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steinhauer___icc_2011_hybrid_equilibria_poster.pdf2011-08-17 09:18:15Loren Steinhauer
steinhauer___icc_2011_hybrid_equilibria___short_paper.pdf2011-08-17 09:17:14Loren Steinhauer

Hybrid equilibria of axisymmetric, divertor tori, with application to field-reversed configurations

Author: Loren C Steinhauer
Requested Type: Consider for Invited
Submitted: 2011-05-28 13:57:35


Contact Info:
University of Washington
Box 352250
Seattle, WA   98195

Abstract Text:
High-beta plasmas of interest to fusion energy are poorly captured by fluid or even extended-fluid models. In local regions of low magnetic field (O-point, X-points) as well as regions with steep gradients (separatrix, SOL) the applicability of even the gyroviscous model is questionable. An adequate treatment of the ion species thus calls for an approach that is fully kinetic. The electrons can still be treated as a massless fluid. The label “hybrid equilibrium” describes this combination of fully-kinetic ions and fluid electrons.

Kinetic ion equilibria are solutions to the steady Vlasov equation. In axisymmetric geometries the distribution function can be expressed in terms of the two constants of motion, the Hamiltonian H and the canonical angular momentum Ptheta. The rigid rotor (RR) paradigm is just such a solution. However, RR equilibria fail in one critical respect for divertor tori: they do not account for the rapid loss of plasma outside the separatrix and its consequent effect on the distribution function. This effect can be captured by recognizing the ion confinement boundary in H-Ptheta space and solving the Fokker-Planck equation for the migration of ions out of the confined and into the unconfined region. This gives rise to an “end-loss” distribution. It differs from the familiar loss-cone distribution in that it depends on both velocity and real space. For reasonable approximations the distribution as well as its moments, e.g. density, flow, temperature, have analytic forms.

The remaining ingredients of the equilibrium system are the electron/potential model and Maxwell’s equations. A small set of three parameters is sufficient to offer adequate flexibility in specifying the electron temperature profile and the potential. Maxwell’s equation (an extended form of the Grad-Shafranov equation) can then be solved by a conventional relaxation procedure. This has been done on a personal computer with modest computation times of several seconds.

Calculated hybrid equilibria yield insight into long-standing anomalies about the SOL thickness in FRCs, as will be explained in some detail. Future work will address how the kinetic ion treatment affects local as well as global confinement properties at high-beta.

Characterization: D1

This topic obviously connects with FRC physics, but also applies to any high-beta, diverted axisymmetric torus, including high-beta divertor tokamaks (e.g. spherical tokamaks).

University of Washington

Workshop on Innovation in Fusion Science (ICC2011) and
US-Japan Workshop on Compact Torus Plasma
August 16-19, 2011
Seattle, Washington

ICC 2011