Advanced Plasma TheoryM. N. Rosenbluth |
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Page 78
... 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 and q as in the case of the solution for fo ( at first ) ...
... 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 and q as in the case of the solution for fo ( at first ) ...
Page 163
... zero - order equilibrium condition of eq . ( 7 ) may be written as ( 15 ) - F - F " . The usual boundary conditions are that both y and W should vanish at infinity or at conducting boundaries , located at uμ1 , μ2 . 3. General remarks ...
... zero - order equilibrium condition of eq . ( 7 ) may be written as ( 15 ) - F - F " . The usual boundary conditions are that both y and W should vanish at infinity or at conducting boundaries , located at uμ1 , μ2 . 3. General remarks ...
Page 209
... zero - frequency part of this function , we see that the term involving the arbitrary coefficient drops out of the expression , leaving ( A - 5.6 ) HZF ( 4 ) H + b1 ( k ) ab ' ( k ) ĉt ab ( k ) ] b ' ( k ) êt ZF where the subscript ZF ...
... zero - frequency part of this function , we see that the term involving the arbitrary coefficient drops out of the expression , leaving ( A - 5.6 ) HZF ( 4 ) H + b1 ( k ) ab ' ( k ) ĉt ab ( k ) ] b ' ( k ) êt ZF where the subscript ZF ...
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