Bowen et al. (Phys. Rev. Lett. 135, 255201, 2025) showed that in a sub-Alfvénic solar-wind stream observed by Parker Solar Probe, quasilinear resonant heating by parallel ion-cyclotron waves cannot supply the turbulent cascade, while stochastic ion heating - perpendicular energization from turbulence-induced breaking of the ion magnetic moment - matches the cascade rate only when the turbulence's intermittency is included. The paper poses a connected set of open questions: whether quasilinear cyclotron-resonant and stochastic heating are limiting behaviors of one underlying process and how intermittency modifies quasilinear predictions; what governs the transition between intervals where ion-cyclotron-wave heating is energetically significant and sub-Alfvénic intervals where it is marginal (radial evolution, plasma beta, or imbalance); how to determine the stochastic diffusion coefficient observationally and which minor-ion velocity-distribution signatures discriminate resonant from non-resonant heating; and how the partition is constrained by the helicity barrier, extended to electrons, and coupled to magnetic reconnection.

Background

The collisionless heating of the solar wind and corona is a decades-old problem: away from the Sun the plasma is nearly collisionless, so the turbulent energy cascade must be converted into particle heat by kinetic processes rather than by particle-particle collisions. The Parker Solar Probe (PSP) mission has sampled the near-Sun solar wind since 2018, including intervals of sub-Alfvénic wind - regions inside the Alfvén surface where the wind flows slower than the Alfvén speed and remains magnetically connected to the corona - providing the first in-situ measurements of the plasma that the corona feeds.

Two broad classes of mechanism preferentially heat ions perpendicular to the magnetic field. The first is quasilinear resonant heating: quasilinear theory (the standard perturbative treatment of wave-particle interaction) applied to cyclotron resonance, in which a particle gyrating in phase with an electromagnetic wave is steadily energized. In the solar wind the relevant waves are left-hand-polarized, nearly parallel-propagating ion-cyclotron waves (ICWs) at ion-kinetic scales. The second is stochastic heating (SH): a non-resonant random walk in energy driven by repeated encounters with turbulent fluctuations at scales comparable to the ion gyroradius, physically understood as breaking of the ion magnetic moment μ\mu (the first adiabatic invariant, μ=miv⊥2/2B\mu = m_i v_\perp^2/2B). Chandran et al. (2010) estimated the SH energy diffusion coefficient of low-β\beta Alfvénic turbulence as

DE=c1 v⊥ δu3 Ωi e−c2/ϵu,D_E = c_1\, v_\perp\, \delta u^3\, \Omega_i\, e^{-c_2/\epsilon_u},

where v⊥v_\perp is the perpendicular ion speed, δu\delta u the turbulent fluctuation amplitude at the particle's gyroradius, Ωi\Omega_i the ion gyrofrequency, ϵu=δu/v⊥\epsilon_u = \delta u/v_\perp the stochasticity parameter, and c1,c2c_1, c_2 constants of order unity (observational studies adopt c1≈0.75c_1 \approx 0.75, c2≈0.34c_2 \approx 0.34 from test-particle simulations, which integrate particle trajectories through prescribed turbulent fields; β\beta is the ratio of plasma pressure to magnetic pressure). The exponential makes SH extremely sensitive to fluctuation amplitude. Later work generalizes SH to a v⊥v_\perp-dependent diffusion of the ion velocity distribution function (VDF; Klein & Chandran 2016; Cerri et al. 2021), and the diffusion coefficient has been determined in simulations - hybrid-kinetic ones treat ions kinetically and electrons as a fluid - (Arzamasskiy et al. 2019; Vasquez et al. 2020), but not, until very recently, from in-situ data.

Bowen et al. (Phys. Rev. Lett. 135, 255201, 2025) analyzed a low-β\beta, highly imbalanced sub-Alfvénic stream observed by PSP. They computed the quasilinear resonant heating rate by the observed parallel ICWs and the SH rate, and compared both with the local energy transfer (LET) rate, a measurable proxy for the turbulent cascade rate. The parallel ICWs are close to marginal stability and produce net cooling, so resonant heating cannot supply the cascade; SH matches the cascade rate, but only if the intermittency of the turbulence - the heavy-tailed distribution of fluctuation amplitudes, such that heating is dominated by rare events with occurrence probability below about 0.1%, a property long correlated with dissipation (Mallet et al. 2019) - is explicitly included. Without intermittency, SH is more than an order of magnitude too small. Since quasilinear theory is canonically derived under non-intermittent, Gaussian-amplitude assumptions, this raises the central theoretical question of whether the two descriptions can be unified once intermittency is retained.

The problem is embedded in the physics of imbalanced Alfvénic turbulence, quantified by the normalized cross helicity σc\sigma_c (the imbalance between counter-propagating Alfvénic fluctuation energies), and in the helicity barrier proposal (Squire et al. 2022): in strongly imbalanced turbulence, conservation of magnetic helicity throttles the cascade to ion scales and triggers high-frequency cyclotron heating. Johnston, Squire & Meyrand (Phys. Rev. Lett. 135, 095201, 2025) argued from test-particle simulations that stochastic and resonant heating are far limits of a continuum controlled by nonlinear resonance broadening, and hence by σc\sigma_c. Bowen et al. note that this and related quasilinear modeling do not include intermittency. Minor ions such as α\alpha-particles (helium nuclei) are sensitive tracers because resonant and stochastic processes predict different minor-ion heating signatures, including distinct scaling with the mass-to-charge ratio Ai/ZiA_i/Z_i.

Problem Statement

From the Discussion of Bowen et al. (Phys. Rev. Lett. 135, 255201, 2025): determine the quantitative relationship between quasilinear cyclotron-resonant heating and stochastic heating in the near-Sun Alfvénic solar wind, and how the partition between them depends on the turbulence regime. The question decomposes into six linked components. The objective itself comprises the first two: whether and how quasilinear cyclotron-resonant and stochastic heating are unified once intermittency is retained (component 1), and what sets the partition between them across turbulence regimes (component 2); a solution resolves the objective when it supplies the intermittency-incorporating account answering these two questions. Components 3-6 - the observational discriminants, the helicity-barrier constraint, the electron extension, and the reconnection interplay - supply the constraints and extensions through which those questions can be sharpened, and a solution may address any of them, but they need not be resolved for the objective to count as resolved.

  1. Unification with intermittency. Establish whether quasilinear cyclotron-resonant heating (including by oblique ion-cyclotron waves) and stochastic heating are limiting behaviors of a common underlying process across turbulence regimes, and how intermittency modifies quasilinear predictions. Existing unified theories (Johnston-Squire-Meyrand test-particle phenomenology; Johnston & Squire quasilinear theory; Mallet et al. coherent-fluctuation theory) do not incorporate intermittency, which the observations show is necessary to reach cascade-level heating rates.

  2. The transition and regime map. Determine what governs the transition between intervals where parallel-ion-cyclotron-wave quasilinear resonant heating is energetically significant (as reported by PSP at larger heliocentric distances, e.g. 15-55 solar radii) and sub-Alfvénic intervals where the waves are near marginality and do not supply the cascade: radial evolution, local plasma beta, imbalance (cross helicity), or other turbulence properties - and whether it supports signatures of preferential heating near the Alfvén surface.

  3. Observational discriminants. Determine the stochastic diffusion coefficient DED_E empirically from in-situ measurements - constraining the coefficients c1,c2c_1, c_2 and the v⊥v_\perp-dependence - and identify signatures in minor-ion (e.g. alpha-particle) velocity distribution functions that discriminate between resonant and non-resonant heating pathways. The direct proton measurement has now been demonstrated for one sub-Alfvénic stream (Ervin et al. 2026); its generalization across regimes and to minor ions remains to be done, and the theoretically predicted minor-ion mass-to-charge signatures await observational test.

  4. Electron extension. Extend the analysis to electrons and to electron-scale intermittent structures, assessing whether analogous stochastic magnetic-moment breaking or current-sheet-associated mechanisms contribute to electron heating.

  5. Reconnection interplay. Determine how reconnection-generated structures and reconnection onset statistics in Alfvénic turbulence modify stochastic heating, given the relative infrequency of reconnection events observed by PSP in the sub-Alfvénic stream, and clarify the relative importance of reconnection heating and Alfvénic-turbulence dissipation for heating the lower corona.

  6. Helicity-barrier constraints. Determine whether a helicity barrier (or other nonlinear constraint on imbalanced turbulence) operates in these streams and how it sets the partition between stochastic and resonant cyclotron processes, including how intermittent effects on quasilinear cyclotron interactions clarify this interplay.

The mandatory components are not independent questions but facets of one quantitative account of how collisionless dissipation of Alfvénic turbulence near the Sun is partitioned between resonant and stochastic mechanisms.

References

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