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Direct Measurement of Diffusion Coefficients: Evidence for Diffusive Stochastic Heating in Collisionless Plasmas

Open questions in collisionless plasma dissipation can be addressed using space-based observations in different astrophysical environments, with implications for both astrophysical and laboratory plasma systems. We study a low-𝛽, highly imbalanced, sub-Alfvénic stream observed by Parker Solar Probe (PSP) to identify and distinguish between signatures of stochastic heating (SH) and resonant heating (RH) by parallel ion cyclotron waves (∥-ICWs). Prior work studying this stream [Trevor A. Bowen et al., Stochastic heating in the sub-Alfvénic solar wind, Phys. Rev. Lett. 135, 255201 (2025)] showed that the SH rate, accounting for intermittency, matched the amplitude of the local energy transfer (LET) rate, while the RH rate did not. This comparison relied on a number of assumptions regarding the nature of the diffusive process and the calculation of the LET rate. We introduce a novel technique of inverting the proton guiding center equation to empirically measure velocity-space diffusion coefficients using three-dimensional proton velocity distribution functions, from the ion electrostatic analyzer (the Solar Probe Analyzer for Ions) on PSP. Measured diffusion coefficients are used to determine phase-space heating rates, leading to a calculation of a fully kinetic heating rate independent of assumptions made in prior work. We show that scale-dependent analytic expressions for SH via noncoherent fluctuations match the empirical measurements from PSP data, provided that we account for intermittency in the heating calculation. In contrast, the derived heating rates for SH that accounts for the effects of the helicity barrier and heating rates for RH via ∥-ICWs do not peak in the same region of velocity space as the empirical measurements, nor do they reach the required magnitude. Our approach provides novel methodology to uniquely identify and constrain heating processes in collisionless plasmas and shows evidence of a Fokker-Planck-like diffusive process in the near-Sun solar wind.

Plasma kinetic theory

Shock waves in collisionless plasmas.

Theoretical models for collisionless plasma shock waves in terms of nonlinear, magnetosonic, constant profile waves, turbulent- and electrostatic-shock structures, etc

Tidman, D. A.

Stationary collector in a collisionless plasma

The effect of a neutral collecting body in a collisionless plasma on the plasma distribution in its immediate neighborhood is discussed. When a magnetic field is present an electron plasma with a neutralizing background charge has empty velocity space regions at points near a collector even though the distribution is Maxwellian far from the collector. For a thin cylinder, the collected collisionless plasma current is a function of the angle between the cylinder axis and the magnetic field with the minimum current collected when the cylinder and field lines are parallel.

Grebowsky, J. M.

Shock waves in collisionless plasmas

Book on shock waves in collisionless plasmas covering basic equations and classification of shock structures, magnetosonic waves, shocks and solitons, electrostatic shocks and solitons, etc

Krall, N. A.

Dielectric and permeability effects in collisionless plasmas

Using the unabridged Maxwell equations (including vectors D, E and H) new effects in collisionless plasmas are uncovered. In a steady state, it is found that spatially varying energy density of the electric field (E perpendicular) orthogonal to B produces electric current leading, under certain conditions, to the relationship P perpendicular + B(2)/8 pi-epsilon E perpendicular(2)/8 pi = constant, where epsilon is the dielectric constant of the plasma for fields orthogonal to B. In steady state quasi-two-dimensional flows in plasmas, a general relationship between the components of electric field parallel and perpendicular to B is found. These effects are significant in geophysical and astrophysical plasmas. The general conditions for a steady state in collisionless plasma are deduced. With time variations in a plasma, slow compared to ion-gyroperiod, there is a general current, (j-asterisk), which includes the well-known polarization current, given by J-asterisk = d/dt (E x M) + (P x B) x B B(-2) where M and P are the magnetization and polarization vectors respectively.

Cole, K. D.

Cyclotron waves in a collisionless plasma

Plasma waves with resonances near electron cyclotron frequency investigated in long collisionless plasma column - wavelength dispersion curves and relations

PLASMA WAVE