Electrostatically trapped electrons in thermal-barrier tandem mirrors

Abstract

Electron confinement in the plug regions of thermal-barrier tandem mirrors is examined. Analytical and numerical (Fokker-Planck code) approaches are presented for small-to-intermediate mirror ratios including the effects of passing particles and electron heating. Steady-state trapped-electron densities and mean energies from the theory and code agree to within 20% for mirror ratios 0 < R < 2.2 with and without passing particles. Electron heating and detrapping by strong RF diffusion is demonstrated computationally for parameters expected in the TMX-U experiment. * Work performed under the auspices of the US Department of Energy by the Lawrence Livermore National Laboratory under contract number W-7405-ENG-48.

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

“…Equation (2) applies when the ratio R of the magnetic field at the edge of the potential well to that at the middle is bigger than about T e p / $ p b . Extension to smaller mirror ratios is considered in Refs [5][6][7] and is also discussed in the present paper.…”

X-Point Heating, Potentials, and Temperature Asymmetries in Edge Plasmas

“…The instantaneous parallel current Jli oc &!/as also\peaks near the x point, because' of a transition of the mode from electromagnetic to electrostatic as the x point is I,\,., approached: this transition occurs [S] indicates significant variability (within the ranges indicated) in the S-point quantities during the course of a shot. 3 Heating and Potential Models : In this section we address whether there might be a connection between locahzed "…”

“…Hence one is led to consider the limit of long L,f,. There are theoretical and computational studies [2], [3] which develop a theory of collisional particle and energy exchange between electrostatically trapped and passing electrons and provide the basis for calculation of potentials and temperature differences. The essential results are equations for the rate of change of trapped density nt,.…”

“…and nt is spelled out in Ref. [3]. Many papers have derived expressions for G,,starting with Pastukhov's [7] and continuing through an elegant expansion treatment by Khudik [S].…”

“…' from the turbulent sources in both short and, iong mean-free-path limits. Perhaps surprisingly, the latter approximation can produce stronger asymmetries for the parameters of interest, because of the limited rate of energy exchange between electrons trapped in the potential well near the X point and those passing to the rest of the flux surface [2], [3].…”