Classical diffusion in a field-reversed mirror

Abstract

Classical transport of particles and heat in field-reversed mirrors is discussed. The X-points (field nulls on axis) are shown to have no deleterious effect on transport; this conclusion is true for any transport model. For an elongated Hill's vortex equilibrium the classical diffusion coefficient is calculated analytically and used to construct an analytic solution to the transport equation for particles or energy ; this yields exact results for particle and energy confinement times. These life-times are roughly 3 to 6 times shorter than previous heuristic estimates. Experimentally determined life-times are within a factor of 3 to 4 of our estimates. To assess the impact of these results on reactor designs, the authors construct an analytic reactor model in which neutral-beam input balances ion heat loss. Energy loss due to synchrotron radiation is calculated analytically and shown to be negligible, even with no wall reflection. Formulas are presented which give the reactor parameters in terms of plasma temperature, energy multiplication factor Q, and allowed neutron wall loading. The effect of anomalous resistivity is incorporated heuristically by assuming an anomalous resistivity which is enhanced by a factor A over classical resistivity. For large A the minimum power of a reactor scales as A11/6. A = 50 gives a reactor design which still seems reasonable, but A = 200 leads to extremely large, high-power reactors.

Gyrokinetic particle simulation of a field reversed configuration

“…Confinement is significantly affected by radial diffusion through the edge, 28,29 where particles may move from the closed field lines of the core to the open field lines of the SOL. A number of analytical studies have been made of classical transport in simple equilibria [30][31][32][33] and using quasi-steady 1-D plasma profiles. [34][35][36] Numerical models of transport have included more details using both simple 1-D and 2-D equilibria.…”

Inductive sustainment of oblate field-reversed configurations with the assistance of magnetic diffusion, shaping, and finite-Larmor radius stabilization

“…The classical outward diffusion is proportional to the plasma resistivity, which is typically close to the collisional Spitzer resistivity in these stable argon plasmas, though large uncertainties preclude a more systematic analysis. This mechanism is directly analogous to the resistive decay of a prolate FRC, 57 but with the addition of the inward pinch.…”

“…46 From a transport perspective, the oblate shape maximizes the shortest distance between the hot plasma core and the cooler edge; for diffusive transport, this geometry maximizes the confinement times. 57 From a formation standpoint, the technique of spheromak merging has been utilized to form largeflux oblate FRCs. 44,58,59 In principle, many of the sustainment techniques noted above are applicable to the oblate FRC.…”

“…Note that the same formulation describes the evolution of unsustained FRCs ͑either prolate or oblate͒ if E is set to zero. 57 This peaking of the pressure gradient and balance of the particle fluxes has been studied during inductive sustainment ͑7.5 kV solenoid voltage in this case͒. Radial scans of the triple Langmuir probe were conducted over many repeatable discharges, in order to measure profiles of the electron temperature and density; these profiles are shown in the bottom row of Fig.…”

A one-and-a-quarter-dimensional transport code for field-reversed configuration studies: A user's guide for CFRX

“…Auerbach and Condit studied classical diffusion based on magnetohydrodynamics. 11 Nguyen and Kammash used a similar approach, but employed a more generalized Ohm's law. 12 Tuszewski and Linford investigated the particle transport induced by the lower-hybrid-drift, instability.…”