Effective plasma heat conductivity in 'braided' magnetic field-II. Percolation limit

For pt.I see ibid., vol.33, no.7, p.795-807 (1991). This paper is devoted to the problem of anomalous transport across a magnetic field that includes a small stochastic component delta B. The perturbation is assumed to be so strongly stretched along the background magnetic field B0 that the parameter R is large: R identical to b0L0/ delta >>1 (here b0 identical to delta Bperpendicular to /B0<<1, and L0 is the longitudinal and delta the transverse correlation length of the magnetic perturbation). This strong turbulence limit, which is opposite to the quasi-linear one (R<<1), has certain notable features. The principal result is that the main transport is concentrated in very thin regions, being fractal sets with the dimension df, which can range in value from 2 to 2.75, depending on the spectrum of the magnetic perturbation. These regions consist of a small fraction of magnetic lines that percolate, that is, walk from the nonperturbed magnetic flux surfaces to a distance large compared to the transverse correlation length delta . Due to such a strong inhomogeneity of the transport distribution, as well as the long correlations, the standard transport averaging techniques fail, and one should make use of the percolation theory methods. Thus the strong turbulence regime is referred to here as the percolation limit. In comparison with the quasi-linear limit, the percolation limit has several additional intermediate regimes and the expressions for the effective heat conductivity chi eff include the critical exponents of 2-D percolation theory. The estimates of chi eff are obtained both in the collisional and collisionless limits, including the case of nonstationary magnetic perturbations.