1+1 dimensional relativistic magnetohydrodynamics with longitudinal acceleration

Abstract

Non-central heavy-ion collisions generate the strongest magnetic field of the order of 10 18 − 10 19 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 non-central heavy-ion collisions. We investigate the longitudinal acceleration effects on the 1+1 dimensional relativistic magnetohydrodynamics with transverse magnetic fields. We analyze the proper time evolution of the system energy density. 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. PACS numbers: 12.38.Mh,24.85.+p,25.75.Nq

Accelerating longitudinal expansion of resistive relativistic magnetohydrodynamics in heavy ion collisions

“…• We remind that the relation between fluid rapidity and space time rapidity is Y = λη, where λ is called the acceleration parameter [35]. So, we can write…”

“…The next step is to solve the conservation equations; the main idea for solving eqs. (29,30) is to change these two couple partial differential equations (PDEs) into two ordinary differential equations (ODEs) with a given initial condition (τ 0 , 0) = 0 [35]. The combination of the energy and Euler equations (29,30) can be rewritten as follows:…”

“…Now, the presence of EM fields in relativistic heavy ion collisions requires to solve the problem, e.g., in the context of relativistic magneto-hydrodynamics (RMHD). Several papers are present in the literature, which perform analytical and numerical calculations within RMHD, by assuming infinite electrical conductivity (Ideal RMHD) [26]- [35]. However, it has been deduced from lattice QCD calculations [36]- [39] that the electrical conductivity of the plasma under investigation corresponds to the ambient temperature and that a finite value could be more appropriate.…”

Ideal spin hydrodynamics from Wigner function approach

“…Recent developments in the relativistic hydrodynamics include the effective theory approach [26][27][28], the derivation using the local equilibrium distribution functions [29][30][31][32] introduced in [9]. The second order hydrodynamical equations can be derived in many approaches, such as the generating function method [33], relaxation time approximation [34,35], and entropy current analysis based on the second law of thermodynamics [36][37][38][39].…”

Generalization of Bantilan-Ishi-Romatschke flow to magnetohydrodynamics

“…As it is discussed earlier, such an assumption is in agreement with the successes of relativistic hydrodynamics. A different approach is assumed in [34,35], in which the kinematical modifications of the fluid due to external magnetic fields are studied. In these works, the magnetic fields are assumed to be external in the sense that they need not satisfy the Maxwell equations, Recently a novel exact analytical solution to relativistic hydrodynamics is presented in [36] that breaks rotational and longitudinal boost symmetries that are assumed by Bjorken and Gubser flows.…”