Advanced Plasma TheoryM. N. Rosenbluth |
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Page 77
... 0 Ui U1 = U¡ , No U 2л qFo dq dw . 1 = r f qFo dq dw . Thus 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 ...
... 0 Ui U1 = U¡ , No U 2л qFo dq dw . 1 = r f qFo dq dw . Thus 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 ...
Page 78
... zero order which we use to find E ̧ ) . To proceed to zero order in ( 16 ) we need J to zero order which by ( 18 ) involves f ' . Because of ( 11 ) eq . ( 9 ) may be solved for f ' but not uniquely ; only up to a function of t , r , w ...
... zero order which we use to find E ̧ ) . To proceed to zero order in ( 16 ) we need J to zero order which by ( 18 ) involves f ' . Because of ( 11 ) eq . ( 9 ) may be solved for f ' but not uniquely ; only up to a function of t , r , w ...
Page 163
... 0 ] . Expanding about this solution in powers of S1 , one finds that when Im ( p ) 0 either Re ( p ) = 0 ( 1 ) ( so that the growth rate is insignificant ) ; or else the zero - order current layer must have sharp resistivity gradients ...
... 0 ] . Expanding about this solution in powers of S1 , one finds that when Im ( p ) 0 either Re ( p ) = 0 ( 1 ) ( so that the growth rate is insignificant ) ; or else the zero - order current layer must have sharp resistivity gradients ...
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