Implicit particle-in-cell codes offer advantages over their explicit counterparts in that they suffer weaker stability constraints on the need to resolve the higher frequency modes of the system. This feature may prove particularly valuable for modeling the interaction of high-intensity laser pulses with overcritical plasmas, in the case where the electrostatic modes in the denser regions are of negligible influence on the physical processes under study. To this goal, we have developed the new two-dimensional electromagnetic code ELIXIRS (standing for ELectromagnetic Implicit X-dimensional Iterative Relativistic Solver) based on the relativistic extension of the so-called Direct Implicit Method [D. Hewett and A. B. Langdon, J. Comp. Phys. extbf{72}, 121(1987)]. Dissipation-free propagation of light waves into vacuum is achieved by an adjustable-damping electromagnetic solver. In the high-density case where the Debye length is not resolved, satisfactory energy conservation is ensured by the use of high-order weight factors. In this paper, we first present an original derivation of the electromagnetic direct implicit method within a Newton iterative scheme. Its linear properties are then investigated through numerically solving the relation dispersions obtained for both light and plasma waves, accounting for finite space and time steps. Finally, our code is successfully benchmarked against explicit particle-in-cell simulations for two kinds of physical problems: plasma expansion into vacuum and relativistic laser-plasma interaction. In both cases, we will demonstrate the robustness of the implicit solver for crude discretizations, as well as the gains in efficiency which can be realized over standard explicit simulations.
展开▼
机译：隐式单元格内的粒子编码提供了优于其显式对应粒子的优势，因为它们在解决系统更高频率模式的需求方面受到较弱的稳定性约束。在密集区域中的静电模式对所研究的物理过程的影响可以忽略不计的情况下，此功能对于模拟高强度激光脉冲与超临界等离子体的相互作用可能特别有价值。为了实现这一目标，我们在所谓的直接隐式方法[D.]的相对论性扩展基础上，开发了新的二维电磁代码ELIXIRS（代表电磁隐式X维迭代相对论解算器）。 Hewett和A. B. Langdon，J. Comp。物理 textbf {72}，121（1987）]。光波到真空的无耗散传播是通过可调阻尼电磁求解器实现的。在德比长度无法解决的高密度情况下，通过使用高阶权重因子可以确保令人满意的节能效果。在本文中，我们首先提出牛顿迭代方案中电磁直接隐式方法的原始推导。然后，通过数值求解光波和等离子波的关系色散，并考虑有限的空间和时间步长，来研究其线性特性。最后，我们的代码已成功针对两种物理问题进行了显式的单元内粒子模拟测试：等离子体膨胀成真空和相对论性激光-等离子体相互作用。在这两种情况下，我们都将证明隐式求解器对粗离散化的鲁棒性，以及可以通过标准显式模拟实现的效率提高。
展开▼
