The Bootstrap Current
A self-generated toroidal current driven by the plasma pressure gradient through trapped-particle dynamics.
Current from a pressure gradient
In a torus, a radial pressure gradient drives a toroidal current with no external drive. The mechanism is neoclassical: trapped particles on banana orbits carry a net momentum, and collisions transfer it to passing particles, producing a parallel current. This is the bootstrap current, essential for steady-state operation because it reduces the current that must be driven externally.
j_bootstrap ~ -(1/B_pol) * sqrt(eps) * dp/drThe current scales with the square root of the inverse aspect ratio eps (the trapped fraction) and inversely with the poloidal field, and it points to reduce the external current-drive burden when the pressure profile is favorable.
Bootstrap fraction
The bootstrap fraction is the ratio of bootstrap current to total current. Advanced steady-state scenarios aim for high bootstrap fraction so that little inductive or auxiliary current drive is needed. Too much off-axis bootstrap current, however, can flatten or reverse the current profile and destabilize modes.
How it is computed
- Solve the drift-kinetic equation on each flux surface for the parallel flow response
- Use analytic coefficients (Sauter or Hirshman formulas) as fast surrogates
- Couple bootstrap current back into the equilibrium and current-diffusion solve
Because bootstrap current changes the q-profile, which changes the pressure gradient, which changes the bootstrap current, the calculation is iterated to self-consistency with the equilibrium.
Relevance
High bootstrap fraction is a design goal for compact devices. For the Hyperion breeder spherical tokamak, the naturally large trapped fraction at low aspect ratio makes bootstrap current a significant contributor, evaluated with drift-kinetic and neoclassical tools.