Hosking integral in non-helical Hall cascade. (20th February 2023)

• Record Type: Journal Article
• Authors: Brandenburg, Axel
• Is Part Of: Journal of plasma physics. Volume 89:Number 1(2023)
• Publication Date: 2023-02-20
• Subjects: plasma nonlinear phenomena; Plasma (Ionized gases) -- Periodicals; 530.4405
• DOI: 10.1017/S0022377823000028
• Languages: English
• ISSNs: 0022-3778

Abstract

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 non-helical Hall cascade.