Conditions for plasma evolution to the\ strong general Woltjer-Taylor state

TL;DR

This paper corrects previous proofs and establishes conditions under which plasma evolves exponentially towards a strong Woltjer-Taylor state, emphasizing the role of Joule heating and introducing new measures for state assessment.

Contribution

It provides a rigorous proof of plasma evolution to the Woltjer-Taylor state and introduces new criteria for reaching the strong/general state.

Findings

Plasma exponentially evolves to the Woltjer-Taylor state due to Joule heat.

Zero Woltjer-Taylor states are physically unfeasible.

New quantities $ heta_{ abla imes oldsymbol{B},oldsymbol{B}}$ and $R$ are proposed to evaluate state evolution.

Abstract

We find that the proof in the recent paper$\textsuperscript{\cite{14}}$ can not justify the authors' conclusion. We provide a real proof that any state will eventually evolves to the Woltjer-Taylor state exponentially. However, this kind of evolution is is mainly due to Joule heat, which also makes the magnetic field vanishes exponentially. Zero Woltjer-Taylor states are not physically attractive. Instead of examine $\Delta$, we introduce the quantity $\theta_{\nabla \times \vec{B},\vec{B}}$ and $R$ to examine if the plasma reaches to the strong (general) Woltjer-Taylor state, and then derive the condition for the evolution to the strong/general Woltjer-Taylor state.