Classical collisional theory of beam-driven plasma currents

A variational calculation of the current produced in a plasma by fast beam particles is presented. A new energy polynomial expansion of the classical Spitzer function is obtained and used to derive an accurate analytic expression for the beam-driven current j/sub parallel/, which includes the effects of electron-electron collisions and is valid for all values of v-bar/sub b/=v/sub b//v/sub e/ and effective charge Z-bar. This analytic result is in excellent agreement with previous numerical calculations. An accurate rational form for the beam-driven current as a function of beam velocity is obtained by patching the large and small v-bar/sub b/ asymptotic expansions of j/sub parallel/