In the process of solving radiation hydrodynamics, the non-physics results often leads to the failure of the solution. In this paper, for radiation hydrodynamics based on maximum entropy approximation under the condition of one-dimensional spherical symmetry, the positive schemes of the operator splitting method are given; the calculation method of spherical symmetric source term is improved, and the time step limitation is reduced; the reconstructing Eddington factor is used instead of the direct reconstructing radiation flux to avoid the non-physics results brought by the reconstructing process. Finally, some examples are given to verify the correctness of the method.

We have studied the evolution of the heavy ions that expand in a cold background plasma. Two typical conditions are considered where only the debris ion’s initial total mass is significantly different. The work aims to illustrate the complex scaling behavior of the debris evolution in the early time of the High Altitude Nuclear Explosions (HANE). The simulation is performed via the hybrid model, in which the ions and electrons are treated as classical particles and mass-less fluid, respectively. Due to the imbalance of the electric and magnetic force on the debris ions, these debris particles will evolve into different collective patterns at the later times. These patterns manifest a rather different stopping behavior of the debris ions and an opposite drifting direction of the electron fluid. Further numerical and analytical calculations demonstrate that the imbalance depends not only on the number densities of the plasma ions, but also on the spatial variations of the magnetic fields. Our work reveals that the behavior of the debris ions scales non-linearly with their initial total mass, and this non-linearity complicates the scaling from laser experiment to HANE.