Exact axisymmetric Taylor states for shaped plasmas

We present a general construction for exact analytic Taylor states in axisymmetric toroidal geometries. In this construction, the Taylor equilibria are fully determined by specifying the aspect ratio, elongation, and triangularity of the desired plasma geometry. For equilibria with a magnetic X-point, the location of the X-point must also be specified. The flexibility and simplicity of these solutions make them useful for verifying the accuracy of numerical solvers and for theoretical studies of Taylor states in laboratory experiments.

[1]  T. Gray,et al.  Observation of a relaxed plasma state in a quasi-infinite cylinder. , 2013, Physical review letters.

[2]  S. Hudson,et al.  Minimally constrained model of self-organized helical states in reversed-field pinches. , 2013, Physical review letters.

[3]  T. W. Kornack,et al.  Scaling studies of spheromak formation and equilibrium , 1998 .

[4]  Allen H. Boozer,et al.  Chandrasekhar-Kendall modes and Taylor relaxation in an axisymmetric torus , 2005 .

[5]  J. Freidberg,et al.  “One size fits all” analytic solutions to the Grad–Shafranov equation , 2010 .

[6]  R. L. Dewar,et al.  Computation of multi-region relaxed magnetohydrodynamic equilibria , 2012, 1211.3072.

[7]  L. Woltjer,et al.  A THEOREM ON FORCE-FREE MAGNETIC FIELDS. , 1958, Proceedings of the National Academy of Sciences of the United States of America.

[8]  Hong Li,et al.  Woltjer-Taylor state without Taylor's conjecture: plasma relaxation at all wavelengths. , 2012, Physical review letters.

[9]  R. J. Hastie,et al.  The Taylor relaxed state in tokamaks and the sawtooth collapse , 1989 .

[10]  George Marklin,et al.  Spheromak Formation by Steady Inductive Helicity Injection , 2006 .

[11]  M. Schaffer.  Exponential Taylor states in circular cylinders , 1987 .

[12]  J. B. Taylor,et al.  Relaxation of toroidal plasma and generation of reverse magnetic fields , 1974 .

[13]  P. Bellan,et al.  Motion and equilibrium of a spheromak in a toroidal flux conserver , 1991 .

[14]  R. Kress,et al.  On constant-alpha force-free fields in a torus , 1986 .

[15]  R J Fonck,et al.  Tokamak startup using point-source dc helicity injection. , 2009, Physical review letters.

[16]  J B Taylor,et al.  Relaxation and magnetic reconnection in plasmas , 1986 .

[17]  J. Greene,et al.  Noncircular, finite aspect ratio, local equilibrium model , 1998 .

[18]  J. Sprott,et al.  Equilibrium studies of a poloidal divertor pinch with a reversed toroidal field , 1987 .

[19]  A. Bondeson,et al.  The CHEASE code for toroidal MHD equilibria , 1996 .

[20]  P. J. Mc Carthy,et al.  Analytical solutions to the Grad–Shafranov equation for tokamak equilibrium with dissimilar source functions , 1999 .