Plasma confinement in multiple-mirror systems. I: Theory

For an intermediate mean free path regime where λ ≪ L, the system length, but where λ ≫ lm, the scale length of the magnetic field variation, it is found that the confinement time τmm of ions in a multipole mirror system scales quadratically with the system length. When either inequality is not satisfied, a transition is found to a scaling which is more closely proportional to L. For the high density regime this corresponds to magnetohydrodynamic flow. By comparison with numerical and experimental results a criterion is found for the transition from the quadratic to the linear scaling. The value of τmm = ML2/(2lcν¯) found from diffusion theory is in good agreement with a more accurate analytic treatment which is valid in the limit of λ/M ≪ lc, where M is the mirror ratio, Lc is the cell length, and ν is the average ion velocity. Good agreement is also obtained with a self-consistent numerical computation.