Hosking integral in non-helical Hall cascade

The Hosking integral, which characterizes magnetic helicity fluctuations in subvolumes, is known to govern the decay of magnetically dominated turbulence. Here we show that, when evolution field controlled by motion electrons only, as neutron star crusts, still but now it has effectively different dimensions than ordinary magnetohydrodynamic (MHD) This causes correlation length increase with time $t$ like $t^{4/13}$ instead $t^{4/9}$ MHD. energy density decreases $t^{-10/13}$, slower MHD, where decays $t^{-10/9}$. These new analytic results agree earlier numerical simulations for nonhelical Hall cascade.