Unified understanding of relation between m-point singular solutions in Euler equation in a point-vortex system and vortex crystals composed of electron plasma strings

2015 Fiscal Year Final Research Report

• Project/Area Number: 26800202
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Kanazawa University
• Principal Investigator: Soga Yukihiro 金沢大学, 数物科学系, 助教 (90525148)
• Research Collaborator: YATSUYANAGI Yuichi 静岡大学, 教育学部, 准教授 ; OHTSUKA Hiroshi 金沢大学, 理工研究域数物科学系, 教授
• Project Period (FY): 2014-04-01 – 2016-03-31
• Keywords: 非中性プラズマ / オイラー方程式

Outline of Final Research Achievements

The final goal of this research is to reveal a physical mechanisms of a vortex crystal observed in non-neutral plasmas in terms of statistical physics. Before proceeding with the vortex crystal experiments, phase space trajectories of two discrete electron vortex strings have been observed in order to confirm a equivalence between electron vortices and 2D Euler fluid. In a result, the deterioration of the equivalence was observed due to non-ideal electric field at both ends of the trap. This non-ideal effects could be suppressed by applying a stepwise potential at the boundary.
In mathematics it is well known that m-point singular solution exists to 2D Euler equation for point-vortex system in an annulus boundary. Unstable equilibrium solutions of few electron vortex strings have been observed by calculating the potential distribution in the annulus boundary. We speculate that these solutions correspond to the m-point singular solution of mathematics.

Free Research Field

プラズマ物理