Propagation velocity of changes to confinement

Abstract

Transient and non-transient changes to confinement properties of a tokamak equilibrium arise from several different plasma phenomena: a heat pulse triggered by a sawtooth; a cold pulse triggered by impurity injection or a giant ELM; the L ↔ H transitions triggered at the edge can produce a fast response in temperature towards the centre; MHD instabilities like sawtooth collapse, ELM or ‘outer’ mode cause negative-positive changes to the local energy density. Such changes to the confinement properties propagate through the plasma on timescales which are much smaller than the confinement time itself. A model to describe this based on turbulent guiding centre drift motion is developed. The theory for the non-linear model focuses on the propagation of perturbations to the plasma temperature and density. The model predicts a fluctuation-turbulence spectrum which agrees with that observed in experimental fluctuation measurements, apart from the predicted long wavelength part, which is not measured experimentally. A turbulence theory for the guiding centre velocity correlation function is developed in five steps, three of which have often been used in work on turbulence. Step 1 is the random phase approximation. Step 2 is the Markovian approximation. Step 3 is the discrete to continuum approximation. Step 4 is the solution of a prototype non-linear equation for one single harmonic. Step 5 is the solution of a non-linear equation for the entire spectrum of fluctuations using statistical techniques. The solution can be studied in two regimes. The long term or steady state regime has commonly been used in many turbulence theories. On the other hand the short term or ballistic regime predicts that perturbations propagate by advective or wave-like transport relevant to transient changes. The propagation speed is the characteristic guiding centre fluid drift velocity scaled by the ratio between the energy in the fluctuations and the thermal energy. Its magnitude agrees with experimental observations. The validity of the approximations in each of the five steps is discussed, together with how appropriate these are to a tokamak equilibrium with shear.