This work presents the application of a novel flow-based kinetic method^[1] to simulate z-pinch plasma dynamics in cylindrical (r,z) geometry with two velocity dimensions. The approach leverages continuous normalizing flows (CNF) ^[2] to track distribution functions along Newton-Lorentz characteristics, combining the precision of Vlasov methods with the flexibility of particle approaches, while avoiding statistical noise inherent to PIC simulations. As in particle methods, marker points move in phase space, but their associated distributions are updated via CNF-based transformations. Field quantities and moments are computed through SPH-like scatter-point integration with optimized smoothing kernels for cylindrical geometry, maintaining both local and global conservation properties.
The method demonstrates significant computational advantages over traditional PIC simulations in z-pinch relevant regimes. Its superior convergence rate of O(N^(-1.4)) in 2D2V phase space, compared to PIC's O(N^(-1/2)), enables accurate plasma evolution modeling using orders of magnitude fewer markers. This efficiency is particularly valuable for z-pinch simulations where high-density regions and sharp gradients pose challenges for conventional methods. The framework's adaptive capabilities allow strategic marker placement in regions of interest, such as current sheets and areas of MRT instability development.
The implementation leverages GPU acceleration for parallel computation of characteristic trajectories and field solving, promising substantial performance improvements for large-scale simulations. The method's modular nature facilitates integration with additional physics modules, while its robust handling of high-density regions makes it particularly suitable for z-pinch physics.
Research is ongoing to fully characterize the method's performance in capturing various z-pinch phenomena, including MRT instabilities, and results will be presented at the conference. This work represents a promising direction toward efficient, high-fidelity kinetic modeling of z-pinch dynamics.
[1] Zhu, Bowen & Wu, Jian & Lu, Yuanbo. (2025). A Flow-Based Hybrid Approach for Kinetic Plasma Simulations: Bridging Direct Vlasov and Particle Methods. 10.48550/arXiv.2501.16390.
[2] Chen, Ricky TQ, et al. "Neural ordinary differential equations." Advances in neural information processing systems 31 (2018).
 

kinetic simulation,Z-Pinch,continuous normalizing flows,Smooth particle hydrodynamic method,GPU