Ramit Bhattacharyya - Spontaneous current sheet formation: Numerical study

Spontaneous current sheet formation is an ubiquitous plasma phenomenon with both theoretical and observational implications. Theoretically it takes our understanding well beyond the standard concept of continuous magnetic fields. Observationally, resistive dissipation of these current sheets into thermal energy may play an important role in coronal heating. The motivation for this work is to understand the dynamical aspect of current sheet formation through specially designed numerical experiments.

The plasma is considered to be of infinite electrical conductivity, incompressible, viscid and described by the single-fluid MHD equations. The current sheets are known to form at the separation layer between two interacting flux surfaces. For direct visualization and hence more insight into the complex process of current sheet formation, the magnetic field is expressed in terms of intersecting magnetic flux surfaces.

The objective is to locate the current sheets both in time and space as they form by analyzing different sections of these flux surfaces. The numerical experiments are performed on a customized version of the EULAG modeling system developed by Piotr Smolarkiewicz. Computations with 128³ and 180³ uniform grid resolutions have been performed and analyzed. In the following, a brief excerpt of obtained results is presented to convey the general idea. This specific set belongs to a 128³ run with a static flow and prescribed cylindrical flux surfaces as the initial condition. With time, as the flow builds up, different sections of these surfaces interact with each other and undulate (Figure 1). From 96 time units (seconds) onward numerical dissipation sets in and the flux surfaces start to break.

Figure 1. Temporal evolution of a given set of flux surfaces

t = 0 s	t = 32 s	t = 96 s	t = 192 s

Figure 2 represents the time evolution of a section of the above flux surfaces on a Cartesian plane (in this case xy plane).

Figure 2. Time evolution of a given cross section of the flux surfaces on a Cartesian plane

t = 0 s	t = 48 s
t = 72 s	t = 80 s

The observed necking and breaking of the flux surfaces in presence of numerical dissipation are the omnipresent signs for current sheet formation.

The methodology and the results described here are a stepping stone and motivation for future studies in this direction with more realistic scenarios including the effects of Navier-Stokes flow,
electrical resistivity and twisted magnetic field lines.

ASP Spotlight Januray 2009
For more ASP spotlights click here http://www.asp.ucar.edu/spotlight/archive.jsp