Scaling law of electron confinement in a zero beta polywell device

Orbital theory simulation was applied to an electron trap that uses a cube shaped magnetic cusp known as a Polywell device. The purpose of this device is to create a virtual cathode in order to achieve nuclear fusion using inertial electrostatic confinement. 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 with numerical simulations showed good agreement over a parameter range that spanned several orders of magnitude for the current. In addition, power loss from electrons exiting the trap was estimated in order to obtain minimum power requirement to maintain a virtual cathode within the device.