Monte Carlo sampling of negative-temperature plasma states

A Monte Carlo procedure is used to generate N-particle configurations compatible with two-temperature canonical equilibria in two dimensions, with particular attention to nonlinear plasma gyrokinetics. An unusual feature of the problem is the importance of a nontrivial probability density function P-0(phi), the probability of realizing a set phi of Fourier amplitudes associated with an ensemble of uniformly distributed, independent particles. This quantity arises because the equilibrium distribution is specified in terms of phi, whereas the sampling procedure naturally produces particle states Gamma; phi and Gamma are related via a gyrokinetic Poisson equation, highly nonlinear in its dependence on Gamma. Expansion and asymptotic methods are used to calculate P-0(phi) analytically; excellent agreement is found between the large-N asymptotic result and a direct numerical calculation. The algorithm is tested by successfully generating a variety of states of both positive and negative temperature, including ones in which either the longest- or shortest-wavelength modes are excited to relatively large amplitudes.