# Bootstrap current

The bootstrap current is a Neoclassical toroidal current produced in the presence of a pressure gradient, associated with the existence of trapped (banana) particles in toroidal magnetic confinement systems. These trapped particles must be able to complete their (banana) orbits, so a requirement for the existence of the bootstrap current is νei < νb (the collision frequency is less than the banana bounce frequency). The difference in particle density on banana orbits crossing a given radial position r then leads to a net toroidal current at r. The bootstrap current is estimated (roughly) as [1]

$j_{b} \sim -\varepsilon^{1/2}\frac{1}{B_p}\frac{dp}{dr}$

Here, ε is the inverse aspect ratio a/R, Bp the poloidal magnetic field, and p the pressure. More precise estimates can be made by simulating particle orbits.

## References

1. K. Miyamoto, Plasma Physics and Controlled Nuclear Fusion, Springer-Verlag (2005) ISBN 3540242171