Ion Stochastic Heating by Wave-induced Field Line Curvature in Space Plasmas

Abstract Finite-amplitude low-frequency Alfvén waves are commonly found in space plasmas and play a crucial role in ion heating. The nonlinear interaction between oblique Alfvén wave spectrum and ions is studied. We find that, as the number of wave modes increases, ions are more likely to exhibit chaotic motion and experience stochastic heating. We extend the effective relative curvature radius ( P eff ) criterion—recently proposed by us for monochromatic waves—to continuous wave spectra and confirm that the chaos threshold ( P eff ≲ 25) remains valid for the breakdown of magnetic moment conservation and the onset of chaos. This criterion is more easily satisfied with increasing wave modes, implying that stochastic heating is nearly ubiquitous in solar wind and coronal Alfvénic turbulence. We identify a three-stage anisotropic heating process: preferential perpendicular heating at early times, quasi-isotropic heating at intermediate times, and preferential parallel heating at late times, which we quantitatively explain using a uniform solid-angle distribution model. We further derive an analytical scaling law for the stochastic heating rate, Q / ( Ω i m i v A 2 ) = H ( α ) v ˜ 3 B ˜ w 3 ω ˜ 1 ω ˜ 1 + Δ ω ˜ , governed by wave amplitude, frequency, bandwidth, propagation angle, and initial ion drift speed in wave reference frame. This heating arises from wave-induced field line curvature, providing a new physical picture for ion kinetic heating in astrophysical plasmas.