Gromov ground state in phase space engineering for fusion energy

Area of Science:

• Plasma Physics
• Theoretical Physics
• Fusion Energy

Background:

• Radio frequency (RF) waves are crucial for phase space engineering in both thermal Deuterium-Tritium (D-T) fusion and nonthermal advanced fuel fusion.
• Fundamental constraints, including Liouville's theorem (volume preservation) and Gromov's nonsqueezing theorem, limit achievable phase space manipulations.

Purpose of the Study:

• To investigate the implications of Gromov's nonsqueezing theorem on phase space engineering for fusion.
• To define and explore the concept of a "Gromov ground state" beyond the standard Gardner ground state.

Main Methods:

• Analysis of phase space transformations under volume-preserving and symplectic map constraints.
• Identification of a Gardner ground state that is forbidden by Gromov's nonsqueezing theorem.

Main Results:

• Gromov's nonsqueezing theorem imposes stricter constraints than Liouville's theorem, potentially leading to higher-energy ground states.
• A specific example of a Gardner ground state that violates Gromov's theorem is presented.

Conclusions:

• The existence of a "Gromov ground state" (lowest energy state accessible by smooth symplectic maps) is posed as a significant challenge.
• A conjecture is proposed that the linear version of the Gromov ground state problem is solvable, offering a potential simplification.