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The interchange instability is a type of
plasma instability The stability of a plasma is an important consideration in the study of plasma physics. When a system containing a plasma is at equilibrium, it is possible for certain parts of the plasma to be disturbed by small perturbative forces acting on it ...
seen in magnetic fusion energy that is driven by the gradients in the
magnetic pressure In physics, magnetic pressure is an energy density associated with a magnetic field. In SI units, the energy density P_B of a magnetic field with strength B can be expressed as :P_B = \frac where \mu_0 is the vacuum permeability. Any magnetic fie ...
in areas where the confining magnetic field is curved. The name of the instability refers to the action of the plasma changing position with the magnetic field lines (i.e. an interchange of the lines of force in space) without significant disturbance to the geometry of the external field. The instability causes flute-like structures to appear on the surface of the plasma, and thus the instability is also known as the flute instability. The interchange instability is a key issue in the field of
fusion energy Fusion power is a proposed form of power generation that would generate electricity by using heat from nuclear fusion reactions. In a fusion process, two lighter atomic nuclei combine to form a heavier nucleus, while releasing energy. Devices de ...
, where magnetic fields are used to confine a plasma in a volume surrounded by the field. The basic concept was first noted in a 1954 paper by
Martin David Kruskal Martin David Kruskal (; September 28, 1925 – December 26, 2006) was an American mathematician and physicist. He made fundamental contributions in many areas of mathematics and science, ranging from plasma physics to general relativity and ...
and
Martin Schwarzschild Martin Schwarzschild (May 31, 1912 – April 10, 1997) was a German-American astrophysicist. Biography Schwarzschild was born in Potsdam into a distinguished German Jewish academic family. His father was the physicist Karl Schwarzschild and ...
, which demonstrated that a situation similar to the
Rayleigh–Taylor instability The Rayleigh–Taylor instability, or RT instability (after Lord Rayleigh and G. I. Taylor), is an instability of an interface between two fluids of different densities which occurs when the lighter fluid is pushing the heavier fluid. Drazin ( ...
in classic fluids existed in magnetically confined plasmas. The problem can occur anywhere where the magnetic field is concave with the plasma on the inside of the curve.
Edward Teller Edward Teller ( hu, Teller Ede; January 15, 1908 – September 9, 2003) was a Hungarian-American theoretical physicist who is known colloquially as "the father of the hydrogen bomb" (see the Teller–Ulam design), although he did not care for ...
gave a talk on the issue at a meeting later that year, pointing out that it appeared to be an issue in most of the fusion devices being studied at that time. He used the analogy of
rubber band A rubber band (also known as an elastic band, gum band or lacky band) is a loop of rubber, usually ring or oval shaped, and commonly used to hold multiple objects together. The rubber band was patented in England on March 17, 1845 by Stephen P ...
s on the outside of a blob of jelly; there is a natural tendency for the bands to snap together and eject the jelly from the center. Most machines of that era suffered from other instabilities that were far more powerful, and whether or not the interchange instability was taking place could not be confirmed. This was finally demonstrated beyond doubt by a Soviet
magnetic mirror A magnetic mirror, known as a magnetic trap (магнитный захват) in Russia and briefly as a pyrotron in the US, is a type of magnetic confinement device used in fusion power to trap high temperature plasma using magnetic fields. T ...
machine during an international meeting in 1961. When the US delegation stated they were not seeing this problem in their mirrors, it was pointed out they were making an error in the use of their instrumentation. When that was considered, it was clear the US experiments were also being affected by the same problem. This led to a series of new mirror designs, as well as modifications to other designs like the
stellarator A stellarator is a plasma device that relies primarily on external magnets to confine a plasma. Scientists researching magnetic confinement fusion aim to use stellarator devices as a vessel for nuclear fusion reactions. The name refers to the ...
to add negative curvature. These had cusp-shaped fields so that the plasma was contained within convex fields, the so-called "magnetic well" configuration. In modern designs, the interchange instability is suppressed by the complex shaping of the fields. In the
tokamak A tokamak (; russian: токамáк; otk, 𐱃𐰸𐰢𐰴, Toḳamaḳ) is a device which uses a powerful magnetic field to confine plasma in the shape of a torus. The tokamak is one of several types of magnetic confinement devices being ...
design there are still areas of "bad curvature", but particles within the plasma spend only a short time in those areas before being circulated to an area of "good curvature". Modern stellarators use similar configurations, differing from tokamaks largely in how that shaping is created.


Basic concept

Magnetic confinement systems attempt to hold the plasma within a
vacuum chamber A vacuum chamber is a rigid enclosure from which air and other gases are removed by a vacuum pump. This results in a low-pressure environment within the chamber, commonly referred to as a vacuum. A vacuum environment allows researchers to con ...
using magnetic fields. The plasma particles are electrically charged, and thus see a transverse force from the field due to the Lorentz force. When the particle's original linear motion is superimposed on this transverse force, its resulting path through space is a
helix A helix () is a shape like a corkscrew or spiral staircase. It is a type of smooth space curve with tangent lines at a constant angle to a fixed axis. Helices are important in biology, as the DNA molecule is formed as two intertwined helic ...
, or corkscrew shape. Such a field will thus trap the plasma by forcing it to flow along the lines. One can produce a linear field using an
electromagnet An electromagnet is a type of magnet in which the magnetic field is produced by an electric current. Electromagnets usually consist of wire wound into a coil. A current through the wire creates a magnetic field which is concentrated in ...
in the form of a solenoid wrapped around a tubular vacuum chamber. In this case, the plasma will orbit the lines running down the center of the chamber and be prevented from moving outward towards the walls. This does not confine the plasma along the length of the tube, and it will rapidly flow out the ends. Designs that prevented this from occurring appeared in the early 1950s and experiments began in earnest in 1953. However, all of these devices proved to leak plasma at rates far higher than expected. In May 1954,
Martin David Kruskal Martin David Kruskal (; September 28, 1925 – December 26, 2006) was an American mathematician and physicist. He made fundamental contributions in many areas of mathematics and science, ranging from plasma physics to general relativity and ...
and
Martin Schwarzschild Martin Schwarzschild (May 31, 1912 – April 10, 1997) was a German-American astrophysicist. Biography Schwarzschild was born in Potsdam into a distinguished German Jewish academic family. His father was the physicist Karl Schwarzschild and ...
published a paper demonstrating two effects that meant plasmas in magnetic fields were inherently unstable. One of the two effects, which became known as the
kink instability A kink instability (also kink oscillation or kink mode), is a current-driven plasma instability characterized by transverse displacements of a plasma column's cross-section from its center of mass without any change in the characteristics of the ...
, was already being seen in early
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 simp ...
experiments and occurred slowly enough to be captured on movie film. The topic of stability immediately gained significance in the field. The other instability noted in the paper considered an infinite sheet of plasma held up against gravity by a magnetic field. It suggested there would be behaviour similar to that in classical physics when one heavy fluid is supported by a lighter one, which leads to the
Rayleigh–Taylor instability The Rayleigh–Taylor instability, or RT instability (after Lord Rayleigh and G. I. Taylor), is an instability of an interface between two fluids of different densities which occurs when the lighter fluid is pushing the heavier fluid. Drazin ( ...
. Any small vertical disturbance in an initially uniform field would result in the field pulling on the charges laterally and causing the initial disturbance to be further magnified. As large sheets of plasma were not common in existing devices, the outcome of this effect was not immediately obvious. It was not long before a corollary became obvious; the initial disturbance resulted in a curved interface between the plasma and the external field, and this was inherent to any design that had a convex area in the field. In October 1954 a meeting of the still-secret
Project Sherwood Project Sherwood was the codename for a United States program in controlled nuclear fusion during the period it was classified. After 1958, when fusion research was declassified around the world, the project was reorganized as a separate division w ...
researchers was held at
Princeton University Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the ...
's Gun Club building.
Edward Teller Edward Teller ( hu, Teller Ede; January 15, 1908 – September 9, 2003) was a Hungarian-American theoretical physicist who is known colloquially as "the father of the hydrogen bomb" (see the Teller–Ulam design), although he did not care for ...
brought up the topic of this instability and noted that two of the major designs being considered, the
stellarator A stellarator is a plasma device that relies primarily on external magnets to confine a plasma. Scientists researching magnetic confinement fusion aim to use stellarator devices as a vessel for nuclear fusion reactions. The name refers to the ...
and the
magnetic mirror A magnetic mirror, known as a magnetic trap (магнитный захват) in Russia and briefly as a pyrotron in the US, is a type of magnetic confinement device used in fusion power to trap high temperature plasma using magnetic fields. T ...
, both had large areas of such curvature and thus should be expected to be inherently unstable. He further illustrated it by comparing the situation to
jello Jell-O is an American brand offering a variety of powdered gelatin dessert (fruit-flavored gels/jellies), pudding, and no-bake cream pie mixes. The original gelatin dessert ( genericized as jello) is the signature of the brand. "Jell-O" is a r ...
being held together with
rubber band A rubber band (also known as an elastic band, gum band or lacky band) is a loop of rubber, usually ring or oval shaped, and commonly used to hold multiple objects together. The rubber band was patented in England on March 17, 1845 by Stephen P ...
s; while such a setup might be created, any slight disturbance would cause the rubber bands to contract and eject the jello. This exchange of position appeared to be identical to the mirror case in particular, where the plasma naturally wanted to expand while the magnetic fields had an internal tension. No such behaviour had been seen in experimental devices, but as the situation was considered further, it became clear it would be more obvious in areas of greater curvature, and existing devices used relatively weak magnetic fields with relatively flat fields. This nevertheless presented a significant problem; a key measure of the attractiveness of a reactor design was its '' beta'', the ratio of magnetic field strength to confined plasma - higher beta meant more plasma for the same magnet, which was a significant factor in cost. However, higher beta also implied more curvature in these devices, which would make them increasingly unstable. This might force reactors to operate at low beta and be doomed to be economically unattractive. As the magnitude of the problem became clear, the meeting turned to the question of whether or not there was any arrangement that was naturally stable. Jim Tuck was able to provide a solution; the picket fence reactor concept had been developed as a solution to another problem,
bremsstrahlung ''Bremsstrahlung'' (), from "to brake" and "radiation"; i.e., "braking radiation" or "deceleration radiation", is electromagnetic radiation produced by the deceleration of a charged particle when deflected by another charged particle, typicall ...
losses, but he pointed out that its field arrangement would be naturally stable under the conditions shown in the Kruskal/Schwarzschild paper. Nevertheless, as Amasa Bishop noted; The correctness of the simplified model was then called into question and led to further study. The answer appeared at a follow-up meeting at
Berkeley Berkeley most often refers to: *Berkeley, California, a city in the United States **University of California, Berkeley, a public university in Berkeley, California * George Berkeley (1685–1753), Anglo-Irish philosopher Berkeley may also refer ...
in February 1955, where
Harold Grad Harold Grad (January 23, 1923 in New York City – November 17, 1986) was an American applied mathematician. His work specialized in the application of statistical mechanics to plasma physics and magnetohydrodynamics. Work In statistical mechan ...
of
New York University New York University (NYU) is a private research university in New York City. Chartered in 1831 by the New York State Legislature, NYU was founded by a group of New Yorkers led by then- Secretary of the Treasury Albert Gallatin. In 1832, th ...
,
Conrad Longmire Conrad Lee Longmire (August 23, 1921 – March 22, 2010) was an American theoretical physicist who was best known as the discoverer of the mechanism behind high-altitude electromagnetic pulse. In 1961, Longmire was awarded the Ernest Orlando Law ...
of Los Alamos and Edward A. Frieman of Princeton presented independent developments that all proved the effect to be real, and worse, should be expected at ''any'' beta, not just high beta. Further work at Los Alamos demonstrated that the effect should be seen in both the mirror and stellarator. The effect is most obvious in the
magnetic mirror A magnetic mirror, known as a magnetic trap (магнитный захват) in Russia and briefly as a pyrotron in the US, is a type of magnetic confinement device used in fusion power to trap high temperature plasma using magnetic fields. T ...
device. The mirror has a field that runs along the open center of the cylinder and bundles together at the ends. In the center of the chamber the particles follow the lines and flow towards either end of the device. There, the increasing magnetic
density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...
causes them to "reflect", reversing direction and flowing back into the center again. Ideally, this will keep the plasma confined indefinitely, but even in theory there a critical angle between the particle trajectory and the axis of the mirror where particles can escape. Initial calculations showed that the loss rate through this process would be small enough to not be a concern. In practice, all mirror machines demonstrated a loss rate far higher than these calculations suggested. The interchange instability was one of the major reasons for these losses. The mirror field has a cigar shape to it, with increasing curvature at the ends. When the plasma is located in its design location, the electrons and ions are roughly mixed. However, if the plasma is displaced, the non-uniform nature of the field means the ion's larger orbital radius takes them outside the confinement area while the electrons remain inside. It is possible the ion will hit the wall of the container, removing it from the plasma. If this occurs, the outer edge of the plasma is now net negatively charged, attracting more of the positively charged ions, which then escape as well. This effect allows even a tiny displacement to drive the entire plasma mass to the walls of the container. The same effect occurs in any reactor design where the plasma is within a field of sufficient curvature, which includes the outside curve of toroidal machines like the
tokamak A tokamak (; russian: токамáк; otk, 𐱃𐰸𐰢𐰴, Toḳamaḳ) is a device which uses a powerful magnetic field to confine plasma in the shape of a torus. The tokamak is one of several types of magnetic confinement devices being ...
and
stellarator A stellarator is a plasma device that relies primarily on external magnets to confine a plasma. Scientists researching magnetic confinement fusion aim to use stellarator devices as a vessel for nuclear fusion reactions. The name refers to the ...
. As this process is highly non-linear, it tends to occur in isolated areas, giving rise to the flute-like expansions as opposed to mass movement of the plasma as a whole.


History

In the 1950s, the field of theoretical
plasma physics Plasma ()πλάσμα
, Henry George Liddell, R ...
emerged. The confidential research of the war became declassified and allowed the publication and spread of very influential papers. The world rushed to take advantage of the recent revelations on
nuclear energy Nuclear energy may refer to: *Nuclear power, the use of sustained nuclear fission or nuclear fusion to generate heat and electricity * Nuclear binding energy, the energy needed to fuse or split a nucleus of an atom *Nuclear potential energy ...
. Although never fully realized, the idea of
controlled thermonuclear fusion Fusion power is a proposed form of power generation that would generate electricity by using heat from nuclear fusion reactions. In a fusion process, two lighter atomic nuclei combine to form a heavier nucleus, while releasing energy. Devices de ...
motivated many to explore and research novel configurations in plasma physics. Instabilities plagued early designs of artificial
plasma confinement In plasma physics, plasma confinement refers to the act of maintaining a plasma in a discrete volume. Confining plasma is required in order to achieve fusion power. There are two major approaches to confinement: magnetic confinement Magnetic co ...
devices and were quickly studied partly as a means to inhibit the effects. The analytical equations for interchange instabilities were first studied by Kruskal and Schwarzschild in 1954. They investigated several simple systems including the system in which an
ideal fluid In physics, a perfect fluid is a fluid that can be completely characterized by its rest frame mass density \rho_m and ''isotropic'' pressure ''p''. Real fluids are "sticky" and contain (and conduct) heat. Perfect fluids are idealized models in whi ...
is supported against
gravity In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
by a magnetic field (the initial model described in the last section). In 1958, Bernstein derived an energy principle that rigorously proved that the change in potential must be greater than zero for a system to be stable. This energy principle has been essential in establishing a stability condition for the possible instabilities of a specific configuration. In 1959,
Thomas Gold Thomas Gold (May 22, 1920 – June 22, 2004) was an Austrian-born American astrophysicist, a professor of astronomy at Cornell University, a member of the U.S. National Academy of Sciences, and a Fellow of the Royal Society (London). Gold was ...
attempted to use the concept of interchange motion to explain the circulation of plasma around the Earth, using data from
Pioneer III The Pioneer III railcar was a short/medium-distance coach designed and built by the Budd Company in 1956 with an emphasis on weight savings. A single prototype was built, but declines in rail passenger traffic resulted in a lack of orders so Bu ...
published by
James Van Allen James Alfred Van Allen (September 7, 1914August 9, 2006) was an American space scientist at the University of Iowa. He was instrumental in establishing the field of magnetospheric research in space. The Van Allen radiation belts were named aft ...
. Gold also coined the term “ magnetosphere” to describe “the region above the ionosphere in which the magnetic field of the Earth has a dominant control over the motions of gas and fast
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 pa ...
s.” Marshall Rosenthal and Conrad Longmire described in their 1957 paper how a
flux tube A flux tube is a generally tube-like (cylindrical) region of space containing a magnetic field, B, such that the cylindrical sides of the tube are everywhere parallel to the magnetic field lines. It is a graphical visual aid for visualizing a mag ...
in a
planetary magnetic field 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 dynamo. ...
accumulates charge because of opposing movement of the
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 and
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 ...
s in the background plasma. Gradient, curvature and centrifugal drifts all send ions in the same direction along the planetary rotation, meaning that there is a positive build-up on one side of the flux tube and a negative build-up on the other. The separation of charges established an electric field across the flux tube and therefore adds an E x B motion, sending the flux tube toward the planet. This mechanism supports our interchange instability framework, resulting in the injection of less dense gas radially inward. Since Kruskal and Schwarzschild's papers a tremendous amount of theoretical work has been accomplished that handle multi-dimensional configurations, varying boundary conditions and complicated
geometries This is a list of geometry topics. Types, methodologies, and terminologies of geometry. * Absolute geometry * Affine geometry * Algebraic geometry * Analytic geometry * Archimedes' use of infinitesimals * Birational geometry * Complex geomet ...
. Studies of planetary magnetospheres with
space probes Space is the boundless three-dimensional extent in which objects and events have relative position and direction. In classical physics, physical space is often conceived in three linear dimensions, although modern physicists usually conside ...
has helped the development of interchange instability theories, especially the comprehensive understanding of interchange motions in
Jupiter Jupiter is the fifth planet from the Sun and the largest in the Solar System. It is a gas giant with a mass more than two and a half times that of all the other planets in the Solar System combined, but slightly less than one-thousandth t ...
and Saturn’s magnetospheres.


Instability in a plasma system

The single most important property of a plasma is its stability. MHD and its derived equilibrium equations offer a wide variety of plasmas configurations but the stability of those configurations have not been challenged. More specifically, the system must satisfy the simple condition where ? is the change in potential energy for degrees of freedom. Failure to meet this condition indicates that there is a more energetically preferable state. The system will evolve and either shift into a different state or never reach a steady state. These instabilities pose great challenges to those aiming to make stable plasma configurations in the lab. However, they have also granted us an informative tool on the behavior of plasma, especially in the examination of planetary magnetospheres. This process injects hotter, lower density plasma into a colder, higher density region. It is the MHD analog of the well-known Rayleigh-Taylor instability. The Rayleigh-Taylor instability occurs at an interface in which a lower density liquid pushes against a higher density liquid in a gravitational field. In a similar model with a gravitational field, the interchange instability acts in the same way. However, in planetary magnetospheres co-rotational forces are dominant and change the picture slightly.


Simple models

Let’s first consider the simple model of a plasma supported by a magnetic field B in a uniform gravitational field g. To simplify matters, assume that the internal energy of the system is zero such that static equilibrium may be obtained from the balance of the gravitational force and the magnetic field pressure on the boundary of the plasma. The change in the potential is then given by the equation: ? If two adjacent flux tubes lying opposite along the boundary (one fluid tube and one magnetic flux tube) are interchanged the volume element doesn’t change and the field lines are straight. Therefore, the magnetic potential doesn’t change, but the gravitational potential changes since it was moved along the
z axis Z (or z) is the 26th and last letter of the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. Its usual names in English are ''zed'' () and ''zee'' (), with an occas ...
. Since the change in is negative the potential is decreasing. A decreasing potential indicates a more energetically favorable system and consequently an instability. The origin of this instability is in he J × B forces that occur at the boundary between the plasma and magnetic field. At this boundary there are slight ripple-like perturbations in which the low points must have a larger current than the high points since at the low point more gravity is being supported against the gravity. The difference in
current Currents, Current or The Current may refer to: Science and technology * Current (fluid), the flow of a liquid or a gas ** Air current, a flow of air ** Ocean current, a current in the ocean *** Rip current, a kind of water current ** Current (stre ...
allows negative and
positive charge Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons respe ...
to build up along the opposite sides of the valley. The charge build-up produces an E field between the hill and the valley. The accompanying E × B drifts are in the same direction as the ripple, amplifying the effect. This is what is physically meant by the “interchange” motion. These interchange motions also occur in plasmas that are in a system with a large
centrifugal force In Newtonian mechanics, the centrifugal force is an inertial force (also called a "fictitious" or "pseudo" force) that appears to act on all objects when viewed in a rotating frame of reference. It is directed away from an axis which is parall ...
. In a cylindrically symmetric plasma device, radial electric fields cause the plasma to rotate rapidly in a column around the axis. Acting opposite to the gravity in the simple model, the centrifugal force moves the plasma outward where the ripple-like perturbations (sometimes called “flute” instabilities) occur on the boundary. This is important for the study of the magnetosphere in which the co-rotational forces are stronger than the opposing gravity of the planet. Effectively, the less dense “bubbles” inject radially inward in this configuration. Without gravity or an
inertial force A fictitious force is a force that appears to act on a mass whose motion is described using a non-inertial frame of reference, such as a linearly accelerating or rotating reference frame. It is related to Newton's second law of motion, which trea ...
, interchange instabilities can still occur if the plasma is in a curved magnetic field. If we assume the potential energy to be purely magnetic then the change in potential energy is: . If the fluid is
incompressible In fluid mechanics or more generally continuum mechanics, incompressible flow ( isochoric flow) refers to a flow in which the material density is constant within a fluid parcel—an infinitesimal volume that moves with the flow velocity. An eq ...
then the equation can be simplified into . Since (to maintain pressure balance), the above equation shows that if the system is unstable. Physically, this means that if the
field lines A field line is a graphical visual aid for visualizing vector fields. It consists of an imaginary directed line which is tangent to the field vector at each point along its length. A diagram showing a representative set of neighboring field l ...
are toward the region of higher plasma density then the system is susceptible to interchange motions. To derive a more rigorous stability condition, the perturbations that cause an instability must be generalized. The momentum equation for a resistive MHD is linearized and then manipulated into a linear force operator. Due to purely mathematical reasons, it is then possible to split the analysis into two approaches: the normal mode method and the energy method. The normal mode method essentially looks for the
eigenmode In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted ...
s and eigenfrequencies and summing the solutions to form the general solution. The energy method is similar to the simpler approach outlined above where is found for any arbitrary perturbation in order to maintain the condition . These two methods are not exclusive and can be used together to establish a reliable diagnosis of the stability.


Observations in space

The strongest evidence for interchange transport of plasma in any magnetosphere is the observation of injection events. The recording of these events in the magnetospheres of Earth, Jupiter and Saturn are the main tool for the interpretation and analysis of interchange motion.


Earth

Although
spacecraft A spacecraft is a vehicle or machine designed to fly in outer space. A type of artificial satellite, spacecraft are used for a variety of purposes, including communications, Earth observation, meteorology, navigation, space colonization, p ...
have travelled many times in the inner and outer orbit of Earth since the 1960s, the spacecraft was the first major plasma experiment performed that could reliably determine the existence of radial injections driven by interchange motions. The analysis revealed the frequent injection of a hot plasma cloud is injected inward during a substorm in the outer layers of the magnetosphere. The injections occur predominantly in the night-time hemisphere, being associated with the
depolarization In biology, depolarization or hypopolarization is a change within a cell, during which the cell undergoes a shift in electric charge distribution, resulting in less negative charge inside the cell compared to the outside. Depolarization is ess ...
of the neutral sheet configuration in the tail regions of the magnetosphere. This paper then implies that 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 ...
region is a major mechanism in which the magnetosphere stores and releases energy through the interchange mechanism. The interchange instability also has been found to have a limiting factor on the night side
plasmapause The plasmasphere, or inner magnetosphere, is a region of the Earth's magnetosphere consisting of low-energy (cool) plasma. It is located above the ionosphere. The outer boundary of the plasmasphere is known as the plasmapause, which is defined ...
thickness olf et al. 1990 In this paper, the plasmapause is found to be near the geosynchronous orbit in which the centrifugal and gravitational potential exactly cancel out. This sharp change in plasma pressure associated with the plasma pause enables this instability. A mathematical treatment comparing the growth rate of the instability with the thickness of the plasmapause boundary revealed that the interchange instability limits the thickness of that boundary.


Jupiter

Interchange instability plays a major role in the radial transport of plasma in the
Io plasma torus The magnetosphere of Jupiter is the cavity created in the solar wind by the planet's magnetic field. Extending up to seven million kilometers in the Sun's direction and almost to the orbit of Saturn in the opposite direction, Jupiter's magnetosp ...
at Jupiter. The first evidence of this behavior was published by Thorne et al. in which they discovered “anomalous plasma signatures” in the Io torus of Jupiter’s magnetosphere. Using the data from the spacecraft Galileo’s energetic particle detector (EPD), the study looked at one specific event. In Thorne et al. they concluded that these events had a density differential of at least a factor of 2, a spatial scale of km and an inward velocity of about km/s. These results support the theoretical arguments for interchange transport. Later, more injections events were discovered and analyzed from Galileo. Mauk et al. used over 100 Jovian injections to study how these events were dispersed in energy and time. Similar to injections of Earth, the events were often clustered in time. The authors concluded that this indicated the injection events were triggered by
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 sol ...
activity against the Jovian magnetosphere. This is very similar to the magnetic storm relationship injection events have on Earth. However, it was found that Jovian injections can occur at all local time positions and therefore can’t be directly related to the situation in Earth’s magnetosphere. Although the Jovian injections aren’t a direct analog of Earth’s injections, the similarities indicate that this process plays a vital role in the storage and release of energy. The difference may lie in the presence of Io in the Jovian system. Io is a large producer of plasma mass because of its volcanic activity. This explains why the bulk of interchange motions are seen in a small radial range near Io.


Saturn

Recent evidence from the spacecraft Cassini has confirmed that the same interchange process is prominent on Saturn. Unlike Jupiter, the events happen much more frequently and more clearly. The difference lies in the configuration of the magnetosphere. Since Saturn’s gravity is much weaker, the gradient/ curvature drift for a given particle energy and L value is about 25 times faster. Saturn’s magnetosphere provides a much better environment for the study of interchange instability under these conditions even though the process is essential in both Jupiter and Saturn. In a case study of one injection event, the
Cassini Plasma Spectrometer Cassini may refer to: People * Cassini (surname) * Oleg Cassini (1913-2006), American fashion designer :Cassini family: * Giovanni Domenico Cassini (1625–1712), Italian mathematician, astronomer, engineer, and astrologer * Jacques Cassini (167 ...
(CAPS) produced characteristic radial profiles of plasma densities and temperatures of the plasma particles that also allowed the calculation of the origin of the injection and the radial propagation velocity. The electron density inside the event was lowered by a factor of about 3, the
electron temperature Plasma parameters define various characteristics of a plasma, an electrically conductive collection of charged particles that responds ''collectively'' to electromagnetic forces. Plasma typically takes the form of neutral gas-like clouds or char ...
was higher by an order of magnitude than the background, and there was a slight increase in the magnetic field.{{Cite journal, last1=Rymer, first1=A. M., last2=Smith, first2=H. T., last3=Wellbrock, first3=A., last4=Coates, first4=A. J., last5=Young, first5=D. T., date=2009-08-13, title=Discrete classification and electron energy spectra of Titan's varied magnetospheric environment, journal=Geophysical Research Letters, language=en, volume=36, issue=15, pages=n/a, doi=10.1029/2009gl039427, bibcode=2009GeoRL..3615109R, issn=0094-8276, url=http://discovery.ucl.ac.uk/139344/1/2009GL039427.pdf, doi-access=free The study also used a model of pitch angle distributions to estimate the event originated between 9 and had a radial speed of about 260+60/-70 km/s. These results are similar to the Galileo results discussed earlier. The similarities imply that the Saturn and Jupiter processes are the same.


See also

*
Plasma stability The stability of a plasma is an important consideration in the study of plasma physics. When a system containing a plasma is at equilibrium, it is possible for certain parts of the plasma to be disturbed by small perturbative forces acting on it ...
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Magnetic mirror A magnetic mirror, known as a magnetic trap (магнитный захват) in Russia and briefly as a pyrotron in the US, is a type of magnetic confinement device used in fusion power to trap high temperature plasma using magnetic fields. T ...
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Fusion power Fusion power is a proposed form of power generation that would generate electricity by using heat from nuclear fusion reactions. In a fusion process, two lighter atomic nuclei combine to form a heavier nucleus, while releasing energy. Devices de ...


References

Plasma instabilities