Cross-field transport and ballooning stability in neutral beam heated ASDEX divertor tokamak plasmas below and at the β limit are analysed by computer simulations. It is found that the discharges below the limit are ballooning stable and exhibit H transport. No gradual reduction of confinement happens when beta approaches the limit (‘hard’ β limit). The degradation of energy confinement at the β limit is shown to be due to enhanced electron heat conduction. Resistive ballooning modes with high wavenumbers are found to be marginally stable or unstable in a radial zone where the electron heat diffusivity is enhanced by a factor of four. Broader zones correspond to stronger degradation of global energy confinement. The diffusion coefficient is raised much less than the electron heat diffusivity. Fast flattening of the current profile which keeps resistive ballooning modes close to marginal stability seems to occur. Such modes with high wavenumbers generate small scale, fluctuating Br fields which can cause magnetic braiding. It is shown that the confinement properties at the β limit are consistent with transport in stochastic magnetic fields.
The response of the electron temperature profiles to changes in heating profile is investigated analytically and by transport code simulations. A heat conduction model with local empirical scalings of the electron thermal diffusivity χe is used. It is found that the Te-profile responds rather insensitively, owing to double radial integration of the heating power density. By scanning the target density and injection energy of neutral beam heated ASDEX plasmas it is shown that only small profile changes in the conductive electron heat flux are achieved. In density scans these changes are further diminished by the convective power loss. The theoretically predicted variation in Te(r)/Te(0) is correspondingly weak and does not exceed the measured profile change. The observed Te profile invariance is thus produced by local transport models with a diffusive electron heat flux proportional to dTe/dr. Consequently, it is not necessary to introduce a χe(r) which adjusts to the profile of the conductive electron heat flux or which non-linearly depends on the electron temperature gradient.
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