A Selection Principle for Weak KAM Solutions via Freidlin–Wentzell Large Deviation Principle of Invariant Measures

Gao, Yuan; Liu, Jian-Guo

doi:10.1137/22M1519717

Abstract This article is devoted to the memory of Yuri P Raizer, who passed away in 2021. He left a noticeable trace in gas discharge physics. The principle of minimal power (the state that requires minimal power is most probable) is thoroughly used in his books. Although the fundamental laws of physics do not imply this ad hoc principle, a detailed analysis of underlying phenomena can often reveal why nature prefers this path. Raizer illustrated this principle for plasma stratification, formation of electrode spots, discharge constriction, the shape of an arc channel, etc. We argue that the nonlinearity of equations describing gas discharges can often justify the realization of a plasma state maintained at minimal electric power. This nonlinearity appears because small groups of energetic electrons often control the ionization processes. The number of these electrons depends strongly on the ratio of the electric field to gas density, E / N . Under certain conditions, the ionization rate can also depend nonlinearly on electron density due to stepwise ionization and Coulomb collisions. We use the principle of minimal power to illustrate some of Raizer’s contributions to gas discharge physics from a single point of view. We demonstrate that nonlinearity of ionization processes in gas discharges can substantiate this principle for plasma stratification. However, striations of s , p , and r types in neon could exist with minimal or no ionization enhancement. This reminds us of Raizer’s warning that applying the minimal power principle could lead to erroneous predictions, and a proper theory is required in each case to justify its use. ‘The phenomenon of striations satisfies the principle of minimal power’ – Yuri Raizer

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