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Effect of magnetically trapped electrons on the plug potential in thermal-barrier tandem mirrors

The problem of potential formation in a thermal-barrier tandem-mirror machine in which the plug and barrier are combined in a single cell is considered. In particular, the effect of hot, magnetically confined barrier electrons on formation of the potential difference Φpb between the plug and barrier regions is evaluated. This is done using a fit to a portion of the hot-electron distribution function and the formalism of Cohen, Bernstein, Doming and Rowlands, which gives the collisional loss rate for particles trapped in a well in the presence of an arbitrary distribution of passing particles. The energy flux associated with the flow of particles across the separatrix dividing the passing and trapped portions of velocity space is also derived in terms of the particle and energy fluxes in the absence of passing particles. Numerical examples appropriate for MFTF-B and TMX-U are presented.