Electrostatic Instabilities in Finite Mirror-Confined Plasmas

Abstract

Three classes of electrostatic instabilities deemed likely to be encountered in magnetic mirror‐confined plasmas are examined theoretically: (A) a convective type, maser‐like in nature, with waves propagating essentially parallel to the field lines; (B) a nonconvective (absolute) instability, arising in the presence of radial density gradients; and (C) a limiting case of (B), not requiring radial density gradients for its stimulation. All three instabilities, which owe their origin to the loss‐cone nature of the particle distributions, exhibit critical conditions for onset or growth that are sensitively dependent on the shape of the distribution functions. These conditions are least restrictive for plasmas that have reached a state of collisional equilibrium in confining fields of high mirror ratio. In this limit (C) disappears and the critical conditions imposed by (A) and (B) are not unduly restrictive. In particular, at high plasma densities it is required: (1) for adequate stability against (A), the length of the plasma between the mirrors must not be greater than about 300 to 500 ion‐orbit radii, and (2) to satisfy conditions (on the radial density gradient) imposed by (B), the plasma dimensions transverse to the field must also be of the same order; i.e., the plasma must be roughly spherical. Examples are also given which show that the confinement of highly peaked distributions leads to required conditions of orders of magnitude more restrictive than those found for well‐randomized distributions.