Mathematical model of the current density for the 30-cm engineering model thruster

Mathematical models are presented for both the singly and doubly charged ion current densities downstream of the 30-cm engineering model thruster with 0.5% compensated dished grids. These models are based on the experimental measurements of Vahrenkamp at a 2-amp ion beam operating condition. The cylindrically symmetric beam of constant velocity ions is modeled with continuous radial source and focusing functions across 'plane' grids with similar angular distribution functions. A computer program is used to evaluate the double integral for current densities in the near field and to obtain a far field approximation beyond 10 grid radii. The utility of the model is demonstrated for (1) calculating the directed thrust and (2) determining the impingement levels on various spacecraft surfaces from a two-axis gimballed, 2 x 3 thruster array.