Abstract
Stochastic heating refers to an increase in the average magnetic moment of charged particles interacting with electromagnetic fluctuations whose frequencies are much smaller than the particles' cyclotron frequencies. This type of heating arises when the amplitude of the gyroscale fluctuations exceeds a certain threshold, causing particle orbits in the plane perpendicular to the magnetic field to become stochastic rather than nearly periodic. We consider the stochastic heating of protons by Alfvén-wave (AW) and kinetic-Alfvén-wave (KAW) turbulence, which may make an important contribution to the heating of the solar wind. Using phenomenological arguments, we derive the stochastic-proton-heating rate in plasmas in which β p ∼ 1 - 30, where β p is the ratio of the proton pressure to the magnetic pressure. (We do not consider the β p ≳ 30 regime, in which KAWs at the proton gyroscale become non-propagating.) We test our formula for the stochastic-heating rate by numerically tracking test-particle protons interacting with a spectrum of randomly phased AWs and KAWs. Previous studies have demonstrated that at β p ≲1, particles are energized primarily by time variations in the electrostatic potential and thermal-proton gyro-orbits are stochasticized primarily by gyroscale fluctuations in the electrostatic potential. In contrast, at β p ≳ 1, particles are energized primarily by the solenoidal component of the electric field and thermal-proton gyro-orbits are stochasticized primarily by gyroscale fluctuations in the magnetic field.
Highlights
In the mid-twentieth century several authors published hydrodynamic models of the solar wind that imposed a fixed temperature at the coronal base and took thermalDownloaded from https://www.cambridge.org/core
Summary In this paper we use phenomenological arguments to derive an analytic formula for the rate at which thermal protons are stochastically heated by Alfvén waves (AWs)/KAW turbulence at Downloaded from https://www.cambridge.org/core
At βp ∼ 1 − 30, the motion of a proton’s effective guiding centre is dominated by the interaction between the proton and gyroscale fluctuations in the magnetic field, whose amplitude is denoted δBρ
Summary
Perpendicular ion heating is the dominant form of heating in the near-Sun solar wind (Esser et al 1999; Marsch 2006; Cranmer et al 2009; Hellinger et al 2013) This discrepancy suggests that AW/KAW turbulence in the solar wind dissipates via some nonlinear mechanism Dmitruk, Matthaeus & Seenu 2004; Markovskii et al 2006; Lehe, Parrish & Quataert 2009; Schekochihin et al 2009; Chandran et al 2010; Servidio et al 2011; Lynn et al 2012; Xia et al 2013; Kawazura, Barnes & Schekochihin 2018) This suggestion is supported by studies that find a correlation between ion temperatures and fluctuation amplitudes in solar-wind measurements and numerical simulations (e.g. Wu et al 2013; Grošelj et al 2017; Hughes et al 2017; Vech, Klein & Kasper 2018).
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