非理想横向磁流体力学的新自相似旋转解
Novel self-similar rotating solutions of non-ideal transverse magnetohydrodynamics
摘要：
在超相对论横向磁流体力学（MHD）框架下研究了非理想流体中电磁场和热力学场的演化，其本质特征是电场和磁场横向于流体速度。将相对论流体动力学的自相似解方法推广到非守恒电荷情形，求解了非理想横向磁流体动力学微分方程，得到了两组新的自相似解。第一组原来是一个升压不变的和精确的解决方案，其特征在于非旋转的电场和磁场。第二组是一个非升压不变的解决方案，其特征在于旋转的电场和磁场。旋转随着增加的速度$η$而发生，因为角速度由$ω_{0}\equiv\frac{\partialζ}{\partialη}=\frac{\partialϕ}{\partialη}$定义，其中$ζ$和$ϕ$是电矢量和磁矢量相对于流体的局部静止坐标系中的某个轴的角度。对于这两组解，电场和磁场彼此平行或反平行。执行一个完整的数值分析，有限的电导率，以及电和磁的磁化率的介质上的旋转和非旋转MHD解决方案的演变的影响进行了探索，和角速度$ω_{0}$和这些量之间的相互作用进行了仔细检查。电磁场的寿命和电磁化流体的温度的演变示出受$ω_{0}$。
英文摘要：
The evolution of electromagnetic and thermodynamic fields in a non-ideal fluid are studied in the framework of ultrarelativistic transverse magnetohydrodynamics (MHD), which is essentially characterized by electric and magnetic fields being transverse to the fluid velocity. Extending the method of self-similar solutions of relativistic hydrodynamics to the case of non-conserved charges, the differential equations of non-ideal transverse MHD are solved, and two novel sets of self-similar solutions are derived. The first set turns out to be a boost-invariant and exact solution, which is characterized by non-rotating electric and magnetic fields. The second set is a non-boost-invariant solution, which is characterized by rotating electric and magnetic fields. The rotation occurs with increasing rapidity $η$, as the angular velocity is defined by $ω_{0}\equiv\frac{\partialζ}{\partialη}=\frac{\partialϕ}{\partialη}$, with $ζ$ and $ϕ$ being the angles of electric and magnetic vectors with respect to a certain axis in the local rest frame of the fluid. For both sets of solutions, the electric and magnetic fields are either parallel or anti-parallel to each other. Performing a complete numerical analysis, the effects of finite electric conductivity as well as electric and magnetic susceptibilities of the medium on the evolution of rotating and non-rotating MHD solutions are explored, and the interplay between the angular velocity $ω_{0}$ and these quantities is scrutinized. The lifetime of electromagnetic fields and the evolution of the temperature of the electromagnetized fluid are shown to be affected by $ω_{0}$.
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