Abstract
The Power Transform method of integrating the nonlinear Vlasov equation is applied to two physically significant problems and the solutions are compared with the results of the Fourier-Hermite method. The problems considered are one dimensional, with periodic boundary conditions and involve (1) Landau damping in a Maxwellian plasma, and (2) the two-beam instability with equal electron beams. The Power Transform method is discussed and several truncation techniques are presented. It is found that an extrapolation procedure can be used which allows a truncation of the infinite matrix without causing numerical instabilities in the nonlinear system. Close quantitative agreement between the results of the two methods is found.
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