Optical Emission Spectroscopy Measurements of keV Apparent Ion Temperatures in Avalanche Energy's Centrifugal Mirror Machine

Abstract

Newly formed ions in $E \times B$ devices are rapidly accelerated by strong radial electric fields and execute large cycloidal orbits in the presence of an axial magnetic field. At locations where these orbits intersect, ions originating from different birth radii arrive with substantially different velocities, producing a non-Maxwellian velocity distribution with a large velocity variance. Through Coulomb collisions and collective interactions, this distribution relaxes toward a drifting Maxwellian in the rotating frame. Here, we present the first optical emission spectroscopy (OES) measurements of the line-of-sight-convolved ion-velocity distribution, from which an apparent ion temperature is determined, in Avalanche Energy's centrifugal mirror machine. High-resolution $H_α$ spectra obtained along five chordal lines-of-sight spanning the plasma radius are analyzed using two complementary models representing limiting cases of the ion dynamics: a collisionless cycloidal model based on the ion-velocity distribution arising from deterministic single-particle orbits, and a rotating Gaussian model based on collisions and collective processes that fully randomize the cycloidal motion into a drifting Maxwellian in the rotating frame. Combined, these approaches bracket the possible degree of velocity-space relaxation and provide a stringent test of the inferred ion energies. Both models reproduce the measured spectra relatively well and yield density-weighted apparent ion temperatures of $1.40\pm0.43$ keV for the rotating Gaussian model and $1.55\pm0.24$ keV for the cycloidal model. These results provide direct spectroscopic evidence that strong $E \times B$ rotation in a device only a few centimeters in size can generate ion populations with keV energy spreads.