Advanced Plasma Theory, Volume 25M. N. Rosenbluth |
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Page 88
... tion for stability as can be shown by the last proof of condition d ) in Section 2'4 . The analogous equation here is W ( A , 4 ) = Σ a ; K ( An , An ) ∞ , and K is positive definite . To obtain an explicit energy principle it is ...
... tion for stability as can be shown by the last proof of condition d ) in Section 2'4 . The analogous equation here is W ( A , 4 ) = Σ a ; K ( An , An ) ∞ , and K is positive definite . To obtain an explicit energy principle it is ...
Page 186
... tion between the two directions of velocity is arbitrary . One may re - express the Poisson equation ( 3.2 ) in terms of the form ( 3.4 ) for the distribution functions , converting the velocity integral to an energy integral by means ...
... tion between the two directions of velocity is arbitrary . One may re - express the Poisson equation ( 3.2 ) in terms of the form ( 3.4 ) for the distribution functions , converting the velocity integral to an energy integral by means ...
Page 207
... tion of the expression ( A - 4.3 ) expressing this variation in terms of 8P ,, SQr . If we now separate terms of first order in @ , we find that ( A - 4.6 ) is satisfied to this order and that we may satisfy the requirement ( A - 4.7 ) ...
... tion of the expression ( A - 4.3 ) expressing this variation in terms of 8P ,, SQr . If we now separate terms of first order in @ , we find that ( A - 4.6 ) is satisfied to this order and that we may satisfy the requirement ( A - 4.7 ) ...
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