A research team from the University of Science and Technology of China (USTC) has developed a novel ray-tracing method that successfully addresses the limitations of traditional algorithms in curvilinear coordinate systems by innovatively introducing a rasterization step. This method can be widely applied to laser-plasma interaction simulations in inertial confinement fusion, plasma sources, and digital optical diagnostics.

In science fiction movies, we often see powerful laser weapons. In reality, when high-power lasers interact with matter, they ionize it into plasma, which acts like an "irregular mirror" that bends, reflects, and even absorbs incident laser light. To accurately predict laser propagation paths in plasma, scientists use "ray-tracing" techniques. Imagine a laser beam composed of countless light rays. Each ray's direction changes during propagation due to plasma density distribution, similar to sunlight refracting through a water glass, except that plasma's "refractive index" varies continuously with position. Ray-tracing technology calculates these specific ray paths to understand how laser energy transfers to plasma.

This technology is particularly crucial in inertial confinement fusion research, where scientists use multiple laser beams to heat and compress deuterium-tritium targets, attempting to achieve controlled nuclear fusion in laboratories. Improving fusion efficiency requires precise control of laser energy transport and deposition. However, traditional ray-tracing methods become computationally inefficient when handling spherical or cylindrical targets, seriously hindering numerical simulation development. The main challenge lies in requiring ray trajectories to be split into segments matching grid topology, with ray birth and end points coinciding with grid faces, significantly increasing algorithm complexity and reducing computational efficiency.

Recently, the USTC team proposed a rasterization-based ray-tracing method with three core innovations: 1) decoupling ray trajectory calculation from energy deposition using adaptive-step Runge-Kutta integration, eliminating the requirement for rays to terminate at grid boundaries; 2) introducing rasterization techniques for energy deposition, allocating ray energy loss based on intersection relationships with fluid grids; 3) establishing a unified, concise tracing framework supporting various curvilinear coordinate systems and reduced-dimensional simulations.

The work was published in High Power Laser Science and Engineering (Tao Tao, Zhujun Li, Kejian Qian, Xian Jiang, Guannan Zheng, Rui Yan, Haoran Liu, Qing Jia, Jun Li, Hang Ding, Jian Zheng, "A rasterization-based ray-tracing method for laser–plasma interactions," High Power Laser Sci. Eng. 13, 03000e37)

Graphic description Figure 1: Ray-tracing demonstration: (a) Traditional cell-avg ray trajectory constrained by computational grid vs. adaptive RK ray trajectory; (b) Target in 2D cylindrical coordinates and corresponding ray tracing in virtual 3D grid; (c) Target in 2D spherical coordinates and corresponding ray tracing in virtual 3D grid.

Graphic description Figure 2: Test cases: (a) Plasma Luneberg focusing lens; (b) Doppler frequency shift; (c) Laser-driven gas sphere target.

The team validated the new algorithm through three typical test cases: First, the plasma Luneberg lens demonstrated the algorithm's high tracking precision by focusing parallel incident laser beams into a point focus through specially distributed plasma. Second, plasma Doppler shift verification showed the algorithm's capability to capture complex laser-plasma interaction processes, achieving a relative error of only 10⁻⁴ compared to analytical solutions, while traditional algorithms showed errors up to 18%. Third, laser-driven gas sphere simulation demonstrated the algorithm's stability in practical applications by integrating it into the DRIM multiphase radiation hydrodynamics program with hybrid MPI+OpenMP parallel strategy, achieving near-linear speedup.

This method lays the foundation for developing universal ray-tracing toolkits and will extend to more complex optical phenomena, such as nonlinear laser-plasma interactions. The team is also developing modules for synthetic optical diagnostics, aiming to achieve digital twins of multi-modal optical diagnostic data for fusion and various plasma industrial applications.