Detailed shape analysis of tandem-mirror end-loss-ion energy spectra

Equations have been derived for relating the shape of measured end-loss-ion energy spectra in tandem-mirror magnetic-fusion experiments to key plasma parameters. The authors assume a collisional central-cell ion distribution. Equation parameters include the end-cell peak potential, the potential at the end-cell inner mirror peak, the magnetic field at the peak-potential position, and the central-cell ion temperature. These equations have been used to obtain good fits to end-loss-ion energy spectra from the Tandem Mirror Experiment-Upgrade (TMX-U). An especially interesting application of this analysis is to TMX-U operating conditions where strong deuteron and proton end losses occur simultaneously. Independent fits to these two quite different spectra, using the spectra-shape equations, give the same value of peak potential. Such consistency gives credibility to the usefulness of this type of analysis.