Through 2D3V PIC simulations of freely decaying sub-ion turbulence, intermittent localized regions with $\mathbf{E} \cdot \mathbf{B} \neq 0$ are found to be statistically associated with reductions in the magnitude of magnetic helicity while evolving in the early electron-scale interaction phase. Motivated by this behavior, 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 our simulations we demonstrate such plateaus to remain approximately invariant even as the usual Saffman helicity integral plateau value $I_H$ 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.
In ideal magnetohydrodynamics (MHD), the total magnetic helicity H V = V dV h, with h = A • B the magnetic helicity density, is gauge-invariant and conserved in a simply connected domain when ∂V is a magnetic, impermeable boundary, or otherwise arranged so boundary terms vanish [1][2][3][4][5]. As a global topological measure of field-line twist, writhe, and linkage [6,7], H V plays a central organizing role in magnetic relaxation and turbulent decay. In high-Lundquist-number plasmas, magnetic helicity often remains comparatively well conserved, provided boundary fluxes are weak [8][9][10][11]. Because resistive dissipation is gradient-weighted and thus acts most strongly at small scales [12], and because helical turbulence tends to transfer magnetic helicity to larger scales [13][14][15][16][17][18], the total magnetic helicity usually decays more slowly than magnetic energy at high Lundquist numbers, making it a natural approximate invariant that constrains the late-time decay of magnetic turbulence [19][20][21][22][23].
For fully helical fields dominated by a single energycontaining scale, L (see, e.g., Eq. 55), conservation of magnetic helicity implies B 2 L ∼ const [16,24,25], with the B (or B rms ) the rms magnetic field. A distinct but common situation arises when the configuration is globally nonhelical in the sense that net magnetic helicity cancels, even though strong local magnetic helicity fluctuations persist. For such configurations, Hosking and Schekochihin [26] proposed a Saffman-type integral built from two-point correlations of magnetic helicity density,
with ⟨•⟩ an ensemble average. Under suitable scale separation, I H (R) can develop an intermediate-range plateau * dionli@psfc.mit.edu that is approximately conserved. Indeed, Zhou et al. [27] confirmed that I H (R) approaches an R-independent asymptote I H for L ≪ R ≪ L sys [see also 28,29], with L sys the system domain size. Under the same scaleseparation/localization assumptions, conservation of I H yields B 4 L 5 ∼ const in 3D [26,[30][31][32].
A key limitation of these helicity-based constraints is that many astrophysical and space plasmas do not remain in the ideal-MHD regime across all dynamically active scales [33][34][35][36][37]. Once the ideal-MHD ordering breaks down, magnetic helicity need not be conserved even in the absence of explicit resistive dissipation, because the magnetic helicity density obeys the general evolution law [3,38]
with φ the electric potential. The source term -2cE • B implies that any localized nonideal region with E • B ̸ = 0 permits magnetic helicity change [39]. This mechanism is particularly relevant at sub-ion scales, where electrons can be strongly non-frozen-in within electron diffusion regions (EDRs) [33,40] and E • B is not controlled by a small resistivity, becoming dynamically significant [41][42][43][44][45][46][47]. Such localized nonideal regions arise naturally in kinetic turbulence. A broad body of kinetic [48][49][50][51] and hybrid-kinetic [52][53][54][55][56] work, together with in-situ spaceplasma evidence [57][58][59][60][61][62], has shown in a wide variety of settings that turbulence rapidly generates intermittent current sheets at ion scales, many of these sheets reconnect, and reconnection commonly coincides with localized dissipation and heating signatures. In sufficiently thin current sheets, reconnection can occur in an “electron-only” mode [33,40], with observational [63][64][65] and numerical [66][67][68][69][70] evidence for electron-only reconnection (EOR) having grown substantially over the last decade. Thus the classical magnetic helicity constraint that organizes MHD decay competes with localized ki-netic nonideality at the very scales where turbulence becomes most intermittent. This competition motivates two closely related questions: i) How does collisionless, reconnection-mediated nonideality modify magnetic helicity at sub-ion scales? ii) If the traditional ideal MHD magnetic helicity constraint is compromised, is there a first-principles kinetic analogue that can still provide a practically useful decay constraint?
In this paper we provide possible answers to both questions in the specific setting of freely decaying 2D3V turbulence at sub-ion scales. In Section II, using magnetic helicity balance and reconnection energetics, we find evidence that during the early kinetic phase the intermittent E • B ̸ = 0 term is statistically associated with structurehandedness proxies and is often accompanied by a reduction in the magnitude of magnetic helicity contained within individual coherent structures. In Section III, we develop a fully kinetic reformulation that can be used to motivate decay constraints. Starting from the Vlasov-Maxwell system and taking velocity moments without closure, we write the canonical vorticity transport [71][72][73][74][75] for each species and obtain a local continuity equation with a kinetic source term. We then absorb the timeintegrated
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