Heat pulse propagation in chaotic 3-dimensional magnetic fields

Abstract: Heat pulse propagation in $3$-D chaotic magnetic fields is studied by solving the parallel heat transport equation using a Lagrangian-Green's function (LG) method. The LG method provides an efficient and accurate technique that circumvents limitations of finite elements and finite difference methods. The main two problems addressed are: (i) The dependence of the radial transport on the magnetic field stochasticity (controlled by the amplitude of the perturbation, $\epsilon$); and (ii) The role of reversed shear configurations on pulse propagation. In all the cases considered there are no magnetic flux surfaces. However, radial transport is observed to depend strongly on $\epsilon$ due to the presence of high-order magnetic islands and Cantori that act as quasi-transport barriers that preclude the radial penetration of heat pulses within physically relevant time scale. The dependence of the magnetic field connection length, $\ell_B$, on $\epsilon$ is studied in detail. The decay rate of the temperature maximum, $\langle T \rangle_{max}(t)$, the time delay of the temperature response as function of the radius, $\tau$, and the radial heat flux $\langle {{\bf q}\cdot {\hat e}\psi} \rangle$, are also studied as functions of the magnetic field stochasticity and $\ell_B$. In all cases, the scaling of $\langle T \rangle{max}$ with $t$ transitions from sub-diffusive, $\langle T \rangle_{max} \sim t^{-1/4}$, at short times ($\chi_\parallel t< 10^5$) to a significantly slower scaling at longer times ($\chi_\parallel t > 10^5$). A strong dependence on $\epsilon$ is also observed on $\tau$ and $\langle {{\bf q}\cdot {\hat e}_\psi} \rangle$. The radial propagation of pulses in fully chaotic fields considerably slows down in the shear reversal region and, as a result, $\tau$, in reversed shear configurations is an order of magnitude longer than the one in monotonic $q$-profiles.