Time and space dependence of the electromagnetic field in relativistic heavy-ion collisions

Exact analytical solution for the space-time evolution of electromagnetic field in electrically conducting nuclear matter produced in heavy-ion collisions is discussed. It is argued that the parameter that controls the strength of the matter effect on the field evolution is σÎ3b, where σ is electrical conductivity, Î3 is the Lorentz boost-factor, and b is the characteristic transverse size of the matter. When this parameter is of the order 1 or larger, which is the case at the Relativistic Heavy Ion Collider and the Large Hadron Collider, the space-time dependence of the electromagnetic field completely differs from that in vacuum. Disciplines Astrophysics and Astronomy | Physics Comments This article is from Physical Review C 88 (2013): 024911, doi: 10.1103/PhysRevC.88.024911. Posted with permission. This article is available at Iowa State University Digital Repository: http://lib.dr.iastate.edu/physastro_pubs/127 PHYSICAL REVIEW C 88, 024911 (2013) Time and space dependence of the electromagnetic field in relativistic heavy-ion collisions Kirill Tuchin Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA (Received 1 July 2013; published 28 August 2013) Exact analytical solution for the space-time evolution of electromagnetic field in electrically conducting nuclear matter produced in heavy-ion collisions is discussed. It is argued that the parameter that controls the strength of the matter effect on the field evolution is σγ b, where σ is electrical conductivity, γ is the Lorentz boost-factor, and b is the characteristic transverse size of the matter. When this parameter is of the order 1 or larger, which is the case at the Relativistic Heavy Ion Collider and the Large Hadron Collider, the space-time dependence of the electromagnetic field completely differs from that in vacuum. DOI: 10.1103/PhysRevC.88.024911 PACS number(s): 25.75.−q In relativistic heavy-ion collisions, production of valence quarks in the central rapidity region (baryon stopping) is suppressed [1]. Hence, Z valence quarks of each nucleus continue to travel after heavy-ion collision along the straight lines in opposite directions. These valence quarks carry total electric charge 2Ze that creates electromagnetic field in the interaction region. Unlike the valence quarks, gluons and sea quarks are produced mostly in the central rapidity region, i.e., in a plane perpendicular to the collision axis. It has been argued in Refs. [2,3] that high-multiplicity events in heavyion collisions can be effectively described using relativistic hydrodynamics. In particular, matter produced in heavy-ion collisions can be characterized by a few transport coefficients. This approach has enjoyed remarkable phenomenological success (see, e.g., Ref. [4]). Since sea quarks carry an electric charge, the electromagnetic field created by valence quarks depends on the permittivity , permeabilityμ, and conductivity σ of the produced matter. Consider the electromagnetic field created by a point charge e moving along the positive z axis with velocity v. It is governed by the following Maxwell equations: ∇ · B = 0 , ∇ × E = − ∂t , (1) ∇ · D = eδ(z− vt)δ(b) , (2) ∇ × H = ∂ D ∂t + σ E + ev ẑδ(z− vt)δ(b) , where r = z ẑ + b (such that b · ẑ = 0) is the position of the observation point. Performing the Fourier transform