Aspects Of Electromagnetic Fields In Heavy Ion Collisions

Nuclear matter under extreme conditions such as high temperatures and densities exist in the universe and becomes the research frontier of nuclear physics.Strong in-teraction is involved among nucleons in nuclear matter and is described by Quantum Chromodynamics(QCD),the fundamental theory of the strong force.Due to color con-finement quarks and gluons are always confined inside nucleons of nuclear matter under normal conditions.However at high temperatures or/and densities nuclear matter can undergo a deconfinement phase transition to form a new state of matter known as the quark-gluon plasma(QGP)made of free quarks and gluons.The QGP can be produced in high-energy collisions of heavy ions,sometimes called "big bang in the lab".Two main heavy ion accelerator facilities that are devoted to the QGP physics are LHC at CERN and RHIC at BNL which help us explore the strong interaction and better under-stand the evolution of the early universe.Peripheral collisions of heavy ions can generate strong magnetic fields and huge an-gular momenta.These strong fields can induce various anomalous transport phenomena such as the Chiral Magnetic Effect(CME)and Chiral Vortical Effect(CVE).It is ex-pected that the CME can lead to charge separation along the direction of the magnetic field.Lots of experimental studies have been carried out in search of the CME signal however it is a great challenge to distinguish the CME signal from the background.For a quantitative study of these effects,a precise space-time description of the magnetic field is necessary.To search for the CME researchers have also proposed collisions of isobars(for example Ru-96 and Zr-96).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.For more accurate calculations one can use the Lienard-Wiechert potential or solve the Maxwell's equations to obtain magnetic fields at early time of heavy ion collisions.However the QGP is a good electric conductor.Due to conducting behaviour and non-vanishing con-ductivity of the QGP,the evolution of the electric and magnetic field is also affected.In the first part of the thesis we give a theoretical derivation of the Lienard-Wiechert potential and analytical expressions of the electromagnetic field by solving Maxwell's equations through Green's function method in the presence of the electric and chiral conductivity.Then we use these results to analyze the evolution and behavior of elec-tromagnetic fields in isobaric collisions.We also check the effect of the impact parame-ter and compare the electric and magnetic field generated by isobars.Our results based on simulations using the MC-Glauber model show that the electric and magnetic field with the electric and chiral conductivity decay at slower rate than without conductivi-ties.While comparing ratios of the electric and magnetic field for isobars we notice that they follow the expected ratio 44/40=1.1 from the fact that Ru has 44 protons and Zr has 40 protons.Another main approach to study the QGP evolution is by the model of relativis-tic hydrodynamics.In presence of the magnetic field the model can be extended to magneto-hydrodynamics(MHD)by including the coupled equations of the fluid and magnetic field as well as the evolution equation of the magnetic field.In the second part of the thesis we study the anomalous MHD with the longitudinal boost invariance and CME.We also include the electric conductivity in the relativistic MHD.Usually numerical results of the MHD with the CME can be highly unstable.Therefore we give analytical solutions which provide us a simple physical picture of this complicated pro-cess and can be a test of numerical simulations.To obtain analytical solutions,firstly we use the MHD with longitudinal boost invariance.Then we consider an electrically neutral fluid to avoid acceleration of the fluid.Then we search for the electromag-netic fields which do not change the velocity of the Bjorken flow.Finally we solve the Maxwell's equations and the anomalous conservation equation to obtain approximate analytical solutions for two equations of states,one for the dense limit with high chem-ical potentials and the other for the hot limit with high temperatures.We also compare analytical solutions with numerical results.The results show that analytical solutions work well in large chiral fluctuations or weak fields.We also compute the electromag-netic field in the lab frame to discuss the coupling between the electromagnetic field and chiral current.It is expected that rotation and polarization are naturally correlated in heavy ion collisions.Huge angular momenta generated in peripheral heavy ion collisions can be estimated by various models.How the global polarization can be measured experimen-tally is what we look for.In the third part of the thesis we study the global polarization effect in heavy ion collisions.Experimentally,the global polarization can be measured by the weak decay of the A hyperon into a proton and a pion.However the method used in experiments is by averaging in A's rest frame.In this thesis we propose another method for measuring the global polarization of A and A hyperons based on Lorentz transformation.The advantage of the method is that the event average is taken over mo-menta in the lab frame instead of A's rest frame.We use the UrQMD model to produce an ensemble of A hyperon four-momenta and compare our method with that used in experiments.We show that all of them work equally well in obtaining the global polar-ization of ? hyperons in the lab frame.We hope our method can be used in experiments in the future.