Modeling of large amplitude plasma blobs in three-dimensions

Abstract

Fluctuations in fusion boundary and similar plasmas often have the form of filamentary structures, or blobs, that convectively propagate radially. This may lead to the degradation of plasma facing components as well as plasma confinement. Theoretical analysis of plasma blobs usually takes advantage of the so-called Boussinesq approximation of the potential vorticity equation, which greatly simplifies the treatment analytically and numerically. This approximation is only strictly justified when the blob density amplitude is small with respect to that of the background plasma. However, this is not the case for typical plasma blobs in the far scrape-off layer region, where the background density is small compared to that of the blob, and results obtained based on the Boussinesq approximation are questionable. In this report, the solution of the full vorticity equation, without the usual Boussinesq approximation, is proposed via a novel numerical approach. The method is used to solve for the evolution of 2D and 3D plasma blobs in a regime where the Boussinesq approximation is not valid. The Boussinesq solution under predicts the cross field transport in 2D. However, in 3D, for parameters typical of current tokamaks, the disparity between the radial cross field transport from the Boussinesq approximation and full solution is virtually non-existent due to the effects of the drift wave instability. V C 2014 AIP Publishing LLC.

Electromagnetic effects on dynamics of high-beta filamentary structures

“…The Boussinesq approximation gives reasonably accurate results for blobs with moderate blob to ambient plasma density ratio. 13 Finite ion temperature effects can enhance polarization drift, modifying the blob propagation speed. 9 For the case of large blob to ambient plasma density ratio,ñ=n 0 , the finite ion temperature may dominate standard vorticity term, r Á ½enr ?…”

Dynamics of 3D isolated thermal filaments

“…so that, by substitution of equation (18) into equation (21) and then by substitution into equation (20) an expression for the sheath heat flux is given by…”

“…The velocities in each regime, alongside the fundamental filament size vary as the temperature and density in the filament change (keeping pressure fixed) with a general increase as the temperature is increased and the density decreased. Angus et al [21] and Omotani et al [18] have recently shown that, with the Boussinesq assumption relaxed the inertial regime velocity scaling is better represented by taking Figure 1. Scaling of the 2D filament characteristic velocity in the inertial regime (IL, broken lines) calculated from equation (30) and in the sheath limited regime (SL, solid lines) calculated from equation (31) for the following cases: δn = 2, δT = 0 (red), δn = 1, δT = 1 (black) and δn = 0, δT = 2 (blue).…”

Isotope effect on filament dynamics in fusion edge plasmas

“…For low collisionality, the electric potential in the blob evolves towards establishment of a Boltzmann relation in phase with the electron density along B, so that n e ∼ exp(−φ) ∼ φ. This leads to reduced radial particle transport, and the resulting spatial alignment of the potential with the blob density perturbation produces a rotating vortex along contours of constant density, the so-called Boltzmann spinning [33,34]. Large collisionality leads to a delay in the build-up of the potential within the blob, so that the radial interchange driving can compete with the parallel evolution, and the perpendicular propagation is similar to the 2-d scenario.…”