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

We derive an 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's 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 with analytic results. Both numerical and analytic results agree very well for the scale of high-energy heavy ion collisions. The spacetime profiles of electromagnetic fields in noncentral Au + Au collisions have been calculated based on these analytic formula as well as exact numerical solutions.