Linear and Nonlinear Theory of Grid Excitation of Low Frequency Waves in a Plasma
CALIFORNIA UNIV LOS ANGELES PLASMA PHYSICS GROUP
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The steady-state excitation of longitudinal waves by a pair of idealized grids immersed in a collisionless plasma and driven at a frequency small compared with the ion plasma frequency is investigated theoretically. In linear theory the Fourier-inversion integral which determines the spatial behavior of the potential in the plasma is expressed as a sum of two integrals which embody the interactions of phase-velocity components of the wave with ions and electrons. An appropriate choice of the deformed contour of integration permits evaluation of the response as the sum of the residue of the dominant ion-acoustic pole and of the two branch-cut integrals. A perturbation-series expansion of the potential and the species distribution functions in the nonlinear Vlasov equation yields a hierarchy of equations. In each order the equations are linear in the perturbation quantities of that order and have driving terms composed of quadratic combinations of lower-order quantities.
- Plasma Physics and Magnetohydrodynamics