Nonambipolar Transport by Trapped Particles in Tokamaks

Small nonaxisymmetric perturbations of the magnetic field can greatly change the performance of tokamaks through nonambipolar transport. A number of theories have been developed, but the predictions were not consistent with experimental observations in tokamaks. This Letter provides a resolution, with a generalized analytic treatment of the nonambipolar transport. It is shown that the discrepancy between theory and experiment can be greatly reduced by two effects: (1) the small fraction of trapped particles for which the bounce and precession rates resonate; (2) the nonaxisymmetric variation in the field strength along the perturbed magnetic field lines rather than along the unperturbed magnetic field lines. The expected sensitivity of the International Thermonuclear Experimental Reactor to nonaxisymmetries is also discussed.

Figure 1

The typical rotational damping rate ($/\mathrm{s}$) for present tokamaks, which is proportional to diffusivity divided temperature, as a function of ion-ion collision frequency for two different rotations. Each evaluation uses ${\Gamma }_{1/\nu }$ ($1/\nu$ regime), ${\Gamma }_{{\nu }_{-}\sqrt{\nu }}$ (${\nu }_{-}{\nu }^{1/2}$ regime), ${\Gamma }_0$ (${\mathrm{\text{resonance}}}_{-}0$), $l>0$ ${\Gamma }_l$ (resonance), and $\Gamma =\max \{l|{\Gamma }_l,{\Gamma }_{{\nu }_{-}\sqrt{\nu }}\}$ (general).

Figure 2

Comparison between the nonambipolar ($D_{NA})$ and ambipolar ($D_A)$ diffusions as a function of ion-ion collision frequency for two different rotations.