ON VARIATIONAL FINITE-DIFFERENCE SCHEME STABILITY OF THE PARTICLE METHOD FOR VLASOV EQUATIONS IN SELF-CONSISTENT ELECTROSTATIC APPROXIMATION. PT. 1. SUFFICIENT CONDITIONS FOR ACTUAL STABILITY

Yu.A. Bondarenko
VANT. Ser. Mat. Mod. Fiz. Proc 1991. Вып.3. С. 15-23.

      Stability of small particle coordinate perturbations is investigated in variational leap-frog-type difference schemes for collisionless plasma in a self-consistent electric field. Difference schemes involving arbitrary macroparticle structures having an arbitrary number of degrees of freedom and basic functions for describing electric field potential are examined. Sufficient conditions are obtained for actual stability of such schemes that is those sufficient for stability of ρ harmonics having physical instability (their growth is not prevented by decreasing the timestep size in a difference scheme) and also for ordinary stability over initial data for others.

      Stability of small particle coordinate perturbations in difference schemes of the particle leap-frog-type method is investigated for collisionlfcjs plasma in a self-consistent electric field for the case of arbitrary macroparticle structure having an arbitrary number of degrees of freedom and arbitrary basic functions for describing electric field potential. For difference schemes, instability presence is proved which is not removable by decreasing the timestep size and its correspondence with that of small plasma particle coordinate perturbations is established for differential equations of particle motion. Bo.th upper and lower estimates were obtained for maximum growth increments of unstable perturbations in difference schemes under consideration which are then checked for a one-dimensional case.
      For a one-dimensional case, sufficient stability conditions obtained in the first part are shown to give a finite (nonzero) acceptable timestep value inversely proportional to plasma frequency as the grid for the potential becomes finer and the number of particles decreasing in size grows simultaneously.