Heat pulse propagation in chaotic three-dimensional magnetic fields

Abstract

Heat pulse propagation in three-dimensional chaotic magnetic fields is studied by solving numerically the parallel heat transport equation using a Lagrangian Green's function (LG) method. The LG method provides an efficient and accurate technique that circumvents known limitations of finite elements and finite difference methods. The main two problems addressed are (i) the dependence of the radial transport of heat pulses on the level of magnetic field stochasticity (controlled by the amplitude of the magnetic field perturbation, ϵ), and (ii) the role of reversed shear magnetic field configurations on heat pulse propagation. In all the cases considered there are no magnetic flux surfaces. However, the radial transport of heat pulses is observed to depend strongly on ϵ due to the presence of high-order magnetic islands and Cantori. These structures act as quasi-transport barriers which can actually preclude the radial penetration of heat pulses within physically relevant time scales. The dependence of the magnetic field connection length, ℓB, on ϵ is studied in detail. Regions where ℓB is large, correlate with regions where the radial propagation of the heat pulse slows down or stops. The decay rate of the temperature maximum, 〈T〉max(t), the time delay of the temperature response as function of the radius, τ, and the radial heat flux , are also studied as functions of the magnetic field stochasticity and ℓB. In all cases it is observed that the scaling of 〈T〉max with t transitions from sub-diffusive, 〈T〉max ∼ t−1/4, at short times (χ∥t < 105) to a significantly slower, almost flat scaling at longer times (χ∥t > 105). A strong dependence on ϵ is also observed on τ and . Even in the case when there are no flux surfaces nor magnetic field islands, reversed shear magnetic field configurations exhibit unique transport properties. The radial propagation of heat pulses in fully chaotic fields considerably slows down in the shear reversal region and, as a result, the delay time of the temperature response in reversed shear configurations is about an order of magnitude longer than the one observed in monotonic q-profiles. The role of separatrix reconnection of resonant modes in the shear reversal region, and the role of shearless Cantori in the observed phenomena are also discussed.