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A magnetic sail is a proposed method of
spacecraft propulsion Spacecraft propulsion is any method used to accelerate spacecraft and artificial satellites. In-space propulsion exclusively deals with propulsion systems used in the vacuum of space and should not be confused with space launch or atmospheric e ...
that uses a static magnetic field to deflect a
plasma Plasma or plasm may refer to: Science * Plasma (physics), one of the four fundamental states of matter * Plasma (mineral), a green translucent silica mineral * Quark–gluon plasma, a state of matter in quantum chromodynamics Biology * Blood pla ...
wind of
charged particle In physics, a charged particle is a particle with an electric charge. It may be an ion, such as a molecule or atom with a surplus or deficit of electrons relative to protons. It can also be an electron or a proton, or another elementary particle, ...
s radiated by the
Sun The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...
or a Star thereby transferring momentum to accelerate or decelerate a spacecraft. Most approaches require little to no propellant and thus are a form of
Field propulsion Field propulsion is the concept of spacecraft propulsion where no propellant is necessary but instead momentum of the spacecraft is changed by an interaction of the spacecraft with external force fields, such as gravitational and magnetic fields f ...
. A magnetic sail could also thrust against a planetary
ionosphere The ionosphere () is the ionized part of the upper atmosphere of Earth, from about to above sea level, a region that includes the thermosphere and parts of the mesosphere and exosphere. The ionosphere is ionized by solar radiation. It plays an ...
or
magnetosphere In astronomy and planetary science, a magnetosphere is a region of space surrounding an astronomical object in which charged particles are affected by that object's magnetic field. It is created by a celestial body with an active interior dynam ...
. Important use cases are: a modest force from the solar wind sustainable for a long period of time; deceleration in the interstellar medium and the plasma wind of a destination Star following
interstellar travel Interstellar travel is the hypothetical travel of spacecraft from one star system, solitary star, or planetary system to another. Interstellar travel is expected to prove much more difficult than interplanetary spaceflight due to the vast dif ...
at relativistic speeds achieved by some other means; and efficient deceleration in a planetary ionosphere. Plasma characteristics for the
Solar wind The solar wind is a stream of charged particles released from the upper atmosphere of the Sun, called the corona. This plasma mostly consists of electrons, protons and alpha particles with kinetic energy between . The composition of the sola ...
, a planetary ionosphere and the
interstellar medium In astronomy, the interstellar medium is the matter and radiation that exist in the space between the star systems in a galaxy. This matter includes gas in ionic, atomic, and molecular form, as well as dust and cosmic rays. It fills interstella ...
and the specifics of the magnetic sail design determine achievable performance; such as, thrust, required power and mass.


History of concept

Dana Andrews and
Robert Zubrin Robert Zubrin (; born April 9, 1952) is an American aerospace engineer, author, and advocate for human exploration of Mars. He and his colleague at Martin Marietta, David Baker, were the driving force behind Mars Direct, a proposal in a 1990 res ...
first proposed the magnetic sail concept in 1988.D. G. Andrews and R. Zubrin, "Magnetic Sails and Interstellar Travel", Paper IAF-88-553, 1988 Andrews was working on use of a magnetic scoop to gather interstellar material as propellant for a nuclear electric
ion drive An ion thruster, ion drive, or ion engine is a form of electric propulsion used for spacecraft propulsion. It creates thrust by accelerating ions using electricity. An ion thruster ionizes a neutral gas by extracting some electrons out of ...
spacecraft, allowing the craft to operate in a similar manner to a
Bussard ramjet The Bussard ramjet is a theoretical method of spacecraft propulsion proposed in 1960 by the physicist Robert W. Bussard, popularized by Poul Anderson's novel '' Tau Zero'', Larry Niven in his ''Known Space'' series of books, Vernor Vinge in h ...
. Andrews asked Zubrin to help compute the magnetic scoop drag against the interplanetary medium, which turned out to be much greater than the ion drive thrust. The ion drive component of the system was dropped, and use of the concept of using the magnetic scoop as a magnetic sail or Magsail (MS) was born. Published magsail analysis was done for interstellar in 1988, interplanetary in 1989, planetary orbital propulsion in 1991 and a detailed design in 2000. Freeland did further analysis in 2015 for Project Icarus that used a more accurate model of the magnetic field and showed that the Andrews and Zubrin results for drag (thrust) were optimistic by a factor of 3.1 In 2016 Gros published results for magsail use for deceleration in the Interstellar medium. In 2017, Crowl documented an analysis for a mission starting near the Sun and destined for
Planet nine Planet Nine is a hypothetical planet in the outer region of the Solar System. Its gravitational effects could explain the peculiar clustering of orbits for a group of extreme trans-Neptunian objects (ETNOs), bodies beyond Neptune that orb ...
. Another mission profile for the magsail is heliocentric transfers, as described in 2013 by Quarta, in 2019 by Bassetto, and in 2020 by Perakis. A drawback of the magsail design was that a large (50–100 km radius) superconducting loop weighing on the order of was required. In 2000, Winglee proposed a Mini-Magnetospheric Plasma Propulsion (M2P2) design that injected low energy plasma into a much smaller coil with much lower mass that required low power. Simulations predicted impressive performance relative to mass and required power, a major factor being a claimed 1/r magnetic field falloff rate as compared with the classical 1/r^3 falloff rate of a
magnetic dipole In electromagnetism, a magnetic dipole is the limit of either a closed loop of electric current or a pair of poles as the size of the source is reduced to zero while keeping the magnetic moment constant. It is a magnetic analogue of the electric ...
in a vacuum. A number of critiques raised issues: that the assumed magnetic field falloff rate was optimistic and that thrust was overestimated as well, an analysis indicating that predicted thrust was over ten orders of magnitude optimistic since the majority of the solar wind momentum was delivered to the magnetotail and current leakages through the magnetopause and not to the spacecraft, and that conservation of magnetic flux in the region outside the magnetosphere was not considered. Starting in 2003 Funaki and others published a series of theoretical, simulation and experimental investigations at JAXA in collaboration with Japanese universities addressing some of the issues from criticisms of M2P2 and named their approach the MagnetoPlasma Sail (MPS). In 2011 Funaki and Yamakawa authored a chapter in a book that is a good reference for magnetic sail theory and concepts. MPS research resulted in many published papers that advanced the understanding of physical principles for magnetic sails. Results published in 2013 by Funaki and others found that best performance occurred when the injected plasma had a lower density and velocity than considered in M2P2 where ion drift created an equatorial ring current that augmented the magnetic moment of the coil, which simulations indicated achieved a thrust gain on the order of 10 for smaller magnetospheres as compared with an MHD modeled magnetic sail. Investigations continued reporting increased thrust experimentally and numerically considering use of an
Magnetoplasmadynamic thruster A magnetoplasmadynamic (MPD) thruster (MPDT) is a form of electrically powered spacecraft propulsion which uses the Lorentz force (the force on a charged particle by an electromagnetic field) to generate thrust. It is sometimes referred to as L ...
(aka MPD Arc jet in Japan), multiple antenna coils, and a multi-pole MPD thruster. John Slough of the University of Washington documented in 2004 and 2006 results of NASA Institute of Advanced Concepts (NIAC) funded research, development and experimentation for a more efficient method to generate the static magnetic dipole for a magnetic sail using a design called the Plasma magnet (PM). The design used a pair of small perpendicularly oriented coils powered by an alternating current to generate a Rotating magnetic field (RMF) operating a frequency too fast for positively charged ions to react, but slow enough to force electrons into co-rotation with the RMF without creating excessive collisions. This system created a large current disc composed of electrons captured from the plasma wind within a static disk of captured positive ions. The reports predicted substantial improvements in terms of reduced coil size (and hence mass) and markedly lower power requirements for significant thrust. An important factor in these predictions was a hypothesized 1/r magnetic field falloff rate as assumed for M2P2. In 2022 a spaceflight trial dubbed Jupiter Observing Velocity Experiment (JOVE) proposed using a
Plasma magnet A plasma magnet is a proposed spacecraft propulsion device that uses a dipole magnetic field to capture energy from the solar wind. The field acts as a sail, using the captured energy to propel the spacecraft analogously to how the wind propels a sa ...
based sail for a spacecraft named Wind Rider using the solar wind to accelerate away from a point near Earth and decelerate against the magnetosphere of Jupiter. A 2012 study by Kirtley and Slough investigated using the plasma magnet technology to use the plasma in the ionosphere of a planetary as a braking mechanism and was called the Plasma Magnetoshell. This paper restated the magnetic field falloff rate for a plasma magnet as 1/r2. Kelly and Little in 2019 and 2021 published simulation results showing that the magnetoshell was more efficient than
Aerocapture Aerocapture is an orbital transfer maneuver in which a spacecraft uses aerodynamic drag force from a single pass through a planetary atmosphere to decelerate and achieve orbit insertion. Aerocapture uses a planet's or moon's atmosphere to accom ...
braking for orbital insertion around Neptune. In 2021 Zhenyu Yang and others published an analysis, numerical calculations and experimental verification for a propulsion system that was a combination of the magnetic sail and the
Electric sail An electric sail (also known as an electric solar wind sail or an E-sail) is a proposed form of spacecraft propulsion using the dynamic pressure of the solar wind as a source of thrust. It creates a "virtual" sail by using small wires to form an ...
called an electromagnetic sail. A superconducting magsail coil augmented by an
electron gun An electron gun (also called electron emitter) is an electrical component in some vacuum tubes that produces a narrow, collimated electron beam that has a precise kinetic energy. The largest use is in cathode-ray tubes (CRTs), used in nearly ...
at the coil's center generates an electric field as in an electric sail that deflects positive ions in the plasma wind thereby providing additional thrust, which could reduce overall system mass.


Modes of operation

Magnetic sail modes of operation cover the mission profile and environment usually involving plasma such as the
solar wind The solar wind is a stream of charged particles released from the upper atmosphere of the Sun, called the corona. This plasma mostly consists of electrons, protons and alpha particles with kinetic energy between . The composition of the sola ...
, a planetary ionosphere or the
interstellar medium In astronomy, the interstellar medium is the matter and radiation that exist in the space between the star systems in a galaxy. This matter includes gas in ionic, atomic, and molecular form, as well as dust and cosmic rays. It fills interstella ...
. A
plasma Plasma or plasm may refer to: Science * Plasma (physics), one of the four fundamental states of matter * Plasma (mineral), a green translucent silica mineral * Quark–gluon plasma, a state of matter in quantum chromodynamics Biology * Blood pla ...
environment has fundamental parameters of the number of ions of type i (with
atomic number The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of an atomic nucleus. For ordinary nuclei, this is equal to the proton number (''n''p) or the number of protons found in the nucleus of every ...
Z_i) in a unit volume n_i, the average mass of each ion type accounting for isotopes m_i (kg), and the number of electrons per unit volume n_e each with
electron mass The electron mass (symbol: ''m''e) is the mass of a stationary electron, also known as the invariant mass of the electron. It is one of the fundamental constants of physics. It has a value of about or about , which has an energy-equivalent of a ...
m_e (kg). A plasma is quasi-neutral meaning that on average there is no electrical charge, that is n_e=\textstyle \sum_ Z_i n_i. An average mass density per unit volume of a plasma environment pe (sw for stellar wind, pi for planetary ionosphere, im for interstellar medium) is \textstyle \rho_ = n_e m_e + \sum_n_i m_i (kg/m3). The velocity distribution of ions and electrons is another important parameter but often analyses use only the average velocity for a plasma wind v_ (m/s).


Acceleration/ deceleration in a stellar plasma wind

A commonly encountered magnetic sail use case is creating drag against a plasma wind from that accelerates a spacecraft away from the Sun or a star. Many designs, analyses, simulations and experiments focus on this use case. The
solar wind The solar wind is a stream of charged particles released from the upper atmosphere of the Sun, called the corona. This plasma mostly consists of electrons, protons and alpha particles with kinetic energy between . The composition of the sola ...
is a time varying stream of plasma that flows outwards from the Sun. Near the Earth's orbit at 1
Astronomical Unit The astronomical unit (symbol: au, or or AU) is a unit of length, roughly the distance from Earth to the Sun and approximately equal to or 8.3 light-minutes. The actual distance from Earth to the Sun varies by about 3% as Earth orbits t ...
(AU) the plasma flows at velocity v_ ranging from 250 to 750 km/s (155-404 mi/s) with a density ranging between 3 and 10
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no kn ...
s,
proton A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...
s, and
alpha particle Alpha particles, also called alpha rays or alpha radiation, consist of two protons and two neutrons bound together into a particle identical to a helium-4 nucleus. They are generally produced in the process of alpha decay, but may also be produce ...
s per cm3 along with a few heavier
ion An ion () is an atom or molecule with a net electrical charge. The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by conve ...
s per cubic centimeter. Assuming that 8% of the solar wind is helium and the remainder hydrogen, the average solar wind plasma mass density at 1 AU is 4\times10^<\rho_(1)<10^ (kg/m3). At 1 AU most magnetic sail research assumes 6 protons per cm3 corresponding to a density of \rho_(1) \approx 10−20 and a mean wind velocity v_=500 km/s. On average, the plasma density decreases with the square of the distance from the Sun while the velocity is nearly constant, see Figure 4.2. The average mass density as a function of distance a_\odot
Astronomical Units The astronomical unit (symbol: au, or or AU) is a unit of length, roughly the distance from Earth to the Sun and approximately equal to or 8.3 light-minutes. The actual distance from Earth to the Sun varies by about 3% as Earth orbits t ...
(AU) from the Sun is: with the plasma velocity falling off very slowly. The effective solar wind seen by a spacecraft traveling at velocity v_ (positive meaning acceleration away from the star and negative meaning deceleration toward a star) is u_=v_-v_.


Deceleration in interstellar medium

A spacecraft accelerated to very high velocities by other means, such as a fusion rocket or laser pushed lightsail, can decelerate even from relativistic velocitieswithout requiring the use of onboard propellant by using a magnetic sail to create drag against the interstellar medium plasma environment. For example. long duration missions, such as missions aimed to offer terrestrial life alternative evolutionary pathways, e.g. as envisioned by the
Genesis project Genesis may refer to: Bible * Book of Genesis, the first book of the biblical scriptures of both Judaism and Christianity, describing the creation of the Earth and of mankind * Genesis creation narrative, the first several chapters of the Book of ...
, could brake passively using magnetic sails on approach to a distant star. The Sun is the center of the
heliosphere The heliosphere is the magnetosphere, astrosphere and outermost atmospheric layer of the Sun. It takes the shape of a vast, bubble-like region of space. In plasma physics terms, it is the cavity formed by the Sun in the surrounding interstell ...
region that extends radially outwards to a
termination shock The heliosphere is the magnetosphere, astrosphere and outermost atmospheric layer of the Sun. It takes the shape of a vast, bubble-like region of space. In plasma physics terms, it is the cavity formed by the Sun in the surrounding interst ...
at 75-90 AU, a
heliosheath The heliosphere is the magnetosphere, astrosphere and outermost atmospheric layer of the Sun. It takes the shape of a vast, bubble-like region of space. In plasma physics terms, it is the cavity formed by the Sun in the surrounding interst ...
at 80 to 100 AU and then a theoretical heliopause at 120 AU. Beyond this is a relatively low density region called the
Local Bubble The Local Bubble, or Local Cavity, is a relative cavity in the interstellar medium (ISM) of the Orion Arm in the Milky Way. It contains the closest of celestial neighbours and among others, the Local Interstellar Cloud (which contains the Sol ...
which contains
local interstellar cloud The Local Interstellar Cloud (LIC), also known as the Local Fluff, is an interstellar cloud roughly across, through which the Solar System is moving. This feature overlaps a region around the Sun referred to as the solar neighborhood. It is unk ...
(which contains the
Solar System The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar S ...
) and a neighboring
G-Cloud The G-Cloud (or G-Cloud complex) is an interstellar cloud located next to the Local Interstellar Cloud, within the Local Bubble. It is unknown whether the Solar System is embedded in the Local Interstellar Cloud or in the region where the two c ...
complex which contains
Alpha Centauri Alpha Centauri ( Latinized from α Centauri and often abbreviated Alpha Cen or α Cen) is a triple star system in the constellation of Centaurus. It consists of 3 stars: Alpha Centauri A (officially Rigil Kentaurus), Alpha Centaur ...
. Less is known about the ISM than within the heliosphere, but measurements by
Voyager 1 ''Voyager 1'' is a space probe launched by NASA on September 5, 1977, as part of the Voyager program to study the outer Solar System and interstellar space beyond the Sun's heliosphere. Launched 16 days after its twin ''Voyager 2'', ''Voya ...
and
Voyager 2 ''Voyager 2'' is a space probe launched by NASA on August 20, 1977, to study the outer planets and interstellar space beyond the Sun's heliosphere. As a part of the Voyager program, it was launched 16 days before its twin, ''Voyager 1'', on a ...
have provided important data and indirect observations have also provided information. Estimates of the number of particles per cm3 are between 0.005 and 0.5 in the
local bubble The Local Bubble, or Local Cavity, is a relative cavity in the interstellar medium (ISM) of the Orion Arm in the Milky Way. It contains the closest of celestial neighbours and among others, the Local Interstellar Cloud (which contains the Sol ...
and
G-cloud The G-Cloud (or G-Cloud complex) is an interstellar cloud located next to the Local Interstellar Cloud, within the Local Bubble. It is unknown whether the Solar System is embedded in the Local Interstellar Cloud or in the region where the two c ...
, respectively meaning that the ISM plasma mass density is 6\times10^<\rho_<6\times10^. A typical value assumed for approach to Alpha Centauri is the G-cloud value of particle density of 0.1 particles per cm3 corresponding to \rho_\approx 10^. The spacecraft velocity v_ is much greater than the ISM velocity at the beginning of a deceleration maneuver so the effective plasma velocity is approximately v_ \approx v_. Radio emissions of
cyclotron radiation Cyclotron radiation is electromagnetic radiation emitted by non-relativistic accelerating charged particles deflected by a magnetic field. The Lorentz force on the particles acts perpendicular to both the magnetic field lines and the particles' mot ...
due to interaction of charged particles in the interstellar medium as they spiral around the magnetic field lines of a magnetic sail would have a frequency of approximately (120 \, v/c) kHz, where v is the spacecraft velocity and c the speed of light. The Earth's ionosphere would prevent detection on the surface, but a space-based antenna could detect such emissions up to several thousands of light years away. Detection of such radiation could indicate activity of advanced extraterrestrial civilizations.


In a planetary ionosphere

A spacecraft approaching a planet with a significant upper atmosphere such as Saturn or Neptune could use a magnetic sail to decelerate by ionizing neutral atoms such that it behaves as a low beta plasma. The spacecraft velocity v_ is much greater than the planetary ionosphere velocity in a deceleration maneuver so the effective plasma velocity is approximately v_ \approx v_.


In a planetary magnetosphere

Inside or near a planetary
magnetosphere In astronomy and planetary science, a magnetosphere is a region of space surrounding an astronomical object in which charged particles are affected by that object's magnetic field. It is created by a celestial body with an active interior dynam ...
, a magnetic sail can thrust against or be attracted to a planet's
magnetic field A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
created by a
dynamo file:DynamoElectricMachinesEndViewPartlySection USP284110.png, "Dynamo Electric Machine" (end view, partly section, ) A dynamo is an electrical generator that creates direct current using a commutator (electric), commutator. Dynamos were the f ...
, especially in an
orbit In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as a p ...
that passes over the planet's magnetic poles. When the magnetic sail and planet's magnetic field are in opposite directions an attractive force occurs and when the fields are in the same direction a repulsive force occurs, which is not stable and means to prevent the sail from flipping over is necessary. The thrust that a magnetic sail delivers within a magnetosphere decreases with the fourth power of its distance from the planet's internal magnetic field. When close to a planet with a strong
magnetosphere In astronomy and planetary science, a magnetosphere is a region of space surrounding an astronomical object in which charged particles are affected by that object's magnetic field. It is created by a celestial body with an active interior dynam ...
such as
Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surfa ...
or a
gas giant A gas giant is a giant planet composed mainly of hydrogen and helium. Gas giants are also called failed stars because they contain the same basic elements as a star. Jupiter and Saturn are the gas giants of the Solar System. The term "gas giant" ...
, the magnetic sail could generate more thrust by interacting with the magnetosphere instead of the solar wind. When operating near a planetary or stellar magnetosphere the effect of that magnetic field must be considered if it is on the same order as the gravitational field. By varying the magnetic sail's field strength and orientation a "
perigee An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. For example, the apsides of the Earth are called the aphelion and perihelion. General description There are two apsides in any ellip ...
kick" can be achieved raising the altitude of the orbit's
apogee An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. For example, the apsides of the Earth are called the aphelion and perihelion. General description There are two apsides in any ellip ...
higher and higher, until the magnetic sail is able to leave the planetary magnetosphere and catch the solar wind. The same process in reverse can be used to lower or circularize the apogee of a magsail's orbit when it arrives at a destination planet with a magnetic field. In theory, it is possible for a magnetic sail to launch directly from the surface of a planet near one of its magnetic poles, repelling itself from the planet's magnetic field. However, this requires the magnetic sail to be maintained in its "unstable" orientation. A launch from Earth required superconductors with 80 times the current density of the best known high-temperature superconductors as of 1991. In 2022 a spaceflight trial dubbed Jupiter Observing Velocity Experiment (JOVE) proposed using a
plasma magnet A plasma magnet is a proposed spacecraft propulsion device that uses a dipole magnetic field to capture energy from the solar wind. The field acts as a sail, using the captured energy to propel the spacecraft analogously to how the wind propels a sa ...
to decelerate against the magnetosphere of Jupiter.


Physical principles

Physical principles involved include: interaction of magnetic fields with moving charged particles; an artificial magnetosphere model analogous to the
Earth's magnetosphere In astronomy and planetary science, a magnetosphere is a region of space surrounding an astronomical object in which charged particles are affected by that object's magnetic field. It is created by a celestial body with an active interior dyn ...
, MHD and kinematic mathematical models for interaction of an artificial magnetosphere with a plasma flow characterized by density and velocity, and performance measures; such as, force achieved, energy requirements and the mass of the magnetic sail system.


Magnetic field interaction with charged particles

An ion or electron with charge in a plasma moving at velocity in a
magnetic field A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
and
electric field An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field fo ...
is treated as an idealized point charge in the
Lorentz force In physics (specifically in electromagnetism) the Lorentz force (or electromagnetic force) is the combination of electric and magnetic force on a point charge due to electromagnetic fields. A particle of charge moving with a velocity in an elect ...
\mathbf = q\,\mathbf + q\,\mathbf \times \mathbf. This means that the force on an ion or electron is proportional to the product of their charge and velocity component v perpendicular to the magnetic field . A magnetic sail design introduces a magnetic field into a plasma flow which under certain conditions deflects the electrons and ions from their original trajectory with the particle's momentum transferred to the sail and hence the spacecraft thereby creating thrust. An
electric sail An electric sail (also known as an electric solar wind sail or an E-sail) is a proposed form of spacecraft propulsion using the dynamic pressure of the solar wind as a source of thrust. It creates a "virtual" sail by using small wires to form an ...
uses an electric field that under certain conditions interact with charged particles to create thrust.


Artificial magnetospheric model

The characteristics of the
Earth's magnetosphere In astronomy and planetary science, a magnetosphere is a region of space surrounding an astronomical object in which charged particles are affected by that object's magnetic field. It is created by a celestial body with an active interior dyn ...
have been widely studied as a basis for magnetic sails. The figure shows streamlines of charged particles from a plasma wind from the Sun (or a star) or an effective wind when decelerating in the ISM flowing from left to right. A source attached to a spacecraft generates a magnetic field. Under certain conditions at the boundary where magnetic pressure equals the plasma wind kinetic pressure an artificial
magnetopause The magnetopause is the abrupt boundary between a magnetosphere and the surrounding plasma. For planetary science, the magnetopause is the boundary between the planet's magnetic field and the solar wind. The location of the magnetopause is d ...
forms at a characteristic length L (m) from the field source. The ionized plasma wind particles create a current sheet, known as the Chapman-Ferraro current along the magnetopause, which compresses the magnetic field lines facing the oncoming plasma wind by a factor of 2 at magnetopause as shown in Figure 2a. The magnetopause deflects charged particles, which affects their streamlines and increases the density at magnetopause. A magnetospheric bubble or cavity forms that has very low density downstream from the magnetopause. Upstream from the magnetopause a
bow shock In astrophysics, a bow shock occurs when the magnetosphere of an astrophysical object interacts with the nearby flowing ambient plasma such as the solar wind. For Earth and other magnetized planets, it is the boundary at which the speed of ...
develops. Simulation results often show the particle density through use of color with an example shown in the figure according to the legend in the lower left. This figure uses aspects of the general structure from Figure 3 Figure 1 and Figure 2a, and aspects of the plasma density from Figure 1, and Figure 2.


Magnetohydrodynamic model

Magnetic sail designs operating in a plasma wind share a theoretical foundation based upon a
magnetohydrodynamic Magnetohydrodynamics (MHD; also called magneto-fluid dynamics or hydro­magnetics) is the study of the magnetic properties and behaviour of electrically conducting fluids. Examples of such magneto­fluids include plasmas, liquid metals, ...
(MHD) model, sometimes called a fluid model, from
plasma physics Plasma ()πλάσμα
, Henry George Liddell, R ...
for an artificially generated
magnetosphere In astronomy and planetary science, a magnetosphere is a region of space surrounding an astronomical object in which charged particles are affected by that object's magnetic field. It is created by a celestial body with an active interior dynam ...
. Under certain conditions, the plasma wind and the magnetic sail are separated by a
magnetopause The magnetopause is the abrupt boundary between a magnetosphere and the surrounding plasma. For planetary science, the magnetopause is the boundary between the planet's magnetic field and the solar wind. The location of the magnetopause is d ...
that blocks the charged particles, which creates a drag force that transfers (at least some) momentum to the magnetic sail, which then applies thrust to the attached spacecraft. The figure depicts the MHD model. Starting from the left a plasma wind in a plasma environment (e.g., stellar, ISM or an ionosphere) of effective velocity v_ with density \rho_ (kg/m3) encounters a spacecraft with time-varying velocity v_ (m/s) that is positive if accelerating and negative if decelerating. The apparent plasma wind velocity from the spacecraft's viewpoint is u_=v_-v_. The spacecraft and field source generate a
magnetic field A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
that creates a magnetospheric bubble extending out to a magnetopause preceded by a bow shock that deflects electrons and ions from the plasma wind At magnetopause the field source magnetic pressure equals the kinetic pressure of the plasma wind at a standoff shown at the bottom of the figure. The characteristic length L (m) is that of a circular sail of effective blocking area S=\pi \, R_^2 where R_ \approx L is the effective magnetopause radius. Under certain conditions the plasma wind pushing on the artificial magnetosphere bow shock and magnetopause creates a force F_w (N) on the magnetic field source that is physically attached to the spacecraft so that at least part of the force F_w causes a force F_on the spacecraft, accelerating it when sailing downwind or decelerating when sailing into a headwind. Under certain conditions and in some designs, some of the plasma wind force may be lost as indicated by F_ on the right side. All magnetic sail designs assume a standoff between plasma wind pressure p_w and magnetic pressure p_B of the same form with parameters specific to a plasma environment, differing only in a constant coefficient C_ as follows: where u (m/s) is the apparent wind velocity and \rho(kg/m3) is the plasma wind density for a specific plasma environment, B_ (T) the magnetic field strength at
magnetopause The magnetopause is the abrupt boundary between a magnetosphere and the surrounding plasma. For planetary science, the magnetopause is the boundary between the planet's magnetic field and the solar wind. The location of the magnetopause is d ...
, ''μ0'' (H/m) is the
vacuum permeability The vacuum magnetic permeability (variously ''vacuum permeability'', ''permeability of free space'', ''permeability of vacuum''), also known as the magnetic constant, is the magnetic permeability in a classical vacuum. It is a physical constant, ...
and C_ is a constant that differs by reference as follows for C_=2 corresponding to p_wmodeled as
dynamic pressure In fluid dynamics, dynamic pressure (denoted by or and sometimes called velocity pressure) is the quantity defined by:Clancy, L.J., ''Aerodynamics'', Section 3.5 :q = \frac\rho\, u^2 where (in SI units): * is the dynamic pressure in pascals ( ...
with no magnetic field compression, C_=1 for p_wmodeled as
ram pressure Ram pressure is a pressure exerted on a body moving through a fluid medium, caused by relative bulk motion of the fluid rather than random thermal motion. It causes a drag force to be exerted on the body. Ram pressure is given in tensor form as ...
with no magnetic field compression and C_=1/2 for p_w modeled as ram pressure with magnetic field compression by a factor of 2 Equation can be solved to yield the required magnetic field B_ (T) that satisfies the pressure balance at magnetopause standoff as: The solar wind plasma density decreases in inverse proportion to the square of the distance d from the Sun and hence from the above, B_ decreases in inverse proportion to d. Since magnetic field strength at radius r is B\propto 1/r^3 this means that the magnetic sail magnetopause radius R_ will increase with distance from the Sun, where the increased effective size of a sail compensates for the reduced dynamic pressure of the solar wind. The force derived by a magnetic sail for a plasma environment is determined from MHD equations as reported by many researchers is: where C_d is a
coefficient of drag In fluid dynamics, the drag coefficient (commonly denoted as: c_\mathrm, c_x or c_) is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water. It is used in the drag e ...
determined by numerical analysis and/or simulation, \rho u^2/2 (Pa) is the dynamic wind pressure, and S=\pi R_^2 (m2) is the effective blocking area of the magnetic sail with magnetopause radius R_ \approx L (m). Note that this equation has the same form as the
drag equation In fluid dynamics, the drag equation is a formula used to calculate the force of drag experienced by an object due to movement through a fully enclosing fluid. The equation is: F_\, =\, \tfrac12\, \rho\, u^2\, c_\, A where *F_ is the drag force ...
in
fluid dynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) an ...
. C_d is a function of coil attack angle on thrust and steering angle. The
power Power most often refers to: * Power (physics), meaning "rate of doing work" ** Engine power, the power put out by an engine ** Electric power * Power (social and political), the ability to influence people or events ** Abusive power Power may a ...
(W) of the plasma wind is the product of velocity and a constant force where equation was used to derive the right-side yielding the same result as equation (9).


MHD applicability test

Through analysis, numerical calculation, simulation and experimentation an important condition for a magnetic sail to generate significant force is the MHD applicability test, that states that the standoff distance L must be significantly greater than the ion
gyroradius The gyroradius (also known as radius of gyration, Larmor radius or cyclotron radius) is the radius of the circular motion of a charged particle in the presence of a uniform magnetic field. In SI units, the non-relativistic gyroradius is given by :r_ ...
, also called the Larmor radius or cyclotron radius: where ''m_i'' (kg) is the ion mass, v_\perp (m/s) is the velocity of ions perpendicular to the magnetic field, , q, (C) is the
elementary charge The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a fundame ...
of the ion, B_x (T) is the magnetic field strength at the point of reference x and C_ is a constant that differs by source with C_=1 and C_=2''.'' In the solar plasma wind at 1 AU with m_i (kg) the
proton mass A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...
, v\perp = v_ = 500 km/s, B_x=B_ = 36 nT with C_=0.5 at from equation at magnetopause and C_=2 then r_g \approx 72 km. The MHD applicability test is the ratio r_g/L. The figure plots C_d on the left axis and lost thrust on the right axis versus the ratio r_g/L. When r_g/L<1, C_d=3.6 is maximum, at r_g/L\approx 1, C_d=2.7, a decrease of 25% from the maximum and at r_g/L\approx 2, C_d\approx 1.5, a 45% decrease. As r_g/L increases beyond one, C_d decreases meaning less thrust from the plasma wind transfers to the spacecraft and is instead lost to the plasma wind. In 2004, Fujita published numerical analysis using a hybrid PIC simulation using a magnetic dipole model that treated electrons as a fluid and a kinematic model for ions to estimate the coefficient of drag C_d for a magnetic sail operating in the radial orientation resulting in the following approximate formula:The lost thrust is T_=(1-C_d(r_g/L))/3.6.


Coil attack angle effect on thrust and steering angle

In 2005 Nishida and others published results from numerical analysis of an MHD model for interaction of the solar wind with a magnetic field of current flowing in a coil that momentum is indeed transferred to the magnetic field produced by field source and hence to the spacecraft . Thrust force derives from the momentum change of the solar wind, pressure by the solar wind on the magnetopause from equation and Lorentz force from currents induced in the magnetosphere interacting with the field source. The results quantified the coefficient of drag, steering (i.e., thrust direction) angle with the solar wind, and torque generated as a function of attack angle (i.e., orientation) The figure illustrates how the attack (or coil tilt) angle \alpha _t orientation of the coil creates a steering angle for the thrust vector and also torque imparted to the coil. Also shown is the vector for the
interplanetary magnetic field The interplanetary magnetic field (IMF), now more commonly referred to as the heliospheric magnetic field (HMF), is the component of the solar magnetic field that is dragged out from the solar corona by the solar wind flow to fill the Solar Syst ...
(IMF), which at 1 AU varies with waves and other disturbances in the solar wind, known as
space weather Space weather is a branch of space physics and aeronomy, or heliophysics, concerned with the time varying conditions within the Solar System, including the solar wind, emphasizing the space surrounding the Earth, including conditions in the ma ...
. For a coil with radial orientation (like a Frisbee) the attack angle \alpha _t= 0 degrees and with axial orientation (like a parachute) \alpha _t=90 degrees. The Nishida 2005 results reported a coefficient of drag C_d that increased non-linearly with attack angle from a minimum of 3.6 at \alpha _t=0 to a maximum of 5 at \alpha _t=90 degrees. The steering angle of the thrust vector is substantially less than the attack angle deviation from 45 degrees due to the interaction of the magnetic field with the solar wind. Torque increases from \alpha _t= 0 degrees from zero at to a maximum at \alpha _t=45 degrees and then decreases to zero at \alpha _t=90 degrees. A number of magnetic sail design and other papers cite these results. In 2012 Kajimura reported simulation results that covered two cases where MHD applicability occurs with r_g/L=1.125 and where a kinematic model is applicable r_g/L=0.125 to compute a coefficient of drag C_d and steering angle. As shown in Figure 4 of that paper when MHD applicability occurs the results are similar in form to Nishida 2005 where the largest C_d occurs with the coil in an axial orientation. However, when the kinematic model applies, the largest C_d occurs with the coil in an radial orientation. The steering angle is positive when MHD is applicable and negative when a kinematic model applies. The 2012 Nishida and Funaki published simulation results for a coefficient of drag C_D, coefficient of lift C_L and a coefficient of moment C_M for a coil radius of R_c=100 km and magnetopause radius R_=500 km at 1 AU. These results included the effect of the interplanetary magnetic field (IMF, which can significantly increase the thrust of a magnetic sail at 1 AU).


Magnetic field model

In a design, either the magnetic field source strength or the magnetopause radius R_\approx L the characteristic length must be chosen. A good approximation for a magnetic field falloff rate f_o, 1\leq f_o \leq3 for a distance R_0 \leq r \leq R_ from the field source to magnetopause starts with the equation: where B(R_0) is the magnetic field at a radius R_0 near the field source that falls off near the source as 1/r^3 as follows: where C_0 is a constant multiplying the
magnetic moment In electromagnetism, the magnetic moment is the magnetic strength and orientation of a magnet or other object that produces a magnetic field. Examples of objects that have magnetic moments include loops of electric current (such as electromagnets ...
\mathbf m (A m2) to make B(r) match a target value at r>>R_0. When far from the field source, a magnetic dipole is a good approximation and choosing the above value of B(R_0) with C_0 =2 near the field source was used by Andrews and Zubrin. The Amperian loop model for the magnetic moment is \mathbf m = I_c S, where I_c (A) is the current and S= \pi \, R_c^2 is the surface area (m2) for a coil (loop) of radius R_c(m). Assuming that R_0 \approx R_c and substituting the expression for the magnetic moment \mathbf m into equation yields the following: When the magnetic field source strength B(R_0) is specified, substituting B_ from the pressure balance analysis from equation into the above and solving for R_ yields the following: This is the expression for L when f_o=3 with C_=1/2 from equation (4), with C_=2 from equation (4), and the magnetopause distance of the Earth. This equation shows directly how a decreased falloff rate f_o dramatically increases the effective sail area S=\pi R_^2 for a given field source magnetic moment \mathbf m and B_ determined from the pressure balance equation . Substituting this into equation yields the plasma wind force as a function of falloff rate f_o , plasma density \rho (kg/m3), coil radius R_c \approx R_0 (m), coil current I_c (A) and plasma wind velocity u (m/s) as follows: using equation for B(R_0) and equation for B_. This is the same expression as equation (10b) when f_o=3 and C_=1/2 , equation (108) and equation (5) with other numerical coefficients grouped into the C_d term. Note that force increases as falloff rate decreases. When the design target is the magnetopause radius R_ , the required field source strength is then determined directly from equation as follows:which then determines the magnetic moment \mathbf m from equation and plasma wind force from equation .


General kinematic model

When the MHD applicability test of r_g/L <1 then a kinematic simulation model more accurately predicts force transferred from the plasma wind to the spacecraft. In this case the effective sail blocking area A_e < S=\pi L^2. The left axis of the figure is for plots of magnetic sail force versus characteristic length L. The solid black line plots the MHD model force F_ from equation . The green line shows the value of ion gyroradius r_g \approx 72 km from equation . The dashed blue line plots the hybrid MHD/kinematic model from equation from Fujita04. The red dashed line plots a curve fit to simulation results from Ashida14. Although a good fit for these parameters, the curve fit range of this model does not cover some relevant examples. Additional simulation results from Hajiwara15 are shown for the MHD and kinematic model as single data points as indicated in the legend. These models are all in close agreement. The kinematic models predict less force than predicted by the MHD model. In other words, the fraction T_ of thrust force predicted by the MHD model is lost when r_g/L<1 as plotted on the right axis. The solid blue and red lines show T_ for Fujita04 and Ashida18 respectively, indicating that operation with L less than 10% of r_g will have significant loss. Other factors in a specific magnetic sail design may offset this loss for values of L.


Performance measures

Important measures that determine the relative performance of different magnetic sail systems include: mass of the field source generator and its power and energy requirements; thrust achieved; thrust to weight ratio, any limitations and constraints, and propellant system exhausted, if any . Mass of the field source M_ in the Magsail design was relatively large and subsequent designs strove to reduce this measure. Total spacecraft mass is M_=M_+M_p, where M_p is the payload mass. Power requirements are significant in some designs and add to field source mass. Thrust is the plasma wind force F_w for a particular plasma environment with acceleration a=F_w/M_. The thrust to weight ratio F_w/M_is also an important performance measure. Other limitations and constraints may be specific to a particular design. The M2P2 and MPS designs, as well as potentially the plasma magnet design, exhaust some plasma as part of inflating the magnetospheric bubble and these cases also have a
specific impulse Specific impulse (usually abbreviated ) is a measure of how efficiently a reaction mass engine (a rocket using propellant or a jet engine using fuel) creates thrust. For engines whose reaction mass is only the fuel they carry, specific impulse i ...
and effective exhaust velocity performance measure.


Proposed magnetic sail systems


Magsail (MS)

The figure shows the magsail design consisting of a loop of
superconducting Superconductivity is a set of physical properties observed in certain materials where Electrical resistance and conductance, electrical resistance vanishes and magnetic field, magnetic flux fields are expelled from the material. Any material e ...
wire of radius R_c (m) on the order of 100 km that carries a direct current I_c (A) that generates a magnetic field, which was modeled according to the Biot-Savart law inside the loop and as a
magnetic dipole In electromagnetism, a magnetic dipole is the limit of either a closed loop of electric current or a pair of poles as the size of the source is reduced to zero while keeping the magnetic moment constant. It is a magnetic analogue of the electric ...
far outside the loop. With respect to the plasma wind direction a magsail may have a radial (or normal) orientation r an axial orientation that can be adjusted to provide torque for steering. In non-axial configurations lift is generated that can change the spacecraft's momentum. The loop connects via shroud lines (or tethers) to the spacecraft in the center. Because a loop carrying current is forced outwards towards a circular shape by its magnetic field, the sail could be deployed by unspooling the conductor wire and applying a current through it via the peripheral platforms. The loop must be adequately attached to the spacecraft in order to transfer momentum from the plasma wind and would pull the spacecraft behind it as shown in the axial configuration in the right side of the figure.


MHD model

Analysis of magsail performance was done using a simulation and a fluid (i.e., MHD) model with similar results observed for one case. The magnetic moment of a current loop is \mathbf m= I_c \pi R_c^2 for a current of I_c (A) and a loop of radius R_c. Close to the loop, the magnetic field at a distance z along the center-line axis perpendicular to the loop is derived from the Biot-Savart law in Section 5-2, equation (25) as follows. At a distance far from the loop center the magnetic field is approximately that produced by a
magnetic dipole In electromagnetism, a magnetic dipole is the limit of either a closed loop of electric current or a pair of poles as the size of the source is reduced to zero while keeping the magnetic moment constant. It is a magnetic analogue of the electric ...
. Since the pressure at the magnetospheric boundary is doubled due to compression of the magnetic field and is the following at a point along the center-line axis at a distance z=L_Z for the target magnetopause standoff distance from equation (5). Equating this to the dynamic pressure for a plasma environment p_=\rho \, u_^2 /2, inserting B_(0) from equation and solving for L_Z yields equation (6). Andrews and Zubrin derived equation (8) for the drag force of the sail F_D that determined the characteristic length L_Z for a tilt angle but according to Section 6.5 of Freeland an error was made in numerical integration in choosing the ellipse downstream from the magnetopause instead of the ellipse upstream that made those results optimistic by a factor of approximately 3.1, which should be used to correct any drag force results using equation (8). Instead, this article uses the approximation from equation (108) for a spherical bubble that corrects this error and is close to the analytical formula for the axial configuration as the force for the Magsail as follows In 2004 Toivanen and Janhunen did further analysis on the Magsail that they called a Plasma Free MagnetoPause (PFMP) that produced similar results to that of Andrews and Zubrin.


Coil mass and current (CMC)

The minimum required mass to carry the current in equation or other magnetic sail designs is defined in equation (9) and equation (3) as follows: where J_e (A/m2) is the superconductor critical current density and \delta_c (kg/m3) is the coil material density, for example 6,500 for a superconductor. The physical mass of the coil is where r_c (m) is the radius of the superconductor wire, for example that necessary to handle the tension for a particular use case, with the N_ factor (e.g., 3) accounting for mass of the tether (or shroud) lines. Note that M_c(phy) with N_=0 must be no less than M_c(min) in order for the coil to carry the current I_c. Setting equation with N_=0 equal to equation and solving for r_c yields the minimum required coil radius If operated within the solar system, high temperature
superconducting wire Superconducting wires are electrical wires made of superconductive material. When cooled below their transition temperatures, they have zero electrical resistance. Most commonly, conventional superconductors such as niobium-titanium are used, ...
(HTS) is necessary to make the magsail practical since the current required is large. However, protection from solar heating is necessary closer to the Sun, for example by highly reflective coatings. If operated in interstellar space low temperature superconductors (LTS) could be adequate since the temperature of a vacuum is 2.7 K, but radiation and other heat sources from the spacecraft may render LTS impractical. The critical current carrying capacity of the promising HTS YBCO coated superconductor wire increases at lower temperatures with a current density J_e(A/m2) of 6x1010 at 77 K and 9x1011 at 5 K. The superconductor critical current is defined as I_=J_e \pi r_c^2 (A) for a coil wire of radius r_c (m).


Magsail kinematic model (MKM)

The MHD applicability test of equation fails in some ISM deceleration cases and a kinematic model is necessary, such as the one documented in 2017 by
Claudius Gros Claudius Gros (born 18 February 1961 in Mainz, Germany) is a German physicist. Career Finishing his studies in physics 1985 at the ETH Zürich with a thesis on heavy Fermions, Gros continued for a PhD in theoretical solid-state physics. Usi ...
summarized here. A spacecraft with an overall mass m_ and velocity v follows equation (1) of motion as: where F_ (N) is force predicted by this model, n_p is the proton number density (m−3), m_p is the
proton A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...
mass (kg), \rho = m_p n_p (kg/m3) the plasma density, and A_G(v) (m2) the effective reflection area. This equation assumes that the spacecraft encounters A_G(v) n_p v particles per second and that every particle of mass m_p is completed reflected. Note that this equation is of the same form as with C_d=4, interpreting the C_d term as just a number. Gros numerically determined the effective reflection area A_G(v) by integrating the degree of reflection of approaching protons interacting with the superconducting loop magnetic field according to the Biot-Savart law. The reported result was independent of the loop radius R_c. An accurate curve fit as reported in Figure 4 to the numerical evaluation for the effective reflection area for a magnetic sail in the axial configuration from equation (8) was where \pi R_c^2 (m2) is the area enclosed by the current carrying loop, c (m/s) the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
, and the value I_G=1.55\cdot10^ (A) determined a good curve fit for I=105 A, the current through the loop. In 2020, Perakis published an analysis that corroborated the above formula with parameters selected for the solar wind and reported a force no more than 9% less than the Gros model for I=105 A and R_c=100 m with the coil in an axial orientation.. That analysis also reported on the effect of magsail tilt angle on lift and side forces for a use case in maneuvering within the solar system. For comparison purposes, the effective sail area determined for the magsail by Zubrin from equation with the 3.1 correction factor from Freeland applied and using the same velocity value (resolving the discrepancy noted by Gros) as follows: The figure shows the normalized effective sail area normalized by the coil area \pi R_c^2 for the MKM case from Gros of equation and for Zubrin from equation for I \approx I_G, R_c=100 km, and n_p=0.1 (cm-3) for the
G-cloud The G-Cloud (or G-Cloud complex) is an interstellar cloud located next to the Local Interstellar Cloud, within the Local Bubble. It is unknown whether the Solar System is embedded in the Local Interstellar Cloud or in the region where the two c ...
on approach to Alpha Centauri corresponding to ISM density \rho_=1.67\times10^ (kg/m3) consistent with that from Freeland plotted versus the spacecraft velocity relative to the speed of light \beta =v/c. A good fit occurs for these parameters, but for different values of R_c and I the fit can vary significantly. Also plotted is the MHD applicability test of ion gyroradius divided by magnetopause radius r_g/R_ <1 from equation on the secondary axis. Note that MHD applicability occurs at v/c < 1%. For comparison, the 2004 Fujita C_d as a function of r_g/R_ from the MHD applicability test section is also plotted. Note that the Gros model predicts a more rapid decrease in effective area than this model at higher velocities. The normalized values of A_G(v) and A_Z(v) track closely until \beta = v/c \approx 10% after which point the Zubrin magsail model of Equation becomes increasingly optimistic and equation is applicable instead. Since the models track closely up to \beta \approx 10%, with the kinematic model underestimating effective sail area for smaller values of \beta (hence underestimating force), equation is an approximation for both the MHD and kinematic region. The Gros model is pessimistic for \beta < 0.1%. Gros used the analytic expression for the effective reflection area A_G(v) from equation for explicit solution for the required distance x_f to decelerate to final velocity v_f \approx 0.013 c from equation (10) given an initial velocity v_0 (m/s) for a spacecraft mass m_ (kg) as follows: where g(v)=ln^(\frac ). When v_f=0 the above equation is defined in equation (11) as x_, which enabled a closed form solution of the velocity at a distance x, v(x) in equation (12) with numerical integration required to compute the time required to decelerate in equation (14). Equation (16) used this result to compute and optimal current that minimized x_ as I_=e \beta_0 I_G where \beta_0=v_0/c. In 2017 Crowl optimized coil current for the ratio of effective area A(v) over total mass m_ and derived the result I_=e^3 \, \beta_0 I_G in equation (15). That paper used results from Gros for the stopping distance x_ and time to decelerate. The figure plots the distance traveled while decelerating x_d (ly) and time required to decelerate t_d (yr) given a starting relative velocity \beta_0 = v_0/c and a final velocity v_f=0.013 c (m/s) consistent with that from Freeland for the same parameters above. Equation gives the magsail mass M_s as 97 tonnes assuming 100 tonnes of payload mass M_p using the same values used by Freeland of J_e = 1011 (A/m2) and \delta_c =6,500 (kg/m3) for the superconducting coil. Equation gives Force for the magsail multiplied by C_d=4 for the Andrews/Zubrin model to align with equation definition of force from the Gros model.
Acceleration In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by the ...
is force divided by mass,
velocity Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity is a ...
is the integral of acceleration over the deceleration time interval t_d (yr) and deceleration distance traveled x_d (ly) is the integral of the velocity over t_d (yr). Numerical integration resulted in the lines plotted in the figure with deceleration distance traveled plotted on the primary vertical axis on the left and time required to decelerate on the secondary vertical axis on the right. Note that the MHD Zubrin model and the Gros kinematic model predict nearly identical values of deceleration distance up to \beta_0~ 5% of light speed, with the Zubrin model predicting less deceleration distance and shorter deceleration time at greater values of \beta_0. This is consistent with the Gros model predicting a smaller effective area A(v) at larger values of \beta_0. The value of the closed form solution for deceleration distance x_f from for the same parameters closely tracks the numerical integration result.


Specific designs and mission profiles

In 1990 Andrews and Zubrin reported on an example for solar wind parameters one AU away from the Sun, with n_i = 5 \times 10^ (m−3) with only protons as ions, apparent wind velocity u_=500 (km/s) the field strength required to resist the
dynamic pressure In fluid dynamics, dynamic pressure (denoted by or and sometimes called velocity pressure) is the quantity defined by:Clancy, L.J., ''Aerodynamics'', Section 3.5 :q = \frac\rho\, u^2 where (in SI units): * is the dynamic pressure in pascals ( ...
of the solar wind is 50 nT from equation . With radius R_c=100 km and magnetospheric bubble of L = reported a thrust of 1980 newtons and a coil mass of 500 tonnes. For the above parameters with the correction factor of 3.1 applied to equation yields the same thrust and equation yields the same coil mass. Results for another 4 solar wind cases were reported, but the MHD applicability test of equation failed in these cases. In 2015 Freeland documented in detail an interstellar deceleration use case for approach to Alpha Centaturi as part of a study to update Project Icarus with R_c=260 km, an initial R_ of 1,320 km and ISM density \rho_=1.67\times10^ kg/m3, almost identical to the n(H I) measurement of 0.098 cm−3 by Gry in 2014. The Freeland study predicted deceleration from 5% of light speed in approximately 19 years. The coil parameters J_e=1011 (A/m2), r_= 5 mm, \rho_=6,500 (kg/m3), resulted in an estimated coil mass is M_c(phy)=1,232 tonnes. Although the critical current density J_e was based upon a 2000 Zubrin NIAC report projecting values through 2020, the assumed value is close to that for commercially produced YBCO coated superconductor wire in 2020. The mass estimate may be optimistic since it assumed that the entire coil carrying mass is superconducting while 2020 manufacturing techniques place a thin film on a non-superconducting substrate. For the interstellar medium plasma density \rho_=1.67x10−22 with an apparent wind velocity 5% of light speed, the ion gyroradius is 570 km and thus the design value for R_ meets the MHD applicability test of equation . Equation gives the required coil current as I_c~7,800 kA and from equation M_c(min)= 338 tonnes; however, but the corresponding superconducting wire minimum radius from equation is r_c(min) =1 mm, which would be insufficient to handle the decelerating thrust force of F_ ~ 100,000 N predicted by equation and hence the design specified r_= 5 mm to meet structural requirements. In a complete design, the mass of shielding the coil to maintain critical temperature and survive abrasion in outer space and other infrastructure must also be included. Appendix A estimates these as 90 tonnes for wire shielding and 50 tonnes for the spools and other magsail infrastructure. Freeland compared this magsail deceleration design with one where both acceleration and deceleration were performed by a fusion engine and reported that the mass of such a "dirty Icarus" design was over twice that with the magsail used for deceleration. An Icarus design published in 2020 used a
Z-pinch In fusion power research, the Z-pinch (zeta pinch) is a type of plasma confinement system that uses an electric current in the plasma to generate a magnetic field that compresses it (see pinch). These systems were originally referred to simply ...
fusion drive in an approach called
Firefly The Lampyridae are a family of elateroid beetles with more than 2,000 described species, many of which are light-emitting. They are soft-bodied beetles commonly called fireflies, lightning bugs, or glowworms for their conspicuous production ...
that dramatically reduced mass of the fusion drive and made fusion only drive performance comparable to the fusion and magsail design. In 2017 Gros reported numerical examples for the Magsail kinematic model that used different parameters and coil mass models than those used by Freeland. For a high speed mission to
Alpha Centauri Alpha Centauri ( Latinized from α Centauri and often abbreviated Alpha Cen or α Cen) is a triple star system in the constellation of Centaurus. It consists of 3 stars: Alpha Centauri A (officially Rigil Kentaurus), Alpha Centaur ...
with initial velocity before deceleration v_0=c/10 using a coil mass of 1500 tons and a coil radius of R=1600 km. The estimated stopping distance was x_of 0.37 (ly) and a total travel time of 58 years with 1/3 being deceleration. In 2017 Crowl documented a design for a mission starting near the Sun and destined for
Planet nine Planet Nine is a hypothetical planet in the outer region of the Solar System. Its gravitational effects could explain the peculiar clustering of orbits for a group of extreme trans-Neptunian objects (ETNOs), bodies beyond Neptune that orb ...
approximately 1,000 AU distant that employed the Magsail kinematic model. The design accounted for the Sun's gravity as well as the impact of elevated temperature on the superconducting coil, composed of meta-stable
metallic hydrogen Metallic hydrogen is a phase of hydrogen in which it behaves like an electrical conductor. This phase was predicted in 1935 on theoretical grounds by Eugene Wigner and Hillard Bell Huntington. At high pressure and temperatures, metallic hydroge ...
, which has a mass density of 3,500 (kg/m3) about half that of other superconductors. The mission profile used the Magsail to accelerate away from 0.25 to 1.0 AU from the Sun and then used the Magsail to brake against the Local ISM on approach to Planet nine for a total travel time of 29 years. Parameters and coil mass models differ from those used by Freeland. Another mission profile uses a magsail oriented at an attack angle to achieve heliocentric transfer between planets moving away from or toward the Sun. In 2013 Quarta and others used Kajimura 2012 simulation results that described the lift (steering angle) and torque to achieve a Venus to Earth transfer orbit of 380 days with a coil radius of R_c~1 km with characteristic acceleration a_c=1 mm/s2. In 2019 Bassetto and others used the Quarta "thick" magnetopause model and predicted a Venus to Earth transfer orbit of approximately 8 years for a coil radius of R_c~1 km. with characteristic acceleration a_c=0.1 mm/s2. In 2020 Perakis used the Magsail kinematic model with a coil radius of R_c=350 m, current I_c=104 A and spacecraft mass of 600 kg that changed attack angle to accelerate away from the Earth orbit and decelerate to Jupiter orbit within 20 years.


Mini-magnetospheric plasma propulsion (M2P2)

In 2000 Winglee and others proposed a design order to reduce the size and weight of a magnetic sail and named it mini-magnetospheric plasma propulsion (M2P2). The figure based upon illustrates the M2P2 design, which is the same as the Magneto plasma sail (MPS) design. Starting at the center with a
solenoid upright=1.20, An illustration of a solenoid upright=1.20, Magnetic field created by a seven-loop solenoid (cross-sectional view) described using field lines A solenoid () is a type of electromagnet formed by a helix, helical coil of wire whose ...
coil of radius R_H (m) of N_t=1,000 turns carrying a radio frequency current that generates a helicon wave that injects plasma fed from a source into a coil of radius R_c (m) that carries a current of I_c (A), which generates a magnetic field. The excited injected plasma enhances the magnetic field and generates a miniaturized magnetosphere around the spacecraft, analogous to the heliopause where the Sun injected plasma encounters the interstellar medium,
coronal mass ejection A coronal mass ejection (CME) is a significant release of plasma and accompanying magnetic field from the Sun's corona into the heliosphere. CMEs are often associated with solar flares and other forms of solar activity, but a broadly accepted ...
s or the Earth's
magnetotail In astronomy and planetary science, a magnetosphere is a region of space surrounding an astronomical object in which charged particles are affected by that object's magnetic field. It is created by a celestial body An astronomical object, c ...
. The injected plasma created an environment that analysis and simulations showed had a magnetic field with a falloff rate of 1/r as compared with the classical model of a 1/r^3 falloff rate, making the much smaller coil significantly more effective. The pressure of the inflated
plasma Plasma or plasm may refer to: Science * Plasma (physics), one of the four fundamental states of matter * Plasma (mineral), a green translucent silica mineral * Quark–gluon plasma, a state of matter in quantum chromodynamics Biology * Blood pla ...
along with the stronger magnetic field pressure at a larger distance due to the lower falloff rate would stretch the magnetic field and inflate a magnetospheric bubble around the spacecraft. The 2000 Winglee paper described a design and reported results adapted from the Earth's magnetosphere. Parameters for the coil and solenoid were R_H=2.5 cm and for the coil R_c= 0.1 m, 6 orders of magnitude less than the magsail coil with correspondingly much lower mass. An estimate for the weight of the coil was 10 kg and 40 kg for the plasma injection source and other infrastructure. Reported results from Figure 2 were B_0 \approx 4x10-3 T at R_ \approx 10 km and from Figure 3 an extrapolated result with a plasma injection jet force F_ \approx10−3 N resulting in a thrust force of F_ \approx 1 N. The magnetic-only sail force from equation is F_w=3x10−11 N and thus M2P2 reported a thrust gain of 4x1010. Since M2P2 injects ionized gas at a rate of m_(kg/s) that can be viewed as a propellant it has a ''
specific impulse Specific impulse (usually abbreviated ) is a measure of how efficiently a reaction mass engine (a rocket using propellant or a jet engine using fuel) creates thrust. For engines whose reaction mass is only the fuel they carry, specific impulse i ...
'' I_=F_/m_/g_0 where g_0 (m/s2) is the acceleration of
Earth's gravity The gravity of Earth, denoted by , is the net acceleration that is imparted to objects due to the combined effect of gravitation (from mass distribution within Earth) and the centrifugal force (from the Earth's rotation). It is a vector quantity ...
. Winglee stated m_=0.5 (kg/day) and therefore I_=17,621. The equivalent exhaust velocity v_e=g_0 \, I_ is 173 km/s for 1 N of thrust force. Winglee assumed total propellant mass of 30 kg and therefore propellant would run out in 60 days. In 2003, Khazanov published
MagnetoHydroDynamic Magnetohydrodynamics (MHD; also called magneto-fluid dynamics or hydro­magnetics) is the study of the magnetic properties and behaviour of electrically conducting fluids. Examples of such magneto­fluids include plasmas, liquid metals, ...
(MHD) and kinetic studies that confirmed some aspects of M2P2 but raised issues that the sail size was too small, and that very small thrust would result and also concluded that the hypothesized 1/r magnetic field falloff rate was closer to 1/r^2. The plasma density plots from Khazanov indicated a relatively high density inside the magnetospheric bubble as compared with the external solar wind region that differed significantly from those published by Winglee where the density inside the magnetospheric bubble was much less than outside in the external solar wind region. A detailed analysis by Toivanen and others in 2004 compared a theoretical model of Magsail, dubbed Plasma-free Magnetospheric Propulsion (PFMP) versus M2P2 and concluded that the thrust force predicted by Winglee and others was over ten orders of magnitude optimistic since the majority of the solar wind momentum was delivered to the magnetotail and current leakages through the magnetopause and not to the spacecraft. Their comments also indicated that the magnetic field lines may not close near enough to the coil to achieve significant transfer of force. Their analysis made an analogy to the
Heliospheric current sheet The heliospheric current sheet, or interplanetary current sheet, is a surface separating regions of the heliosphere where the interplanetary magnetic field points toward and away from the Sun. A small electrical current with a current density of ...
as an example in astrophysics where the magnetic field could falloff at a rate of between 1/r and 1/r^2. They also analyzed current sheets reported by Winglee from the magnetopause to the spacecraft in the windward direction and a current sheet in the magnetotail. Their analysis indicated that the current sheets needed to pass extremely close to the spacecraft to impart significant force could generate significant heat and render this leverage impractical. In 2005, Cattell and others published comments regarding M2P2 that included a lack of magnetic flux conservation in the region outside the magnetosphere that was not considered in the Khazanov studies. Their analysis concluded in Table 1 that Winglee had significantly underestimated the required sail size, mass, required magnetic flux and asserted that the hypothesized 1/r magnetic field falloff rate was not possible. The expansion of the magnetic field using injected plasma was demonstrated in a large vacuum chamber on
Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surfa ...
, but quantification of thrust was not part of the experiment. The accompanying presentation has some good animations that illustrate physical principles described in the report. A 2004 Winglee paper primarily focused on usage of M2P2 for electromagnetic shielding. Beginning in 2003, the Magneto plasma sail design further investigated the plasma injection augmentation of the magnetic field, used larger coils and reported more modest gains.


Magnetoplasma sail (MPS)

In 2003 Funaki and others proposed an approach similar to the M2P2 design and called it the MagnetoPlasma Sail (MPS) that started with a coil R_c=0.2 m and a magnetic field falloff rate of f_o=1.52 with injected plasma creating an effective sail radius of L=26 km and assumed a conversion efficiency that transferred a fraction of the solar wind momentum to the spacecraft. Simulation results indicated a significant increase in magnetosphere size with plasma injection as compared to the Magsail design, which had no plasma injection. Analysis showed how adjustment of the MPS steering angle created force that could reach the outer planets. A satellite trial was proposed. Preliminary performance results were reported but later modified in subsequent papers. Many MPS papers have been published on the magnetic sail contributing to the understanding of general physical principles of an artificial magnetosphere, its magnetohydrodynamic model, and the design approach for computing the magnetopause distance for a given magnetic field source are documented in the linked sections of this article. In 2004 Funaki and others analyzed MPS cases where R_c=10 m and R_c=100 m as summarized in Table 2 predicting a characteristic length L of 50 and 450 km producing significant thrust with mass substantially less than the Magsail and hence significant acceleration. This paper detailed the MHD applicability test of equation that the characteristic length must be greater than the ion
gyroradius The gyroradius (also known as radius of gyration, Larmor radius or cyclotron radius) is the radius of the circular motion of a charged particle in the presence of a uniform magnetic field. In SI units, the non-relativistic gyroradius is given by :r_ ...
r_g (m) to effectively transfer solar wind momentum to the spacecraft. In 2005 Yamakawa and others further described a potential trial. An analogy with the Earth's magnetosphere and magnetopause in determining the penetration of plasma irregularities into the magnetopause defines the key parameter of a local kinetic plasma beta as the ratio of the dynamic pressure p_of the injected plasma over the magnetic pressure p_ as followswhere \rho_l (kg/m3) is the local plasma density, u_l (m/s) is the local velocity of the plasma and B_l (T) is the local magnetic field. Simulations have shown that the kinetic beta is smallest near the field source, at magnetopause and the bow shock. The kinetic \beta_k differs from the thermal plasma beta \beta_i=p_/p_ whis the ratio of the plasma thermal pressure to the magnetic pressure, with terms: p_=n \, k_B \,T is the plasma pressure with n (m−3) the number density, k_B (J/K) the
Boltzmann constant The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constant, ...
and T (eV) the ion temperature; and p_ = B^2/(2 \mu_0)the magnetic pressure for magnetic field B (T) and \mu_0 (H/m)
vacuum permeability The vacuum magnetic permeability (variously ''vacuum permeability'', ''permeability of free space'', ''permeability of vacuum''), also known as the magnetic constant, is the magnetic permeability in a classical vacuum. It is a physical constant, ...
. In the context of the MPS, \beta_k determines the propensity of the injected plasma flow to stretch the magnetic field while \beta_i specifies the relative energy of the injected plasma. In 2005 Funaki and others published numerical analysis showing f_0=1.88 for \beta_k=0.1. In 2009 Kajimura published simulation results with \beta_k=5 and \beta_i ranging from 6 to 20 that the magnetic field falloff rate f_0 with argon and xenon plasma injected into the polar region was f_0=2.1 and with argon plasma injected into the equatorial region was f_0=1.8. If \beta_k>1 then the Injection of a high-velocity, high-density plasma into a magnetosphere as proposed in M2P2 freezes the motion of a magnetic field into the plasma flow and was believed to inflate the magnetosphere. However experiments and numerical analysis determined that the solar wind cannot compress the magnetosphere and momentum transfer to the spacecraft is limited since momentum is transferred to injected plasma flowing out of the magnetosphere, similar to another criticism of M2P2. An alternative is to reduce the plasma injection velocity and density to result in \beta_k<1 to achieve a plasma in equilibrium with the inflated magnetic field and therefore induce an equatorial diamagnetic current in the same direction as the coil current as shown in the figure, thereby increasing the magnetic moment of the MPS field source and consequently increasing thrust. In 2013 Funaki and others published simulation and theoretical results regarding how characteristics of the injected plasma affected thrust gain through creation of an equatorial ring current. They defined thrust gain for MPS as G_=F_/F_: the ratio of the force generated by low beta plasma injection F_ divided by that of a pure magnetic sail F_ from equation with f_o =3 and C_=0.5 for r_g\leq L or from equation for r_g>L. They reported G_ of approximately 40 for magnetospheres less than the MHD applicability test and 3.77 for a larger magnetosphere where MHD applicability occurred, larger than values reported in 2012 of 20 and 3.3, respectively. Simulations revealed that optimum thrust gain occurred for \beta_k<1 and \beta_i \approx 10. In 2014 Arita, Nishida and Funaki published simulation results indicating that plasma injection created an equatorial ring current and that the plasma injection rate had a significant impact on thrust performance, with the lowest value simulated having the best performance of a thrust gain G_ of 3.77 with \beta_i \approx 25. They also reported that MPS increased the height of the magnetosphere by a factor of 2.6, which is important since it increases the effective sail blocking area. In 2014 Ashida and others documented Particle In Cell (PIC) simulation results for a kinematic model for cases where r_g >> L where MHD is not applicable. Equation (12) of their study included the additional force of the injected plasma jet F_ consisting of momentum and static pressure of ions and electrons and defined thrust gain as F_/(F_+F_), which differs from the definition of a term by the same name in other studies. It represents the gain of MPS over that of simply adding the magnetic sail force and the plasma injection jet force. For the values cited in the conclusion, F_/F_ is 7.5 in the radial orientation. Since a number of results were published by different authors at different times, the figure summarizes the reported thrust gain G_ versus magnetosphere size (or characteristic length L) with the source indicated in the legend as follows for simulation results Arita14, Ashida14, Funaki13, and Kajimura10. Simulation results require significant compute time, for example it took 1024 CPUs 4 days to simulate the simplest case and 4096 CPUs one week to simulate a more complex case. A thrust gain between 2 and 10 is common with the larger gains with a magnetic nozzle injecting plasma in one direction in opposition to the solar wind. The MHD applicability test of equation for the solar wind is L \approx72 km. Therefore, the estimated force of the MPS is that of equation multiplied by the empirically determined thrust gain G_ from the figure multiplied by the percentage thrust loss T_ from equation For example, using solar wind parameters \rho=8x10−21 kg/m3 and u=500 km/s then r_g=72 km and B_=4x10−8 T. With L=105 m for f_o=3 then r_g < L and T_\approx 11% from equation . The magnetic field only force with a coil radius of R_c=6,300 m and coil current I_c=1.6x106 A yields B_0=1.6x10−4 T from equation and with C_d=5 the magnetic force only is 175 N from equation . Determining G_ \approx4 from the figure at L=105 m as the multiplier for the magnetic-only force then the MPS force F_ \approx700 N. Since MPS injects ionized gas at a rate of m_(kg/s) that can be viewed as a propellant it has a ''
specific impulse Specific impulse (usually abbreviated ) is a measure of how efficiently a reaction mass engine (a rocket using propellant or a jet engine using fuel) creates thrust. For engines whose reaction mass is only the fuel they carry, specific impulse i ...
'' I_=F_/m_/g_0 where g_0 (m/s2) is the acceleration of
Earth's gravity The gravity of Earth, denoted by , is the net acceleration that is imparted to objects due to the combined effect of gravitation (from mass distribution within Earth) and the centrifugal force (from the Earth's rotation). It is a vector quantity ...
. Funaki and Arita stated m_=0.31 (kg/day). Therefore I_=28,325 (s) per newton of thrust force. The equivalent exhaust velocity v_e=g_0 \, I_ is 278 km/s per newton of thrust force. In 2015 Kajimura and others published simulation results for thrust performance with plasma injected by a magnetic nozzle, a technology used in
VASIMR The Variable Specific Impulse Magnetoplasma Rocket (VASIMR) is an electrothermal thruster under development for possible use in spacecraft propulsion. It uses radio waves to ionize and heat an inert propellant, forming a plasma, then a magnetic ...
. They reported a thrust gain G_ of 24 when the ion
gyroradius The gyroradius (also known as radius of gyration, Larmor radius or cyclotron radius) is the radius of the circular motion of a charged particle in the presence of a uniform magnetic field. In SI units, the non-relativistic gyroradius is given by :r_ ...
r_g (see equation ) was comparable to the characteristic length L , at the boundary of the MHD applicability test. The optimal result occurred with a thermal \beta_i \approx 1 with some decrease for higher values of thermal beta. In 2015 Hagiwara and Kajimura published experimental thrust performance test results with plasma injection using a
magnetoplasmadynamic thruster A magnetoplasmadynamic (MPD) thruster (MPDT) is a form of electrically powered spacecraft propulsion which uses the Lorentz force (the force on a charged particle by an electromagnetic field) to generate thrust. It is sometimes referred to as L ...
(aka MPD thruster or MPD Arcjet) in a single direction opposite the solar wind direction and a coil with the axial orientation. This meant that F_ provided additional propulsive force. Density plots explicitly show the increased plasma density upwind of the bow shock originating from the MPD thruster. They reported that F_>>F_+F_showing how MPS inflated the magnetic field to create more thrust than the magnetic sail alone plus that of the <>. The conclusion of the experiment was that the thrust gain G_ was approximately 12 for a scaled characteristic length of L = 60 km. In the above figure, note the significant improvement in thrust gain at L = 60 km.as compared with only plasma injection. In this example, using solar wind parameters \rho=8x10−21 kg/m3 and u=500 km/s then r_g=72 km and B_=4x10−8 T. With L=60 km for f_o=3 then r_g \approx L and T_\approx 28% from equation . The magnetic field only force with a coil radius of R_c=2,900 m and coil current I_c=1.6x106 A yields B_0=3.5x10−4 T from equation and with C_d=5 the magnetic force only is 51 N from equation . Given G_=12 as the multiplier for the magnetic only force then the MPS force F_ \approx611 N. In 2017 Ueno published a design proposing use of multiple coils to generate a more complex magnetic field to increase thrust production. In 2020 Murayama and others published additional experimental results for a multi-pole MPD thruster. In 2020 Peng and others published MHD simulation results for a magnetic dipole with plasma injection operating in
Low Earth orbit A low Earth orbit (LEO) is an orbit around Earth with a period of 128 minutes or less (making at least 11.25 orbits per day) and an eccentricity less than 0.25. Most of the artificial objects in outer space are in LEO, with an altitude never mor ...
at 500 km within the Earth's
Ionosphere The ionosphere () is the ionized part of the upper atmosphere of Earth, from about to above sea level, a region that includes the thermosphere and parts of the mesosphere and exosphere. The ionosphere is ionized by solar radiation. It plays an ...
where the ion number density is approximately 1011 (m−3). As reported in Figure 3, the magnetic field strength initially falls off as 1/r and then approaches 1/r2 at larger distances from the dipole. The radius of the artificial mini-magnetosphere could extend up to 200 m for this scenario. They reported that the injected plasma reduced magnetic field fall off rate and created of a drift current, similar to earlier reported MPS results for the solar wind.


Plasma magnet (PM)

The plasma magnet (PM) sail design introduced a different approach to generate a static magnetic dipole as illustrated in the figure. As shown in the detailed view on the right the field source is two relatively small crossed perpendicularly oriented antenna coils each of radius R_c (m), each carrying a sinusoidal
alternating current Alternating current (AC) is an electric current which periodically reverses direction and changes its magnitude continuously with time in contrast to direct current (DC) which flows only in one direction. Alternating current is the form in whic ...
(AC) with the total current of ''I_c'' (A) generated by an onboard power supply. The AC current applied to each coil is out of phase by 90 degrees and consequently generates a
rotating magnetic field A rotating magnetic field is the resultant magnetic field produced by a system of coils symmetrically placed and supplied with polyphase currents. A rotating magnetic field can be produced by a poly-phase (two or more phases) current or by a singl ...
(RMF) with
rotational speed Rotational frequency (also known as rotational speed or rate of rotation) of an object Rotation around a fixed axis, rotating around an axis is the frequency of rotation of the object. Its unit is revolution per minute (rpm), cycle per second ...
\omega_(rad/s) chosen that is fast enough that positive ions do not rotate but the less massive electrons rotate at this speed. The figure illustrates rotation using color coded contours of constant magnetic strength, not magnetic field lines. In order to inflate the magnetospheric bubble the thermal plasma beta \beta_t must be high and initially a plasma injection may be necessary, analogous to inflating a balloon when small and internal tension is high. After initial inflation, protons and rotating electrons are captured from the plasma wind through the leaky magnetopause and as shown in the left create a current disc shown as transparent red in the figure with darker shading indicating greatest density near the coil pair and extending out to the magnetopause radius ''Rmp'', which is orders of magnitude larger than the coil radius ''Rc'' (figure not drawn to scale). See RMDCartoon.avi for an animation of this effect. The induced current disc carries a direct current I_ (A) orders of magnitude larger than the input alternating current ''I_c'' (A) and forms a static dipole magnetic field oriented perpendicular to the current disc reaching a standoff balance with the plasma wind pressure at distance R_ \approx L at the magnetopause boundary according to the MHD model of an artificial magnetosphere. The magnetic field falloff rate was assumed to be f_o =1 is described in detail in, but as described by Khazanov, restated by Kirtley and Slough and several MPS studies concluded that f_o is closer to 2. The falloff rate f_o is a critical parameter in the determination of performance. The RMF-induced rotating disc of electrons has current density j_\theta(r) (A/m2) at distance ''r'' from the antenna as given by equation (5) for f_o=1 and equation (4) for f_o=2, which states that flux conservation requires this falloff rate, consistent with a criticism of M2P2 by Cattell as follows: where B(R_0) (T) is the magnetic field at radius R_0 \approx R_c (m) near the antenna coils. Note that the current density is highest at r=R_0 and falls off at a rate of f_o+1. A critical condition for the plasma magnet design from equation (1a) provides a lower bound on the RMF frequency \omega_ (rad/s) as follows so that electrons in the plasma wind are magnetized and rotate but the ions are not magnetized and do not rotate: where \omega_ (rad/s) is the
ion gyrofrequency Plasma parameters define various characteristics of a Plasma (physics), plasma, an electrically conductive collection of charged particles that responds ''collectively'' to electromagnetic forces. Plasma typically takes the form of neutral gas-li ...
in the RMF near the antenna coils, Z is charge number of the ion, e (C) is the
elementary charge The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a fundame ...
, and m_i (kg) is the (average) mass of the ion(s). Specifying the magnetic field near the coils at radius R_0 is critical since this is where the current density is greatest. Choosing a magnetic field at magnetopause yields a lower value of \omega_ but ions closer to the coils will rotate. Another condition is that \omega_ be small enough such that collisions are extremely unlikely. The required power to generate the RMF P_ is derived by integrating the product of the square of the current density from equation and the resistivity of the plasma \eta_p (kg/m3) from R_0to R_ with the result as follows: where \eta_p (W m) is the
Spitzer resistivity The Spitzer resistivity (or plasma resistivity) is an expression describing the electrical resistance in a plasma, which was first formulated by Lyman Spitzer in 1950. The Spitzer resistivity of a plasma decreases in proportion to the electron temp ...
of the plasma of ~1.2x10−3 T_e where ''T_e'' is the electron temperature assumed to be 15 eV. The above result is the same as equation (7) for f_o=1 and equation (5) for f_o=2. Starting with the definition of plasma wind power from equation , rearranging and recognizing that equation can be substituted and then using equation yields the following expression which is the same as equation (10) for f_o=1. Note that solution for P_ and R_0 must also satisfy equation . A number of the examples cited assume a magnetopause radius R_ that does not meet the MHD applicability test of equation . From the definition of power in physics a constant force is power divided by velocity, the force generated by the plasma magnet (PM) sail is as follows Note that as the falloff rate f_o increases that the force derived from the plasma wind decreases, or to maintain the same force P_ and/or R_0 must increase. Equation gives the mass for each physical coil of radius R_c (m). Since the RMF requires alternating current and semiconductors are not efficient at higher frequencies, aluminum was specified with mass density \delta_c = 2,700 (kg/m3). Estimates of the coil mass are optimistic by a factor of 4 \pi since only one coil was sized and the coil circumference was specified as R_c instead of 2 \pi R_c. The coil resistance is the product of coil material resistivity \eta_c (Ω m) (e.g., ~3x10−8 for aluminum) and the coil length 2 \pi R_c (m) divided by the coil wire cross sectional area where r_c (m) is the radius of the coil wire as follows: Some additional power must compensate for resistive loss but it is orders of magnitude less than P_. The peak current carried by a coil is specified by the RMF power and coil resistance from the definition of electrical power in physics as follows: The current induced in the disc by the RMF I_ (A) is the integral of the current density j(r,f_o) from equation on the surface of the disc with inner radius R_c and outer radius R_ with result: the same as equation (11) from Slough for f_o=1. Laboratory experiments validated that the RMF creates a magnetospheric bubble, electron temperature near the coils increases and that thrust was generated. Since the scale of a terrestrial experiment is limited simulations or a flight trial was recommended. Some of these concepts adapted to an ionospheric plasma environment were carried on in the Magnetoshell magnetic design. In 2022 Freeze, Greason and others published a detailed design for a
plasma magnet A plasma magnet is a proposed spacecraft propulsion device that uses a dipole magnetic field to capture energy from the solar wind. The field acts as a sail, using the captured energy to propel the spacecraft analogously to how the wind propels a sa ...
based sail for a spacecraft named Wind Rider that would use solar wind force to accelerate away from near Earth and decelerate against the magnetosphere of Jupiter in a spaceflight trial mission called Jupiter Observing Velocity Experiment (JOVE). This design employed a pair of superconducting coils each with radius R_c of 9 (m), an alternating current of I_c of 112 (A) with  \omega_/(2\pi) of 4 (Hz). For example, using solar wind parameters \rho=8x10−21 kg/m3 and u=500 km/s then r_g=72 km and B_=4x10−8 T. With L=105 m and f_o=2 then r_g < L. With a coil radius of R_c=1,000 m yields B_0=4x10−4 T from equation . The required RMF power from equation is 13 kW with a required AC coil current I_c=10 A from equation resulting in an induced current of I_=2 kA from equation . With C_d=5 the plasma magnet force from equation is 197 N. The magnetic force only for the above parameters is 2.8 N from equation and therefore the plasma magnet thrust gain is 71. Using f_o=1 creates very optimistic performance numbers, but since Slough changed this to f_o=2 in 2012, this case is not compared in this article.


Plasma magnetoshell (PMS)

A 2012 study by Kirtley and Slough investigated the plasma magnet technology for use in the ionosphere of a planet as a braking mechanism in an approach dubbed plasma magnetoshell. The magnetoshell creates drag by ionizing neutral atoms in a planet's ionosphere then magnetically deflecting them. A tether attaching the plasma magnet coils to the spacecraft transfers momentum such that orbital insertion occurs. Analytical models, laboratory demonstrations and mission profiles to Neptune and Mars were described. In 2017 Kelly described using a single-coil magnet with 1/r3 magnetic field falloff rate and more experimental results. In 2019 Kelly and Little published simulation results for magnetoshell performance scaling. A magnet with radius R_c=1 m was tethered to a spacecraft with batteries for 1,000 seconds of operation (longer than aerocapture designs). The simulations assumed a magnet mass M_c=1,000 kg and total magnetoshell system mass of 1,623 kg, suitable for a
Cassini–Huygens ''Cassini–Huygens'' ( ), commonly called ''Cassini'', was a space research, space-research mission by NASA, the European Space Agency (ESA), and the Italian Space Agency (ASI) to send a space probe to study the planet Saturn and its system, i ...
or
Juno Juno commonly refers to: *Juno (mythology), the Roman goddess of marriage and queen of the gods *Juno (film), ''Juno'' (film), 2007 Juno may also refer to: Arts, entertainment and media Fictional characters *Juno, in the film ''Jenny, Juno'' *Ju ...
size orbiter. The planet's mass and atmosphere atomic composition and density determine a threshold velocity where magnetoshell operation is feasible. Saturn and Neptune have a hydrogen atmosphere and a threshold velocity of approximately 22 km/s. In a Neptune mission a \Delta v=6 km is required for a 5,000 kg spacecraft and must average 50 kN for the maneuver duration. The model overestimates performance for N2 (Earth, Titan) and CO2 (Venus, Mars) atmospheres since multiple ion species are created and more complex interactions occur. Furthermore, the relatively lower mass of Venus and Mars reduces the threshold velocity below that of feasible magnetoshell operation. The paper states that
aerocapture Aerocapture is an orbital transfer maneuver in which a spacecraft uses aerodynamic drag force from a single pass through a planetary atmosphere to decelerate and achieve orbit insertion. Aerocapture uses a planet's or moon's atmosphere to accom ...
technologies are mature enough for these mission profiles. In 2021 Kelly and Little published further details for use of drag-modulated plasma aerocapture (DMPA) that when compared to Adaptable Deployable Entry and Placement Technology (ADEPT) for drag-modulated aerocapture (DMA) to Neptune that could deliver 70% higher orbiter mass and experience 30% lower stagnation heating.


Beam powered magsail (BPM)

A beam-powered of M2P2 variant, MagBeam was proposed in 2011. In this design a magnetic sail is used with
beam-powered propulsion Beam-powered propulsion, also known as directed energy propulsion, is a class of aircraft or spacecraft propulsion that uses energy beamed to the spacecraft from a remote power plant to provide energy. The beam is typically either a microwave or a ...
, by using a high-power
particle accelerator A particle accelerator is a machine that uses electromagnetic fields to propel charged particles to very high speeds and energies, and to contain them in well-defined beams. Large accelerators are used for fundamental research in particle ...
to fire a beam of charged particles at the spacecraft. The magsail would deflect this beam, transferring momentum to the vehicle, that could provide higher acceleration than a solar sail driven by a
laser A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The fir ...
, but a charged particle beam would disperse in a shorter distance than a laser due to the electrostatic repulsion of its component particles. This dispersion problem could potentially be resolved by accelerating a stream of sails which then in turn transfer their momentum to a magsail vehicle, as proposed by
Jordin Kare Jordin T. Kare (October 24, 1956 – July 19, 2017) was a physicist and aerospace engineer known for his research on laser propulsion. In particular, he was responsible for Mockingbird, a conceptual design for an extremely small (75 kg dry ...
.


Performance comparison

The table below compares performance measures for the magnetic sail designs with the following parameters for the solar wind (sw) at 1 AU: velocity u_= 500 km/s, number density n_i= 5x106 (m−3), ion mass m_i = 1.67x10−27 kg a
proton mass A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...
, resulting in mass density \rho_= m_i n_i = 8.4x10−21 (kg/m3), and coefficient of drag C_d=5 where applicable. Equation gives the magnetic field at magnetopause as B_≈ 36 nT, equation gives the ion gyroradius r_g ≈ 72 km for C_=2. Table entries in boldface are from a cited source as described in the following: Equation determines force for the Magsail (MS) divided by the Freeland correction factor 3.1, equation defines the force for the
plasma magnet (PM) A plasma magnet is a proposed spacecraft propulsion device that uses a dipole magnetic field to capture energy from the solar wind. The field acts as a sail, using the captured energy to propel the spacecraft analogously to how the wind propels a sa ...
with the assumed magnetic field falloff rate f_o=2. The force for the magnetic sail alone F_ is from equation . Thrust gain G_T for the magneto plasma sail (MPS) is the simulation and/or experimentally determined value with force defined equation to account for thrust loss due to operation in a kinematic region. The last column headed MPS+MPD adds a magnetoplasma dynamic thruster (MPD) that has a higher thrust gain as determined by experiment and simulation. Further details are in the section for the specific design. For designs other than MPS and MPS+MPD, the thrust gain G_T is the achieved force from the first row divided by the force of a magnetic sail alone in the second row. The magnetopause distance R_ \approx L (m) and the coil radius R_c(m) are design parameters. Equation with r=R_ defines the magnetic field near the coil(s) as B_0=B(R_0)=B_(R_/R_0)^ (T). The superconducting coil designs used a critical current density J_c=2x106 (A/m) to account for warmer temperatures in the solar system. The plasma magnet uses AC power and cannot use a superconducting coil and assumed an aluminum coil with material density \delta_c = 2,700 kg/m3 and coil wire radius r_c=5 mm. All other designs assumed a superconducting coil with material density \delta_c =6,500 kg/m3, coil wire radius r_c=5 mm, and critical current \max I_c \approx 1.6 x106 A, above which the coil becomes a normal conductor. The magnetopause distance R_ \approx L and coil radius R_c for superconducting-coil based designs were adjusted to meet this critical current constraint. The values for the plasma magnet used a value of R_c for f_o=2 selected to minimize time to velocity and distance. The MPS values for R_ \approx L and R_c were chosen to match the thrust gain from simulation and scaled experimental results and meet the superconducting-coil critical current constraint. Equation gives the physical coil mass M_c(phy) (kg) assuming a coil wire radius r_c=5 mm. Equation gives the plasma magnet alternating current I_c . Equation gives the direct current I_c with C_0=2 for all other designs. The plasma magnet RMF uses the input alternating current I_c (kA) to rotate electrons in captured plasma to create an induced direct current disc carrying I_ kA as defined in equation . Designs with a superconducting coil do not require continuous power (but may require power for other functions, such as cooling); however, the plasma magnet design requires a continuous power source as specified in equation . An estimate for the plasma magnet power supply mass assumes ~3 kg/W for
nuclear power in space Nuclear power in space is the use of nuclear power in outer space, typically either small fission systems or radioactive decay for electricity or heat. Another use is for scientific observation, as in a Mössbauer spectrometer. The most common ...
. Other mass was assumed to be 10 tonnes for MS and 1 tonne of other mass for plasma magnet and MPS. Acceleration a is the thrust force F (N) from the first row divided by the total mass (coil plus other). An optimistic approximation is constant acceleration a (m/s2), for which the time to reach a target velocity V (km/s) of 10% of the solar wind velocity is T_V \approx V/a (days) and time to cover a specified distance D ≈ 7.8x108 km (approximate distance from Earth to Jupiter) is T_D \approx \sqrt (days). For comparison purposes the time for a
Hohmann transfer In astronautics, the Hohmann transfer orbit () is an orbital maneuver used to transfer a spacecraft between two orbits of different altitudes around a central body. Examples would be used for travel between low Earth orbit and Moon, the Moon, ...
from Earth orbit to Jupiter orbit is 2.7 years (almost 1,000 days) but that would allow orbital insertion whereas a magnetic sail would do a flyby unless the magnetosphere and gravity of Jupiter could provided deceleration. Another comparison is the
New Horizons ''New Horizons'' is an Interplanetary spaceflight, interplanetary space probe that was launched as a part of NASA's New Frontiers program. Engineered by the Johns Hopkins University Applied Physics Laboratory (APL) and the Southwest Research ...
interplanetary space probe with a 30 kg payload that flew by Jupiter after 405 days on its way to Pluto. The best time to velocity T_V and distance T_D performance occurs for the PM and MPS designs due primarily to much reduced coil and other mass. As described in the M2P2 section, several criticisms asserted that the falloff rate f_o=1 was questionable and hence it was not included in this table. Simulations and experiments as described in the MPS section showed that f_o=2 is valid with injection of plasma to inflate the magnetic field in a manner similar to M2P2. As described in the PM section, plasma is not injected but instead captured to achieve a falloff rate of f_o=2, with calculations assuming f_o=1 being very optimistic. The classic Magsail (MS) design generates the most thrust force and has considerable mass but still has relatively good time performance. Parameters for the other designs were chosen to yield comparable time performance subject to the constraints previously described. As described above and further detailed in the section for the respective design, this article contains the equations and parameters to compute performance estimates for different parameter choices.


Criticisms and advantages/disadvantages


Criticisms

In 1994 Vulpetti published a critical review regarding viability of space propulsion based on solar wind momentum flux. The paper highlighted technology challenges in terms of the magnetic field source, energy required and interaction between the solar wind and the spacecraft's magnetic field, summarizing that these issues were not insurmountable. The major unresolved issue is spacecraft and mission design that account for the potentially highly variable solar wind velocity and plasma density that could complicate maneuvers by a spacecraft employing magnetic sail technology. Some means of modulating thrust is necessary. If the mission objective is to rapidly escape the solar system then the paper states that this is less of an issue. In 2006 Bolonkin published a paper that questioned the theoretical viability of a Magsail and described common mistakes. Equation (2) states that the magnetic field of electrons rotating in the large coil was greater than and opposed the magnetic field generated by the current in the coil and hence no thrust would result. In 2014 Vulpetti published a rebuttal that summarized plasma properties, in particular the fact that plasma is quasi-neutral and noted in equation (B1) that the Bolonkin paper equation (2) assumed that the plasma had a large net negative electrical charge. The plasma charge varies statistically over short intervals and the maximum value has negligible impact on Magsail performance. Furthermore, he argued that observations by many spacecraft have observed compression of a magnetic field by dynamic (or ram) pressure that did not depend on particle charges. In 2017, Gros published results that differed from prior magsail work. A major result was the Magsail kinetic model of equation that is a curve fit to numerical analysis of proton trajectories impacted by a large current carrying superconducting coil. The curve fit scaling relation for the effective sail area A(v) was logarithmic cubed with argument c I / (v I_G) with I the loop current, I_G the curve fit parameter, v the ship velocity and c the speed of light. This differed from the power law scaling A(v) \sim (v/c)^\alpha of prior work. The Gros paper could not trace back this difference to underlying physical arguments and noted that the results are inconsistent, stating that the source for these discrepancies was unclear. Appendix B questioned whether a bow shock will form if the initial spacecraft velocity v_0 is large, for example for deceleration after interstellar travel, since the predicted effective sail area A_G(v) is small in this case. One difference is that this analysis used the coil radius R_c for computation of the ion gyroradius as compared with prior work use of the magnetopause radius R_


Advantages and disadvantages

One advantage of magnetic or solar sails over (chemical or ion) reaction thrusters is that little to no reaction mass is depleted or carried in the craft. Acceleration or deceleration against a planetary magnetosphere is possible. A disadvantage for interplanetary travel is that acceleration is only in the direction of a plasma wind away from the Sun or a star or deceleration in only in the direction opposite to the plasma wind from the Sun or a star. Only deceleration is possible in the
interstellar medium In astronomy, the interstellar medium is the matter and radiation that exist in the space between the star systems in a galaxy. This matter includes gas in ionic, atomic, and molecular form, as well as dust and cosmic rays. It fills interstella ...
.


Fictional uses in popular culture

''Magnetic sails'' have become a popular
trope Trope or tropes may refer to: Arts, entertainment, and media * Trope (cinema), a cinematic convention for conveying a concept * Trope (literature), a figure of speech or common literary device * Trope (music), any of a variety of different things ...
in many works of
science fiction Science fiction (sometimes shortened to Sci-Fi or SF) is a genre of speculative fiction which typically deals with imaginative and futuristic concepts such as advanced science and technology, space exploration, time travel, parallel unive ...
although the
solar sail Solar sails (also known as light sails and photon sails) are a method of spacecraft propulsion using radiation pressure exerted by sunlight on large mirrors. A number of spaceflight missions to test solar propulsion and navigation have been p ...
is more popular: # The ancestor of the magsail, the Bussard magnetic scoop, first appeared in science-fiction in
Poul Anderson Poul William Anderson (November 25, 1926 – July 31, 2001) was an American fantasy and science fiction author who was active from the 1940s until the 21st century. Anderson wrote also historical novels. His awards include seven Hugo Awards and ...
's 1967 short story ''To Outlive Eternity'', which was followed by the novel ''
Tau Zero ''Tau Zero'' is a hard science fiction novel by American writer Poul Anderson. The novel was based upon the short story "To Outlive Eternity" appearing in ''Galaxy Science Fiction'' in 1967. It was first published in book form in 1970. The book i ...
'' in 1970. # The magsail appears as a crucial plot device in ''The Children's Hour'', a ''
Man-Kzin Wars ''The Man-Kzin Wars'' is a series of military science fiction anthologies and is the name of the first. The short stories detail the eponymous conflicts between mankind and the Kzinti, set in Larry Niven's ''Known Space'' universe. However, Nive ...
'' novel by
Jerry Pournelle Jerry Eugene Pournelle (; August 7, 1933 – September 8, 2017) was an American scientist in the area of operations research and human factors research, a science fiction writer, essayist, journalist, and one of the first bloggers. In the 1960s ...
and S.M. Stirling (1991). # It also features prominently in the science-fiction novels of
Michael Flynn Michael Thomas Flynn (born December 24, 1958) is a retired United States Army lieutenant general and conspiracy theorist who was the 24th U.S. National Security Advisor for the first 22 days of the Trump administration. He resigned in light of ...
, particularly in ''The Wreck of the River of Stars'' (2003); this book is the tale of the last flight of a magnetic sail ship when
fusion rocket A fusion rocket is a theoretical design for a rocket driven by fusion propulsion that could provide efficient and sustained acceleration in space without the need to carry a large fuel supply. The design requires fusion power technology beyond cu ...
s based on the Farnsworth-Hirsch Fusor have become the preferred technology. #
GURPS The ''Generic Universal RolePlaying System'', or ''GURPS'', is a tabletop role-playing game system designed to allow for play in any game setting. It was created by Steve Jackson Games and first published in 1986 at a time when most such systems w ...
Spaceships features both
solar sail Solar sails (also known as light sails and photon sails) are a method of spacecraft propulsion using radiation pressure exerted by sunlight on large mirrors. A number of spaceflight missions to test solar propulsion and navigation have been p ...
s and magnetic sails as possible methods of spacecraft propulsion. Although not referred to as a "magnetic sail", the concept was used in the novel Encounter with Tiber by
Buzz Aldrin Buzz Aldrin (; born Edwin Eugene Aldrin Jr.; January 20, 1930) is an American former astronaut, engineer and fighter pilot. He made three spacewalks as pilot of the 1966 Gemini 12 mission. As the Lunar Module ''Eagle'' pilot on the 1969 A ...
and
John Barnes John Charles Bryan Barnes MBE (born 7 November 1963) is a former professional football player and manager. He currently works as an author, commentator and pundit for ESPN and SuperSport. Initially a quick, skilful left winger, he moved to cent ...
as a braking mechanism to decelerate starships from relativistic speed.


See also

* * interacts with magnetosphere in similar manner to magsail * (Magnetized beamed plasma propulsion)a beam-powered variant of
mini-magnetospheric plasma propulsion A magnetic sail is a proposed method of spacecraft propulsion that uses a static magnetic field to deflect a plasma wind of charged particles radiated by the Sun or a Star thereby transferring momentum to accelerate or decelerate a spacecraft. ...
(M2P2). * Other methods of spacecraft propulsion used to change the velocity of spacecraft and artificial satellites. *


References


External links


プラズマ・核融合学会誌 - 磁気プラズマセイルの研究と深宇宙探査への挑戦
PDF)
九州大学大学院 - MPSにおける磁気インフレーションに関する研究
PDF)
JAXA - プラズマセイル
PDF)
神戸大学大学院 - 惑星間航行システム開発に向けたマルチスケール粒子シミュレーション
PDF)
JAXA - 磁気プラズマセイルの推力発生メカニズムの解明
PDF) {{DEFAULTSORT:Magnetic Sail Spacecraft propulsion Spacecraft components Electrodynamics Magnetic propulsion devices