Non-thermal advanced fuel fusion trades the requirement of a large amount of recirculating tritium in the system for that of large recirculating power. Phase space engineering technologies utilizing externally injected electromagnetic fields can be applied to meet the challenge of maintaining non-thermal particle distributions at a reasonable cost. The physical processes of the phase space engineering are studied from a theoretical and algorithmic perspective. It is emphasized that the operational space of phase space engineering is limited by the underpinning symplectic dynamics of charged particles. The phase space incompressibility according to the Liouville theorem is just one of many constraints, and Gromov's non-squeezing theorem determines the minimum footprints of the charged particles on every conjugate phase space plane. In this sense and level of sophistication, the mathematical abstraction of phase space engineering is symplectic topology. To simulate the processes of phase space engineering, such as the Maxwell demon and electromagnetic energy extraction, and to accurately calculate the minimum footprints of charged particles, recently developed structure-preserving geometric algorithms can be used. The family of algorithms conserves exactly, on discretized spacetime, symplecticity and thus incompressibility, non-squeezability, and symplectic capacities. The algorithms apply to the dynamics of charged particles under the influence of external electromagnetic fields as well as the charged particle-electromagnetic field system governed by the Vlasov-Maxwell equations.

翻译：非热先进聚变燃料聚变以系统需要大量循环功率为代价，从而避免使用大量循环氚。利用外部注入电磁场的相空间工程技术可用于应对以合理成本维持非热粒子分布的挑战。本文从理论和算法角度研究相空间工程的物理过程。强调相空间工程的操作空间受限于带电粒子的基础辛动力学。根据刘维尔定理的相空间不可压缩性仅仅是众多约束之一，而格罗莫夫非挤压定理决定了每个共轭相空间平面上带电粒子的最小足迹。在此意义和复杂程度上，相空间工程的数学抽象是辛拓扑。为了模拟相空间工程的过程（如麦克斯韦妖和电磁能量提取）并精确计算带电粒子的最小足迹，可采用近期发展的保结构几何算法。这类算法在离散时空上精确保持辛性，从而保持不可压缩性、非挤压性和辛容量。这些算法适用于外部电磁场作用下带电粒子的动力学，以及由弗拉索夫-麦克斯韦方程组控制的带电粒子-电磁场系统。