Kinetic Route to Helicity-Constrained Decay

Abstract

Through 2D3V PIC simulations of freely decaying sub-ion turbulence, intermittent localized regions with $\mathbf{E} \cdot \mathbf{B} \neq 0$ are found, in the early electron-scale interaction phase, to be statistically associated with decreases in $|H_{V_s}|$, the fixed-gauge structure-integrated magnetic-helicity diagnostic. This structure-level behavior coincides with a decline of the Saffman helicity-variance plateau value $I_H$. Motivated by these observations, we propose a source-compensated, history-dependent helicity density that satisfies an exact local balance identity by construction, enabling Saffman-type two-point correlation integrals which, under standard flux-decorrelation assumptions, can exhibit intermediate-scale plateaus that are roughly time-independent. In the simulations, such plateaus are observed to remain approximately invariant over the measured kinetic interval even as $I_H$ evolves during the early kinetic stage. Under approximate single-scale self-similarity, the plateau behavior of the magnetic integral is consistent with the 2D decay constraint $BL \sim \text{const}$. For initially net-helical configurations, we observe rapid development of mixed-signed magnetic-helicity patches and a decrease of the global fractional helicity, such that the decay over the kinetic interval is again most consistent with the cancellation-dominated scaling constraint.