PPPL-3729 is available in <a href="PPPL-3729.pdf">pdf</a> format (1 MB).

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<b>Monte Carlo Sampling of Negative-temperature Plasma States
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<b>Authors:</b> John A. Krommes and Sharadini Rath
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<b>Date of PPPL Report:</b> July 2002
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<b>Submitted to:</b> Physical Review E</p>


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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<sub>0</sub>(<Font Face = "symbol">f</Font Face = "symbol">), the probability of realizing a set {<Font Face = "symbol">f</Font Face = "symbol">} of Fourier amplitudes associated with an ensemble of uniformly distributed, independent particles. This quantity arises because the equilibrium distribution is specified in terms of {<Font Face = "symbol">f</Font Face = "symbol">}, whereas the sampling procedure naturally produces particles states <Font Face = "symbol">G</Font Face = "symbol">; {<Font Face = "symbol">f</Font Face = "symbol">} and <Font Face = "symbol">G</Font Face = "symbol"> are related via a gyrokinetic Poisson equation, highly nonlinear in its dependence on <Font Face = "symbol">G</Font Face = "symbol">. Expansion and asymptotic methods are used to calculate P<sub>0</sub>(<Font Face = "symbol">f</Font Face = "symbol">) 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 very large amplitudes.




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