arXiv subjects

Daniel Verscharen

Publications and source records attributed to Daniel Verscharen.

At least 73 records · Page 4Linked to original sources

arXiv2021

Power Anisotropy, Dispersion Signature and Turbulence Diffusion Region in the 3D Wavenumber Domain of Space Plasma Turbulence

We explore the multi-faceted important features of turbulence (e.g., anisotropy, dispersion, diffusion) in the three-dimensional (3D) wavenumber domain ($k_\parallel$, $k_{\perp,1}$, $k_{\perp,2}$), by employing the k-filtering technique to the high-quality measurements of fields and particles from the MMS multi-spacecraft constellation. We compute the 3D power spectral densities (PSDs) of magnetic and electric fluctuations (marked as $\rm{PSD}(δ\mathbf{B}(\mathbf{k}))$ and $\rm{PSD}(δ\mathbf{E}'_{\langle\mathbf{v}_\mathrm{i}\rangle}(\mathbf{k}))$), both of which show a prominent spectral anisotropy in the sub-ion range. We give the first 3D image of the bifurcation between power spectra of the electric and magnetic fluctuations, by calculating the ratio between $\rm{PSD}(δ\mathbf{E}'_{ \langle\mathbf{v}_\mathrm{i}\rangle}(\mathbf{k}))$ and $\rm{PSD}(δ\mathbf{B}(\mathbf{k}))$, the distribution of which is related to the non-linear dispersion relation. We also compute the ratio between electric spectra in different reference frames defined by the ion bulk velocity, that is $\mathrm{PSD}(δ{\mathbf{E}'_{\mathrm{local}\ \mathbf{v}_\mathrm{i}}})/\mathrm{PSD}(δ{\mathbf{E}'_{ \langle\mathbf{v}_\mathrm{i}\rangle}})$, to visualize the turbulence ion diffusion region (T-IDR) in wavenumber space. The T-IDR has an anisotropy and a preferential direction of wavevectors, which is generally consistent with the plasma wave theory prediction based on the dominance of kinetic Alfvén waves (KAW). This work manifests the worth of the k-filtering technique in diagnosing turbulence comprehensively, especially when the electric field is involved.

physics.plasm-ph↗

arXiv2021

Three-dimensional magnetic reconnection in particle-in-cell simulations of anisotropic plasma turbulence

We use 3D fully kinetic particle-in-cell simulations to study the occurrence of magnetic reconnection in a simulation of decaying turbulence created by anisotropic counter-propagating low-frequency Alfvén waves consistent with critical-balance theory. We observe the formation of small-scale current-density structures such as current filaments and current sheets as well as the formation of magnetic flux ropes as part of the turbulent cascade. The large magnetic structures present in the simulation domain retain the initial anisotropy while the small-scale structures produced by the turbulent cascade are less anisotropic. To quantify the occurrence of reconnection in our simulation domain, we develop a new set of indicators based on intensity thresholds to identify reconnection events in which both ions and electrons are heated and accelerated in 3D particle-in-cell simulations. According to the application of these indicators, we identify the occurrence of reconnection events in the simulation domain and analyse one of these events in detail. The event is related to the reconnection of two flux ropes, and the associated ion and electron exhausts exhibit a complex three-dimensional structure. We study the profiles of plasma and magnetic-field fluctuations recorded along artificial-spacecraft trajectories passing near and through the reconnection region. Our results suggest the presence of particle heating and acceleration related to small-scale reconnection events within magnetic flux ropes produced by the anisotropic Alfvénic turbulent cascade in the solar wind. These events are related to current structures of order a few ion inertial lengths in size.

physics.space-ph↗

arXiv2020

Design and Optimization of a High-Time-Resolution Magnetic Plasma Analyzer (MPA)

In-situ measurements of space plasma throughout the solar system require high time resolution to understand the plasma's kinetic fine structure and evolution. In this context, research~is conducted to design instruments with the capability to acquire the plasma velocity distribution and its moments with high cadence. We study a new instrument design, using a constant magnetic field generated by two permanent magnets, to analyze solar wind protons and $α$-particles with high time resolution. We determine the optimal configuration of the instrument in terms of aperture size, sensor position, pixel size and magnetic field strength. We conduct this analysis based on analytical calculations and SIMION simulations of the particle trajectories in our instrument. We evaluate the velocity resolution of the instrument as well as Poisson errors associated with finite counting statistics. Our instrument is able to resolve Maxwellian and $κ$-distributions for both protons and $α$-particles. This method retrieves measurements of the moments (density, bulk speed and temperature) with a relative error below 1%. Our instrument design achieves these results with an acquisition time of only 5 ms, significantly faster than state-of-the-art electrostatic analyzers. Although the instrument only acquires one-dimensional cuts of the distribution function in velocity space, the simplicity and reliability of the presented instrument concept are two key advantages of our new design.

physics.ins-det↗

arXiv2020

Possible coexistence of kinetic Alfvén and ion Bernstein modes in sub-ion scale compressive turbulence in the solar wind

We investigate compressive turbulence at sub-ion scales with measurements from the Magnetospheric MultiScale Mission. The tetrahedral configuration and high time resolution density data obtained by calibrating spacecraft potential allow an investigation of the turbulent density fluctuations in the solar wind and their three-dimensional structure in the sub-ion range. The wave-vector associated with the highest energy density at each spacecraft frequency is obtained by application of the Multi-point signal resonator technique to the four-point density data. The fluctuations show a strong wave-vector anisotropy $k_{\perp}\gg k_{\parallel}$ where the parallel and perpendicular symbols are with respect to the mean magnetic field direction. The plasma frame frequencies show two populations, one below the proton cyclotron frequency $ω<Ω_{ci}$ consistent with kinetic Alfvén wave (KAW) turbulence. The second component has higher frequencies $ω> Ω_{ci}$ consistent with ion Bernstein wave (IBW) turbulence. Alternatively, these fluctuations may constitute KAWs that have undergone multiple wave-wave interactions causing a broadening in the plasma frame frequencies. The scale-dependent kurtosis in this wave-vector region shows a reduction in intermittency at the small scales which can also be explained by the presence of wave activity. Our results suggest that small-scale turbulence exhibits linear-wave properties of kinetic Alfvén and possibly ion-Bernstein/magnetosonic waves. Based on our results, we speculate that these waves may play a role in describing the observed reduction in intermittency at sub ion scales.

physics.space-ph↗

arXiv2020

Using dimensionality reduction and clustering techniques to classify space plasma regimes

Collisionless space plasma environments are typically characterised by distinct particle populations. Although moments of their velocity distribution functions help in distinguishing different plasma regimes, the distribution functions themselves provide more comprehensive information about the plasma state, especially at times when the distribution function includes non-thermal effects. Unlike moments, however, distribution functions are not easily characterised by a small number of parameters, making their classification more difficult to achieve. In order to perform this classification, we propose to distinguish between the different plasma regions by applying dimensionality reduction and clustering methods to electron distributions in pitch angle and energy space. We utilise four separate algorithms to achieve our plasma classifications: autoencoders, principal component analysis, mean shift, and agglomerative clustering. We test our classification algorithms by applying our scheme to data from the Cluster-PEACE instrument measured in the Earth's magnetotail. Traditionally, it is thought that the Earth's magnetotail is split into three different regions (the plasma sheet, the plasma sheet boundary layer, and the lobes), that are primarily defined by their plasma characteristics. Starting with the ECLAT database with associated classifications based on the plasma parameters, we identify 8 distinct groups of distributions, that are dependent upon significantly more complex plasma and field dynamics. By comparing the average distributions as well as the plasma and magnetic field parameters for each region, we relate several of the groups to different plasma sheet populations, and the rest we attribute to the plasma sheet boundary layer and the lobes. We find clear distinctions between each of our classified regions and the ECLAT results.

physics.plasm-ph↗

arXiv2020

A Quasi-Linear Diffusion Model for Resonant Wave-Particle Instability in Homogeneous Plasma

In this paper, we develop a model to describe the generalized wave-particle instability in a quasi-neutral plasma. We analyze the quasi-linear diffusion equation for particles by expressing an arbitrary unstable and resonant wave mode as a Gaussian wave packet, allowing for an arbitrary direction of propagation with respect to the background magnetic field. We show that the localized energy density of the Gaussian wave packet determines the velocity-space range in which the dominant wave-particle instability and counter-acting damping contributions are effective. Moreover, we derive a relation describing the diffusive trajectories of resonant particles in velocity space under the action of such an interplay between the wave-particle instability and damping. For the numerical computation of our theoretical model, we develop a mathematical approach based on the Crank-Nicolson scheme to solve the full quasi-linear diffusion equation. Our numerical analysis solves the time evolution of the velocity distribution function under the action of a dominant wave-particle instability and counteracting damping and shows a good agreement with our theoretical description. As an application, we use our model to study the oblique fast-magnetosonic/whistler instability, which is proposed as a scattering mechanism for strahl electrons in the solar wind. In addition, we numerically solve the full Fokker-Planck equation to compute the time evolution of the electron-strahl distribution function under the action of Coulomb collisions with core electrons and protons after the collisionless action of the oblique fast-magnetosonic/whistler instability.

physics.space-ph↗

arXiv2020

Wave Composition, Propagation, and Polarization of MHD Turbulence within 0.3AU as Observed by PSP

Turbulence, a ubiquitous phenomenon in interplanetary space, is crucial for the energy conversion of space plasma at multiple scales. This work focuses on the propagation, polarization and wave composition properties of the solar wind turbulence within 0.3AU, and its variation with heliocentric distances at MHD scales (from 10s to 1000s in the spacecraft frame). We present the probability density function of propagation wavevectors (${\rm{PDF}}(k_\parallel,k_\perp)$) for solar wind turbulence winthin 0.3 AU for the first time: (1) wavevectors cluster quasi-(anti-)parallel to the local background magnetic field for $kd_{\rm i}<0.02$, where $d_{\rm i}$ is the ion inertial length; (2) wavevectors shift to quasi-perpendicular directions for $kd_{\rm i}>0.02$. Based on our wave composition diagnosis, we find that: the outward/anti-sunward Alfvén mode dominates over the whole range of scales and distances, the spectral energy density fraction of the inward/sunward fast mode decreases with distance, and the fractional energy densities of the inward and outward slow mode increase with distance. The outward fast mode and inward Alfvén mode represent minority populations throughout the explored range of distances and scales. On average, the degree of anisotropy of the magnetic fluctuations defined with respect to the minimum variation direction decreases with increasing scale, with no trend in distance at all scales. Our results provide comprehensive insight into the scenario of transport and transfer of the solar wind fluctuations/turbulence in the inner heliosphere.

physics.space-ph↗

arXiv2020

Statistics of Solar Wind Electron Breakpoint Energies Using Machine Learning Techniques

Solar wind electron velocity distributions at 1 au consist of a thermal "core" population and two suprathermal populations: "halo" and "strahl". The core and halo are quasi-isotropic, whereas the strahl typically travels radially outwards along the parallel and/or anti-parallel direction with respect to the interplanetary magnetic field. With Cluster-PEACE data, we analyse energy and pitch angle distributions and use machine learning techniques to provide robust classifications of these solar wind populations. Initially, we use unsupervised algorithms to classify halo and strahl differential energy flux distributions to allow us to calculate relative number densities, which are of the same order as previous results. Subsequently, we apply unsupervised algorithms to phase space density distributions over ten years to study the variation of halo and strahl breakpoint energies with solar wind parameters. In our statistical study, we find both halo and strahl suprathermal breakpoint energies display a significant increase with core temperature, with the halo exhibiting a more positive correlation than the strahl. We conclude low energy strahl electrons are scattering into the core at perpendicular pitch angles. This increases the number of Coulomb collisions and extends the perpendicular core population to higher energies, resulting in a larger difference between halo and strahl breakpoint energies at higher core temperatures. Statistically, the locations of both suprathermal breakpoint energies decrease with increasing solar wind speed. In the case of halo breakpoint energy, we observe two distinct profiles above and below 500 km/s. We relate this to the difference in origin of fast and slow solar wind.

physics.space-ph↗

arXiv2020

Polytropic Behavior of Solar Wind Protons Observed by Parker Solar Probe

A polytropic process describes the transition of a fluid from one state to another through a specific relationship between the fluid density and temperature. The value of the polytropic index that governs this relationship determines the heat transfer and the effective degrees of freedom during the process. In this study, we analyze solar wind proton plasma measurements, obtained by the Faraday cup instrument on-board Parker Solar Probe. We examine the large-scale variations of the proton plasma density and temperature within the inner heliosphere explored by the spacecraft. We also address a polytropic behavior in the density and temperature fluctuations in short-time intervals, which we analyze in order to derive the effective polytropic index of small time-scale processes. The large-scale variations of the solar wind proton density and temperature which are associated with the plasma expansion through the heliosphere, follow a polytropic model with a polytropic index ~5/3. On the other hand, the short time-scale fluctuations which may be associated with turbulence, follow a model with a larger polytropic index. We investigate possible correlations between the polytropic index of short time-scale fluctuations and the plasma speed, plasma beta, and the magnetic field direction. We discuss the scenario of mechanisms including energy transfer or mechanisms that restrict the particle effective degrees of freedom.

physics.space-ph↗

arXiv2020

Magnetic Energy Transfer and Distribution between Protons and Electrons for Alfvénic Waves at Kinetic Scales in Wavenumber Space

Turbulent dissipation is considered a main source of heating and acceleration in cosmological plasmas. The alternating current Joule-like term, $\langleδj \cdot δE\rangle$, is used to measure the energy transfer between electromagnetic (EM) fields and particles. Because the electric field depends on the reference frame, in which frame to calculate $\langleδj\cdot δE\rangle$ is an important issue. We compute the scale-dependent energy transfer rate spectrum in wavevector space, and investigate the electric-field fluctuations in two reference frames: $δE$ in the mean bulk flow frame and $δE'$ in the local bulk flow frame (non-inertial reference frame). Considering Alfvénic waves, we find that $\langleδj\cdotδE^\prime\rangle$, which neglects the contribution of work done by the ion inertial force, is not consistent with the magnetic field energy damping rate ($2γδB^2$) according to linear Maxwell-Vlasov theory, while $\langleδj\cdot δE\rangle$ is exactly the same as $2γδB^2$ in wavenumber space $(k_\parallel, k_\perp)$, where $γ$ is the linear damping rate. Under typical conditions of solar wind at 1 au, we find in our theoretical calculation that the field energy is mainly converted into proton kinetic energy leaving the residual minor portion for electrons. Although the electrons gain energy in the direction perpendicular to the mean magnetic field, they return a significant fraction of their kinetic energy in the parallel direction. Magnetic-field fluctuations can transfer particle energy between the parallel and perpendicular degrees of freedom. Therefore, $\langleδj_\parallel\cdot δE_\parallel\rangle$ and $\langleδj_\perp\cdot δE_\perp\rangle$ cannot solely describe the energy transfer in parallel direction and perpendicular direction, respectively.

physics.space-ph↗

arXiv2020

Dependence of kinetic plasma waves on ion-to-electron mass ratio and light-to-Alfvén speed ratio

The magnetization $|Ω_{\mathrm e}|/ω_{\mathrm{e}}$ is an important parameter in plasma astrophysics, where $Ω_{\mathrm e}$ and $ω_{\mathrm{e}}$ are the electron gyro-frequency and electron plasma frequency, respectively. It only depends on the mass ratio $m_{\mathrm i}/m_{\mathrm e}$ and the light-to-Alfvén speed ratio $c/v_{\mathrm{Ai}}$, where $m_{\mathrm i}$ ($m_{\mathrm e}$) is the ion (electron) mass, $c$ is the speed of light, and $v_{\mathrm{Ai}}$ is the ion Alfvén speed. Nonlinear numerical plasma models such as particle-in-cell simulations must often assume unrealistic values for $m_{\mathrm i}/m_{\mathrm e}$ and for $c/v_{\mathrm{Ai}}$. Because linear theory yields exact results for parametric scalings of wave properties at small amplitudes, we use linear theory to investigate the dispersion relations of Alfvén/ion-cyclotron and fast-magnetosonic/whistler waves as prime examples for collective plasma behaviour depending on $m_{\mathrm i}/m_{\mathrm e}$ and $c/v_{\mathrm{Ai}}$. We analyse their dependence on $m_{\mathrm i}/m_{\mathrm e}$ and $c/v_{\mathrm{Ai}}$ in quasi-parallel and quasi-perpendicular directions of propagation with respect to the background magnetic field for a plasma with $β_j\sim1$, where $β_j$ is the ratio of the thermal to magnetic pressure for species $j$. Although their dispersion relations are largely independent of $c/v_{\mathrm{Ai}}$ for $c/v_{\mathrm{Ai}}\gtrsim 10$, the mass ratio $m_{\mathrm i}/m_{\mathrm e}$ has a strong effect at scales smaller than the ion inertial length. Moreover, we study the impact of relativistic electron effects on the dispersion relations. Based on our results, we recommend aiming for a more realistic value of $m_{\mathrm i}/m_{\mathrm e}$ than for a more realistic value of $c/v_{\mathrm{Ai}}$ in non-relativistic plasma simulations if such a choice is necessary, although $\dots$

physics.space-ph↗

arXiv2020

Evolution of the Earth's Magnetosheath Turbulence: A statistical study based on MMS observations

Composed of shocked solar wind, the Earth's magnetosheath serves as a natural laboratory to study the transition of turbulence from low Alfv{é}n Mach number, $M_\mathrm{A}$, to high $M_\mathrm{A}$. The simultaneous observations of magnetic field and plasma moments with unprecedented high temporal resolution provided by NASA's \textit{Magnetospheric Multiscale} Mission enable us to study the magnetosheath turbulence at both magnetohydrodynamics (MHD) and sub-ion scales. Based on 1841 burst-mode segments of MMS-1 from 2015/09 to 2019/06, comprehensive patterns of the spatial evolution of magnetosheath turbulences are obtained: (1) from the sub-solar region to the flanks, $M_\mathrm{A}$ increases from $<$ 1 to $>$ 5. At MHD scales, the spectral indices of the magnetic-field and velocity spectra present a positive and negative correlation with $M_\mathrm{A}$. However, no obvious correlations between the spectral indices and $M_\mathrm{A}$ are found at sub-ion scales. (2) from the bow shock to the magnetopause, the turbulent sonic Mach number, $M_{\mathrm{turb}}$, generally decreases from $>$ 0.4 to $<$ 0.1. All spectra steepen at MHD scales and flatten at sub-ion scales, representing a positive/negative correlations with $M_\mathrm{turb}$. The break frequency increases by 0.1 Hz when approaching the magnetopause for the magnetic-field and velocity spectra, while it remains at 0.3 Hz for the density spectra. (3) In spite of some differences, similar results are found for the quasi-parallel and quasi-perpendicular magnetosheath. In addition, the spatial evolution of magnetosheath turbulence is found to be independent of the upstream solar wind conditions, e.g., the Z-component of the interplanetary magnetic field and the solar wind speed.

physics.space-ph↗

arXiv2019

The multi-scale nature of the solar wind

The solar wind is a magnetized plasma and as such exhibits collective plasma behavior associated with its characteristic spatial and temporal scales. The characteristic length scales include the size of the heliosphere, the collisional mean free paths of all species, their inertial lengths, their gyration radii, and their Debye lengths. The characteristic timescales include the expansion time, the collision times, and the periods associated with gyration, waves, and oscillations. We review the past and present research into the multi-scale nature of the solar wind based on in-situ spacecraft measurements and plasma theory. We emphasize that couplings of processes across scales are important for the global dynamics and thermodynamics of the solar wind. We describe methods to measure in-situ properties of particles and fields. We then discuss the role of expansion effects, non-equilibrium distribution functions, collisions, waves, turbulence, and kinetic microinstabilities for the multi-scale plasma evolution.

physics.space-ph↗

arXiv2019

Self-induced Scattering of Strahl Electrons in the Solar Wind

We investigate the scattering of strahl electrons by microinstabilities as a mechanism for creating the electron halo in the solar wind. We develop a mathematical framework for the description of electron-driven microinstabilities and discuss the associated physical mechanisms. We find that an instability of the oblique fast-magnetosonic/whistler (FM/W) mode is the best candidate for a microinstability that scatters strahl electrons into the halo. We derive approximate analytic expressions for the FM/W instability threshold in two different $β_{\mathrm c}$ regimes, where $β_{\mathrm c}$ is the ratio of the core electrons' thermal pressure to the magnetic pressure, and confirm the accuracy of these thresholds through comparison with numerical solutions to the hot-plasma dispersion relation. We find that the strahl-driven oblique FM/W instability creates copious FM/W waves under low-$β_{\mathrm c}$ conditions when $U_{0\mathrm s}\gtrsim 3w_{\mathrm c}$, where $U_{0\mathrm s}$ is the strahl speed and $w_{\mathrm c}$ is the thermal speed of the core electrons. These waves have a frequency of about half the local electron gyrofrequency. We also derive an analytic expression for the oblique FM/W instability for $β_{\mathrm c}\sim 1$. The comparison of our theoretical results with data from the \emph{Wind} spacecraft confirms the relevance of the oblique FM/W instability for the solar wind. The whistler heat-flux, ion-acoustic heat-flux, kinetic-Alfvén-wave heat-flux, and electrostatic electron-beam instabilities cannot fulfill the requirements for self-induced scattering of strahl electrons into the halo. We make predictions for the electron strahl close to the Sun, which will be tested by measurements from \emph{Parker Solar Probe} and \emph{Solar Orbiter}.

physics.space-ph↗

arXiv2019

The Impact of Turbulent Solar Wind Fluctuations on Solar Orbiter Plasma Proton Measurements

Solar Orbiter will observe the Sun and the inner heliosphere to study the connections between solar activity, coronal structure, and the origin of the solar wind. The plasma instruments on board Solar Orbiter will determine the three-dimensional velocity distribution functions of the plasma ions and electrons with high time resolution. The analysis of these distributions will determine the plasma bulk parameters, such as density, velocity, and temperature. This paper examines the effects of short-time-scale plasma variations on particle measurements and the estimated bulk parameters of the plasma. For the purpose of this study, we simulate the expected observations of solar wind protons, taking into account the performance of the Proton-Alpha Sensor (PAS) on board Solar Orbiter. We particularly examine the effects of Alfvénic and slow-mode-like fluctuations, commonly observed in the solar wind on timescales of milliseconds to hours, on the observations. We do this by constructing distribution functions from modeled observations and calculate their statistical moments in order to derive plasma bulk parameters. The comparison between the derived parameters with the known input allows us to estimate the expected accuracy of Solar Orbiter proton measurements in the solar wind under typical conditions. We find that the plasma fluctuations due to these turbulence effects have only minor effects on future SWA-PAS observations

physics.space-ph↗

arXiv2019

Parallel-propagating Fluctuations at Proton-kinetic Scales in the Solar Wind are Dominated by Kinetic Instabilities

We use magnetic helicity to characterise solar wind fluctuations at proton-kinetic scales from Wind observations. For the first time, we separate the contributions to helicity from fluctuations propagating at angles quasi-parallel and oblique to the local mean magnetic field, $\mathbf{B}_0$. We find that the helicity of quasi-parallel fluctuations is consistent with Alfvén-ion cyclotron and fast magnetosonic-whistler modes driven by proton temperature anisotropy instabilities and the presence of a relative drift between $α$-particles and protons. We also find that the helicity of oblique fluctuations has little dependence on proton temperature anisotropy and is consistent with fluctuations from the anisotropic turbulent cascade. Our results show that parallel-propagating fluctuations at proton-kinetic scales in the solar wind are dominated by proton temperature anisotropy instabilities and not the turbulent cascade. We also provide evidence that the behaviour of fluctuations at these scales is independent of the origin and macroscopic properties of the solar wind.

physics.space-ph↗

arXiv2019

A Case for Electron-Astrophysics

A grand-challenge problem at the forefront of physics is to understand how energy is transported and transformed in plasmas. This fundamental research priority encapsulates the conversion of plasma-flow and electromagnetic energies into particle energy, either as heat or some other form of energisation. The smallest characteristic scales, at which electron dynamics determines the plasma behaviour, are the next frontier in space and astrophysical plasma research. The analysis of astrophysical processes at these scales lies at the heart of the field of electron-astrophysics. Electron scales are the ultimate bottleneck for dissipation of plasma turbulence, which is a fundamental process not understood in the electron-kinetic regime. Since electrons are the most numerous and most mobile plasma species in fully ionised plasmas and are strongly guided by the magnetic field, their thermal properties couple very efficiently to global plasma dynamics and thermodynamics.

physics.space-ph↗

arXiv2019

Stochastic Ion Acceleration by the Ion-cyclotron Instability in a Growing Magnetic Field

Using 1D and 2D particle-in-cell (PIC) simulations of a plasma with a growing magnetic field $\vec{B}$, we show that ions can be stochastically accelerated by the ion-cyclotron (IC) instability. As $\vec{B}$ grows, an ion pressure anisotropy $p_{\perp,i} > p_{||,i}$ arises, due to the adiabatic invariance of the ion magnetic moment ($p_{||,i}$ and $p_{\perp,i}$ are the ion pressures parallel and perpendicular to $\vec{B}$). When initially $β_i = 0.5$ ($β_i \equiv 8πp_i/|\vec{B}|^2$, where $p_i$ is the ion isotropic pressure), the pressure anisotropy is limited mainly by inelastic pitch-angle scattering provided by the IC instability, which in turn produces a non-thermal tail in the ion energy spectrum. After $\vec{B}$ is amplified by a factor $\sim 2.7$, this tail can be approximated as a power-law of index $\sim 3.4$ plus two non-thermal bumps, and accounts for $2-3\%$ of the ions and $\sim 18\%$ of their kinetic energy. On the contrary, when initially $β_i =2$, the ion scattering is dominated by the mirror instability and the acceleration is suppressed. This implies that efficient ion acceleration requires that initially $β_i \lesssim 1$. Although we focus on cases where $\vec{B}$ is amplified by plasma shear, we check that the acceleration occurs similarly if $\vec{B}$ grows due to plasma compression. Our results are valid in a sub-relativistic regime where the ion thermal energy is $\sim 10\%$ of the ion rest mass energy. This acceleration process can thus be relevant in the inner region of low-luminosity accretion flows around black holes.

astro-ph.HE↗