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

Abstract

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 $ P b 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.

The ambipolar trap

“…Figure 3 gives an idea of ambipolar plasma confinement in a solenoid in which thermal barriers have been introduced. In this case [11], Figure 2. An ambipolar TMX trap: 1, plasma; 2, solenoid coils; 3, baseballtype coils generating quadrupole magnetic fields with minima at the centers of the end mirror cells; 4, interstage C-shaped coils; 5, atomic injectors of the end mirror cells; 6, gas`boxes', or sources of controllable hydrogen inflow followed by ionization in the solenoid; and 7, start plasma guns.…”

“…The number density of high-energy electrons in the thermal barriers can be lowered to its minimum value, while the plasma density in the ion barriers may be optimized independently to increase the capture of ions from the injecting atomic beams. In contrast to single mirror cells, in double mirror cells, the high-energy electrons from the thermal barriers are not scattered into the ion barriers and do not increase the power consumed by the ion barriers [11]. As a result, in traps with thermal barriers, the energy consumption by double mirror cells is lower than that by single mirror cells, despite the double length.…”

Generalized Scaling Laws of the Formation and Effects of Plasma-Confining Potentials for Tandem-Mirror Operations in GAMMA 10

“…Even at this time, however, the physics-mechanism and scaling studies on the basis of the comparison between experimental data and potential theories [6][7][8][9] are reported in a limited number of publications for specific plasma operations alone [10][11][12].…”

Electrostatically trapped electrons in thermal-barrier tandem mirrors

“…In Ref. [11], corresponding expressions for intermediate mirror ratios were obtained from the ansatz that one can extrapolate to low mirror ratio the property that the fluxes for f and f* should be distributed nearly exponentially; specifically, these fluxes were assumed to be distributed as exp(-e) P(e) -exp(-e m ) P(e m ), where e m = 0/(1-R) for R < 1, e m -*• °° for R > 1, and P is a polynomial which can be truncated at zeroth and first order for the f and f* fluxes, respectively. This form accounts for the finite extent of the separatrix 3) for R < 1.…”

“…However, progress has been made on the analytic description of the regimes where ECRH significantly distorts the distribution for barrier electrons but not the distribution for electrons trapped in the plug, and also the regime where ECRH is so strong as to dominate over collisions for all particles not traversing the solenoid. This work is described elsewhere [11,12] as is related computational work [13].…”