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To investigate how magnetic reconnection (MR) accelerates electrons to a power-law energy spectrum in solar flares, we explore the scaling of a kinetic model proposed by Che & Zank (CZ) and compare it to observations. Focusing on thin current sheet MR particle-in-cell (PIC) simulations, we analyze the impact of domain size on the evolution of the electron Kelvin–Helmholtz instability (EKHI). We find that the duration of the growth stage of the EKHI ($t_G\sim {\mathrm{\Omega }}_e^{-1}$) is short and remains nearly unchanged because the electron gyrofrequency Ω_eis independent of domain size. The quasi-steady stage of the EKHI (t_MR) dominates the electron acceleration process and scales linearly with the size of the simulations asL/v_A0, wherev_A0is the Alfvén speed. We use the analytical results obtained by CZ to calculate the continuous temporal evolution of the electron energy spectra from PIC simulations and linearly scale them to solar flare observational scales. For the first time, an electron acceleration model predicts the sharp two-stage transition observed in typical soft–hard–harder electron energy spectra, implying that the electron acceleration model must be efficient with an acceleration timescale that is a small fraction of the duration of solar flares. Our results suggest that we can use PIC MR simulations to investigate the observational electron energy spectral evolution of solar flares if the ratiot_MR/t_Gis sufficiently small, i.e., ≲10%.

 

Ion beam-driven instabilities in a collisionless space plasma with low β, i.e. low plasma and magnetic pressure ratio, are investigated using particle-in-cell (PIC) simulations. Specifically, the effects of different ion drift velocities on the development of Buneman and resonant electromagnetic (EM) right-handed (RH) ion beam instabilities are studied. Our simulations reveal that both instabilities can be driven when the ion beam drift exceeds the theoretical thresholds. The Buneman instability, which is weakly triggered initially, dissipates only a small fraction of the kinetic energy of the ion beam while causing significant electron heating, owing to the small electron-ion mass ratio. However, we find that the ion beam-driven Buneman instability is quenched effectively by the resonant EM RH ion beam instability. Instead, the resonant EM RH ion beam instability dominates when the ion drift velocity is larger than the Alfvén speed, leading to the generation of RH Alfvén waves and RH whistler waves. We find that the intensity of Alfvén waves decreases with decrease of ion beam drift velocity, while the intensity of whistler waves increases. Our results provide new insights into the complex interplay between ion beams and plasma instabilities in low β collisionless space plasmas.

 

On electron kinetic scales, ions and electrons decouple, and electron velocity shear on electron inertial length ∼de can trigger electromagnetic (EM) electron Kelvin–Helmholtz instability (EKHI). In this paper, we present an analytic study of EM EKHI in an inviscid collisionless plasma with a step-function electron shear flow. We show that in incompressible collisionless plasma, the ideal electron frozen-in condition E+ve×B/c=0 must be broken for the EM EKHI to occur. In a step-function electron shear flow, the ideal electron frozen-in condition is replaced by magnetic flux conservation, i.e., ∇×(E+ve×B/c)=0, resulting in a dispersion relation similar to that of the standard ideal and incompressible magnetohydrodynamics KHI. The magnetic field parallel to the electron streaming suppresses the EM EKHI due to magnetic tension. The threshold for the EM mode of the EKHI is (k·ΔUe)2>ne1+ne2ne1ne2[ne1(vAe1·k)2+ne2(vAe2·k)2], where vAe=B/(4πmene)1/2, ΔUe, and ne are the electron streaming velocity shear and densities, respectively. The growth rate of the EM mode is γem∼Ωce, which is the electron gyro-frequency. 

Small-amplitude fluctuations in the magnetized solar wind are measured typically by a single spacecraft. In the magnetohydrodynamics (MHD) description, fluctuations are typically expressed in terms of the fundamental modes admitted by the system. An important question is how to resolve an observed set of fluctuations, typically plasma moments such as the density, velocity, pressure, and magnetic field fluctuations, into their constituent fundamental MHD modal components. Despite its importance in understanding the basic elements of waves and turbulence in the solar wind, this problem has not yet been fully resolved. Here, we introduce a new method that identifies between wave modes and advected structures such as magnetic islands or entropy modes and computes the phase information associated with the eligible MHD modes. The mode-decomposition method developed here identifies the admissible modes in an MHD plasma from a set of plasma and magnetic field fluctuations measured by a single spacecraft at a specific frequency and an inferred wavenumberk_m. We present data from three typical intervals measured by the Wind and Solar Orbiter spacecraft at ∼1 au and show how the new method identifies both propagating (wave) and nonpropagating (structures) modes, including entropy and magnetic island modes. This allows us to identify and characterize the separate MHD modes in an observed plasma parcel and to derive wavenumber spectra of entropic density, fast and slow magnetosonic, Alfvénic, and magnetic island fluctuations for the first time. These results help identify the fundamental building blocks of turbulence in the magnetized solar wind.