DIRECT CALCULATION OF TIME-PERIODIC STATES OF CONTINUUM MODELS OF RADIOFREQUENCY PLASMAS

Time-periodic solutions of the partial differential equation set for a one-dimensional model of a radio-frequency plasma are computed directly by finite-difference discretization of the equations and by Newton's method for computing the time-periodic states of periodically forced ordinary differential equations. The monodromy matrix is computed by integration of the sensitivity equations for one period of the oscillation, and is used to calculate the Jacobian matrix needed for the Newton iteration. An improvement by more than two orders of magnitude in the execution speed of the calculation is achieved by the Newton iteration compared to time integration to a periodic state. The Newton iteration is coupled with continuation methods for tracking solutions in parameter space and with linear stability analysis based on the eigenvalues of the monodromy matrix. The effectiveness of the algorithm is demonstrated by calculations for an argon plasma and the ignition extinction characteristics of the plasma are explained in terms of bifurcation and limit points in the solution families.