Temperature Contours and Ghost Surfaces for Chaotic Magnetic Fields

Steady state solutions for anisotropic heat transport in a chaotic magnetic field are determined numerically and compared to a set of “ghost surfaces”—surfaces constructed via an action-gradient flow between the minimax and minimizing periodic orbits. The ghost surfaces are in remarkable agreement with the temperature contours.

Figure 1

For $\theta <0$: the selected ghost curves (red lines) and cantori (black dots). For $\theta >0$: Poincaré plot (gray dots), ghost curves (red lines), and the temperature contours (black lines) for ${\kappa }_{\perp }/{\kappa }_{\parallel }={10}^{-10}$.

Figure 2

Temperature profile for case shown in Fig. 1.