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Techniques for calculating the drift velocity of an electron moving in a 1/r magnetic field

Lee, J.R.

An electron moving in the magnetic field generated by a current-carrying rod will drift in the direction defined by the rod. The motion can be characterized by two dimensionless parameters,/var epsilon/ = 2eI/mc/sup 3/..gamma beta.. and xi = (v/sub /phi///v)exp(v/sub z///var epsilon/v). The drift velocity can be computed by numerical integration for arbitrary values of /var epsilon/ and xi. Analytic solutions are derived for the limiting cases xi = 0 and /vert bar/xi/vert bar/ = xi/sub MAX/. Series solutions are derived that are accurate in the limit /vert bar/xi//var epsilon//vert bar/ << 1. A simple algorithm is developed that has an error of less than +- 0.08% for /var epsilon/ greater than or equal to 2. 14 refs., 18 figs.