Speaker
Jeffrey Freidberg
Description
See the full Abstract at http://ocs.ciemat.es/EPS2018ABS/pdf/P2.1045.pdf
Surface Current Equilibria for a Stellarator
J. Freidberg1, A. Cerfon2, L. Guazzotto3, D. Malhotra2
1
Plasma Science and Fusion Center MIT, Cambridge MA USA
2
Courant Institute of Mathematical Sciences NYU, NYC NY USA
3
Auburn University, Auburn AL USA
The work presented here is focused on the calculation of 3-D stellarator equilibria using the
well-known surface current model which assumes that all plasma current flows only on a single
surface r = rs (θ , φ ) . The pressure within the surface is a constant and both the interior magnetic
field plus external magnetic field just outside the surface satisfy the vacuum Maxell’s equations.
The model has been investigated for both equilibrium and stability for arbitrary 2-D tokamak
shapes [1]. It has also been used to investigate 3-D stellarator equilibrium and stability in the
context of the large aspect ratio stellarator expansion [2]. A recent 3-D multi-surface stellarator
model has been developed for computing equilibria and is largely focused on the interior solution
[3]. The contribution of the present work is to extend these studies to solve both the interior and
exterior problems for a single 3-D surface model that is valid for arbitrary β , ιH , ιI , ε , and
rs (θ , φ ) . The main advantages of the model are (1) a crisp separation of equilibrium and
stability, (2) reduction of the analysis to an exact 2-D formulation, (3) evaluation of both
equilibrium and stability MHD β limits, and (4) optimization of plasma shape for high
performance with respect to large scale external MHD modes. The model obviously does not
treat internal pressure gradient driven modes, nor take into account neoclassical transport.
Another application of the model is the examination of 3-D tokamak equilibrium perturbations
with the aim of optimizing disruption free operation.
The strategy of our equilibrium analysis is to calculate the interior fields on the plasma
surface by means of a fast 3-D Green’s function procedure. The fields just exterior to the surface
require the solution to a first order, quadratically nonlinear partial differential equation, which is
obtained by the method of characteristics. These fields are all that are needed to completely
determine plasma stability limits. The present work, however, solely focuses on equilibria.
[1] J. P. Freidberg and W. Grossmann, Physics of Fluids 18, 1494 (1975);
[2] D. Sherwell, J. P. Freidberg, and G. Berge, Physics of Fluids 25, 1370 (1982)
[3] S.R. Hudson, R.L. Dewar, G. Dennis, et. al., Phys. Plasmas 19 (2012) 112502
