Decay law of magnetic turbulence with helicity balanced by chiral fermions

Abstract

In plasmas composed of massless electrically charged fermions, chirality can be interchanged with magnetic helicity while preserving the total chirality through the quantum chiral anomaly. The decay of turbulent energy in plasmas such as those in the early Universe and compact stars is usually controlled by certain conservation laws. In the case of zero total chirality, when the magnetic helicity density balances with the appropriately scaled chiral chemical potential to zero, the total chirality no longer determines the decay. We propose that in such a case, an adaptation to the Hosking integral, which is conserved in nonhelical magnetically dominated turbulence, controls the decay in turbulence with helicity balanced by chiral fermions. We show, using a high resolution numerical simulation, that this is indeed the case. The magnetic energy density decays and the correlation length increases with time just like in nonhelical turbulence with vanishing chiral chemical potential. But here, the magnetic helicity density is nearly maximum and shows a scaling with time $t$ proportional to $t^{-2/3}$. This is unrelated to the $t^{-2/3}$ decay of magnetic {\it energy} in fully helical magnetic turbulence. The modulus of the chiral chemical potential decays in the same fashion. This is much slower than the exponential decay previously expected in theories of asymmetric baryon production from the hypermagnetic helicity decay after axion inflation.

6 pages, 4 figures, corrected Fig.2

References in corpus (14)

• The Pencil Code, a modular MPI code for partial differential equations and particles: multipurpose and multiuser-maintained
• Evolution of Primordial Magnetic Fields from Phase Transitions
• Classes of hydrodynamic and magnetohydrodynamic turbulent decay
• Evolution of hydromagnetic turbulence from the electroweak phase transition
• Evolution of the Baryon Asymmetry through the Electroweak Crossover in the Presence of a Helical Magnetic Field
• The turbulent chiral-magnetic cascade in the early universe
• Chiral effects in astrophysics and cosmology
• Reconnection-controlled decay of magnetohydrodynamic turbulence and the role of invariants
• Wash-in leptogenesis after axion inflation
• Relic gravitational waves from the chiral magnetic effect
• Scaling of the Hosking integral in decaying magnetically-dominated turbulence
• Generation of chiral asymmetry via helical magnetic fields
• Hosking integral in nonhelical Hall cascade
• Generation of strong magnetic fields in a nascent neutron star accounting for the chiral magnetic effect

Cited by in corpus (8)

• Chiral magnetohydrodynamics with zero total chirality
• Turbulence with Magnetic Helicity that is Absent on Average
• Chiral anomaly and dynamos from inhomogeneous chemical potential fluctuations
• Inverse cascading for initial MHD turbulence spectra between Saffman and Batchelor
• Turbulent magnetic decay controlled by two conserved quantities
• Relic Gravitational Waves from the Chiral Plasma Instability in the Standard Cosmological Model
• Reality of inverse cascading in neutron star crusts
• Conservation of magnetic-helicity fluctuations due to spatial decorrelation of fluxes in decaying MHD turbulence