Gromov ground state in phase space engineering for fusion energy

TL;DR

This paper explores the fundamental limits of phase space manipulation in fusion energy using Gromov's non-squeezing theorem, proposing a conjecture about the linear Gromov ground state as a simplified solution.

Contribution

It introduces the concept of Gromov ground states in phase space engineering and conjectures a solvable linear case, highlighting new theoretical constraints in fusion energy.

Findings

Gromov's non-squeezing theorem imposes additional constraints beyond Liouville's theorem.

An example of a forbidden Gardner ground state is provided.

The paper conjectures the solvability of the linear Gromov ground state problem.

Abstract

Phase space engineering by RF waves plays important roles in both thermal D-T fusion and non-thermal advanced fuel fusion. But not all phase space manipulation is allowed, certain fundamental limits exist. In addition to Liouville's theorem, which requires the manipulation to be volume-preserving, Gromov's non-squeezing theorem imposes another constraint. The Gardner ground state is defined as the ground state accessible by smooth volume-preserving maps. However, the extra Gromov constraint should produce a higher-energy ground state. An example of a Gardner ground state forbidden by Gromov's non-squeezing theorem is given. The challenge question is: What is the Gromov ground state, i.e., the lowest energy state accessible by smooth symplectic maps? This is a difficult problem. As a simplification, we conjecture that the linear Gromov ground state problem is solvable.