Ion and Electron Current Scaling Issues

Abstract

Studies to scale an IEC device for higher neutron yields or breakeven fusion operation require the prediction of scaling laws that relate the device performance to the ion and electron current. Ion currents contribute to the fusion reaction rate, while a major energy loss channel occurs through electron currents. Early studies focused on ion beam reactions in the compressed central core region. However, due to high background pressures and modest ion currents in early experiments, it soon became apparent that ion beam–background neutral interactions along with charge exchange reactions and ion interactions with absorbed gas on grid wires were dominant factors. These interactions produce nonlinearities that make the development of scaling laws for internal ion source IECs much more complicated than originally recognized. In addition, breakeven calculations for fusion power concepts involve low-pressure potential well physics, so completely different scaling laws come in.Some approximate reaction rate scaling laws based on the ion density, n 1, in the ion beams illustrate how these conditions radically affect operation. Assuming a deuterium gas filling of the IEC, the volumetric reaction rate, r 1,2 (units of m−3 s−1), arising from monoenergetic populations 1 and 2 of colliding deuterons is given by $$ {r}_{1,2}={n}_1{n}_2\sigma \left({v}_{12}\right){v}_{12}, $$ where n 1 and n 2 are the respective population densities and v 12 is the magnitude of the collision velocity in the rest frame of either particle (assuming head-on collisions). The subscripts 1 and 2 may refer to either beam deuterons, gas molecules, or those embedded in a solid target. For a fixed grid voltage, we expect the density of beam deuterons to be proportional to the grid current I grid. Thus for beam–beam reactions, we expect to observe $$ {r}_{1,2}\propto {I}_{grid}^2, $$ whereas for beam–gas reactions, we expect $$ {r}_{1,2}\propto {I}_{grid}. $$