Statistical Theory of Nonadiabatic Magnetic Traps

The trapping and containment of particles injected into a nonadiabatic magnetic mirror trap are considered. The results of numerical orbit calculations are compared with a statistical theory which is shown to give essentially identical results. This statistical theory leads to simple expressions for the mean containment time and the mean density of trapped particles. These results indicate that the most significant factors in the nonadiabatic trapping process are the width of the acceptance cone (i.e., the solid angle in velocity within which the injected particles have a finite chance of capture) and the angular spread of the input beam. Optimum trapping requires that these two quantities be appropriately matched. When this is done the density approaches a limiting value (which is generally below the usually quoted ``Liouville limit'') and the buildup time is a minimum. Provided this matching can be achieved, there appears to be no special merit in using resonant nonadiabatic traps over any other form.