We study the evolution of one-dimensional relativistic jets, using the exact solution of the Riemann problem for relativistic flows. For this purpose, we solve equations for the ideal special relativistic fluid composed of dissimilar particles in flat space-time and the thermodynamics of fluid is governed by a relativistic equation of state. We obtain the exact solution of jets impinging on denser ambient media. The time variation of the cross-section of the jet-head is modelled and incorporated. We present the initial condition that gives rise to a reverse shock. If the jet-head cross-section increases in time, the jet propagation speed slows down significantly and the reverse-shock may recede opposite to the propagation direction of the jet. We show that the composition of jet and ambient medium can affect the jet solution significantly. For instance, the propagation speed depends on the composition and is maximum for a pair-dominated jet, rather than a pure electron-positron or electron-proton jet. The propagation direction of the reverse-shock may also strongly depend on the composition of the jet.

中文翻译：

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具有相对论状态方程的一维相对论射流的精确解

我们使用相对论流动的黎曼问题的精确解来研究一维相对论射流的演化。为此，我们求解了平面时空中由不同粒子组成的理想特殊相对论流体的方程，流体的热力学由相对论状态方程支配。我们获得了射流撞击更密集的环境介质的精确解。对喷射头横截面的时间变化进行建模和合并。我们提出了引起反向冲击的初始条件。如果射流头截面随时间增加，则射流传播速度明显减慢，反向冲击可能会与射流传播方向相反地后退。我们表明射流和环境介质的组成可以显着影响射流溶液。例如，传播速度取决于成分，并且对于以对为主的射流，而不是纯电子-正电子或电子-质子射流，传播速度最大。反向冲击的传播方向也可能在很大程度上取决于射流的成分。