Description of turbulent transport in tokamaks by invariants

In general, turbulent transport drives a plasma toward a state of turbulent equipartition, in which Lagrangian invariants are uniformly distributed. Different invariants decay with different rates, and in tokamaks the frozen-in law of particles in the poloidal magnetic field survives longer than the corresponding law for the toroidal field, assuming that the trapped particles dominate the turbulent transport. Therefore, the plasma profiles depend on the safety factor $\mathrm{q(r),}$ and the condition for convection of trapped particles is that the shear $\mathrm{dq/dr}$ is positive. There are two ways to suppress this convection and thereby enhance confinement. The first one is to reverse the magnetic shear. The energy of typical trapped particles then increases outward instead of inward, which suppresses instabilities. The second method is to eliminate the trapped ions by poloidal rotation, and thereby create a transport barrier.