Parallel heat transport in integrable and chaotic magnetic fieldsa)

The study of transport in magnetized plasmas is a problem of fundamental interest in controlled fusion, space plasmas, and astrophysics research. Three issues make this problem particularly challenging: (i) The extreme anisotropy between the parallel (i.e., along the magnetic field), χ‖, and the perpendicular, χ⊥, conductivities (χ‖/χ⊥ may exceed 1010 in fusion plasmas); (ii) Nonlocal parallel transport in the limit of small collisionality; and (iii) Magnetic field lines chaos which in general complicates (and may preclude) the construction of magnetic field line coordinates. Motivated by these issues, we present a Lagrangian Green’s function method to solve the local and non-local parallel transport equation applicable to integrable and chaotic magnetic fields in arbitrary geometry. The method avoids by construction the numerical pollution issues of grid-based algorithms. The potential of the approach is demonstrated with nontrivial applications to integrable (magnetic island), weakly chaotic (Devil’s st...

[1]  C. Sovinec,et al.  Conductive electron heat flow along magnetic field lines , 2001 .

[2]  Vickie E. Lynch,et al.  Fractional diffusion in plasma turbulence , 2004 .

[3]  S. Hudson,et al.  Temperature contours and ghost surfaces for chaotic magnetic fields. , 2008, Physical review letters.

[4]  M. Rosenbluth,et al.  Electron heat transport in a tokamak with destroyed magnetic surfaces , 1978 .

[5]  Daniil Svyatskiy,et al.  A constrained finite element method satisfying the discrete maximum principle for anisotropic diffusion problems , 2009, J. Comput. Phys..

[6]  S. Kruger,et al.  Nonlocal closures for plasma fluid simulations , 2004 .

[7]  L Chacón,et al.  Local and nonlocal parallel heat transport in general magnetic fields. , 2010, Physical review letters.

[8]  Perkins,et al.  Fluid moment models for Landau damping with application to the ion-temperature-gradient instability. , 1990, Physical review letters.

[9]  Diego del-Castillo-Negrete,et al.  Fractional diffusion models of nonlocal transport , 2006 .

[10]  E. Parker,et al.  Random walk of magnetic lines of force in astrophysics. , 1968 .

[11]  Jet Efda Contributors,et al.  Fractional diffusion models of non-local perturbative transport: numerical results and application to JET experiments , 2008 .

[12]  Steven J. Plimpton,et al.  Nonlinear magnetohydrodynamics simulation using high-order finite elements , 2004 .

[13]  Prateek Sharma,et al.  Preserving monotonicity in anisotropic diffusion , 2007, J. Comput. Phys..

[14]  Sibylle Günter,et al.  Finite element and higher order difference formulations for modelling heat transport in magnetised plasmas , 2007, J. Comput. Phys..

[15]  Sibylle Günter,et al.  Modelling of heat transport in magnetised plasmas using non-aligned coordinates , 2005 .