Anomalous transport and the coupling of plasma diffusion and heat flow

Abstract

Anomalous transport has been observed in heat-pulse tokamak experiments in the form of faster thermal diffusion than expected from thermal conductivity alone. The anomaly is resolved by correct treatment of time-dependent transport, coupling heat flow and plasma diffusion. The diffusion rates are exhibited as invariant eigenvalues appearing in the transport model. We show how these eigenvalues couple the basic transport processes. The thermal diffusion rate is not determined by thermal conductivity, since it is not an eigenvalue with temperature as eigenmode.

Experimental evidence for coupling of plasma particle and heat transport in the TEXT tokamak

“…(heat pulse) should not be compared to Xe qu (equilibrium), but instead, to an incremental thermal diffusivity, Xe nc -Experimental results from the Joint European Torus (JET) have been reconciled using this formalism. 5 Enhanced transport due to increased magnetic or electrostatic fluctuations during the sawtooth cycle has also been proposed as a potential resolution to the discrepancy between perturbative and equilibrium estimates of Xe- 4 Theoretical treatment of the problem by Hossain et al 6 and Bishop and Connor 7 provides yet another possible explanation for the apparent anomaly by including density effects, when solving the heat equation, and formally treating the coupling of plasma diffusion and heat flow. As a consequence, one might expect to observe a strong spatial and temporal correlation between the sawtooth temperature and density perturbations.…”

“…These results provide experimental support for the theoretically predicted coupling of plasma diffusion and heat flow. 6,7 Measurements of the sawtooth density perturbation are made with a multichannel interferometer system possessing high spatial (Ax -1.5 cm) and high phase (An e < 5*\0 ]0 cm -3 ) resolution. 8 An Abel inversion is performed to arrive at the local sawtooth density perturbation profile.…”

“…4 By using this analysis for the data shown, one obtains ^H P =2.25 m 2 /s, which is significantly larger than equilibrium, where Xe qu -1 m 2 /s. However, as was pointed out by Hossain et al, 6 no heat equation in terms of temperature alone can be written without ignoring the coupling of plasma particle diffusion and heat flow. In order to account for this effect, an off-diagonal element 14 of the transport matrix in which a density gradient drives a heat flux must be included, e.g., q e = ~ n e XeVT e -j T e D e Vn e .…”

Turbulent enhancement of particle and heat fluxes during sawtooth oscillations in a tokamak edge plasma

“…7 Fredrickson et al 1 suggested that either an anomalously high value of Xe, due perhaps to fluctuations, or an inward heat pinch could explain the differences in the Xe obtained. Hossain et al 8 found that the different values of Xe could be explained on the basis of coupled heat flow and plasma diffusion, but they could not rule out enhanced transport due to magnetic or electrostatic fluctuations. If turbulent transport is driven by temperature or density gradients (as predicted by many theories), the passage of a heat or density pulse would cause the resulting transport coefficients to be significantly different from their equilibrium values.…”

Experimental measurement of electron particle diffusion from sawtooth-induced density-pulse propagation in the Texas Experimental Tokamak

“…The picture described above is completely analogous to the heat-pulse counterpart and suggests a coupling between the two phenomena. 7,8 An Abel inversion is performed to arrive at the local sawtooth density-perturbation profile. In order to minimize errors near the crash where m = 1 oscillations are often large, a numerical boxcar averaging technique is applied during the plateau region of the discharge where the sawtooth period and amplitude are essentially constant.…”