Nonlinear collective processes and the confinement of a pure-electron plasma

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Abstract
For an electron plasma that is magnetically confined in a cylindrical field geometry, radial expansion occurs only if the angular momentum of the plasma changes. In the absence of external torques, the plasma can be confined forever. Confinement experiments have suggested that the small asymmetries in the confining fields are an important external source of angular momentum. Recent transport experiments show that such field errors may excite waves and thereby enhance radial transport. A detailed theory of the nonlinear couplings between the electrostatic collective modes and perturbing asymmetric fields is presented, with emphasis on three‐wave and induced scattering‐type interactions. Via these interactions, field errors may trigger instabilities. Thresholds for such instabilities are derived and the resulting transfer of angular momentum is analyzed. The theory is applied to a simple model of a long column in order to estimate the field error levels required by the thresholds. The theoretical formalism is based on a variational formulation of the Vlasov–Poisson equations that is well suited to discussing the nonlinear interactions of global modes in bounded equilibria.