Classical Vlasov plasma description through quantum numerical methods

Abstract

The Schrödinger equation describes the motion of a particle in a statistical sense. It consequently possesses the two main properties of the Vlasov equation (dynamic and statistic) and can replace this last equation provided we take sophisticated initial conditions. The scheme must be considered as a new attempt to discretize intelligently the amount of information contained in the phase space distribution and to stop, without destroying it, the flow of information which usually goes to high wavenumbers in velocity space. The method is applied to the breaking of highly nonlinear waves in a cold plasma (usually treated by the Lagrangian method) and to double beam instability. It is shown that such an Eulerian scheme works quite well with a much smaller number of discretized functions than are required in the regular Fourier—Fourier or Fourier-Hermite methods. The central point is the introduction of the phase space Wigner distribution function which is a useful mathematical tool in spite of its poor physical properties.