Advanced Plasma TheoryM. 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 ɑ , 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 ε = ( En ) n we ...
... Maxwell's equations to zero order . - Equation ( 11 ) gives F in terms of ɑ , 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 ε = ( En ) n we ...
Page 77
... Maxwell's equations to minus first order give ( 22 ) ( 23 ) Σε Σe Fo dw dq = 0 , Σ of Foqdwdq = 0 . It is easily shown from ( 11 ) that the time derivative of ( 22 ) is zero if ( 23 ) is satisfied . ( This is just ( do - 1 / dt ) + ...
... Maxwell's equations to minus first order give ( 22 ) ( 23 ) Σε Σe Fo dw dq = 0 , Σ of Foqdwdq = 0 . It is easily shown from ( 11 ) that the time derivative of ( 22 ) is zero if ( 23 ) is satisfied . ( This is just ( do - 1 / dt ) + ...
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 KRUSKAL KULSRUD l'axe magnétique limit lowest order magnetic field Maxwell's equations mode nonlinear obtain Ohm's law P₁ parameter particle périodique 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