Some Mathematical Models for ELM Signal

TL;DR

This paper explores various mathematical models for understanding Edge Localized Modes (ELM) in fusion plasmas, acknowledging the complexity and lack of a comprehensive theory, and aims to inspire further insights through mathematical approaches.

Contribution

It introduces several mathematical modeling approaches for ELM and H-mode, serving as conceptual tools rather than definitive theories.

Findings

Models may inspire better understanding of ELM

Mathematical approaches serve as 'toys' for exploration

No definitive theory provided

Abstract

There is no wide accepted theory for ELM (Edge Localized Mode) yet. Some fusion people feel that we may never get a final theory for ELM and H-mode, since which are too complicated (also related to the unsolved turbulence problem) and with at least three time scales. The only way out is using models. (This is analogous to that we believe quantum mechanics can explain chemistry and biology, but no one can calculate DNA structure from Schrodinger equation directly.) This manuscript gives some possible mathematical approaches to it. I should declare that these are just math toys for me yet. They may inspire to good understandings of ELM and H-mode, may not. Useful or useless, I don't know. One need not take too much care of it. Just for fun and enjoying different interesting ideas.