  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.
