Advanced Plasma Theory, Volume 25M. N. Rosenbluth |
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Page 55
... equations . - The basic equations underlying all three theories will be the Fokker - Planck equation [ 6 ] for the Boltzmann distribution function of each particle and Maxwell's equations for the electromagnetic field . In each of the ...
... equations . - The basic equations underlying all three theories will be the Fokker - Planck equation [ 6 ] for the Boltzmann distribution function of each particle and Maxwell's equations for the electromagnetic field . In each of the ...
Page 75
... Maxwell's equations to zero order . - Equation ( 11 ) gives F in terms of a , n , ɛ as functions of r and t , Also the definitions of q and w depend on a and n . To find the behavior of a = ( E × B ) / B2 , n = B || B | and ɛ = ( En ) n ...
... Maxwell's equations to zero order . - Equation ( 11 ) gives F in terms of a , n , ɛ as functions of r and t , Also the definitions of q and w depend on a and n . To find the behavior of a = ( E × B ) / B2 , n = B || B | and ɛ = ( En ) n ...
Page 77
... Maxwell's equations to minus first order give ( 22 ) ( 23 ) Σε πο F0 dw dq = 0 , Σef Fogdwdq - = 0 . It is easily shown from ( 11 ) that the time derivative of ( 22 ) is zero if ( 23 ) is satisfied . ( This is just ( dot ) + ▽ · J - 1 ...
... Maxwell's equations to minus first order give ( 22 ) ( 23 ) Σε πο F0 dw dq = 0 , Σef Fogdwdq - = 0 . It is easily shown from ( 11 ) that the time derivative of ( 22 ) is zero if ( 23 ) is satisfied . ( This is just ( dot ) + ▽ · J - 1 ...
Common terms and phrases
adiabatic invariant amplitude approximation Boltzmann equation boundary conditions boundary layer calculated cathode coefficient collision components consider constant contraction corresponds courbe critère current density d³k d³v Debye length derived differential equations discharge dispersion relation distribution function eigenvalue electric field electrostatic energy principle equations of motion equilibrium exp[i(k finite fluid theory frequency given Hence instability integral interaction ionized k₁ k₂ KRUSKAL KULSRUD l'axe magnétique limit lowest order m₁ magnetic field Maxwell's equations mode nonlinear obtain Ohm's law P₁ parameter particle perturbation Phys plasma oscillations plasma physics Poisson's equation potential problem quantities R₁ radial region Rendiconti S.I.F. satisfied saturation current solution solving stabilité stability temperature thermal tion v₁ values variables vector velocity voisinage waves in plasmas zero zero-order Απ