SCATTERING LOSS FROM MAGNETIC MIRROR SYSTEMS. I-II.
Abstract
The problem of scattering loss of a plasma of singlycharged ions and electrons from magnetic mirror confinement is considered. Using the adiabatic approximation for the behaviour of a charged particle in the absence of collisions, a method is developed in which collisions are treated as a perturbation. The time behaviour of the distribution function of the ions everywhere in the system is found from the reference distribution' at the mid-plane. The 'square well' approximation is treated in detail. An approximation to the ROSENBLUTH equation is developed which permits the problem to be treated in terms of angular modes and transport coefficients. The transport coefficients involve integrals over the speed distribution of the ions; this speed distribution is the solution of a highly non-linear equation and numerical solutions are given for several mirror ratios. The asymptotic form of the distritution function in both angle and speed is discussed. Results are then presented of a study in which the 'square well' treatment was generalized by the reference distribution method to a class of more realistic mirror machine shapes. It is shown that the rate of change of density and energy in such systems may be considered in terms of equations similar in form to those derived for the 'square well'. Graphs presented of the results to numerical calculations in which the independent parameter was the 'shape' of the system. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 19, 1961
- Accession Number
- AD0613495
Entities
People
- D. J. Bendaniel
- W. P. Allis
Organizations
- Massachusetts Institute of Technology