# Chiral Instabilities and the Onset of Chiral Turbulence in QED Plasmas

## Abstract

We present a first principles study of chiral plasma instabilities and the onset of chiral turbulence in QED plasmas with strong gauge matter interaction ( ${e}^{2}{N}_{f}=64$), far from equilibrium. By performing classical-statistical lattice simulations of the microscopic theory, we show that the generation of strong helical magnetic fields from a helicity imbalance in the fermion sector proceeds via three distinct phases. During the initial linear instability regime the helicity imbalance of the fermion sector causes an exponential growth (damping) of magnetic field modes with right- (left-) handed polarization, for which we extract the characteristic growth (damping) rates. Secondary growth of unstable modes accelerates the helicity transfer from fermions to gauge fields and ultimately leads to the emergence of a self-similar scaling regime characteristic of a decaying turbulence, where magnetic helicity is efficiently transferred to macroscopic length scales. Within this turbulent regime, the evolution of magnetic helicity spectrum can be described by an infrared power spectrum with spectral exponent $\kappa =10.2\pm 0.5$ and dynamical scaling exponents $\alpha =1.14\pm 0.50$ and $\beta =0.37\pm 0.13$.

- Authors:

- Publication Date:

- Research Org.:
- Brookhaven National Lab. (BNL), Upton, NY (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)

- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP); HEP Center for Computational Excellence; SOLLVE Exascale Computing Project; European Research Council (ERC); German Research Foundation (DFG); Government of India; Institute of Mathematical Sciences

- OSTI Identifier:
- 1619873

- Alternate Identifier(s):
- OSTI ID: 1616441

- Report Number(s):
- BNL-213870-2020-JAAM

Journal ID: ISSN 0031-9007; PRLTAO; 191604

- Grant/Contract Number:
- SC0012704; AC02-05CH11231; KA24001022; 17-SC-20-SC; ERC-2015-CoG-681707

- Resource Type:
- Published Article

- Journal Name:
- Physical Review Letters

- Additional Journal Information:
- Journal Name: Physical Review Letters Journal Volume: 124 Journal Issue: 19; Journal ID: ISSN 0031-9007

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 79 ASTRONOMY AND ASTROPHYSICS

### Citation Formats

```
Mace, Mark, Mueller, Niklas, Schlichting, Sören, and Sharma, Sayantan. Chiral Instabilities and the Onset of Chiral Turbulence in QED Plasmas. United States: N. p., 2020.
Web. doi:10.1103/PhysRevLett.124.191604.
```

```
Mace, Mark, Mueller, Niklas, Schlichting, Sören, & Sharma, Sayantan. Chiral Instabilities and the Onset of Chiral Turbulence in QED Plasmas. United States. https://doi.org/10.1103/PhysRevLett.124.191604
```

```
Mace, Mark, Mueller, Niklas, Schlichting, Sören, and Sharma, Sayantan. Fri .
"Chiral Instabilities and the Onset of Chiral Turbulence in QED Plasmas". United States. https://doi.org/10.1103/PhysRevLett.124.191604.
```

```
@article{osti_1619873,
```

title = {Chiral Instabilities and the Onset of Chiral Turbulence in QED Plasmas},

author = {Mace, Mark and Mueller, Niklas and Schlichting, Sören and Sharma, Sayantan},

abstractNote = {We present a first principles study of chiral plasma instabilities and the onset of chiral turbulence in QED plasmas with strong gauge matter interaction (e2Nf=64), far from equilibrium. By performing classical-statistical lattice simulations of the microscopic theory, we show that the generation of strong helical magnetic fields from a helicity imbalance in the fermion sector proceeds via three distinct phases. During the initial linear instability regime the helicity imbalance of the fermion sector causes an exponential growth (damping) of magnetic field modes with right- (left-) handed polarization, for which we extract the characteristic growth (damping) rates. Secondary growth of unstable modes accelerates the helicity transfer from fermions to gauge fields and ultimately leads to the emergence of a self-similar scaling regime characteristic of a decaying turbulence, where magnetic helicity is efficiently transferred to macroscopic length scales. Within this turbulent regime, the evolution of magnetic helicity spectrum can be described by an infrared power spectrum with spectral exponent κ=10.2±0.5 and dynamical scaling exponents α=1.14±0.50 and β=0.37±0.13.},

doi = {10.1103/PhysRevLett.124.191604},

journal = {Physical Review Letters},

number = 19,

volume = 124,

place = {United States},

year = {2020},

month = {5}

}

https://doi.org/10.1103/PhysRevLett.124.191604

*Citation information provided by*

Web of Science

Web of Science

Works referenced in this record:

##
Dynamics of quasiparticles in graphene under intense circularly polarized light

journal, February 2015

- Yudin, Dmitry; Eriksson, Olle; Katsnelson, Mikhail I.
- Physical Review B, Vol. 91, Issue 7

##
Phase space representation of quantum dynamics

journal, August 2010

- Polkovnikov, Anatoli
- Annals of Physics, Vol. 325, Issue 8

##
Chiral magnetic and vortical effects in high-energy nuclear collisions—A status report

journal, May 2016

- Kharzeev, D. E.; Liao, J.; Voloshin, S. A.
- Progress in Particle and Nuclear Physics, Vol. 88

##
Observation of the Chiral-Anomaly-Induced Negative Magnetoresistance in 3D Weyl Semimetal TaAs

journal, August 2015

- Huang, Xiaochun; Zhao, Lingxiao; Long, Yujia
- Physical Review X, Vol. 5, Issue 3

##
Anomalous hydrodynamics kicks neutron stars

journal, September 2016

- Kaminski, Matthias; Uhlemann, Christoph F.; Bleicher, Marcus
- Physics Letters B, Vol. 760

##
Parametric Resonance in Quantum Field Theory

journal, September 2003

- Berges, Jürgen; Serreau, Julien
- Physical Review Letters, Vol. 91, Issue 11

##
$\Lambda $ polarization in peripheral heavy ion collisions

journal, September 2013

- Becattini, F.; Csernai, L. P.; Wang, D. J.
- Physical Review C, Vol. 88, Issue 3

##
The nonlinear glasma

journal, January 2013

- Berges, Jürgen; Schlichting, Sören
- Physical Review D, Vol. 87, Issue 1

##
Long-Range Magnetic Fields in the Ground State of the Standard Model Plasma

journal, September 2012

- Boyarsky, Alexey; Ruchayskiy, Oleg; Shaposhnikov, Mikhail
- Physical Review Letters, Vol. 109, Issue 11

##
Off-equilibrium sphaleron transitions in the glasma

journal, April 2016

- Mace, Mark; Schlichting, Sören; Venugopalan, Raju
- Physical Review D, Vol. 93, Issue 7

##
The growth of chiral magnetic instability in a large-scale magnetic field

journal, April 2019

- Kojima, Yasufumi; Miura, Yuri
- Progress of Theoretical and Experimental Physics, Vol. 2019, Issue 4

##
Status of the chiral magnetic effect and collisions of isobars

journal, June 2017

- Koch, Volker; Schlichting, Soeren; Skokov, Vladimir
- Chinese Physics C, Vol. 41, Issue 7

##
Nonhelical Inverse Transfer of a Decaying Turbulent Magnetic Field

journal, February 2015

- Brandenburg, Axel; Kahniashvili, Tina; Tevzadze, Alexander G.
- Physical Review Letters, Vol. 114, Issue 7

##
Evolution of Magnetic Fields in Freely Decaying Magnetohydrodynamic Turbulence

journal, June 2007

- Campanelli, Leonardo
- Physical Review Letters, Vol. 98, Issue 25

##
Fermion production from real-time lattice gauge theory in the classical-statistical regime

journal, July 2014

- Kasper, V.; Hebenstreit, F.; Berges, J.
- Physical Review D, Vol. 90, Issue 2

##
Chiral Plasma Instabilities

journal, August 2013

- Akamatsu, Yukinao; Yamamoto, Naoki
- Physical Review Letters, Vol. 111, Issue 5

##
Dynamics of Vortices in Chiral Media: The Chiral Propulsion Effect

journal, October 2018

- Hirono, Yuji; Kharzeev, Dmitri E.; Sadofyev, Andrey V.
- Physical Review Letters, Vol. 121, Issue 14

##
Erratum: $\mathrm{\Lambda}$ polarization in peripheral heavy ion collisions [Phys. Rev. C **88** , 034905 (2013)]

journal, June 2016

- Becattini, F.; Csernai, L. P.; Wang, D. J.
- Physical Review C, Vol. 93, Issue 6

##
Chiral magnetic photocurrent in Dirac and Weyl materials

journal, February 2019

- Kaushik, Sahal; Kharzeev, Dmitri E.; Philip, Evan John
- Physical Review B, Vol. 99, Issue 7

##
Non-thermal fixed points: Universal dynamics far from equilibrium

journal, October 2019

- Schmied, Christian-Marcel; Mikheev, Aleksandr N.; Gasenzer, Thomas
- International Journal of Modern Physics A, Vol. 34, Issue 29

##
Magnetohydrodynamics of the early Universe and the evolution of primordial magnetic fields

journal, February 1999

- Son, D. T.
- Physical Review D, Vol. 59, Issue 6

##
Hamiltonian formulation of Wilson's lattice gauge theories

journal, January 1975

- Kogut, John; Susskind, Leonard
- Physical Review D, Vol. 11, Issue 2

##
A PCAC puzzle: π0→γγ in the σ-model

journal, March 1969

- Bell, J. S.; Jackiw, R.
- Il Nuovo Cimento A, Vol. 60, Issue 1

##
Basin of attraction for turbulent thermalization and the range of validity of classical-statistical simulations

journal, May 2014

- Berges, J.; Boguslavski, K.; Schlichting, S.
- Journal of High Energy Physics, Vol. 2014, Issue 5

##
Laminar and Turbulent Dynamos in Chiral Magnetohydrodynamics. II. Simulations

journal, May 2018

- Schober, Jennifer; Rogachevskii, Igor; Brandenburg, Axel
- The Astrophysical Journal, Vol. 858, Issue 2

##
Overpopulated gauge fields on the lattice

journal, October 2012

- Berges, Jürgen; Schlichting, Sören; Sexty, Dénes
- Physical Review D, Vol. 86, Issue 7

##
The pseudo chiral magnetic effect in QED 3

journal, January 2016

- Mizher, Ana Julia; Raya, Alfredo; Villavicencio, Cristián
- Nuclear and Particle Physics Proceedings, Vol. 270-272

##
Chiral vortical effect for bosons

journal, August 2017

- Avkhadiev, Artur; Sadofyev, Andrey V.
- Physical Review D, Vol. 96, Issue 4

##
Nonperturbative methods and extended-hadron models in field theory. III. Four-dimensional non-Abelian models

journal, December 1974

- Dashen, Roger F.; Hasslacher, Brosl; Neveu, André
- Physical Review D, Vol. 10, Issue 12

##
The Turbulent Chiral Magnetic Cascade in the Early Universe

journal, August 2017

- Brandenburg, Axel; Schober, Jennifer; Rogachevskii, Igor
- The Astrophysical Journal, Vol. 845, Issue 2

##
A saddle-point solution in the Weinberg-Salam theory

journal, November 1984

- Klinkhamer, F. R.; Manton, N. S.
- Physical Review D, Vol. 30, Issue 10

##
Recent developments in transport phenomena in Weyl semimetals

journal, November 2013

- Hosur, Pavan; Qi, Xiaoliang
- Comptes Rendus Physique, Vol. 14, Issue 9-10

##
Chiral magnetic effect

journal, October 2008

- Fukushima, Kenji; Kharzeev, Dmitri E.; Warringa, Harmen J.
- Physical Review D, Vol. 78, Issue 7

##
Electromagnetic field and the chiral magnetic effect in the quark-gluon plasma

journal, June 2015

- Tuchin, Kirill
- Physical Review C, Vol. 91, Issue 6

##
Analytic and numerical study of preheating dynamics

journal, December 1996

- Boyanovsky, D.; de Vega, H. J.; Holman, R.
- Physical Review D, Vol. 54, Issue 12

##
Scaling laws in chiral hydrodynamic turbulence

journal, June 2016

- Yamamoto, Naoki
- Physical Review D, Vol. 93, Issue 12

##
Anomalous transport properties of Dirac and Weyl semimetals (Review Article)

journal, June 2018

- Gorbar, E. V.; Miransky, V. A.; Shovkovy, I. A.
- Low Temperature Physics, Vol. 44, Issue 6

##
Chiral Shock Waves

journal, May 2017

- Sen, Srimoyee; Yamamoto, Naoki
- Physical Review Letters, Vol. 118, Issue 18

##
Improved Hamiltonian for Minkowski Yang-Mills theory

journal, December 1996

- Moore, Guy D.
- Nuclear Physics B, Vol. 480, Issue 3

##
Color Glass Condensate in Schwinger–Keldysh QCD

journal, January 2014

- Jeon, Sangyong
- Annals of Physics, Vol. 340, Issue 1

##
Sphalerons and axion dynamics in high-temperature QCD

journal, March 1991

- McLerran, Larry; Mottola, Emil; Shaposhnikov, Mikhail E.
- Physical Review D, Vol. 43, Issue 6

##
Self-Consistent Evolution of Magnetic Fields and Chiral Asymmetry in the Early Universe

journal, January 2012

- Boyarsky, Alexey; Fröhlich, Jürg; Ruchayskiy, Oleg
- Physical Review Letters, Vol. 108, Issue 3

##
Anomalous non-conservation of fermion/chiral number in Abelian gauge theories at finite temperature

journal, April 2018

- Figueroa, Daniel G.; Shaposhnikov, Mikhail
- Journal of High Energy Physics, Vol. 2018, Issue 4

##
Collective modes and instabilities in anisotropically expanding ultrarelativistic plasmas

journal, April 2010

- Rebhan, Anton; Steineder, Dominik
- Physical Review D, Vol. 81, Issue 8

##
Lattice implementation of Abelian gauge theories with Chern–Simons number and an axion field

journal, January 2018

- Figueroa, Daniel G.; Shaposhnikov, Mikhail
- Nuclear Physics B, Vol. 926

##
When Chiral Photons Meet Chiral Fermions: Photoinduced Anomalous Hall Effects in Weyl Semimetals

journal, January 2016

- Chan, Ching-Kit; Lee, Patrick A.; Burch, Kenneth S.
- Physical Review Letters, Vol. 116, Issue 2

##
Ultraviolet cascade in classical Yang-Mills theory

journal, September 2012

- Kurkela, Aleksi; Moore, Guy D.
- Physical Review D, Vol. 86, Issue 5

##
Laminar and Turbulent Dynamos in Chiral Magnetohydrodynamics. I. Theory

journal, September 2017

- Rogachevskii, Igor; Ruchayskiy, Oleg; Boyarsky, Alexey
- The Astrophysical Journal, Vol. 846, Issue 2

##
The effects of topological charge change in heavy ion collisions: “Event by event and violation”

journal, May 2008

- Kharzeev, Dmitri E.; McLerran, Larry D.; Warringa, Harmen J.
- Nuclear Physics A, Vol. 803, Issue 3-4

##
Real-time dynamics with fermions on a lattice

journal, August 1999

- Aarts, Gert; Smit, Jan
- Nuclear Physics B, Vol. 555, Issue 1-2

##
Chiral charge dynamics in Abelian gauge theories at finite temperature

journal, October 2019

- Figueroa, Daniel G.; Florio, Adrien; Shaposhnikov, Mikhail
- Journal of High Energy Physics, Vol. 2019, Issue 10

##
Dynamical evolution of the chiral magnetic effect: Applications to the quark-gluon plasma

journal, October 2015

- Manuel, Cristina; Torres-Rincon, Juan M.
- Physical Review D, Vol. 92, Issue 7

##
Energy source for the magnetic field growth in magnetars driven by the electron-nucleon interaction

journal, October 2015

- Dvornikov, Maxim; Semikoz, Victor B.
- Physical Review D, Vol. 92, Issue 8

##
Relativistic Turbulence: A Long Way from Preheating to Equilibrium

journal, March 2003

- Micha, Raphael; Tkachev, Igor I.
- Physical Review Letters, Vol. 90, Issue 12

##
Energy conservation and the chiral magnetic effect

journal, July 2017

- Kaplan, David B.; Reddy, Sanjay; Sen, Srimoyee
- Physical Review D, Vol. 96, Issue 1

##
Instabilities of an anisotropically expanding non-Abelian plasma: $3\mathrm{D}\mathbf{+}3\mathrm{V}$ discretized hard-loop simulations

journal, January 2013

- Attems, Maximilian; Rebhan, Anton; Strickland, Michael
- Physical Review D, Vol. 87, Issue 2

##
Axial-Vector Vertex in Spinor Electrodynamics

journal, January 1969

- Adler, Stephen L.
- Physical Review, Vol. 177, Issue 5

##
Chiral Magnetic Effect and Anomalous Transport from Real-Time Lattice Simulations

journal, September 2016

- Müller, Niklas; Schlichting, Sören; Sharma, Sayantan
- Physical Review Letters, Vol. 117, Issue 14

##
Universal attractor in a highly occupied non-Abelian plasma

journal, June 2014

- Berges, J.; Boguslavski, K.; Schlichting, S.
- Physical Review D, Vol. 89, Issue 11

##
Anomaly-Induced Dynamical Refringence in Strong-Field QED

journal, August 2016

- Mueller, N.; Hebenstreit, F.; Berges, J.
- Physical Review Letters, Vol. 117, Issue 6

##
Quantum Theory of Fermion Production after Inflation

journal, August 2011

- Berges, Jürgen; Gelfand, Daniil; Pruschke, Jens
- Physical Review Letters, Vol. 107, Issue 6

##
Nonequilibrium study of the chiral magnetic effect from real-time simulations with dynamical fermions

journal, February 2017

- Mace, Mark; Mueller, Niklas; Schlichting, Sören
- Physical Review D, Vol. 95, Issue 3

##
Chiral anomaly and classical negative magnetoresistance of Weyl metals

journal, September 2013

- Son, D. T.; Spivak, B. Z.
- Physical Review B, Vol. 88, Issue 10

##
Chiral magnetohydrodynamic turbulence

journal, July 2017

- Pavlović, Petar; Leite, Natacha; Sigl, Günter
- Physical Review D, Vol. 96, Issue 2

##
Chiral magnetic effect in ZrTe5

journal, February 2016

- Li, Qiang; Kharzeev, Dmitri E.; Zhang, Cheng
- Nature Physics, Vol. 12, Issue 6

##
Numerical study of chiral plasma instability within the classical statistical field theory approach

journal, July 2016

- Buividovich, P. V.; Ulybyshev, M. V.
- Physical Review D, Vol. 94, Issue 2

##
Chiral gravitational waves from chiral fermions

journal, July 2017

- Anber, Mohamed M.; Sabancilar, Eray
- Physical Review D, Vol. 96, Issue 2

##
Covariant and 3 + 1 Equations for Dynamo-Chiral General Relativistic Magnetohydrodynamics

journal, June 2018

- Del Zanna, L.; Bucciantini, N.
- Monthly Notices of the Royal Astronomical Society

##
Equilibrium parity-violating current in a magnetic field

journal, December 1980

- Vilenkin, Alexander
- Physical Review D, Vol. 22, Issue 12

##
Role of the electron mass in damping chiral plasma instability in Supernovae and neutron stars

journal, April 2015

- Grabowska, Dorota; Kaplan, David B.; Reddy, Sanjay
- Physical Review D, Vol. 91, Issue 8

##
Turbulent thermalization

journal, August 2004

- Micha, Raphael; Tkachev, Igor I.
- Physical Review D, Vol. 70, Issue 4