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

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 $Δ$, we introduce the quantity $θ_{\nabla \times \vec{B},\vec{B}}$ 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.