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adiabatic invariant amplitude approximation assumed Boltzmann equation boundary conditions boundary layer calculated cathode charge coefficient collision column components consider const constant contraction corresponds courbe current density Debye length derived differential equations diffusion discharge dispersion relation distribution function double adiabatic theory effect eigenvalue electric field electromagnetic waves electrostatic energy principle equations of motion equilibrium expand experimental finite fluid theory frequency given Hence hydromagnetic inertia-limited instability integral interaction ionized Kruskal Kulsrud l'axe magnétique lignes limit linear theory lowest order magnetic field Maxwell's equations mode negative ions nonlinear obtain Ohm's law parameter particle perturbation Phys plasma oscillations plasma physics Poisson's equation potential pressure problem produced quantities radial region satisfied saturation current self-adjointness solution solving stability surface temperature thermal tion transverse wave values vanish variables vector velocity Vlasov equation waves in plasmas zero zero-order