TY - JOUR

T1 - Generation of chiral asymmetry via helical magnetic fields

AU - Schober, Jennifer

AU - Fujita, Tomohiro

AU - Durrer, Ruth

N1 - Funding Information:
The authors would like to acknowledge the Mainz Institute for Theoretical Physics (MITP) of the DFG Cluster of Excellence (Project ID 39083149), for enabling us to complete a significant portion of this work. J. S. acknowledges the funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant No. 665667 and the Swiss National Science Foundation under Grant No. 185863 as well as the support by the National Science Foundation under Grant No. NSF PHY-1748958. The work of T. F. was supported by JSPS KAKENHI No. 17J09103 and No. 18K13537. R. D. is supported with the Swiss National Science Foundation under Grant No. 200020_182044. The simulations presented in this work were performed on resources at Chalmers Centre for Computational Science and Engineering (C3SE) provided by the Swedish National Infrastructure for Computing (SNIC) as well as on the Baobab cluster at the University of Geneva.
Publisher Copyright:
© 2020 American Physical Society.

PY - 2020/5/15

Y1 - 2020/5/15

N2 - It is well known that helical magnetic fields undergo a so-called inverse cascade by which their correlation length grows due to the conservation of magnetic helicity in classical ideal magnetohydrodynamics (MHD). At high energies above approximately 10 MeV, however, classical MHD is necessarily extended to chiral MHD and then the conserved quantity is H+2μ5/λ with H being the mean magnetic helicity and μ5 being the mean chiral chemical potential of charged fermions. Here, λ is a (phenomenological) chiral feedback parameter. In this paper, we study the evolution of the chiral MHD system with the initial condition of nonzero H and vanishing μ5. We present analytic derivations for the time evolution of H and μ5 that we compare to a series of laminar and turbulent three-dimensional direct numerical simulations. We find that the late-time evolution of H depends on the magnetic and kinetic Reynolds numbers ReM and ReK. For a high ReM and ReK where turbulence occurs, H eventually evolves in the same way as in classical ideal MHD where the inverse correlation length of the helical magnetic field scales with time t as kp t-2/3. For a low Reynolds numbers where the velocity field is negligible, the scaling is changed to kp t-1/2ln(t/tlog). After being rapidly generated, μ5 always decays together with kp, i.e., μ5≈kp, with a time evolution that depends on whether the system is in the limit of low or high Reynolds numbers.

AB - It is well known that helical magnetic fields undergo a so-called inverse cascade by which their correlation length grows due to the conservation of magnetic helicity in classical ideal magnetohydrodynamics (MHD). At high energies above approximately 10 MeV, however, classical MHD is necessarily extended to chiral MHD and then the conserved quantity is H+2μ5/λ with H being the mean magnetic helicity and μ5 being the mean chiral chemical potential of charged fermions. Here, λ is a (phenomenological) chiral feedback parameter. In this paper, we study the evolution of the chiral MHD system with the initial condition of nonzero H and vanishing μ5. We present analytic derivations for the time evolution of H and μ5 that we compare to a series of laminar and turbulent three-dimensional direct numerical simulations. We find that the late-time evolution of H depends on the magnetic and kinetic Reynolds numbers ReM and ReK. For a high ReM and ReK where turbulence occurs, H eventually evolves in the same way as in classical ideal MHD where the inverse correlation length of the helical magnetic field scales with time t as kp t-2/3. For a low Reynolds numbers where the velocity field is negligible, the scaling is changed to kp t-1/2ln(t/tlog). After being rapidly generated, μ5 always decays together with kp, i.e., μ5≈kp, with a time evolution that depends on whether the system is in the limit of low or high Reynolds numbers.

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U2 - 10.1103/PhysRevD.101.103028

DO - 10.1103/PhysRevD.101.103028

M3 - Article

AN - SCOPUS:85085999842

VL - 101

JO - Physical Review D

JF - Physical Review D

SN - 2470-0010

IS - 10

M1 - 103028

ER -