Fermi Acceleration Research Articles

Stochastic acceleration of electrons by chaotic electrostatic field in thundercloud

We investigate stochastic acceleration of electrons moving through a chaotic electrostatic field (CEF). Acceleration mechanism is based on irregular scattering of electrons experiencing random pulses in the CEF. Despite the fact that the pulses have random values and orientations, a specific stochastic acceleration of electrons occurs. This acceleration mechanism is analogous to the well-known second-order Fermi acceleration. It can act in various media, where random inhomogeneities create a chaotically distributed electric field. In this paper the phenomenon is investigated specifically for thunderclouds, where the CEF is formed by randomly distributed charged hydrometeors and ions. We show that acceleration process is threshold: the electron flux is accelerated, if the mean CEF value exceeds a certain threshold value, and decelerated otherwise. Accelerated electrons can form the avalanche of relativistic electrons, producing intense bremstrahlung gamma ray radiation. Proposed stochastic acceleration of electrons in the CEF complements second-order Fermi acceleration, expanding its application to static chaotic fields.

Formation of Pancake, Rolling Pin, and Cigar Distributions of Energetic Electrons at the Dipolarization Fronts (DFs) Driven by Magnetic Reconnection: A Two‐Dimensional Particle‐In‐Cell Simulation

AbstractA two‐dimensional particle‐in‐cell (PIC) simulation is performed to study the formation of the pitch angle distribution of energetic electrons at dipolarization fronts (DFs) driven by magnetic reconnection. The energetic electrons at DFs are originated from the lobe region, and experience a two‐step acceleration process at the reconnection x‐line and the DFs, respectively. Three kinds of pitch angle distributions commonly observed in the magnetotail, Pancake, Rolling pin, and Cigar distributions, are formed in sequence during the propagation of the DFs. In the early stage, Pancake distributions are formed through betatron acceleration. During this stage, the flux of energetic electrons with pitch angles around 0° and 180° is low because these electrons have no time to be reflected many times at the DFs to obtain sufficient Fermi acceleration. However, the electrons with pitch angles around 90° are difficult to be trapped around the DFs for a long time, and their flux saturates quickly; while the electrons with pitch angles around 0° and 180° can be trapped inside the closed field lines and they get continuous Fermi acceleration during the propagation of the DFs. Therefore, in the later stage, the flux of energetic electrons with pitch angles around 0° and 180° gradually increases and at last exceeds that of energetic electrons with pitch angles around 90°, forming Rolling pin and Cigar distributions in sequence.

Quantum dynamics of a nucleon in the Fermi accelerator

The quantum dynamics of a particle in a one-dimensional box with an oscillating wall (the Fermi accelerator) is investigated. The model is applied to the motion of a single nucleon in the mean-field potential of a heavy atomic nucleus whose surface vibrates. By directly solving the time-dependent Schrödinger equation, both the state of the particle and its mean-energy are studied. The effects of the frequency of the wall oscillation on the nucleon’s energy are addressed. Its energy oscillates in phase with the moving wall for all frequencies, showing no chaotic behaviour. There is a large initial peak of the nucleon’s energy as the particle adjusts to the sudden change in the size of the box and a varying relaxation time as it plateaus towards lower energy and a partial equilibrium. Small oscillations in energy continue, since there cannot be a true equilibrium while the wall is moving. The quantum coherence between the different parts of the nucleon’s wave-function in real space is very much preserved. This research lays the foundation for future investigations into quantum tunnelling in the Fermi accelerator.

Simulations of Neutrino and Gamma-Ray Production from Relativistic Black-Hole Microquasar Jets

Recently, microquasar jets have aroused the interest of many researchers focusing on the astrophysical plasma outflows and various jet ejections. In this work, we concentrate on the investigation of electromagnetic radiation and particle emissions from the jets of stellar black hole binary systems characterized by the hadronic content in their jets. Such emissions are reliably described within the context of relativistic magneto-hydrodynamics. Our model calculations are based on the Fermi acceleration mechanism through which the primary particles (mainly protons and electrons) of the jet are accelerated. As a result, a small portion of thermal protons of the jet acquire relativistic energies, through shock-waves generated into the jet plasma. From the inelastic collisions of fast (non-thermal) protons with the thermal (cold) ones, secondary charged and neutral particles (pions, kaons, muons, η-particles, etc.) are created, as well as electromagnetic radiation from the radio wavelength band to X-rays and even very high energy gamma-rays. One of our main goals is, through the appropriate solution of the transport equation and taking into account the various mechanisms that cause energy losses to the particles, to study the secondary particle concentrations within hadronic astrophysical jets. After assessing the suitability and sensitivity of the derived (for this purpose) algorithms on the Galactic MQs SS 433 and Cyg X-1, as a concrete extragalactic binary system, we examine the LMC X-1 located in the Large Magellanic Cloud, a satellite galaxy of our Milky Way Galaxy. It is worth mentioning that, for the companion O star (and its extended nebula structure) of the LMC X-1 system, new observations using spectroscopic data from VLT/UVES have been published a few years ago.

Cluster Observations of Energetic Electron Acceleration Within Earthward Reconnection Jet and Associated Magnetic Flux Rope

AbstractWe study acceleration of energetic electrons in an earthward plasma jet due to magnetic reconnection in the Earth magnetotail for one case observed by Cluster. The case has been selected based on the presence of high fluxes of energetic electrons, Cluster being in the burst mode and Cluster separation being around 1,000 km that is optimal for studies of ion scale physics. We show that two characteristic acceleration mechanisms are operating during this event. First, significant acceleration is achieved inside the magnetic flux pile‐up of the jet, the acceleration mechanism being consistent with betatron acceleration. Second, strong energetic electron acceleration occurs in magnetic flux rope like structure forming in front of the magnetic flux pile‐up region. Energetic electrons inside the magnetic flux rope are accelerated predominantly in the field‐aligned direction and the acceleration can be due to Fermi acceleration in a contracting flux rope.

Cosmic-Ray Acceleration from Turbulence in Molecular Clouds

Abstract Low-energy cosmic rays, in particular protons with energies below 1 GeV, are significant drivers of the thermochemistry of molecular clouds. However, these cosmic rays are also greatly impacted by energy losses and magnetic field transport effects in molecular gas. Explaining cosmic-ray ionization rates of 10−16 s−1 or greater in dense gas requires either a high external cosmic-ray flux, or local sources of MeV–GeV cosmic-ray protons. We present a new local source of low-energy cosmic rays in molecular clouds: first-order Fermi acceleration of protons in regions undergoing turbulent reconnection in molecular clouds. We show from energetic-based arguments there is sufficient energy within the magnetohydrodynamic turbulent cascade to produce ionization rates compatible with inferred ionization rates in molecular clouds. As turbulent reconnection is a volume-filling process, the proposed mechanism can produce a near-homogeneous distribution of low-energy cosmic rays within molecular clouds.

Local Acceleration of Protons to 100 keV in a Quasi‐Parallel Bow Shock

AbstractRecent observations in the quasi‐parallel bow shock by the Magnetospheric Multiscale spacecraft show rapid heating and acceleration of ions up to an energy of about 100 keV. It is demonstrated that a prominent acceleration mechanism is the nonlinear interaction with a spectrum of waves produced by gradient‐driven instabilities, including the lower hybrid drift (LHD) instability, modified two‐stream (MTS) instability, and electron cyclotron drift (ECD) instability. Test‐particle simulations show that the observed spectrum of waves can rapidly accelerate protons up to a few hundreds of keV by the ExB mechanism. The ExB wave mechanism is related to the surfatron mechanism at shocks, but through the coupling with the stochastic heating condition, it produces significant acceleration on much shorter temporal and spatial scales by the interaction with bursts of waves within a cyclotron period. The results of this study are built on the heritage of four‐point measurement techniques developed for the Cluster mission and imply that the concepts of Fermi acceleration, diffusive shock acceleration, and shock drift acceleration are not needed to explain proton acceleration to hundreds of keV at the Earth’s bow shock.

Statistical Properties of Current, Energy Conversion, and Electron Acceleration in Flux Ropes in the Terrestrial Magnetotail

AbstractWe perform a statistical analysis on current density, energy conversion, and electron acceleration in the primary flux ropes (PFRs) and the secondary flux ropes (SFRs) distinguished by out‐of‐plane electron current, respectively. It is found that current filaments are plentiful in both PFRs and SFRs. The closer to the center of the SFRs, the stronger the |J| is. The J•E′ is intermittent in the PFRs. However, J•E′ almost stays positive in the SFRs. The local adiabatic acceleration of the electrons in the PFRs and the SFRs are explored. Fermi and betatron acceleration are closely related to the adjacent magnetic field and bulk flow which can lead to the contraction/relaxation of the PFRs and SFRs and enhance/reduce the gradient of the magnetic field. The acceleration by the parallel electric field is significant in the SFRs. Our results can help to improve the understanding of the PFRs and SFRs and their roles in the magnetotail dynamics.

Ion Acceleration by Foreshock Bubbles

AbstractForeshock bubbles (FBs) form as a result of the interaction between solar wind discontinuities and backstreaming ion beams in the foreshock. They are carried by the solar wind in the anti‐sunward direction and are associated with high energy ions. We employ electromagnetic hybrid (kinetic ions, fluid electrons) simulations and test particle calculations to investigate ion acceleration by FBs. Simulation results show that the maximum energies which the ions attain are not sensitive to the topology of the FBs, which varies from spherical to planar limits. However, the solar wind velocity does control the maximum energies reached by FB acceleration. Test particle calculations show that ion energization takes place through reflection of sunward moving ions from FBs through one or more collisions consistent with second‐order Fermi acceleration. The results also indicate that energy gain does not reach that expected for elastic reflections. Examination of ion energy spectra within different FBs shows a self‐similar pattern consisting of distribution peaked at the solar wind ram energy Esw with a distribution tail that reaches energies of ∼5.6 Esw. This behavior is consistent with second‐order Fermi acceleration and the inherent limitations on energy gain in this process. We also discuss the role of nonlinear structures called foreshock cavitons in the acceleration process.

The double signature of local cosmic-ray acceleration in star-forming regions

Context.Recently, there has been an increased interest in the study of the generation of low-energy cosmic rays (< 1 TeV) in shocks situated on the surface of a protostar or along protostellar jets. These locally accelerated cosmic rays offer an attractive explanation for the high levels of non-thermal emission and ionisation rates observed close to these sources.Aims.The high ionisation rate observed in some protostellar sources is generally attributed to shock-generated UV photons. The aim of this article is to show that when synchrotron emission and a high ionisation rate are measured in the same spatial region, a locally shock-accelerated cosmic-ray flux is sufficient to explain both phenomena.Methods.We assume that relativistic protons and electrons are accelerated according to the first-order Fermi acceleration mechanism, and we calculate their emerging fluxes at the shock surface. These fluxes are used to compute the ionisation rate and the non-thermal emission at centimetre wavelengths. We then apply our model to the star-forming region OMC-2 FIR 3/FIR 4. Using a Bayesian analysis, we constrain the parameters of the model and estimate the spectral indices of the non-thermal radio emission, the intensity of the magnetic field, and its degree of turbulence.Results.We demonstrate that the local cosmic-ray acceleration model makes it possible to simultaneously explain the synchrotron emission along the HOPS 370 jet within the FIR 3 region and the ionisation rate observed near the FIR 4 protocluster. In particular, our model constrains the magnetic field strength (∼250−450 μG), its turbulent component (∼20−40 μG), and the jet velocity in the shock reference frame for the three non-thermal sources of the HOPS 370 jet (between 350 km s−1and 1000 km s−1).Conclusions.Beyond the modelling of the OMC-2 FIR 3/FIR 4 system, we show how the combination of continuum observations at centimetre wavelengths and molecular transitions is a powerful new tool for the analysis of star-forming regions: These two types of observations can be simultaneously interpreted by invoking only the presence of locally accelerated cosmic rays, without having to resort to shock-generated UV photons.

An explanation about the flat radio spectrum for Mrk 421

It is well known that a flat radio spectrum is a common property in the spectral energy distribution of blazars. Although one-zone leptonic models are generally successful in explaining the multi-wave band emission, they are problematic in reproducing the radio spectrum. In the study of Mrk 421, one-zone models suggest that in order to avoid overproducing the radio flux, the minimum electron Lorentz factor should be larger than a few hundred at least, even considering the synchrotron self-absorption effect. This result suggests that the model predicted spectral index in the radio band of Mrk 421 should be -1/3. On the basis of this result, by assuming there is a neglected region that will also contribute the radio emission and its electron energy index naturally originates from the simplest first-order Fermi acceleration mechanism, we can get a superimposed flat radio spectrum. In this paper, a two-zone model is proposed to reproduce the quiescent state spectral energy distribution of Mrk 421. In addition to taking into account the emission from a conventional radiation zone, we further consider emission from the acceleration zone in which particles are accelerated at a shock front. With the present model, our fitting result suggests that the low frequency flat radio spectrum of Mrk 421 might be explained as a superposition of the synchrotron emission from acceleration zone and radiation zone.

Turbulence Upstream and Downstream of Interplanetary Shocks

The paper reviews the interaction of collisionless interplanetary (IP) shocks with the turbulent solar wind. The coexistence of shocks and turbulence plays an important role in understanding the acceleration of particles via Fermi acceleration mechanisms, the geoeffectiveness of highly disturbed sheaths following IP shocks and, among others, the nature of the fluctuations themselves. Although our knowledge of physics of upstream and downstream shock regions has been greatly improved in recent years, many aspects of the IP-shock/turbulence interaction are still poorly known, for example, the nature of turbulence, its characteristics on spatial and temporal scales, how it decays, its relation to shock passage and others. We discuss properties of fluctuations ahead (upstream) and behind (downstream) of IP shock fronts with the focus on observations. Some of the key characteristics of the upstream/downstream transition are 1) enhancement of the power in the inertial range fluctuations of the velocity, magnetic field and density is roughly one order of magnitude, 2) downstream fluctuations are always more compressible than the upstream fluctuations, and 3) energy in the inertial range fluctuations is kept constant for a significant time after the passage of the shock. In this paper, we emphasize that–for one point measurements–the downstream region should be viewed as an evolutionary record of the IP shock propagation through the plasma. Simultaneous measurements of the recently launched spacecraft probing inner parts of the Solar System will hopefully shed light on some of these questions.

Maximally hard radio spectra from Fermi acceleration in pulsar-wind nebulae

ABSTRACT The processes leading to the exceptionally hard radio spectra of pulsar-wind nebulae (PWNe) are not yet understood. Radio photon spectral indices among 29 PWNe from the literature show an approximately normal, α = 0.2 ± 0.2 distribution. We present ∼3σ evidence for a distinct sub-population of PWNe, with a hard spectrum α = 0.01 ± 0.06 near the termination shock and significantly softer elsewhere, possibly due to a recent evacuation of the shock surroundings. Such spectra, especially in the hard sub-population, suggest a Fermi process, such as diffusive shock acceleration (DSA), at its extreme, α = 0 limit. In particular, we show that this limit is approached in DSA for sufficiently anisotropic small-angle scattering, enhanced on either side of the shock for particles approaching the shock front. In the upstream, the spectral hardening is mostly associated with an enhanced energy gain, possibly driven by the same beamed particles crossing the shock. Downstream, the main effect is a diminished escape probability, but this lowers the acceleration efficiency to $\lesssim 25{{\ \rm per\ cent}}$ for α = 0.3 and $\lesssim 1{{\ \rm per\ cent}}$ for α = 0.03.

Energy Dissipation via Magnetic Reconnection Within the Coherent Structures of the Magnetosheath Turbulence

AbstractA series of intermittent coherent structures was observed in magnetosheath turbulence in the form of magnetic peaks. These magnetic peaks are always accompanied with enhancement of local current density, and three of them are studied in detail because of their intense current density. Based on the magnetic field signals, magnetic curvatures, and the toroidal magnetic field lines, three peaks are identified as magnetic flux ropes. In each trailing part of these three peaks, an extremely thin electron current layer was embedded within a much broader ion‐scale current layer. The energy dissipation is evident within the peaks and direct evidence of magnetic reconnection was found within the thinnest electron current layer. The electrons were heated mainly in two regions of magnetic peaks, that is, the reconnecting current layer by parallel electric field and the trailing edges by Fermi and betatron mechanisms. These results suggest that the ion‐scale magnetic peaks are coherent structures associated with energy dissipation and electron heating in the magnetosheath. Thin current layers can be formed in magnetic peaks, and magnetic reconnection can play a significant role for the energy dissipation in magnetic peaks.

Scrutinizing FR 0 radio galaxies as ultra-high-energy cosmic ray source candidates

Fanaroff-Riley (FR) 0 radio galaxies compose a new class of radio galaxies, which are usually weaker but much more numerous than the well-established class of FR 1 and FR 2 galaxies. The latter classes have been proposed as sources of the ultra-high-energy cosmic rays (UHECRs) with energies reaching up to ∼1020 eV. Based on this conjecture, the possibility of UHECR acceleration and survival in an FR 0 source environment is examined in this work.In doing so, an average spectral energy distribution (SED) based on data from the FR 0 catalog (FR0CAT) is compiled. The resulting photon fields are used as targets for UHECRs, which suffer from electromagnetic pair production, photo-disintegration, photo-meson production losses, and synchrotron radiation. Multiple mechanisms are discussed to assess the UHECR acceleration probability, including Fermi-I order and gradual shear accelerations, and particle escape from the source region.This work shows that in a hybrid scenario, combining Fermi and shear accelerations, FR 0 galaxies can contribute to the observed UHECR flux, as long as Γj≳1.6, where shear acceleration starts to dominate over escape. Even in less optimistic scenarios, FR 0s can be expected to contribute to the cosmic-ray flux between the knee and the ankle. Our results are relatively robust with respect to the realized magnetic turbulence model and the speed of the accelerating shocks.

Electron Pitch Angle Distributions Around Dipolarization Fronts at the Off Magnetic Equator

AbstractThe pitch angle distributions of energetic electrons (10 s–200 keV) around the dipolarization front (DF) have been studied extensively. However, the pitch angle distributions of energetic electrons around the DF at the off magnetic equator have been unclear so far. In this study, we present the observations of the DF at the off magnetic equator in the near‐Earth tail. Some properties of the DF at the off magnetic equator are presented. Importantly, the triple‐peaked pitch angle distribution of energetic electrons around the DF is found. Such a new type of distribution is a peak at around 22.5°, 90°, and 157.5°, which is a combinational consequence of betatron acceleration, Fermi acceleration, and magnetic mirror effect. Using an analytical model, we quantitatively reproduce the processes of betatron acceleration, Fermi acceleration, and magnetic mirror effect. These results will further enhance our understanding of the electron dynamics around DFs.

Flux Transfer Events at a Reconnection‐Suppressed Magnetopause: Cassini Observations at Saturn

AbstractWe present the discovery of seven new flux transfer events (FTEs) at Saturn's dayside magnetopause by the Cassini spacecraft and analyze the observations of all eight known FTEs. We investigate how FTEs may differ at Saturn where the magnetopause conditions are likely to diamagnetically suppress magnetic reconnection from occurring. The measured ion‐scale FTEs have diameters close to or above the ion inertial length di∼1–27 (median and mean values of 5 and 8), considerably lower than typical FTEs found at Earth. The FTEs magnetic flux contents are 4–461 kWb (median and mean values of 16 and 77 kWb), considerably smaller (<0.1%) than average flux opened during magnetopause compression events at Saturn. This is in contrast to Earth and Mercury where FTEs contribute significantly to magnetospheric flux transfer. FTEs therefore represent a negligible proportion of the amount of open magnetic flux transferred at Saturn. Due to the likely suppression of the two main growth‐mechanisms for FTEs (continuous multiple x‐line reconnection and FTE coalescence), we conclude that adiabatic expansion is the likely (if any) candidate to grow the size of FTEs at Saturn. Electron energization is observed inside the FTEs, due to either Fermi acceleration or parallel electric fields. Due to diamagnetic suppression of reconnection at Saturn's magnetopause, we suggest that the typical size of FTEs at Saturn is most likely very small, and that there may be more di∼1 FTEs present in the Cassini magnetometer data that have not been identified due to their brief and unremarkable magnetic signatures.

Normal forms and averaging in an acceleration problem in nonholonomic mechanics.

This paper investigates nonholonomic systems (the Chaplygin sleigh and the Suslov system) with periodically varying mass distribution. In these examples, the behavior of velocities is described by a system of the form dvdτ=f2(τ)u2+f1(τ)u+f0(τ),dudτ=-uv+g(τ), where the coefficients are periodic functions of time τ with the same period. A detailed analysis is made of the problem of the existence of modes of motion for which the system speeds up indefinitely (an analog of Fermi's acceleration). It is proved that, depending on the choice of coefficients, variable v has the asymptotics t1k,k=1,2,3. In addition, we show regions of the phase space for which the system, when the trajectories are started from them, is observed to speed up. The proof uses normal forms and averaging in a slightly unusual form since unusual form averaging is performed over a variable that is not fast.

Modeling the spectrum and composition of ultrahigh-energy cosmic rays with two populations of extragalactic sources

We fit the ultrahigh-energy cosmic-ray (UHECR, Egtrsim 0.1 EeV) spectrum and composition data from the Pierre Auger Observatory at energies Egtrsim 5cdot 10^{18} eV, i.e., beyond the ankle using two populations of astrophysical sources. One population, accelerating dominantly protons (^1H), extends up to the highest observed energies with maximum energy close to the GZK cutoff and injection spectral index near the Fermi acceleration model; while another population accelerates light-to-heavy nuclei (^4He, ^{14}N, ^{28}Si, ^{56}Fe) with a relatively low rigidity cutoff and hard injection spectrum. A significant improvement in the combined fit is noted as we go from a one-population to two-population model. For the latter, we constrain the maximum allowed proton fraction at the highest-energy bin within 3.5sigma statistical significance. In the single-population model, low-luminosity gamma-ray bursts turn out to match the best-fit evolution parameter. In the two-population model, the active galactic nuclei is consistent with the best-fit redshift evolution parameter of the pure proton-emitting sources, while the tidal disruption events could be responsible for emitting heavier nuclei. We also compute expected cosmogenic neutrino flux in such a hybrid source population scenario and discuss possibilities to detect these neutrinos by upcoming detectors to shed light on the sources of UHECRs.

Modelling of particle acceleration in the pulsar wind nebulae with bow shocks

The observations of the pulsar wind nebulae (PWNe) indicate the presence of efficient acceleration of positrons and electrons in these sources. The Fermi acceleration in the colliding shock flows can explain the observed hard synchrotron emission spectra of PWNe with bow shocks (BSPWNe). This may result in their maximal luminosities in the far ultraviolet range (FUV; 1250 — 2000 Å, ∼ 6 — 10 eV) due to the synchrotron emission of pairs rather than due to the thermal emission of the shocked interstellar matter. Fine spectroscopic observations of sufficiently bright sources with Hubble Space Telescope could be applied to distinguish between these two scenarios. In this paper we simulate BSPWNe flows structure with the relativistic magnetohydrodynamic code PLUTO, consider particle transport and their synchrotron emission for a number of BSPWNe. We calculate the synchrotron FUV luminosities of these BSPWNe and discuss the prospective of their observation in FUV. We also consider possible contribution of PSR J1741-2054 to the positron excess detected by AMS-02 and PAMELA.