The Computation of FLR Eigenfrequencies in General Geometries
Abstract
Until recently, the calculation of fieldline resonance (FLR) frequencies from magnetic field data, provided by magnetospheric models such as BATSRUS and Tsyganenko (T01), was restricted to orthogonal coordinate systems. With this restriction, only dipolar and axisymmetric configurations are admissible. The matter of addressing more general configurations such as nonaxisymmetric, stretched and twisted field topologies requires the use of a nonorthogonal coordinate system. The appropriate coordinate system can be constrained by defining the magnetic field as the product of matched Euler potentials, B = ∇ α _{i} x ∇ α _{j}, and imposing the condition, ∇ ṡ B = 0, everywhere. As a consequence, the coordinates defining the plane perpendicular to B, α _{i} and α _{j}, must both satisfy the partial differential equation, B ṡ ∇ α _{i,j} = 0. In other words, α _{i,j} must be constant along magnetic field lines. Upon solving this differential equation implicitly using known magnetic field intensities, the metric tensor for the resulting basis can be computed. The elements of this tensor can be substituted directly into the eigenvalue problem for general coordinate systems written in covariant notation. The equation for FLR modes has been developed for arbitrary incompressible magnetospheric conditions and has been specialized to the case where spatial variations are constrained along the magnetic field. The result is a coupled fourthorder system of ordinary differential equations, which can be evaluated numerically. The eigenvalue problem is solved at several latitudes for a broad range of magnetospheric conditions.
 Publication:

AGU Spring Meeting Abstracts
 Pub Date:
 May 2004
 Bibcode:
 2004AGUSMSM53B..07B
 Keywords:

 0654 Plasmas;
 2731 Magnetosphere: outer;
 2752 MHD waves and instabilities;
 7819 Experimental and mathematical techniques;
 7827 Kinetic and MHD theory