In the case that collisions are neglected, particles are trapped in a mirror when they do not appear in the loss cone in velocity space. However, plasma ions and electrons do suffer collisions, which can bring them randomly from the confinement region of velocity space into the loss cone. Upon entering the loss
cone, the particles escape immediately within one transit time t = L/v over the length L of the device. Due to their relatively small mass, electrons diffuse more rapidly both in velocity and coordinate space and hence are first to be scattered into the escape cone and then lost. This initially rapid loss rate causes the build­up of a positive electrostatic potential in the confined plasma which then consists of a surplus of ions having not yet scattered into the loss cone. Since this positive potential tends to retain the remaining electrons in the magnetic bottle, the overall plasma confinement time is governed by the ion escape time as characterized by the ion-ion collision time and can be shown, for ions encountering simultaneous multiple collisions, to be given by

(9.42)

at the plasma temperatures of interest to nuclear fusion, with Aj representing the ion’s atomic mass number.

Current Carrying Bars

The mirror confinement time Хм must also be determined by the size of the
loss cone, and consequently the approximation

(9.43)

can be shown to hold for large values of the so-called mirror ratio Binax / Bmm. By substituting, one obtains

(9.44)

where q, = Z, e has been replaced and C is a constant taken for typical fusion temperatures here to be

C= 1.78 x 1016 s

when Tj is measured in keV, N, in particles per m3 and Хм in seconds. Note that the mirror confinement time depends on the ion temperature and on the ratio Bmax/Bmin. but not on the actual magnitude of В or the plasma size. Evidently, a higher density will enhance the scattering into the loss cone and thus reduce Хм-

We add that the heuristic derivation of Хм presented here refers to a classical treatment in the sense that collective effects such as instabilities are suppressed. Therefore, the above scaling applies when stabilization of those collective perturbations has been provided and then appears to be in good agreement with particle containment times recorded in magnetic mirror device experiments.