Electromagnetic fields with electric and chiral magnetic conductivities in heavy ion collisions

Abstract

We derive analytic formula for electric and magnetic fields produced by a moving charged particle in a conducting medium with the electric conductivity $\sigma$ and the chiral magnetic conductivity ${\sigma }_{\chi }$. We use the Green function method and assume that ${\sigma }_{\chi }$ is much smaller than $\sigma$. The compact algebraic expressions for electric and magnetic fields without any integrals are obtained. They recover the Lienard-Wiechert formula at vanishing conductivities. Exact numerical solutions are also found for any values of $\sigma$ and ${\sigma }_{\chi }$ and are compared to analytic results. Both numerical and analytic results agree very well for the scale of high energy heavy ion collisions. The space-time profiles of electromagnetic fields in non-central Au+Au collisions have been calculated based on these analytic formula as well as exact numerical solutions.

RevTex 4, 7 figures, 13 pages; section III-B has been re-written using dimensionful variables to improve readability; added references and one figure

References in corpus (8)

• The Chiral Magnetic Effect
• Berry Curvature, Triangle Anomalies, and the Chiral Magnetic Effect in Fermi Liquids
• Testing the chiral magnetic and chiral vortical effects in heavy ion collisions
• Chiral anomaly and local polarization effect from quantum kinetic approach
• Lorentz Invariance in Chiral Kinetic Theory
• Electrical conductivity and charge diffusion in thermal QCD from the lattice
• Chiral fermions as classical massless spinning particles
• Chiral Magnetic Effect at Weak Coupling with Relaxation Dynamics

Cited by in corpus (69)

• What can we learn from global spin alignment of $\varphi$ meson in heavy-ion collisions?
• Magnetic Field Induced Polarization Difference between Hyperons and Anti-hyperons
• Magnetic fields in heavy ion collisions: flow and charge transport
• A quark coalescence model for polarized vector mesons and baryons
• Spin alignment of vector mesons in heavy-ion collisions
• Foundations and Applications of Quantum Kinetic Theory
• Improved quark coalescence model for spin alignment and polarization of hadrons
• Effect of intense magnetic fields on reduced-MHD evolution in $\sqrt{s_{\mathrm{NN}}}$ = 200 GeV Au+Au collisions
• Anisotropic transport properties of Hadron Resonance Gas in magnetic field
• Covariant chiral kinetic equation in Wigner function approach
• New developments in relativistic magnetohydrodynamics
• Out-of-Equilibrium Chiral Magnetic Effect from Chiral Kinetic Theory
• Wigner function and pair production in parallel electric and magnetic fields
• Chiral kinetic approach to the chiral magnetic effect in isobaric collisions
• Anomalous magnetohydrodynamics with longitudinal boost invariance and chiral magnetic effect
• Covariant and 3+1 Equations for Dynamo-Chiral General Relativistic Magnetohydrodynamics
• Pseudoscalar condensation induced by chiral anomaly and vorticity for massive fermions
• Wigner functions of massive fermions in strong magnetic fields
• New Developments in Relativistic Fluid Dynamics with spin
• Causality and stability in relativistic viscous non-resistive magneto-fluid dynamics
• One particle distribution function and shear viscosity in magnetic field: a relaxation time approach
• Magnetic field in expanding quark-gluon plasma
• Magneto-Seebeck coefficient and Nernst coefficient of hot and dense hadron gas
• Dynamically flavored description of holographic QCD in the presence of a magnetic field
• Probing the initial longitudinal density profile and electromagnetic field in ultrarelativistic heavy-ion collisions with heavy quarks
• Dynamical magnetic fields in heavy-ion collisions
• Electromagnetic fields from the extended Kharzeev-McLerran-Warringa model in relativistic heavy-ion collisions
• Kinetic theory with spin: From massive to massless fermions
• Boost invariant formulation of the chiral kinetic theory
• Deconfinement and chiral phase transitions in quark matter with a strong electric field
• Chirality Production with Mass Effects-Schwinger Pair Production and the Axial Ward Identity
• Lepton pair photoproduction in peripheral relativistic heavy-ion collisions
• Electromagnetic fields and directed flow in large and small colliding systems at ultrarelativistic energies
• Centrality dependence of photon yield and elliptic flow from gluon fusion and splitting induced by magnetic fields in relativistic heavy-ion collisions
• Charge-dependent directed flows in heavy-ion collisions by Boltzmann-Maxwell equations
• Magnetic field influence on the early time dynamics of heavy-ion collisions
• Space-average electromagnetic fields and EM anomaly weighted by energy density in heavy-ion collisions
• Directed flow of charged particles within idealized viscous hydrodynamics at energies available at the BNL Relativistic Heavy Ion Collider and at the CERN Large Hadron Collider
• Electromagnetic response of hot QCD medium in the presence of background time-varying fields
• Non-relativistic approximate numerical ideal-magneto hydrodynamics of (1+1) D transverse flow in Bjorken scenario
• Relativistic Dissipative Magnetohydrodynamics from the Boltzmann equation for a two-component gas
• The fermion self-energy and damping rate in a hot magnetized plasma
• Directed flow in asymmetric nucleus-nucleus collisions and the inverse Landau-Pomeranchuk-Migdal effect
• Quantum diffusion of electromagnetic fields of ultrarelativistic spin-half particles
• Estimation of electric field in intermediate-energy heavy-ion collisions
• Chiral magnetic effect for chiral fermion system
• Collisional energy loss and the Chiral Magnetic Effect
• The signature of charge dependent directed flow observables by electromagnetic fields in heavy ion collisions
• Electromagnetic instability and Schwinger effect in the Witten-Sakai-Sugimoto model with D0-D4 background
• Recent developments in chiral and spin polarization effects in heavy-ion collisions
• Quark matter under strong electric fields in the Linear Sigma Model coupled with quarks
• Transverse expansion of hot magnetized Bjorken flow in heavy ion collisions
• Electromagnetic field of ultrarelativistic charge in topologically random nuclear matter
• External magnetic field induced paramagnetic squeezing effect in heavy-ion collisions at the LHC
• Mass Spectra and Decay of Mesons under Strong External Magnetic Field
• Accelerating longitudinal expansion of resistive relativistic-magneto-hydrodynamics in heavy ion collisions
• Chiral Cherenkov radiation in the presence of a time-dependent chiral chemical potential
• Relativistic resistive magnetohydrodynamics for a two-component plasma
• Polarization Dynamics in Paramagnet of Charged Quark-Gluon Plasma
• Dynamical Electromagnetic fields and Dynamical Electromagnetic Anomaly in heavy ion collisions at intermediate energies
• Correlation of density fluctuation in a magnetized QCD matter near the critical end point
• The effect of electric and chiral magnetic conductivities on azimuthally fluctuating electromagnetic fields and observables in isobar collisions
• Continuous evolution of electromagnetic field in heavy-ion collisions
• Dynamic Magnetic Response of Quark-Gluon Plasma to Electromagnetic Fields
• Lepton pair production in ultra-peripheral collisions
• Quarks to Cosmos: Particles and Plasma in Cosmological evolution
• Electromagnetic anomaly in the presence of electric and chiral magnetic conductivities in relativistic heavy-ion collisions
• Magnetodynamic Characteristics and QGP Energy Dissipation in RMHD Framework with Relativistic Heavy-Ion Collisions
• Thermoelectric transport coefficients of quark matter