Temperature gradient driven electron transport in NSTX and Tore Supra

Electron thermal fluxes are derived from the power balance for Tore Supra (TS) and NSTX discharges with centrally deposited fast wave electron heating. Measurements of the electron temperature and density profiles, combined with ray tracing computations of the power absorption profiles, allow detailed interpretation of the thermal flux versus temperature gradient. Evidence supporting the occurrence of electron temperature gradient turbulent transport in the two confinement devices is found. With control of the magnetic rotational transform profile and the heating power, internal transport barriers are created in TS and NSTX discharges. These partial transport barriers are argued to be a universal feature of transport equations in the presence of invariant tori that are intrinsic to non-monotonic rotational transforms in dynamical systems. PACS numbers: 52.25.Fi, 52.35.Qz, 52.55.Fa (Some figures in this article are in colour only in the electronic version) 1. Electron transport in tokamaks Turbulent transport of electron thermal energy appears to be ubiquitous in tokamaks. This suggests that it may arise from the small space and time scales associated with electron temperature gradient (ETG) driven drift wave turbulence. Simulations show that, while the source of the turbulence is on the scale of the electron gyroradius ρe, the nonlinear saturated states have large-scale structures on the scale of the collisionless skin depth. Various numerical simulations with two-component fluids, gyrofluids and gyrokinetics show levels of electron diffusivity comparable to that of the ion thermal transport from ion temperature gradient (ITG) driven turbulence. These results support the general conclusion of Kadomtsev [1] that there is an intrinsic level of anomalous electron turbulent transport in toroidal confinement devices. For higher values of βe = 2μ0pe/B and not too low plasma density, the characteristic scale length is the collisionless skin depth δs = c/ωpe, owing to the intrinsic inductive electric field from the magnetic fluctuations. The time scale of relevance is that for the microscale electron dynamics τe = R/ve. Particular theoretical formulae, developed for the electron thermal fluxes with critical gradients, have successfully interpreted transport in Tore Supra (TS) with fast wave electron heating, where thermal fluxes and gradients vary over an order of magnitude in response to radio frequency (RF) power increasing from 0.7 to 7.5 MW [2–4]. These are high βe, helium discharges with 0.65 MA/2.2 T in a classic tokamak geometry with R/a = 2.2 m/0.7 m. An example for TS is shown in figure 1(a) using the integrated CRONOS transport code [5], with the ETG transport model for a stair-stepped fast wave heating profile of 3 and 6 MW. This TS discharge (#18368) has Ip = 0.65 MA, B = 2.2 T, ne(0) = 4 × 1019 m−3 and Te(0) = 4 keV with the fast wave power rising from 3 to 6 MW. The time evolution of the electron temperature Te(r, t) at various radii, the electron energy content We = 3 2 ∫ pe d3x, the loop voltage Vl(t) and the Faraday rotation angles are all shown in figure 1. In figure 1 the dashed curves are the measured and inferred values while the solid curves are derived from the CRONOS code simulation with the ETG mode. In the CRONOS code simulations shown the edge electron temperature is fixed as a boundary condition taken from the experimental data and only the electron diffusivity is taken from three models for making the comparisons. The electron transport formulae derived in Horton et al [4] for TS were applied to NSTX for similar plasma conditions, but 0029-5515/05/080976+10$30.00 © 2005 IAEA, Vienna Printed in the UK 976 Temperature gradient driven electron transport