Relativistic magnetohydrodynamics in one dimension
Abstract
We derive a number of solutions for onedimensional dynamics of relativistic magnetized plasma that can be used as benchmark estimates in relativistic hydrodynamic and magnetohydrodynamic numerical codes. First, we analyze the properties of simple waves of fast modes propagating orthogonally to the magnetic field in relativistically hot plasma. The magnetic and kinetic pressures obey different equations of state, so that the system behaves as a mixture of gases with different polytropic indices. We find the selfsimilar solutions for the expansion of hot strongly magnetized plasma into vacuum. Second, we derive linear hodograph and Darboux equations for the relativistic Khalatnikov potential, which describe arbitrary onedimensional isentropic relativistic motion of cold magnetized plasma and find their general and particular solutions. The obtained hodograph and Darboux equations are very powerful: A system of highly nonlinear, relativistic, timedependent equations describing arbitrary (not necessarily selfsimilar) dynamics of highly magnetized plasma reduces to a single linear differential equation.
 Publication:

Physical Review E
 Pub Date:
 February 2012
 DOI:
 10.1103/PhysRevE.85.026401
 arXiv:
 arXiv:1112.0249
 Bibcode:
 2012PhRvE..85b6401L
 Keywords:

 52.27.Ny;
 47.75.+f;
 47.45.n;
 52.35.Tc;
 Relativistic plasmas;
 Relativistic fluid dynamics;
 Rarefied gas dynamics;
 Shock waves and discontinuities;
 Astrophysics  High Energy Astrophysical Phenomena;
 Physics  Computational Physics;
 Physics  Fluid Dynamics;
 Physics  Plasma Physics
 EPrint:
 accepted by Phys. Rev. E