Fermi Acceleration Research Articles

Electron acceleration in a coil target-driven low-β magnetic reconnection simulation

Magnetic reconnection driven by a capacitor coil target is an innovative way to investigate low-β magnetic reconnection in the laboratory, where β is the ratio of particle thermal pressure to magnetic pressure. Low-β magnetic reconnection frequently occurs in the Earth’s magnetosphere, where the plasma is characterized by β ≲ 0.01. In this paper, we analyze electron acceleration during magnetic reconnection and its effects on the electron energy spectrum via particle-in-cell simulations informed by parameters obtained from experiments. We note that magnetic reconnection starts when the current sheet is down to about three electron inertial lengths. From a quantitative comparison of the different mechanisms underlying the electron acceleration in low-β reconnection driven by coil targets, we find that the electron acceleration is dominated by the betatron mechanism, whereas the parallel electric field plays a cooling role and Fermi acceleration is negligible. The accelerated electrons produce a hardened power-law spectrum with a high-energy bump. We find that injecting electrons into the current sheet is likely to be essential for further acceleration. In addition, we perform simulations for both a double-coil co-directional magnetic field and a single-coil one to eliminate the possibility of direct acceleration of electrons beyond thermal energies by the coil current. The squeeze between the two coil currents can only accelerate electrons inefficiently before reconnection. The simulation results provide insights to guide future experimental improvements in low-β magnetic reconnection driven by capacitor coil targets.

3D MHD Time-dependent Charge State Ionization and Recombination Modeling of the Bastille Day Coronal Mass Ejection

Heavy ion signatures of coronal mass ejections (CMEs) indicate that rapid and strong heating takes place during the eruption and early stages of propagation. However, the nature of the heating that produces the highly ionized charge states often observed in situ is not fully constrained. An MHD simulation of the Bastille Day CME serves as a test bed to examine the origin and conditions of the formation of heavy ions evolving within the CME in connection with those observed during its passage at L1. In particular, we investigate the bimodal nature of the Fe charge state distribution, which is a quintessential heavy ion signature of CME substructure, as well as the source of the highly ionized plasma. We find that the main heating experienced by the tracked plasma structures linked to the ion signatures examined is due to field-aligned thermal conduction via shocked plasma at the CME front. Moreover, the bimodal Fe distributions can be generated through significant heating and rapid cooling of prominence material. However, although significant heating was achieved, the highest ionization stages of Fe ions observed in situ were not reproduced. In addition, the carbon and oxygen charge state distributions were not well replicated owing to anomalous heavy ion dropouts observed throughout the ejecta. Overall, the results indicate that additional ionization is needed to match observation. An important driver of ionization could come from suprathermal electrons, such as those produced via Fermi acceleration during reconnection, suggesting that the process is critical to the development and extended heating of extreme CME eruptions, like the Bastille Day CME.

Cosmic-Ray Drag and Damping of Compressive Turbulence

While it is well known that cosmic rays (CRs) can gain energy from turbulence via second-order Fermi acceleration, how this energy transfer affects the turbulent cascade remains largely unexplored. Here, we show that damping and steepening of the compressive turbulent power spectrum are expected once the damping time becomes comparable to the turbulent cascade time. Magnetohydrodynamic simulations of stirred compressive turbulence in a gas-CR fluid with diffusive CR transport show clear imprints of CR-induced damping, saturating at , where is the turbulent energy input rate. In that case, almost all of the energy in large-scale motions is absorbed by CRs and does not cascade down to grid scale. Through a Hodge–Helmholtz decomposition, we confirm that purely compressive forcing can generate significant solenoidal motions, and we find preferential CR damping of the compressive component in simulations with diffusion and streaming, rendering small-scale turbulence largely solenoidal, with implications for thermal instability and proposed resonant scattering of E ≳ 300 GeV CRs by fast modes. When CR transport is streaming dominated, CRs also damp large-scale motions, with kinetic energy reduced by up to 1 order of magnitude in realistic E CR ∼ E g scenarios, but turbulence (with a reduced amplitude) still cascades down to small scales with the same power spectrum. Such large-scale damping implies that turbulent velocities obtained from the observed velocity dispersion may significantly underestimate turbulent forcing rates, i.e., .

Long-term X-Ray Outburst in the TeV-detected Blazar Mrk 501 in 2021–2022: Further Clues for the Emission and Unstable Processes

This paper presents the results of a detailed X-ray timing and spectral analysis of Mrk 501, which are based mainly on the Swift data obtained during 2021 February–2022 December. The source showed strongly enhanced X-ray activity, characterized by a long-term increase in the baseline 0.3–10 keV flux level superimposed by shorter-term flares on timescales of a few weeks to about 2 months. During some time intervals, Mrk 501 was the brightest blazar in the X-ray sky and, moreover, showed an intense intraday variability, which was sometimes detected within the exposures lasting a few hundred seconds. These instances were characterized by fractional variability amplitudes of 4%–18% and were mostly observed during short-term X-ray flares. The source exhibited extreme spectral properties with dominance of the spectral curvature, frequent occurrence of hard photon indices in the 0.3–10 keV and 0.3–300 GeV bands, and the peak of a synchrotron spectral energy distribution in the hard X-ray range. These properties demonstrate the importance of relativistic magnetic reconnection, first-order Fermi mechanism within the magnetic field of different confinement efficiencies, stochastic acceleration, and hadronic processes. The X-ray and γ-ray fluxes showed a log-normal distribution, which hints at the imprint of accretion disk instabilities on the blazar jet, as well as the possible presence of hadronic cascades and random fluctuations in the particle acceleration rate. The optical–UV and γ-ray variabilities showed a weak or absent correlation with the X-ray flaring activity, which is not consistent with simple leptonic models and requires more complex particle acceleration, emission, and variability scenarios.

Electron Acceleration and Heating during Magnetic Reconnection in the Earth's Quasi-parallel Bow Shock

We perform a 2.5-dimensional particle-in-cell simulation of a quasi-parallel shock, using parameters for the Earth’s bow shock, to examine electron acceleration and heating due to magnetic reconnection. The shock transition region evolves from the ion-coupled reconnection dominant stage to the electron-only reconnection dominant stage, as time elapses. The electron temperature enhances locally in each reconnection site, and ion-scale magnetic islands generated by ion-coupled reconnection show the most significant enhancement of the electron temperature. The electron energy spectrum shows a power law, with a power-law index around 6. We perform electron trajectory tracing to understand how they are energized. Some electrons interact with multiple electron-only reconnection sties, and Fermi acceleration occurs during multiple reflections. Electrons trapped in ion-scale magnetic islands can be accelerated in another mechanism. Islands move in the shock transition region, and electrons can obtain larger energy from the in-plane electric field than the electric potential in those islands. These newly found energization mechanisms in magnetic islands in the shock can accelerate electrons to energies larger than the achievable energies by the conventional energization due to the parallel electric field and shock drift acceleration. This study based on the selected particle analysis indicates that the maximum energy in the nonthermal electrons is achieved through acceleration in ion-scale islands, and electron-only reconnection accounts for no more than half of the maximum energy, as the lifetime of sub-ion-scale islands produced by electron-only reconnection is several times shorter than that of ion-scale islands.

Evidence of Electron Acceleration via Nonlinear Resonant Interactions with Whistler-mode Waves at Foreshock Transients

Shock waves are sites of intense plasma heating and charged particle acceleration. In collisionless solar wind plasmas, such acceleration is attributed to shock drift or Fermi acceleration but also to wave–particle resonant interactions. We examine the latter for the case of electrons interacting with one of the most commonly observed wave modes in shock environments, the whistler mode. Such waves are particularly intense in dynamic, localized regions upstream of shocks, arising from the kinetic interaction of the shock with solar wind discontinuities. These regions, known as foreshock transients, are also sites of significant electron acceleration by mechanisms not fully understood. Using in situ observations of such transients in the Earth’s foreshock, we demonstrate that intense whistler-mode waves can resonate nonlinearly with >25 eV solar wind electrons and accelerate them to ∼100–500 eV. This acceleration is mostly effective for the 50–250 eV energy range, where the accelerated electron population exhibits a characteristic butterfly pitch-angle distribution consistent with theoretical predictions. Such nonlinear resonant acceleration is very fast, implying that this mechanism may be important for injecting suprathermal electrons of solar wind origin into the shock region, where they can undergo further, efficient shock-drift acceleration to even higher energies.

Electron Acceleration by Interaction of Two Filamentary Currents Within a Magnetopause Magnetic Flux Rope

AbstractTwo types of filamentary currents (FCs) were observed inside a magnetic flux rope at the magnetopause by the Magnetospheric Multiscale mission. The first FC is identified as an electron vortex, while the other is a reconnecting current sheet. Stochastic electric fields were generated within the FCs, resulting in electron acceleration up to a few keV, similar to recent simulations of electron acceleration inside vortex, which is a second‐order Fermi acceleration. Furthermore, two FCs propagated at different speeds, causing compression in the region between them. Energetic electrons up to 200 keV were detected in the compressed region and displayed a double power‐law spectrum. Observations suggest that the electrons were mainly accelerated by betatron mechanism in the compressed region. The formation, evolution, and interaction of FCs provide a novel mechanism for electron acceleration. These results clearly show the significance of electron‐scale dynamics within flux rope.

Acceleration of suprathermal protons near an interplanetary shock

Context.Interplanetary collisionless shocks are known to be sources of energetic charged particles up to hundreds of MeV. However, the underlying acceleration mechanisms are still under debate.Aims.We determine the properties of suprathermal protons accelerated by the interplanetary shock on 2021 November 3 with the unprecedented high-resolution measurements by the SupraThermal Electron Proton sensor of the Energetic Particle Detector on board the Solar Orbiter spacecraft, in order to constrain the potential shock acceleration mechanisms.Methods.We first reconstructed the pitch-angle distributions (PADs) of suprathermal protons in the solar wind frame. Then, we studied the evolution of the PADs, the temporal flux profile, and the velocity distribution function of this proton population close to the shock and compared the observations to theoretical predictions.Results.We find that the suprathermal proton fluxes peak ∼12 to ∼24 s before the shock in the upstream region. The proton fluxes rapidly decrease by ∼50% in a thin layer (∼8000 km) adjacent to the shock in the downstream region and become constant farther downstream. Furthermore, the proton velocity distribution functions in the upstream (downstream) region fit a double power law,f(v)∼v−γ, at ∼1000 − 3600 km s−1, with aγof ∼3.4 ± 0.2 (∼4.3 ± 0.7) at velocities (v) below a break at ∼1800 ± 100 km s−1(∼1600 ± 200 km s−1) and aγof ∼5.8 ± 0.3 (∼5.8 ± 0.2) at velocities higher than this. These indices are all smaller than predicted by first-order Fermi acceleration. In addition, the proton PADs in the covered pitch-angle range show anisotropies in the direction away from the shock in the region close to the upstream region and become nearly isotropic farther upstream, while downstream of the shock, they show a tendency of anisotropies towards 90° PA.Conclusions.These results suggest that the acceleration of suprathermal protons at interplanetary shocks are dynamic on a timescale of ∼10 s, that is, few proton gyroperiods. Furthermore, shock-drift acceleration likely plays an important role in accelerating these suprathermal protons.

Super-Fermi acceleration in multiscale MHD reconnection

We investigate the Fermi acceleration of charged particles in 2D MHD anti-parallel plasmoid reconnection, finding a drastic enhancement in energization rate ε ̇ over a standard Fermi model of ε ̇ ∼ ε. The shrinking particle orbit width around a magnetic island due to E → × B → drift produces a ε ̇ ∥ ∼ ε ∥ 1 + 1 / 2 χ power law with χ ∼ 0.75. The increase in the maximum possible energy gain of a particle within a plasmoid due to the enhanced efficiency increases with the plasmoid size and is by multiple factors of 10 in the case of solar flares and much more for larger plasmas. Including the effects of the non-constant E → × B → drift rates leads to further variation in power law indices from ≳ 2 to ≲ 1, decreasing with plasmoid size at the time of injection. The implications for energetic particle spectra are discussed alongside applications to 3D plasmoid reconnection and the effects of a guide field.

Two-step Acceleration of Energetic Electrons at Magnetic Flux Ropes during Turbulent Reconnection

Energetic electrons have been frequently observed during magnetic reconnection in the magnetotail. The acceleration process of the energetic electrons is not fully understood. In this paper, we select for a detailed study a case of energetic electron acceleration from the earlier reported interval of turbulent magnetic reconnection in Earth’s magnetotail observed by the Magnetospheric Multiscale mission. We use the first-order Taylor expansion method to reconstruct the magnetic topology of electron acceleration sites from the data. We find that the energetic electron fluxes increase inside the flux rope forming in front of the magnetic pileup region. We show that the energetic electrons are produced by a two-step process where two different acceleration mechanisms are successively operating outside and inside the flux rope. First, the thermal electrons are energized in the field-aligned direction inside the magnetic pileup region owing to the Fermi mechanism forming a cigar-like distribution. Second, those energized electrons are further accelerated predominately antiparallel to the magnetic field direction by a parallel electric field inside the flux rope. Our findings provide information for a better understanding of the generation of energetic electrons during turbulent reconnection process.

A fermi acceleration model to study the electron acceleration in laser-produced plasma with localized structures formation and turbulence generation

This investigation presents a model based on the nonlinear coupling of waves for studying electron acceleration in laser-produced plasma. The impact of the localized structures formation and turbulence generation on electron acceleration is investigated via a second-order Fermi acceleration mechanism. For this purpose, the dynamical coupled equations of the extraordinary mode laser and the upper hybrid wave are formulated by taking into account relativistic and ponderomotive nonlinearity. These coupled equations are solved by laboratory simulations using pseudo-spectral and finite difference methods. The simulation results show the turbulent wavenumber spectrum associated with the localization of the laser beam. The power-law scaling of turbulence generation has been utilized to study the formation of the thermal tail of energetic electrons, which may be responsible for the acceleration of the electrons. A fractional diffusion method has been exploited to determine electron acceleration. This study also provides a simplified model for a better understanding of the nonlinear progression of the laser beam during propagation inside the magnetized plasma.

Cosmic-Ray Acceleration and Nonthermal Radiation at Accretion Shocks in the Outer Regions of Galaxy Clusters

Cosmology models predict that external accretion shocks form in the outer region of galaxy clusters owing to supersonic gas infall from filaments and voids in the cosmic web. They are characterized by high sonic and Alfvénic Mach numbers, M s ∼ 10–102 and M A ∼ 102–103, and propagate into weakly magnetized plasmas of β ≡ P g /P B ≳ 102. Although strong accretion shocks are expected to be efficient accelerators of cosmic rays (CRs), nonthermal signatures of shock-accelerated CRs around clusters have not been confirmed, and detailed acceleration physics at such shocks has yet to be understood. In this study, we first establish through two-dimensional particle-in-cell simulations that at strong high-β shocks electrons can be pre-energized via stochastic Fermi acceleration owing to the ion Weibel instability in the shock transition region, possibly followed by injection into diffusive shock acceleration. Hence, we propose that the models derived from conventional thermal leakage injection may be employed for the acceleration of electrons and ions at accretion shocks as well. Applying these analytic models to numerical shock zones identified in structure formation simulations, we estimate nonthermal radiation, such as synchrotron and inverse Compton (IC) emission due to CR electrons and π 0-decay γ-rays due to CR protons, around simulated clusters. Our models with injection parameter Q ≈ 3.5–3.8 predict synthetic synchrotron maps, which seem consistent with recent radio observations of the Coma Cluster. However, the detection of nonthermal IC X-rays and γ-rays from accretion shocks would be quite challenging. We suggest that the proposed analytic models may be adopted as generic recipes for CR production at cosmological shocks.

Non-thermal electron acceleration from magnetically driven reconnection in a laboratory plasma

Magnetic reconnection is a ubiquitous astrophysical process that rapidly converts magnetic energy into some combination of plasma flow energy, thermal energy, and non-thermal energetic particles, including energetic electrons. Various reconnection acceleration mechanisms in different low-$\beta$ (plasma-to-magnetic pressure ratio) and collisionless environments have been proposed theoretically and studied numerically, including first- and second-order Fermi acceleration, betatron acceleration, parallel electric field acceleration along magnetic fields, and direct acceleration by the reconnection electric field. However, none of them have been heretofore confirmed experimentally, as the direct observation of non-thermal particle acceleration in laboratory experiments has been difficult due to short Debye lengths for \textit{in-situ} measurements and short mean free paths for \textit{ex-situ} measurements. Here we report the direct measurement of accelerated non-thermal electrons from low-$\beta$ magnetically driven reconnection in experiments using a laser-powered capacitor coil platform. We use kiloJoule lasers to drive parallel currents to reconnect MegaGauss-level magnetic fields in a quasi-axisymmetric geometry. The angular dependence of the measured electron energy spectrum and the resulting accelerated energies, supported by particle-in-cell simulations, indicate that the mechanism of direct electric field acceleration by the out-of-plane reconnection electric field is at work. Scaled energies using this mechanism show direct relevance to astrophysical observations. Our results therefore validate one of the proposed acceleration mechanisms by reconnection, and establish a new approach to study reconnection particle acceleration with laboratory experiments in relevant regimes.

Photons’ Scattering in Relativistic Plasma with Velocity Shear: Generation of High Energy Power-law Spectra

A high energy power law is a common feature in the spectra of many astrophysical objects. We show that the photons in an unmagnetized relativistic plasma composed of electrons and protons with a variable Lorentz factor (or a velocity shear) go through repeated scattering with electrons to gain energy. The escaped population of photons naturally produces a power-law-shaped spectrum making it a photon’s analog to the conventional Fermi acceleration mechanism for charged particles. Thus, this mechanism provides a natural alternative to current explanations of high energy power-law spectra via synchrotron or thermal Comptonization. The model is applicable to any relativistic plasma beam with an arbitrary Lorentz factor profile. We implement the theory to the gamma-ray burst prompt phase and show that the obtained range of the photon indices is compatible with the observed values and the results of Monte Carlo simulations that we carry out independently. Therefore, the observed high energy spectral indices provide a unique indicator of the jet structure.

Properties and Acceleration Mechanisms of Electrons Up To 200keV Associated With a Flux Rope Pair and Reconnection X-Lines Around It in Earth's Plasma Sheet.

The properties and acceleration mechanisms of electrons (<200keV) associated with a pair of tailward traveling flux ropes and accompanied reconnection X-lines in Earth's plasma sheet are investigated with MMS measurements. Energetic electrons are enhanced on both boundaries and core of the flux ropes. The power-law spectra of energetic electrons near the X-lines and in flux ropes are harder than those on flux rope boundaries. Theoretical calculations show that the highest energy of adiabatic electrons is a few keV around the X-lines, tens of keV immediately downstream of the X-lines, hundreds of keV on the flux rope boundaries, and a few MeV in the flux rope cores. The X-lines cause strong energy dissipation, which may generate the energetic electron beams around them. The enhanced electron parallel temperature can be caused by the curvature-driven Fermi acceleration and the parallel electric potential. Betatron acceleration due to the magnetic field compression is strong on flux rope boundaries, which enhances energetic electrons in the perpendicular direction. Electrons can be trapped between the flux rope pair due to mirror force and parallel electric potential. Electrostatic structures in the flux rope cores correspond to potential drops up to half of the electron temperature. The energetic electrons and the electron distribution functions in the flux rope cores are suggested to be transported from other dawn-dusk directions, which is a 3-dimensional effect. The acceleration and deceleration of the Betatron and Fermi processes appear alternately indicating that the magnetic field and plasma are turbulent around the flux ropes.

Long-term multi-wavelength variability and extreme spectral properties of the TeV-detected blazar 1ES 0033+595

Context. The multi-wavelength (MWL) properties of some TeV-detected blazars are still poorly understood. By studying the MWL properties of the BL Lacertae source 1ES 0033+595, we make further progress in our understanding of the instable physical processes responsible for particle acceleration to ultra-relativitic energies and the observed emission properties. Aims. This paper presents the results of a detailed X-ray timing and spectral analysis of the source 1ES 0033+595, allowing us to draw conclusions about the physical mechanisms responsible for particle acceleration and the generation of X-ray emission. We also examined the long-term MWL behaviour of the source and interband cross-correlations. Methods. Our study focused on the observations performed with the X-Ray Telescope on board the Neil Gehrels Swift Observatory (Swift-XRT) in the period 2005–2022. The MWL data sets were obtained with several space and ground-based instruments. We analysed the MWL flaring behaviour during the entire period, as well as in particular subperiods selected on the basis of the X-ray flaring activity of the target; constructed histograms characterising the distributions of the different spectral parameters and MWL fluxes; and checked cross-correlations between these parameters and/or MWL fluxes. The obtained results are compared with the predictions of the various theoretical studies and simulations presented by the different authors to date. Results. The source showed extreme spectral properties with dominance of high spectral curvature, frequent occurrence of very and extremely hard photon indices, and the presence of a synchrotron spectral energy distribution (SED) peak in the hard X-ray range (sometimes at energies beyond 10 keV). These properties reveal the importance of first-order Fermi acceleration with very low initial particle energy distribution, along with the co-existence of stochastic acceleration and hadronic processes. The source was characterised by very uneven and erratic flaring activity in diverse epochs: the period of strong flares (2013–2016) was preceded by a moderate variability and followed by a gradual long-term decrease in MWL flaring activity. We detected a number of instances of intraday 0.3–10 keV variability, which were sometimes observed within a few hundred seconds and explained by the interaction between the relativistic shock front and jet inhomogeneities with strong magnetic fields. The X-ray and γ-ray fluxes showed a lognormal distribution, which hints at the imprint of accretion disc instabilities on the blazar jet.

First-Principles Fermi Acceleration in Magnetized Turbulence.

This Letter provides a concrete implementation of Fermi's model of particle acceleration in magnetohydrodynamic (MHD) turbulence, connecting the rate of energization to the gradients of the velocity of magnetic field lines, which it characterizes within a multifractal picture of turbulence intermittency. It then derives a transport equation in momentum space for the distribution function. This description is shown to be substantiated by a large-scale numerical simulation of strong MHD turbulence. The present general framework can be used to model particle acceleration in a variety of environments.

Active Galactic Nuclei as Potential Sources of Ultra-High Energy Cosmic Rays

Active Galactic Nuclei (AGNs) and their relativistic jets belong to the most promising class of ultra-high-energy cosmic ray (UHECR) accelerators. This compact review summarises basic experimental findings by recent instruments, and discusses possible interpretations and astrophysical constraints on source energetics. Particular attention is given to potential sites and mechanisms of UHECR acceleration in AGNs, including gap-type particle acceleration close to the black hole, as well as first-order Fermi acceleration at trans-relativistic shocks and stochastic shear particle acceleration in large-scale jets. It is argued that the last two represent the most promising mechanisms given our current understanding, and that nearby FR I type radio galaxies provide a suitable environment for UHECR acceleration.

A semiempirical approach to low-energy cosmic ray propagation in the diffuse interstellar medium

Context. We investigate the ionization of the diffuse interstellar medium by cosmic rays by modeling their propagation along the wandering magnetic fields using a Monte Carlo method. We explore how particle trapping and second-order Fermi processes affect the ionization of the medium. Aims. We study how low-energy comic rays propagate in turbulent, translucent molecular clouds, and how they regulate the ionization and both lose and gain energy from the medium. Methods. As a test case, we used high spatial resolution (0.03 pc) CO maps of a well-studied high latitude translucent cloud, MBM 3, to model turbulence. The propagation problem is solved with a modified Monte Carlo procedure that includes trapping, energization, and ionization losses. Results. In the homogeneous medium, trapping and re-energization do not produce a significant effect. In the nonuniform medium, particles can be trapped for a long time inside the cloud. This modifies the cosmic ray distribution due to stochastic acceleration at the highest energies (∼100 MeV). At lower energies, the re-energization is too weak to produce an appreciable effect. The change in the energy distribution does not significantly affect the ionization losses, so ionization changes are due to trapping effects. Conclusions. Our Monte Carlo approach to cosmic ray propagation is an alternative method for solving the transport equation. This approach can be benchmarked to gas observations of molecular clouds. Using this approach, we demonstrate that stochastic Fermi acceleration and particle trapping occurs in inhomogeneous clouds, significantly enhancing their ionization.

Exponential Fermi Acceleration in a Switching Billiard

In this paper we show an infinite measure set of exponentially escaping orbits for a resonant Fermi accelerator, which is realised as a square billiard with a periodically oscillating platform. We use normal forms to describe how the energy changes in a period and we employ techniques for hyperbolic systems with singularities to show the exponential drift of these normal forms on a divided time-energy phase.