One-dimensional model of power balance in an Orbitron fusion reactor

The Orbitron is a small scale fusion reactor that relies on crossed electric and magnetic fields for co-confinement of ions and electrons at fusion-relevant energies. To confine ions, a >100 kV bias is applied across an azimuthally symmetric anode-cathode gap modelled around the geometry of an orbitrap. An ion source injects particles azimuthally into elliptical orbits that precess around the cathode to collide with each other at high energies and fuse. An axial magnetic field confines electrons radially, building density to prevent a space charge limited ion density.

This work presents a simplified analytical ion model that predicts power balance in such a device for a variety of operating parameters and input species. In an assumed cylindrically symmetric configuration, we apply fundamental conservation laws to predict species velocities and densities as functions of radius. We then apply known reaction rate laws to predict fusion and energy generation rates for deuterium-tritium and proton-boron 11 species composition. We further analyze several loss mechanisms including Coulomb collisions, energy loss to background neutral species, and bremsstrahlung radiation and discuss their relative importance. Finally, we discuss operating regimes that would be required to achieve net energy gain and the potential impact of phenomena not captured by the model, such as plasma instabilities.