HOME

TheInfoList



OR:

In the
physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...
of
electromagnetism In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interacti ...
, the Abraham–Lorentz force (also known as the Lorentz–Abraham force) is the reaction force on an accelerating
charged particle In physics, a charged particle is a particle with an electric charge. For example, some elementary particles, like the electron or quarks are charged. Some composite particles like protons are charged particles. An ion, such as a molecule or atom ...
caused by the particle emitting
electromagnetic radiation In physics, electromagnetic radiation (EMR) is a self-propagating wave of the electromagnetic field that carries momentum and radiant energy through space. It encompasses a broad spectrum, classified by frequency or its inverse, wavelength ...
by self-interaction. It is also called the radiation reaction force, the radiation damping force, or the self-force. It is named after the physicists Max Abraham and
Hendrik Lorentz Hendrik Antoon Lorentz ( ; ; 18 July 1853 – 4 February 1928) was a Dutch theoretical physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for their discovery and theoretical explanation of the Zeeman effect. He derive ...
. The formula, although predating the theory of
special relativity In physics, the special theory of relativity, or special relativity for short, is a scientific theory of the relationship between Spacetime, space and time. In Albert Einstein's 1905 paper, Annus Mirabilis papers#Special relativity, "On the Ele ...
, was initially calculated for non-relativistic velocity approximations. It was extended to arbitrary velocities by Max Abraham and was shown to be physically consistent by George Adolphus Schott. The non-relativistic form is called Lorentz self-force while the relativistic version is called the Lorentz–Dirac force or collectively known as Abraham–Lorentz–Dirac force. The equations are in the domain of
classical physics Classical physics refers to physics theories that are non-quantum or both non-quantum and non-relativistic, depending on the context. In historical discussions, ''classical physics'' refers to pre-1900 physics, while '' modern physics'' refers to ...
, not
quantum physics Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...
, and therefore may not be valid at distances of roughly the
Compton wavelength The Compton wavelength is a quantum mechanical property of a particle, defined as the wavelength of a photon whose energy is the same as the rest energy of that particle (see mass–energy equivalence). It was introduced by Arthur Compton in 1 ...
or below.Fritz Rohrlich: ''The dynamics of a charged sphere and the electron'', Am. J. Phys. 65 (11) p. 1051 (1997)
"The dynamics of point charges is an excellent example of the importance of obeying the validity limits of a physical theory. When these limits are exceeded the predictions of the theory may be incorrect or even patently absurd. In the present case, the classical equations of motion have their validity limits where quantum mechanics becomes important: they can no longer be trusted at distances of the order of (or below) the Compton wavelength. ... Only when all distances involved are in the classical domain is classical dynamics acceptable for electrons."
There are, however, two analogs of the formula that are both fully quantum and relativistic: one is called the "Abraham–Lorentz–Dirac–Langevin equation", the other is the self-force on a moving mirror. The force is proportional to the square of the object's
charge Charge or charged may refer to: Arts, entertainment, and media Films * ''Charge, Zero Emissions/Maximum Speed'', a 2011 documentary Music * ''Charge'' (David Ford album) * ''Charge'' (Machel Montano album) * '' Charge!!'', an album by The Aqu ...
, multiplied by the jerk that it is experiencing. (Jerk is the rate of change of
acceleration In mechanics, acceleration is the Rate (mathematics), rate of change of the velocity of an object with respect to time. Acceleration is one of several components of kinematics, the study of motion. Accelerations are Euclidean vector, vector ...
.) The force points in the direction of the jerk. For example, in a
cyclotron A cyclotron is a type of particle accelerator invented by Ernest Lawrence in 1929–1930 at the University of California, Berkeley, and patented in 1932. Lawrence, Ernest O. ''Method and apparatus for the acceleration of ions'', filed: Januar ...
, where the jerk points opposite to the velocity, the radiation reaction is directed opposite to the velocity of the particle, providing a braking action. The Abraham–Lorentz force is the source of the
radiation resistance Radiation resistance is that part of an antenna's feedpoint electrical resistance caused by the emission of radio waves from the antenna. A radio transmitter applies a radio frequency alternating current to an antenna, which radiates the energy ...
of a radio antenna radiating
radio wave Radio waves (formerly called Hertzian waves) are a type of electromagnetic radiation with the lowest frequencies and the longest wavelengths in the electromagnetic spectrum, typically with frequencies below 300 gigahertz (GHz) and wavelengths g ...
s. There are pathological solutions of the Abraham–Lorentz–Dirac equation in which a particle accelerates ''in advance'' of the application of a force, so-called ''pre-acceleration'' solutions. Since this would represent an effect occurring before its cause (
retrocausality Retrocausality, or backwards causation, is a concept of cause and effect in which an effect precedes its cause in time and so a later event affects an earlier one. In quantum physics, the distinction between cause and effect is not made at the mos ...
), some theories have speculated that the equation allows signals to travel backward in time, thus challenging the physical principle of causality. One resolution of this problem was discussed by Arthur D. Yaghjian and was further discussed by Fritz Rohrlich and Rodrigo Medina. Furthermore, some authors argue that a radiation reaction force is unnecessary, introducing a corresponding stress-energy tensor that naturally conserves energy and momentum in Minkowski space and other suitable spacetimes.


Definition and description

The Lorentz self-force derived for non-relativistic velocity approximation v\ll c, is given in
SI units The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of measurement. It is the only system of measurement with official st ...
by: \mathbf_\mathrm = \frac \mathbf = \frac \mathbf = \frac \frac \mathbf or in
Gaussian units Gaussian units constitute a metric system of units of measurement. This system is the most common of the several electromagnetic unit systems based on the centimetre–gram–second system of units (CGS). It is also called the Gaussian unit syst ...
by \mathbf_\mathrm = \frac \mathbf. where \mathbf_\mathrm is the force, \mathbf is the derivative of
acceleration In mechanics, acceleration is the Rate (mathematics), rate of change of the velocity of an object with respect to time. Acceleration is one of several components of kinematics, the study of motion. Accelerations are Euclidean vector, vector ...
, or the third derivative of
displacement Displacement may refer to: Physical sciences Mathematics and physics *Displacement (geometry), is the difference between the final and initial position of a point trajectory (for instance, the center of mass of a moving object). The actual path ...
, also called jerk, ''μ''0 is the
magnetic constant The vacuum magnetic permeability (variously ''vacuum permeability'', ''permeability of free space'', ''permeability of vacuum'', ''magnetic constant'') is the magnetic permeability in a classical vacuum. It is a physical constant, conventionall ...
, ''ε''0 is the electric constant, ''c'' is the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant exactly equal to ). It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time i ...
in
free space A vacuum (: vacuums or vacua) is space devoid of matter. The word is derived from the Latin adjective (neuter ) meaning "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressur ...
, and ''q'' is the
electric charge Electric charge (symbol ''q'', sometimes ''Q'') is a physical property of matter that causes it to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative''. Like charges repel each other and ...
of the particle. Physically, an accelerating charge emits radiation (according to the
Larmor formula In electrodynamics, the Larmor formula is used to calculate the total power radiated by a nonrelativistic point charge as it accelerates. It was first derived by J. J. Larmor in 1897, in the context of the wave theory of light. When any charge ...
), which carries
momentum In Newtonian mechanics, momentum (: momenta or momentums; more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. ...
away from the charge. Since momentum is conserved, the charge is pushed in the direction opposite the direction of the emitted radiation. In fact the formula above for radiation force can be ''derived'' from the Larmor formula, as shown
below Below may refer to: *Earth *Ground (disambiguation) *Soil *Floor * Bottom (disambiguation) *Less than *Temperatures below freezing *Hell or underworld People with the surname * Ernst von Below (1863–1955), German World War I general * Fred Belo ...
. The Abraham–Lorentz force, a generalization of Lorentz self-force for arbitrary velocities is given by: \mathbf_\mathrm =\frac\left(\gamma^2\dot+\frac + \frac+\frac\right) Where \gamma is the Lorentz factor associated with v, the velocity of particle. The formula is consistent with special relativity and reduces to Lorentz's self-force expression for low velocity limit. The covariant form of radiation reaction deduced by Dirac for arbitrary shape of elementary charges is found to be: F^_\mu = \frac \left frac-\frac \left(\frac\frac\right) \right/math>


History

The first calculation of electromagnetic radiation energy due to current was given by George Francis FitzGerald in 1883, in which radiation resistance appears. However, dipole antenna experiments by
Heinrich Hertz Heinrich Rudolf Hertz (; ; 22 February 1857 – 1 January 1894) was a German physicist who first conclusively proved the existence of the electromagnetic waves predicted by James Clerk Maxwell's equations of electromagnetism. Biography Heinri ...
made a bigger impact and gathered commentary by Poincaré on the ''amortissement'' or damping of the oscillator due to the emission of radiation. Qualitative discussions surrounding damping effects of radiation emitted by accelerating charges was sparked by Henry Poincaré in 1891. In 1892,
Hendrik Lorentz Hendrik Antoon Lorentz ( ; ; 18 July 1853 – 4 February 1928) was a Dutch theoretical physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for their discovery and theoretical explanation of the Zeeman effect. He derive ...
derived the self-interaction force of charges for low velocities but did not relate it to radiation losses. Suggestion of a relationship between radiation energy loss and self-force was first made by
Max Planck Max Karl Ernst Ludwig Planck (; ; 23 April 1858 – 4 October 1947) was a German Theoretical physics, theoretical physicist whose discovery of energy quantum, quanta won him the Nobel Prize in Physics in 1918. Planck made many substantial con ...
. Planck's concept of the damping force, which did not assume any particular shape for elementary charged particles, was applied by Max Abraham to find the radiation resistance of an antenna in 1898, which remains the most practical application of the phenomenon. In the early 1900s, Abraham formulated a generalization of the Lorentz self-force to arbitrary velocities, the physical consistency of which was later shown by George Adolphus Schott. Schott was able to derive the Abraham equation and attributed "acceleration energy" to be the source of energy of the electromagnetic radiation. Originally submitted as an essay for the 1908
Adams Prize The Adams Prize is a prize awarded each year by the Faculty of Mathematics at St John's College to a UK-based mathematician for distinguished research in mathematical sciences. The prize is named after the mathematician John Couch Adams and wa ...
, he won the competition and had the essay published as a book in 1912. The relationship between self-force and radiation reaction became well-established at this point.
Wolfgang Pauli Wolfgang Ernst Pauli ( ; ; 25 April 1900 – 15 December 1958) was an Austrian theoretical physicist and a pioneer of quantum mechanics. In 1945, after having been nominated by Albert Einstein, Pauli received the Nobel Prize in Physics "for the ...
first obtained the covariant form of the radiation reaction and in 1938,
Paul Dirac Paul Adrien Maurice Dirac ( ; 8 August 1902 – 20 October 1984) was an English mathematician and Theoretical physics, theoretical physicist who is considered to be one of the founders of quantum mechanics. Dirac laid the foundations for bot ...
found that the equation of motion of charged particles, without assuming the shape of the particle, contained Abraham's formula within reasonable approximations. The equations derived by Dirac are considered exact within the limits of classical theory.


Background

In
classical electrodynamics Classical electromagnetism or classical electrodynamics is a branch of physics focused on the study of interactions between electric charges and currents using an extension of the classical Newtonian model. It is, therefore, a classical field th ...
, problems are typically divided into two classes: # Problems in which the charge and current ''sources'' of fields are specified and the ''fields'' are calculated, and # The reverse situation, problems in which the fields are specified and the motion of particles are calculated. In some fields of physics, such as
plasma physics Plasma () is a state of matter characterized by the presence of a significant portion of charged particles in any combination of ions or electrons. It is the most abundant form of ordinary matter in the universe, mostly in stars (including th ...
and the calculation of transport coefficients (conductivity, diffusivity, ''etc.''), the fields generated by the sources and the motion of the sources are solved self-consistently. In such cases, however, the motion of a selected source is calculated in response to fields generated by all other sources. Rarely is the motion of a particle (source) due to the fields generated by that same particle calculated. The reason for this is twofold: # Neglect of the " self-fields" usually leads to answers that are accurate enough for many applications, and # Inclusion of self-fields leads to problems in physics such as
renormalization Renormalization is a collection of techniques in quantum field theory, statistical field theory, and the theory of self-similar geometric structures, that is used to treat infinities arising in calculated quantities by altering values of the ...
, some of which are still unsolved, that relate to the very nature of matter and energy. These conceptual problems created by self-fields are highlighted in a standard graduate text. ackson
The difficulties presented by this problem touch one of the most fundamental aspects of physics, the nature of the elementary particle. Although partial solutions, workable within limited areas, can be given, the basic problem remains unsolved. One might hope that the transition from classical to quantum-mechanical treatments would remove the difficulties. While there is still hope that this may eventually occur, the present quantum-mechanical discussions are beset with even more elaborate troubles than the classical ones. It is one of the triumphs of comparatively recent years (~ 1948–1950) that the concepts of Lorentz covariance and gauge invariance were exploited sufficiently cleverly to circumvent these difficulties in quantum electrodynamics and so allow the calculation of very small radiative effects to extremely high precision, in full agreement with experiment. From a fundamental point of view, however, the difficulties remain.
The Abraham–Lorentz force is the result of the most fundamental calculation of the effect of self-generated fields. It arises from the observation that accelerating charges emit radiation. The Abraham–Lorentz force is the average force that an accelerating charged particle feels in the
recoil Recoil (often called knockback, kickback or simply kick) is the rearward thrust generated when a gun is being discharged. In technical terms, the recoil is a result of conservation of momentum, for according to Newton's third law the force requ ...
from the emission of radiation. The introduction of
quantum effects Quantum mechanics is the fundamental physical theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is the foundation of a ...
leads one to
quantum electrodynamics In particle physics, quantum electrodynamics (QED) is the Theory of relativity, relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quant ...
. The self-fields in quantum electrodynamics generate a finite number of infinities in the calculations that can be removed by the process of
renormalization Renormalization is a collection of techniques in quantum field theory, statistical field theory, and the theory of self-similar geometric structures, that is used to treat infinities arising in calculated quantities by altering values of the ...
. This has led to a theory that is able to make the most accurate predictions that humans have made to date. (See
precision tests of QED Quantum electrodynamics (QED), a relativistic quantum field theory of electrodynamics, is among the most stringently tested theories in physics. The most precise and specific tests of QED consist of measurements of the electromagnetic fine-structur ...
.) The renormalization process fails, however, when applied to the
gravitational force Newton's law of universal gravitation describes gravity as a force by stating that every particle attracts every other particle in the universe with a force that is proportional to the product of their masses and inversely proportional to the sq ...
. The infinities in that case are infinite in number, which causes the failure of renormalization. Therefore,
general relativity General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the differential geometry, geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of grav ...
has an unsolved self-field problem.
String theory In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and intera ...
and
loop quantum gravity Loop quantum gravity (LQG) is a theory of quantum gravity that incorporates matter of the Standard Model into the framework established for the intrinsic quantum gravity case. It is an attempt to develop a quantum theory of gravity based direc ...
are current attempts to resolve this problem, formally called the problem of radiation reaction or the problem of self-force.


Derivation

The simplest derivation for the self-force is found for periodic motion from the
Larmor formula In electrodynamics, the Larmor formula is used to calculate the total power radiated by a nonrelativistic point charge as it accelerates. It was first derived by J. J. Larmor in 1897, in the context of the wave theory of light. When any charge ...
for the power radiated from a point charge that moves with velocity much lower than that of speed of light: P = \frac \mathbf^2. If we assume the motion of a charged particle is periodic, then the average work done on the particle by the Abraham–Lorentz force is the negative of the Larmor power integrated over one period from \tau_1 to \tau_2: \int_^ \mathbf_\mathrm \cdot \mathbf dt = \int_^ -P dt = - \int_^ \frac \mathbf^2 dt = - \int_^ \frac \frac \cdot \frac dt. The above expression can be integrated by parts. If we assume that there is periodic motion, the boundary term in the integral by parts disappears: \int_^ \mathbf_\mathrm \cdot \mathbf dt = - \frac \frac \cdot \mathbf \bigg, _^ + \int_^ \frac \frac \cdot \mathbf dt = -0 + \int_^ \frac \mathbf \cdot \mathbf dt. Clearly, we can identify the Lorentz self-force equation which is applicable to slow moving particles as: \mathbf_\mathrm = \frac \mathbfA more rigorous derivation, which does not require periodic motion, was found using an
effective field theory In physics, an effective field theory is a type of approximation, or effective theory, for an underlying physical theory, such as a quantum field theory or a statistical mechanics model. An effective field theory includes the appropriate degrees ...
formulation. A generalized equation for arbitrary velocities was formulated by Max Abraham, which is found to be consistent with special relativity. An alternative derivation, making use of theory of relativity which was well established at that time, was found by Dirac without any assumption of the shape of the charged particle.


Signals from the future

Below is an illustration of how a classical analysis can lead to surprising results. The classical theory can be seen to challenge standard pictures of causality, thus signaling either a breakdown or a need for extension of the theory. In this case the extension is to
quantum mechanics Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...
and its relativistic counterpart
quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines Field theory (physics), field theory and the principle of relativity with ideas behind quantum mechanics. QFT is used in particle physics to construct phy ...
. See the quote from Rohrlich in the introduction concerning "the importance of obeying the validity limits of a physical theory". For a particle in an external force \mathbf_\mathrm, we have m \dot = \mathbf_\mathrm + \mathbf_\mathrm = m t_0 \ddot + \mathbf_\mathrm . where t_0 = \frac. This equation can be integrated once to obtain m \dot = \int_t^ \exp \left( - \right ) \, \mathbf_\mathrm(t') \, dt' . The integral extends from the present to infinitely far in the future. Thus future values of the force affect the acceleration of the particle in the present. The future values are weighted by the factor \exp \left( -\right ) which falls off rapidly for times greater than t_0 in the future. Therefore, signals from an interval approximately t_0 into the future affect the acceleration in the present. For an electron, this time is approximately 10^ sec, which is the time it takes for a light wave to travel across the "size" of an electron, the
classical electron radius The classical electron radius is a combination of fundamental Physical quantity, physical quantities that define a length scale for problems involving an electron interacting with electromagnetic radiation. It links the classical electrostatic sel ...
. One way to define this "size" is as follows: it is (up to some constant factor) the distance r such that two electrons placed at rest at a distance r apart and allowed to fly apart, would have sufficient energy to reach half the speed of light. In other words, it forms the length (or time, or energy) scale where something as light as an electron would be fully relativistic. It is worth noting that this expression does not involve the
Planck constant The Planck constant, or Planck's constant, denoted by h, is a fundamental physical constant of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and the wavelength of a ...
at all, so although it indicates something is wrong at this length scale, it does not directly relate to quantum uncertainty, or to the frequency–energy relation of a photon. Although it is common in quantum mechanics to treat \hbar \to 0 as a "
classical limit The classical limit or correspondence limit is the ability of a physical theory to approximate or "recover" classical mechanics when considered over special values of its parameters. The classical limit is used with physical theories that predict n ...
", some speculate that even the classical theory needs renormalization, no matter how the Planck constant would be fixed.


Abraham–Lorentz–Dirac force

To find the relativistic generalization, Dirac renormalized the mass in the equation of motion with the Abraham–Lorentz force in 1938. This renormalized equation of motion is called the Abraham–Lorentz–Dirac equation of motion.


Definition

The expression derived by Dirac is given in signature (− + + +) by F^_\mu = \frac \left frac-\frac \left(\frac\frac\right) \right With Liénard's relativistic generalization of Larmor's formula in the co-moving frame, P = \frac, one can show this to be a valid force by manipulating the time average equation for power: \frac\int_0^t P dt = \frac\int_0^t \textbf \cdot \textbf\,dt.


Paradoxes


Pre-acceleration

Similar to the non-relativistic case, there are pathological solutions using the Abraham–Lorentz–Dirac equation that anticipate a change in the external force and according to which the particle accelerates ''in advance'' of the application of a force, so-called ''preacceleration'' solutions. One resolution of this problem was discussed by Yaghjian, and is further discussed by Rohrlich and Medina.


Runaway solutions

Runaway solutions are solutions to ALD equations that suggest the force on objects will increase exponential over time. It is considered as an unphysical solution.


Hyperbolic motion

The ALD equations are known to be zero for constant acceleration or hyperbolic motion in Minkowski spacetime diagram. The subject of whether in such condition electromagnetic radiation exists was matter of debate until Fritz Rohrlich resolved the problem by showing that hyperbolically moving charges do emit radiation. Subsequently, the issue is discussed in context of energy conservation and
equivalence principle The equivalence principle is the hypothesis that the observed equivalence of gravitational and inertial mass is a consequence of nature. The weak form, known for centuries, relates to masses of any composition in free fall taking the same t ...
which is classically resolved by considering "acceleration energy" or Schott energy.


Self-interactions

However the antidamping mechanism resulting from the Abraham–Lorentz force can be compensated by other nonlinear terms, which are frequently disregarded in the expansions of the retarded Liénard–Wiechert potential.


Landau–Lifshitz radiation damping force

The Abraham–Lorentz–Dirac force leads to some pathological solutions. In order to avoid this,
Lev Landau Lev Davidovich Landau (; 22 January 1908 – 1 April 1968) was a Soviet physicist who made fundamental contributions to many areas of theoretical physics. He was considered as one of the last scientists who were universally well-versed and ma ...
and
Evgeny Lifshitz Evgeny Mikhailovich Lifshitz (; ; 21 February 1915 – 29 October 1985) was a leading Soviet physicist and brother of the physicist Ilya Lifshitz. Work Born into a Ukrainian Jewish family in Kharkov, Kharkov Governorate, Russian Empire (now K ...
came with the following formula for radiation damping force, which is valid when the radiation damping force is small compared with the Lorentz force in some frame of reference (assuming it exists), : g^i= \frac\left\ so that the equation of motion of the charge e in an external field F^ can be written as : mc\frac= \fracF^u_k+g^i. Here u^i=(\gamma,\gamma\mathbf v/c) is the four-velocity of the particle, \gamma=1/\sqrt is the
Lorentz factor The Lorentz factor or Lorentz term (also known as the gamma factor) is a dimensionless quantity expressing how much the measurements of time, length, and other physical properties change for an object while it moves. The expression appears in sev ...
and \mathbf v is the three-dimensional velocity vector. The three-dimensional Landau–Lifshitz radiation damping force can be written as : \mathbf F_ = \frac\left\+\frac\left mathbf E\times\mathbf H+ \frac\mathbf H\times(\mathbf H\times\mathbf v) + \frac\mathbf E(\mathbf v\cdot\mathbf E)\right\frac\left left(\mathbf E + \frac\mathbf v\times\mathbf H\right)^2-\frac(\mathbf E\cdot\mathbf v)^2\right/math> where D/Dt=\partial/\partial t+\mathbf v\cdot\nabla is the
total derivative In mathematics, the total derivative of a function at a point is the best linear approximation near this point of the function with respect to its arguments. Unlike partial derivatives, the total derivative approximates the function with res ...
.


Experimental observations

While the Abraham–Lorentz force is largely neglected for many experimental considerations, it gains importance for plasmonic excitations in larger
nanoparticles A nanoparticle or ultrafine particle is a particle of matter 1 to 100 nanometres (nm) in diameter. The term is sometimes used for larger particles, up to 500 nm, or fibers and tubes that are less than 100 nm in only two directions. At ...
due to large local field enhancements. Radiation damping acts as a limiting factor for the plasmonic excitations in surface-enhanced
Raman scattering In chemistry and physics, Raman scattering or the Raman effect () is the inelastic scattering of photons by matter, meaning that there is both an exchange of energy and a change in the light's direction. Typically this effect involves vibrationa ...
. The damping force was shown to broaden surface plasmon resonances in gold nanoparticles, nanorods and
clusters may refer to: Science and technology Astronomy * Cluster (spacecraft), constellation of four European Space Agency spacecraft * Cluster II (spacecraft), a European Space Agency mission to study the magnetosphere * Asteroid cluster, a small ...
. The effects of radiation damping on
nuclear magnetic resonance Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are disturbed by a weak oscillating magnetic field (in the near field) and respond by producing an electromagnetic signal with a ...
were also observed by
Nicolaas Bloembergen Nicolaas Bloembergen (March 11, 1920 – September 5, 2017) was a Dutch- American physicist and Nobel laureate, recognized for his work in developing driving principles behind nonlinear optics for laser spectroscopy. During his career, he was a ...
and Robert Pound, who reported its dominance over spin–spin and spin–lattice relaxation mechanisms for certain cases. The Abraham–Lorentz force has been observed in the semiclassical regime in experiments which involve the scattering of a relativistic beam of electrons with a high intensity laser. In the experiments, a supersonic jet of helium gas is intercepted by a high-intensity (1018–1020 W/cm2) laser. The laser ionizes the helium gas and accelerates the electrons via what is known as the “laser-wakefield” effect. A second high-intensity laser beam is then propagated counter to this accelerated electron beam. In a small number of cases, inverse-Compton scattering occurs between the photons and the electron beam, and the spectra of the scattered electrons and photons are measured. The photon spectra are then compared with spectra calculated from Monte Carlo simulations that use either the QED or classical LL equations of motion.


Collective effects

The effects of radiation reaction are often considered within the framework of single-particle dynamics. However, interesting phenomena arise when a collection of charged particles is subjected to strong electromagnetic fields, such as in a plasma. In such scenarios, the collective behavior of the plasma can significantly modify its properties due to radiation reaction effects. Theoretical studies have shown that in environments with strong magnetic fields, like those found around
pulsars A pulsar (''pulsating star, on the model of quasar'') is a highly magnetized rotating neutron star that emits beams of electromagnetic radiation out of its magnetic poles. This radiation can be observed only when a beam of emission is pointin ...
and magnetars, radiation reaction cooling can alter the collective dynamics of the plasma. This modification can lead to instabilities within the plasma. Specifically, in the high magnetic fields typical of these astrophysical objects, the momentum distribution of particles is bunched and becomes anisotropic due to radiation reaction forces, potentially driving plasma instabilities and affecting overall plasma behavior. Among these instabilities, the firehose instability can arise due to the anisotropic pressure, and electron cyclotron maser due to population inversion in the rings.


See also

*
Lorentz force In electromagnetism, the Lorentz force is the force exerted on a charged particle by electric and magnetic fields. It determines how charged particles move in electromagnetic environments and underlies many physical phenomena, from the operation ...
* Cyclotron radiation **
Synchrotron radiation Synchrotron radiation (also known as magnetobremsstrahlung) is the electromagnetic radiation emitted when relativistic charged particles are subject to an acceleration perpendicular to their velocity (). It is produced artificially in some types ...
*
Electromagnetic mass Electromagnetic mass was initially a concept of classical mechanics, denoting as to how much the electromagnetic field, or the self-energy, is contributing to the mass of charged particles. It was first derived by J. J. Thomson in 1881 and was ...
*
Radiation resistance Radiation resistance is that part of an antenna's feedpoint electrical resistance caused by the emission of radio waves from the antenna. A radio transmitter applies a radio frequency alternating current to an antenna, which radiates the energy ...
* Radiation damping *
Wheeler–Feynman absorber theory The Wheeler–Feynman absorber theory (also called the Wheeler–Feynman time-symmetric theory), named after its originators, the physicists Richard Feynman and John Archibald Wheeler, is a theory of electrodynamics based on a relativistic correct ...
* Magnetic radiation reaction force


References


Further reading

* See sections 11.2.2 and 11.2.3 * * Donald H. Menzel (1960) ''Fundamental Formulas of Physics'', Dover Publications Inc., , vol. 1, p. 345. * Stephen Parrott (1987) ''Relativistic Electrodynamics and Differential Geometry'', § 4.3 Radiation reaction and the Lorentz–Dirac equation, pages 136–45, and § 5.5 Peculiar solutions of the Lorentz–Dirac equation, pp. 195–204, Springer-Verlag .


External links


MathPages – Does A Uniformly Accelerating Charge Radiate?


* ttp://airccse.com/ijel/papers/1116ijel05.pdf EC. del Río: Radiation of an accelerated charge {{DEFAULTSORT:Abraham-Lorentz force Electrodynamics Electromagnetic radiation Radiation Hendrik Lorentz