fieldaligned

Fieldaligned, often written field-aligned, refers to approaches, coordinates, or data that are oriented along a vector field, typically a magnetic or electric field. In practice, field-aligned coordinate systems rotate or transform standard Cartesian coordinates so one axis runs along the field lines, while the other axes span the perpendicular directions.

In plasma physics and magnetohydrodynamics, field-aligned coordinates simplify anisotropic transport, since diffusion and convection are often much stronger along field lines. A common scheme uses coordinates (s, x, y) where s is distance along a magnetic field line, with x and y labeling field lines or cross-field positions. Field lines may be labeled by flux functions. This alignment reduces numerical stiffness and allows higher accuracy along the direction of the field.

Applications include numerical simulations of fusion devices like tokamaks and stellarators, space plasma models, and geophysical flows. Field-aligned methods appear in finite difference, finite element, and spectral schemes, and in flux-coordinate or field-line-following grids.

Challenges include the topology of the field; field line mapping in three dimensions can be complex, and time-dependent fields require dynamic remapping. Singularities near X-points can complicate calculations, and there can be additional computational overhead. Alternatives include non-aligned grids or adaptive meshing that does not rely on strict alignment with the field.

See also: anisotropic diffusion, magnetic field, coordinate systems, flux coordinates.