Scaling laws of electron confinement and power losses in zero and low beta Polywell devices

Abstract

The Polywell consists of three orthogonal pairs of opposing coil current loops equidistant from the center of the device. The coils produce strong magnetic field gradients to confine a central negative space charge, of electrons, to create a virtual cathode within the Polywell. To investigate electron confinement in the Polywell, we developed an orbital theory simulation, which was then used to simulate electrons in the vacuum magnetic fields of a zero beta (ratio of plasma pressure to magnetic pressure) Polywell. Both empirical and analytical expressions of the electron confinement time and average position within the device were obtained in terms of the current in the field coils, the dimensions of the device, and the kinetic energy of the electrons. Comparisons between the numerical simulations and the analytically derived expressions showed good agreement over a parameter range that spanned several orders of magnitude. Electron recirculation exterior to the Polywell device have been investigated in order to mitigate electron cusp losses. It was observed that without a positive bias placed on the Polywell coils the electron trajectories intersected with the vacuum chamber wall. Recirculating electrons spent approximately an order of magnitude longer outside the device compared to their internal confinement time. Also, the volume required to accommodate the recirculating electrons was calculated to be 90% of the vacuum chamber volume, using the optimum parameters used in the simulation. By modifying the cusp transmission probability to include the electrostatic repulsion effects of the repeller plates we derived new electron confinement time scaling laws. We also predict a significant improvement in the confinement time of electrons. Finally, we derived the electron power loss scaling laws for a thermalised distribution of electrons with and without electrostatic plugging. Also, space charge limited flow effects were considered in the cusp of the device.