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steinhauer_icc_poster.pdf | 2006-03-07 13:37:50 | Loren Steinhauer |

## Computation of equilibria of a flowing two-fluid

Author: Loren Steinhauer

Submitted: 2005-12-15 13:02:22

Co-authors:

Contact Info:

University of Washington

14700 N.E. 95th St., Suite 100

Redmond, WA 98052

US

Abstract Text:

The system of equations for two-fluid equilibria with flow presents difficulties for numerical computation. The first challenge is that it is much more complex than that for static, single-fluid equilibria, which is a single, second-order differential equation with two arbitrary surface functions (Grad-Shafranov equation). The two-fluid system has two second-order differential equations plus a Bernoulli equation and six arbitrary surface functions. Another challenge is that it is a singular-perturbation problem with a small parameter multiplying the highest-order derivatives, i.e. the â€œskin-depthâ€? parameter e Âº li/L where li is the ion skin depth and L is the system size scale. The effect is to â€œstiffenâ€? the differential equations. However, the recently developed nearby-fluids platform [1] overcomes this by an ordering of the â€œarbitraryâ€? surface functions. The result is a â€œsoftenedâ€?, nonsingular problem. Further, it reduces the system to a single second-order differential equation for the magnetic flux function plus the Bernoulli equation for the density. A quasi-one-dimensional form of this has been used to interpret experiments on the TCS experiment at the University of Washington. This was done by a â€œbackwardsâ€? approach, working backwards from magnetic field and flow measurements to infer the surface functions as well as other, unmeasured properties [2].

A two-fluid equilibria solver has been developed for the full two-dimensional problem, i.e. axisymmetric equilibria. The solver employs an iterative approach: using the successive over-relaxation method to â€œupdateâ€? the magnetic flux function and the Newton-Raphson method to update the density. Examples of computed equilibria will be presented. Computed equilibria relevant to experiments show important features missing from the simpler models (static or flowing single-fluid equilibria). For example, there are two distinct sets of characteristic surfaces, one set each for ions and electrons. This gives rise to two separatrices (one for each species) which are well separated, i.e. the plasma â€œedgeâ€? has significant width. This provides a â€œline tyingâ€? effect inside the ion flow separatrix. Further, for plasma parameters of interest, poloidal and toroidal flows seem to go together, i.e. if there is toroidal flow, then a significant poloidal flow also appears.

*This work is supported by the U.S. Department of energy

[1] L.C. Steinhauer and A. Ishida, submitted to Phys. Plasmas, 2005.

[2] L.C. Steinhauer and H.Y. Guo, submitted to Phys. Plasmas, 2005.

Characterization: A1,A2

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