Kakuyūgō kenkyū

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The Power Transform method of integrating the nonlinear Vlasov equation is applied to several physical problems. The problems considerd are one dimensional, with periodic boundary conditiolls.
The nonlinear electric wave behavior of Vlasov plasma is studied numerically for perturbations applied to a Maxwellian plasma. The solution is carried past the point of minimum electrostatic amplitude. After reaching its minimum value, the electrostatic amplitude which is linearly stable grows due to the interaction with particles and mode coupling with the other modes. The effect of a weak beam of electrons on a Maxwellian plasma is studied. The solution for three unstable modes is carried past the point of maximum electrostatic energy. After the initial conditions die out three modes behave as one would expect according to the quasilinear theory, eventually levelling off when the energy of the fields becomes large enough to ditort the ditribution of particles.
The nonlinear response of a Vlasov plasma is calculated for perturbations applied to an inhomogeneous equilibrium and found approach the equilibrium different from the initial one. The response of an initially uniform plasma to a suddenly applied external field is also calculated.
We find that the Power Transform method is amenable to an extraporation procedure which avoids the difficulty of a cutoff and yields an appreciable savings in computer time.

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