On the generation of magnetic helicity by the Kelvin-Helmholtz instability in 2.5D incompressible MHD

We present an exact analytical theory demonstrating that the linear, ideal, incompressible Kelvin-Helmholtz instability (KHI) in a 2.5-dimensional magnetized plasma intrinsically generates a gauge-invariant regional relative magnetic helicity flux. The mechanism arises from the non-self-adjoint, non-normal nature of the MHD KHI operator, which produces a complex phase asymmetry in the eigenfunctions across the shear layer. This phase asymmetry drives a non-zero time-averaged helicity flux through the boundaries of any subvolume enclosing the shear layer, redistributing magnetic helicity within the closed system. We derive a closed-form analytical expression for the helicity injection rate. We apply our theory to solar coronal jets, where the KHI is frequently observed at the interface between the jet and the ambient plasma. For typical jet parameters—\(B_{0}\approx 10\) G, a shear-flow Alfvén Mach number \(M_{A}\approx 1.36\), a layer half-width \(a\approx 100\text{ km}\), and a perturbation wavelength \(\lambda \approx 10^{4}\text{ km}\)—the linear KHI injects helicity at a rate of \(\sim 10^{14}\) Wb² s⁻¹ into the jet boundary region. Over an e-folding time of 8 seconds, the accumulated helicity is comparable to the observed twist in active-region jets, suggesting that the KHI alone can provide the magnetic helicity needed for the helical structure and stability of coronal jets.