Advanced fuel fusion, phase space engineering, and structure-preserving geometric algorithms

Abstract

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.

Figures (5)

• Figure 1: Tritium self-sustainability is still an engineering challenge. For the tritium burning fraction and breeding return currently achievable, there is a large amount of recirculating tritium in the system, and the required tritium recycling and recovery rate is in the range of 99.9%.
• Figure 2: A Maxwell demon guarding a one-way door. The blue balls inside (representing backward-moving particles) are bounced back at the door, and the red balls outside (representing forward-moving particles) are allowed in.
• Figure 3: Not all phase space manipulations by a Maxwell demon driven by electromagnetic fields are possible. The phase space volume of the ions needs to be conserved according to the Liouville theorem. If the operation is confined in the $(x,v_{x})$ plane, incompressibility rules out the possibility of forming a cold, focused, energetic beam as shown in (b), which would be ideal for fusion reactions.
• Figure 4: Gardner ground state is reached by "doing a Lebesgue integral".
• Figure 5: Gromov's non-squeezing theorem. No symplectic map $\varphi$ can squeeze the ball $B^{2n}(r)$ into the cylinder $Z_{j}^{2n}(R)$ when $r>R.$ But for any $r\le R,$ the ball $B^{2n}(r)$ is already inside the cylinder $Z_{j}^{2n}(R)$. The ball $B^{2n}(r)$ in phase space is "rigid".