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Register a new userThree dimensional particle-in-cell simulation of particle acceleration by circularly polarised inertial Alfven waves in a transversely inhomogeneous plasma
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D. Tsiklauri
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The process of particle acceleration by left-hand, circularly polarised inertial Alfven waves (IAW) in a transversely inhomogeneous plasma is studied using 3D particle-in-cell simulation. A cylindrical tube with, transverse to the background magnetic field, inhomogeneity scale of the order of ion inertial length is considered on which IAWs with frequency $0.3 omega_{ci}$ are launched that are allowed to develop three wavelength. As a result time-varying parallel electric fields are generated in the density gradient regions which accelerate electrons in the parallel to magnetic field direction. Driven perpendicular electric field of IAWs also heats ions in the transverse direction. Such numerical setup is relevant for solar flaring loops and earth auroral zone. This first, 3D, fully-kinetic simulation demonstrates electron acceleration efficiency in the density inhomogeneity regions, along the magnetic field, of the order of 45% and ion heating, in the transverse to the magnetic field direction, of 75%. The latter is a factor of two times higher than the previous 2.5D analogous study and is in accordance with solar flare particle acceleration observations. We find that the generated parallel electric field is localised in the density inhomogeneity region and rotates in the same direction and with the same angular frequency as the initially launched IAW. Our numerical simulations seem also to suggest that the knee often found in the solar flare electron spectra can alternatively be interpreted as the Landau damping (Cerenkov resonance effect) of IAWs due to the wave-particle interactions.
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Dispersive Alfven waves (DAWs) offer, an alternative to magnetic reconnection, opportunity to accelerate solar flare particles. We study the effect of DAW polarisation, L-, R-, circular and elliptical, in different regimes inertial and kinetic on the efficiency of particle acceleration. We use 2.5D PIC simulations to study how particles are accelerated when DAW, triggered by a solar flare, propagates in transversely inhomogeneous plasma that mimics solar coronal loop. (i) In inertial regime, fraction of accelerated electrons (along the magnetic field), in density gradient regions is ~20% by the time when DAW develops 3 wavelengths and is increasing to ~30% by the time DAW develops 13 wavelengths. In all considered cases ions are heated in transverse to the magnetic field direction and fraction of the heated particles is ~35%. (ii) The case of R-circular, L- and R- elliptical polarisation DAWs, with the electric field in the non-ignorable transverse direction exceeding several times that of in the ignorable direction, produce more pronounced parallel electron beams and transverse ion beams in the ignorable direction. In the inertial regime such polarisations yield the fraction of accelerated electrons ~20%. In the kinetic regime this increases to ~35%. (iii) The parallel electric field that is generated in the density inhomogeneity regions is independent of m_i/m_e and exceeds the Dreicer value by 8 orders of magnitude. (iv) Electron beam velocity has the phase velocity of the DAW. Thus electron acceleration is via Landau damping of DAWs. For the Alfven speeds of 0.3c the considered mechanism can accelerate electrons to energies circa 20 keV. (v) The increase of mass ratio from m_i/m_e=16 to 73.44 increases the fraction of accelerated electrons from 20% to 30-35% (depending on DAW polarisation). For the mass ratio m_i/m_e=1836 the fraction of accelerated electrons would be >35%.
A possible solution to the unexplained high intensity hard x-ray (HXR) emission observable during solar flares was investigated via 3D fully relativistic, electromagnetic particle-in-cell (PIC) simulations with realistic ion to electron mass ratio. A beam of accelerated electrons was injected into a magnetised, Maxwellian, homogeneous and inhomogeneous background plasma. The electron distribution function was unstable to the beam-plasma instability and was shown to generate Langmuir waves, while relaxing to plateau formation. In order to estimate the role of the background density gradient on an unbound (infinite spatial extent) beam, three different scenarios were investigated: a) a uniform density background; b) a weak density gradient, n_R/n_L=3; c) a strong gradient case, n_R/n_L=10, where n_R and n_L denote background electron densities on the left and right edges of the simulation box respectively. The strong gradient case produced the largest fraction of electrons beyond 15 v_th. Further, two cases (uniform and strong gradient background) with spatially localized beam injections were performed aiming to show drifts of the generated Langmuir wave wavenumbers, as suggested in previous studies. For the strong gradient case, the Langmuir wave power is shown to drift to smaller wavenumbers, as found in previous quasi-linear simulations.
In the previous works harmonic, phase-mixed, Alfven wave dynamics was considered both in the kinetic and magnetohydrodynamic regimes. Up today only magnetohydrodynamic, phase-mixed, Gaussian Alfven pulses were investigated. In the present work we extend this into kinetic regime. Here phase-mixed, Gaussian Alfven pulses are studied, which are more appropriate for solar flares, than harmonic waves, as the flares are impulsive in nature. Collisionless, phase-mixed, dispersive, Gaussian Alfven pulse in transversely inhomogeneous plasma is investigated by particle-in-cell (PIC) simulations and by an analytical model. The pulse is in inertial regime with plasma beta less than electron-to-ion mass ratio and has a spatial width of 12 ion inertial length. The linear analytical model predicts that the pulse amplitude decrease is described by the linear Korteweg de Vries (KdV) equation. The numerical and analytical solution of the linear KdV equation produces the pulse amplitude decrease in time as $t^{-1}$. The latter scaling law is corroborated by full PIC simulations. It is shown that the pulse amplitude decrease is due to dispersive effects, while electron acceleration is due to Landau damping of the phase-mixed waves. The established amplitude decrease in time as $t^{-1}$ is different from the MHD scaling of $t^{-3/2}$. This can be attributed to the dispersive effects resulting in the different scaling compared to MHD, where the resistive effects cause the damping, in turn, enhanced by the inhomogeneity. Reducing background plasma temperature and increase in ion mass yields more efficient particle acceleration.
We herein investigate shock formation and particle acceleration processes for both protons and electrons in a quasi-parallel high-Mach-number collisionless shock through a long-term, large-scale particle-in-cell simulation. We show that both protons and electrons are accelerated in the shock and that these accelerated particles generate large-amplitude Alfv{e}nic waves in the upstream region of the shock. After the upstream waves have grown sufficiently, the local structure of the collisionless shock becomes substantially similar to that of a quasi-perpendicular shock due to the large transverse magnetic field of the waves. A fraction of protons are accelerated in the shock with a power-law-like energy distribution. The rate of proton injection to the acceleration process is approximately constant, and in the injection process, the phase-trapping mechanism for the protons by the upstream waves can play an important role. The dominant acceleration process is a Fermi-like process through repeated shock crossings of the protons. This process is a `fast process in the sense that the time required for most of the accelerated protons to complete one cycle of the acceleration process is much shorter than the diffusion time. A fraction of the electrons is also accelerated by the same mechanism, and have a power-law-like energy distribution. However, the injection does not enter a steady state during the simulation, which may be related to the intermittent activity of the upstream waves. Upstream of the shock, a fraction of the electrons is pre-accelerated before reaching the shock, which may contribute to steady electron injection at a later time.
Previous studies [Malara et al ApJ, 533, 523 (2000)] considered small-amplitude Alfven wave (AW) packets in Arnold-Beltrami-Childress (ABC) magnetic field using WKB approximation. In this work linearly polarised Alfven wave dynamics in ABC magnetic field via direct 3D MHD numerical simulation is studied for the first time. Gaussian AW pulse with length-scale much shorter than ABC domain length and harmonic AW with wavelength equal to ABC domain length are studied for four different resistivities. While it is found that AWs dissipate quickly in the ABC field, surprisingly, AW perturbation energy increases in time. In the case of the harmonic AW perturbation energy growth is transient in time, attaining peaks in both velocity and magnetic perturbation energies within timescales much smaller than resistive time. In the case of the Gaussian AW pulse velocity perturbation energy growth is still transient in time, attaining a peak within few resistive times, while magnetic perturbation energy continues to grow. It is also shown that the total magnetic energy decreases in time and this is governed by the resistive evolution of the background ABC magnetic field rather than AW damping. On contrary, when background magnetic field is uniform, the total magnetic energy decrease is prescribed by AW damping, because there is no resistive evolution of the background. By considering runs with different amplitudes and by analysing perturbation spectra, possible dynamo action by AW perturbation-induced peristaltic flow and inverse cascade of magnetic energy have been excluded. Therefore, the perturbation energy growth is attributed to a new instability. The growth rate appears to be dependent on the value of the resistivity and spatial scale of the AW disturbance. Thus, when going beyond WKB approximation, AW damping, described by full MHD equations, does not guarantee decrease of perturbation energy.
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