1 + 1 dimensional relativistic magnetohydrodynamics with longitudinal acceleration

Nonentral heavy-ion collisions generate the strongest magnetic field of the order of 1018–1019 Gauss due to the electric current produced by the positively charged spectators that travel at nearly the speed of light. Such transient electromagnetic fields may induce various novel effects in the hydrodynamic description of the quark gluon plasma for noncentral heavy-ion collisions. We investigate the longitudinal acceleration effects on the 1+1 dimensional relativistic magnetohydrodynamics (MHD) with homogenous transverse magnetic fields. Exact solution of such MHD with a special equation of state (EoS) is presented, and we analyze the proper time evolution of the system energy density for general EoS. We find that the longitudinal acceleration parameter λ*, magnetic field decay parameter a, equation of state κ, and initial magnetization σ0 have nontrivial effects on the evolutions of the system energy density and temperature profile.