Hamiltonians and fluctuations of continuous plasma models

Summary

Comments on the nature of turbulence in macroscopically confined plasmas, in contrast to turbulence in hydrodynamics, are made in the introduction. It is suggested that equilibrium statistics may be a reasonable approach for plasma fluctuations. For that purpose, non-linear drift wave equations are derived from two-fluid theory. This helps to construct continuous plasma models with simple Hamiltonians, which allows canonical distributions to be defined explicitly. Partition functions and correlation functions can be calculated analytically in the one-dimensional case as functional integral averages over canonical distributions. This leads to a Lorentz spectrum ink-space, which has the observed plateau behaviour for smallk, but disagrees with thek ⁻³-dependence for largek. Through explicit calculations of the correlation function are not feasible in the two-dimensional case, the reasonable assumption of its exponential behaviour leads to good agreement with the experiment. In particular, the observedk ⁻³ behaviour for largek is now confirmed theoretically. The open problem of saturation levels of fluctuations is discussed in the conclusions.