Collisional Diffusion in a Toroidal Pinch

Abstract

Transverse diffusion coefficients in a toroidal pinch are investigated for three regions of collision frequencies. The configuration of a toroidal pinch is characterized by a large poloidal magnetic field B P comparable to a toroidal magnetic field B T . We calculated diffusion coefficients following the scheme of Galeev and Sagdeev. In a toroidal pinch particles can be trapped in a local magnetic mirror formed by both a toroidal magnetic field and a poloidal magnetic field. Furthermore B P ≃ B T reduces the connection length of a toroidal pinch. Transverse diffusion coefficients including these effects are shown to be smaller than D GS which is given by Galeev and Sagdeev. in the banana region \(D_{\bot}{\simeq}D_{\text{GS}}\sqrt{\delta/\varepsilon}\) is obtained and in the plateau region D ⊥ ≃ D GS (δ 2 / ε 2 ), where ε denotes an aspect ratio and a small parameter δ denotes the inhomogeneity of the toroidal magnetic field in the toroidal pinch. Here it is noted that a safety factor included in D ⊥ may be smaller than or comparable to unity. In the MHD region D ⊥ also includes a factor δ/ ε .