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A plasma confined in a mirror machine can be expected to develop an electrostatic potential with respect to its surroundings. This potential arises because of the intrinsically different rate of diffusion in velocity space of the electrons and ions. When the temperature of the confined electrons is comparable to or smaller than the ion temperature, the potential will be positive, and will vary within the plasma. The variation of plasma potential with position in a mirror machine is calculated for conditions where: (a) the electron temperature is small compared to ion temperature and (b) electrons and ions are separately in diffusion equilibrium with the mirror losses. It is shown in an example that the plasma potential tends to concentrate near the mirrors, and that its variation, between the mirrors, is relatively insensitive to the total potential. Applications and extensions of the calculations are suggested.

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.

In a pulsed experiment a magnetically guided plasma stream is reflected by a double electrode structure. Space‐charge‐limited densities up to 4×1011 cm−3 are calculated and verified. An application to stopper one end of a mirror fusion reactor is discussed.