Theoretical Study Of Relativistic Magnetohydrodynamics

In the early Universe at temperatures greater than 1012K,the ordinary matter composed of protons and neutrons was dissolved into a plasma the quarks and the gluons.Such a primor-dial state of matter is called the quark-gluon plasma(QGP),and its properties are currently under active investigation by using the relativistic heavy-ion collisions at the Relativistic Heavy Ion Collider(RHIC)and at the Large Hadron Collider(LHC).The theoretical basis for studying QGP is provided by the color SU(3)gauge theory of strong interaction,the quantum chromodynamics(QCD).To make a connection between QCD predictions and experimental data,it is essential to formulate a general framework of describing the space-time evolution of hot and dense matter produced in relativistic heavy-ion collisions.The relativistic hydrodynamics supplemented with suitable initial conditions is known be one such framework.In recent years,the importance of considering dissipative effects beyond the assumption of perfect QGP fluid has been recognized both theoretically and experimentally.We introduce the basic laws of thermodynamics and derive the thermodynamic relations that will be used later in this thesis and a brief review of relativistic ideal fluid dynamics.We derive the general form of the conserved currents of an ideal fluid and their equations of mo-tion.We postulate the thermodynamic relations in a covariant notation using the definition of hydrodynamic four-velocity and derive a covariant version of Navier-Stokes theory using the second law of thermodynamics.We discuss the problems of Navier-Stokes theory in the relativistic regime,i.e.,the acausality and instability of this theory.We also review Israel-Stewart theory and show how to derive causal fluid dynamical equations from the second law of thermodynamics.Peripheral collisions of heavy ions can generate strong magnetic fields and huge angu-lar momentum.The strength of the magnetic field generated in heavy ion collisions can be estimated to be about 1018 Gauss at RHIC energies and 1019 Gauss at LHC energies.Such transient electromagnetic fields may induce various novel effects in the hydrodynamic de-scription of the quark gluon plasma for noncentral heavy-ion collisions.In presence of the magnetic field the model can be extended to magnetohydrodynamics(MHD)by including the coupled equations of the fluid and magnetic field as well as the evolution equation of the magnetic field.The basics of relativistic magnetohydrodynamics and relativistic ideal magnetohydro-dynamics are first introduced.We present the work on the analytic solution of the Bjorken flow in 1+1 dimensional relativistic ideal magnetohydrodynamics,which is also the theo-retical basis of our first work.As we know,QGP expanding in the beam direction can be described by considering a boost invariant 1+1D Bjorken flow,that is known to be a good approximation at mid-rapidity.It leads to a flat rapidity distribution of final particle,which is inconsistent with observations at RHIC and LHC.However,it has been pointed out that in realistic situation the energy density at mid-rapidity decreases faster than in the Bjorken flow.Although the Bjorken solution is widely used,the longitudinal expansion dynamics of hydrodynamics seems to be able to offer a more realistic estimation for the initial energy density estimation and the final state description.We investigate the longitudinal accelera-tion effects on the 1+1 dimensional relativistic magnetohydrodynamics 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 ?*,magnetic field de-cay parameter a,equation of state ?,and initial magnetization ?0 have nontrivial effects on the evolutions of the system energy density and temperature profile.Finally,the work on analytic solutions of Bjorken flow in 1+1dimensional relativistic magnetohydrodynamics in a uniform transverse magnetic field with magnetization effect is introduced,which is also the theoretical basis of our first work.In addition,the work on relativistic dissipative mag-netohydrodynamics is also presented,and this work has some inspiration for our third work.Then the earliest work on anomalous fluids is presented,where some transport coefficients could be determined from thermodynamic relations,and this piece of content is currently the new trend.Then we introduce our second work,we study the evolution of the longitudinal expansion of an ideal fluid with finite electrical conductivity,which is subject to the electro-magnetic(EM)fields.In the framework of resistive relativistic magnetohydrodynamics,we find an exact analytical solution for the EM fields and for the acceleration of the fluid.Inspired by work related to spin hydrodynamics,based on the theoretical foundation of viscous fluids,we extend it to the initial theory of viscous fluids with angular momentum,and introduce the first-order dissipative quantities to describe the viscous fluids based on ideal fluids,in which we use the matching condition,dissipative tensor decomposition,def-inition of velocity field and other standard techniques for derivation of viscous fluids,and derive the first-order theory of viscous fluids with angular momentum by the second law of thermodynamics,hoping to provide hydrodynamic model that can explain the ? hyperon polarization effect.