Visualizing Plasma Equilibria
A magnetohydrodynamic equilibrium is described by nested flux surfaces; visualizing them clarifies confinement geometry and boundary shape.
What an equilibrium is
A toroidal plasma in force balance is described by the Grad-Shafranov equation, whose solution is the poloidal flux function. Level sets of that function are the flux surfaces: nested surfaces on which pressure and other quantities are roughly constant. Visualizing an equilibrium means showing these surfaces, the field they imply, and the derived profiles.
Poloidal cross-section
The most informative single view is a poloidal cut showing flux-surface contours, the magnetic axis, and the last closed flux surface or separatrix. Shape parameters read directly from this view: elongation, and triangularity, which measures how the outer surface is pushed inward or outward at top and bottom.
- Nested contours reveal the confinement region.
- The separatrix marks the boundary between closed and open field lines.
- Color can overlay pressure, safety factor, or current density.
Profiles alongside geometry
Equilibrium geometry pairs with one-dimensional profiles versus a flux-surface label: pressure, safety factor q, and current. Showing the cross-section and the profiles together links spatial shape to the physics. See Profile Plots.
Three dimensions
Flux surfaces are toroidal; a 3D view helps convey the actual geometry, using transparent nested isosurfaces or a cutaway. Field structure on those surfaces is a vector-field problem (Field-Line Tracing).
Kronos use
The Hyperion breeder is a spherical tokamak with negative triangularity of -0.30; visualizing its equilibrium makes that inward-shaped boundary and the compact aspect ratio legible. All fields shown are simulation output.