Hosking integral in nonhelical Hall cascade

Abstract

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

9 pages, 4 figures, 2 tables

References in corpus (8)

• Nonhelical inverse transfer of a decaying turbulent magnetic field
• Simulations of Electron Magnetohydrodynamic Turbulence
• Classes of hydrodynamic and magnetohydrodynamic turbulent decay
• Magnetic Axis Drift and Magnetic Spot Formation in Neutron Stars with Toroidal Fields
• Powering Central Compact Objects with a Tangled Crustal Magnetic Field
• Scaling of the Hosking integral in decaying magnetically-dominated turbulence
• Hall cascade with fractional magnetic helicity in neutron star crusts
• Thermal luminosity degeneracy of magnetized neutron stars with and without hyperon cores

Cited by in corpus (8)

• Chiral magnetohydrodynamics with zero total chirality
• Decay law of magnetic turbulence with helicity balanced by chiral fermions
• Turbulence with Magnetic Helicity that is Absent on Average
• Inverse cascading for initial MHD turbulence spectra between Saffman and Batchelor
• Turbulent magnetic decay controlled by two conserved quantities
• Confronting the neutron star population with inverse cascades
• Reality of inverse cascading in neutron star crusts
• Conservation of magnetic-helicity fluctuations due to spatial decorrelation of fluxes in decaying MHD turbulence