Safety factor (plasma physics)

The concept was first developed by Martin David Kruskal and Vitaly Shafranov, who noticed that the plasma in pinch effect reactors would be stable if q was larger than 1.

A plasma generated in the center of the cylinder would be confined to run along the lines down the inside of the tube, keeping it away from the walls.

One can close the ends by bending the solenoid around into a circle, forming a torus (a ring or donut).

In this case, the particles will still be confined to the middle of the cylinder, and even if they move along it they would never exit the ends - they would circle the apparatus endlessly.

A particle orbiting such a field line will find itself near the outside of the confinement area at some times, and near the inside at others.

The net effect of the drift over a period of several orbits along the long axis of the reactor nearly adds up to zero.

[2] The effect of the helical field is to bend the path of a particle so it describes a loop around the cross section of the containment cylinder.

In the case of an axisymmetric system, which was common in earlier fusion devices, it is more common to use the safety factor, which is simply the inverse of the rotational transform: The safety factor is essentially a measure of the "windiness" of the magnetic fields in a reactor.

Toroidal arrangements are a major class of magnetic fusion energy reactor designs.

These are subject to a number of inherent instabilities that cause the plasma to exit the confinement area and hit the walls of the reactor on the order of milliseconds, far too rapidly to be used for energy generation.

Areas where the plasma is slightly further from the centerline will experience a force outwards, causing a growing bulge that will eventually reach the reactor wall.

from both sides and moving the major radius R to the other side of the equality produces: Which produces the simple rule of thumb that as long as the safety factor is greater than one at all points in the plasma, it will be naturally stable to this major class of instabilities.