A relativistic form of Boltzmann's transport equation in the absence of collisions

Clemmow, P. C.; Willson, A. J.

doi:10.1017/s0305004100032151

Cited by 37 publications

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“…As was shown by TAuB [8], CLEMMOW and WILLSO~ [9], and LIr~nART [10], the collision-free Boltzmann equation can be put in certain relativistic noncovariant forms, while Ks.N-ITI GOTO [11] gave a covariant form of the relativistic Boltzmann equation. In 1965, ABONYI [12] showed that the forms proposed by TAUB, CLEMMOW and WILLSON and LINnART are equivalent, the form given by KE~-ITI Goro being valid only for the "four-power free" forces.…”

Section: Lntroductionmentioning

confidence: 98%

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The relativistic Boltzmann equation and the macroscopic equations of conservation

Merches

Agop

1978

Acta Physica

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Slarting with the relativistic collision-free Boltzmann equation, a covariant transport equation is found; this leads to equations of conservation in magnetohydrodynamies, both in Galilean and general coordinate systems. lntroductionThe method of derivation of the macroscopic transport equations by means of averaging the Boltzmann equation is a well-known and useful procedure (see e.g.[1]--[6]). By using ttlis method, one of the authors obtained a generalization of the Poynting's theorem fora moving conductor medium [7]. AH these papers are concerned with the nonrelativistic formulation of the problem.As was shown by TAuB [8], CLEMMOW and WILLSO~ [9], and LIr~nART [10], the collision-free Boltzmann equation can be put in certain relativistic noncovariant forms, while Ks.N-ITI GOTO [11] gave a covariant form of the relativistic Boltzmann equation. In 1965, ABONYI [12] showed that the forms proposed by TAUB, CLEMMOW and WILLSON and LINnART are equivalent, the form given by KE~-ITI Goro being valid only for the "four-power free" forces. The relativistic Boltzmann equation was used by TAVB [8] in order to obtain a transport equation, leading to the equations of conservation of mass, energy and momentum in relativistic hydrodynamics. This was done in the usual manner, by using a noncovariant transport equation.It is the purpose of the present paper to gire a covariant formulation of the transport equation and to obtain the covariant equations of conservation in relativistic magnetohydrodynamics. The transport equationWc sha11 use the relativistic forro of the collision-frce Boltzmann equation proposed by [u s 0 d_m~lK s 0 / f=0; s=1,2,3,4,8x s Su s ] ,Acta Phy~ Academiae Scienliarum llungarieae 44s 1978

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Section: Lntroductionmentioning

confidence: 98%

“…If the microscopic velocity four rector uf is defined by Ur = <ttr > q Wr ' (9) where <Ur> iS the macroscopic (mean) velocity four vector, and w r the deviation from (Ur>, and observe that (wr> = 0, then we get successively: …”

Section: Galilean Coordinatesmentioning

confidence: 99%

The relativistic Boltzmann equation and the macroscopic equations of conservation

Merches

Agop

1978

Acta Physica

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“…In general, the particle distribution function / depends on the variables t, x and ijr. It is convenient to present the Vlasov relativistic kinetic equation (Clemmow & Willson 1956) in those variables in the form…”

Section: Gyrokinetics Of Resonant Particles 179mentioning

confidence: 99%

“…Moreover relativisitic effects have not been taken into account; these can be very important in resonant conditions because the difference between frequencies at cyclotron resonances is very sensitive to relativisitic changing of the gyrofrequency of particles. In addition, relativistic effects can strongly change the dispersion relation for waves (Clemmow & Willson 1956). A relativistic kinetic theory in the particular case of electron-cyclotron resonance has been developed by Bernstein & Baxter (1981), but is not consistent.…”

Section: Introductionmentioning

confidence: 99%

Gyrokinetics of resonant particles in a collisionless plasma

1985

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A consistent drift-kinetic theory is developed for the interaction of resonant particles in a relativistic magnetized plasma with HF (high-frequency) wave packets for arbitrary ratio of the gyroradius to the wavelength. Gyrokinetic equations for the plasma particles are obtained for Čerenkov and cyclotron resonances as well as for those at the harmonics of the gyrofrequency, the half-integer cyclotron resonances and those with the beats of two wave packets. The periodic parts of the distribution function for the relativistic non-uniform and non-stationary plasma are calculated.

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“…Work based on approximations of the equilibrium distribution function with and without streaming cannot be applied to fusion reaction chambers, relativistic electron beam experiments necessitating the fusion of nuclei, etc. (Clemmow & Willson 1956;Kursunoglu 1961;Buti 1963aButi , b, 1972. Misra (1975) derived dispersion relations for transverse and longitudinal waves propagating in a Vlasov plasma valid for relativistic and nonrelativistic temperatures for one-component electron plasma.…”

Section: Introductionmentioning

confidence: 99%

Electromagnetic waves in a relativistic plasma stream: fusion instability

Mohanty

Misra

1982

J. Plasma Phys.

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A relativistic form of Boltzmann's transport equation in the absence of collisions

Abstract: With the neglect of collisions, a relativistic form of Boltzmann's transport equation is derived and its invariance under a Lorentz transformation is established.

Cited by 37 publications

References 0 publications

The relativistic Boltzmann equation and the macroscopic equations of conservation

The relativistic Boltzmann equation and the macroscopic equations of conservation

Gyrokinetics of resonant particles in a collisionless plasma

Electromagnetic waves in a relativistic plasma stream: fusion instability

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