Evolutionary tracks and isochrones of the inverse Hall cascade

Decaying MHD turbulence can exhibit an inverse cascade, which means that the height of the spectrum of magnetic energy in the subinertial range increases with time. However, there is evidence for a resistive dependence of the inverse transfer speed. It is unclear whether this is caused by reconnection, which is known to depend on resistivity. Here, we show that in the Hall cascade, where no momentum equation is solved, and the induction term is replaced by what corresponds to the negative Lorentz force in MHD, there is still a resistive dependence of the inverse transfer speed, but no such dependence is found for an analogous numerical reconnection experiment. This suggests that the resistive dependence of the inverse transfer speed is not necessarily related to reconnection.