Fermi Acceleration Research Articles

Acceleration behaviors of Fermi accelerator model excited by Van der Pol oscillator

In this paper, we investigate on dynamics of a generalized Fermi accelerator model with a moving wall described by a nonlinear Van der Pol oscillator. Different acceleration behaviors appear due to the discontinuity brought by impact and the stationary periodic excitation of the moving wall. Utilizing the theory of discontinuous dynamical systems, acceleration mechanism of the particle is studied and the analytical conditions for stick motion and grazing motion are obtained. By the use of generic mappings between different boundaries including stick and non-stick motions, periodic motions of the Fermi accelerator can be constructed, and corresponding local stability and bifurcations can be discussed according to mapping dynamics. Finally, different acceleration behaviors including periodic, chatter and stick motions are presented and illustrated.

Electron acceleration and formation of power-law spectra of energetic electrons during the merging process of multiple magnetic islands: particle-in-cell simulations

Magnetic reconnection is considered to be one important source to produce energetic electrons. In this paper, two-dimensional (2D) particle-in-cell (PIC) simulations are performed to investigate electron acceleration during the merging process of multiple magnetic islands in a current sheet with a strong guide field. Due to the existence of the strong guide field, we can analyze the contributions of the parallel electric field, Fermi, and betatron mechanisms to the electron acceleration with the guiding-center theory. During the coalescence process of magnetic islands, the islands merge each other continuously until only one large island remains. Energetic electrons are generated during such process, and the electrons with sufficient high energy develop a power-law spectrum. We also investigate the dependence of the index of the power-law spectra on the shape of magnetic islands, electron plasma beta, the number of magnetic islands, and the guide field.

A Fast Fermi Acceleration at Mars Bow Shock

AbstractWe report, for the first time, strong evidences that a fast Fermi mechanism is taking place at the Mars bow shock. The MAVEN spacecraft observations from the Solar Wind Electron Analyzer instrument show electron flux spikes with energies up to ∼1.5 keV. These spikes are associated with sunward propagating electrons and appear when the interplanetary field line threading the spacecraft is connected near the Martian bow shock tangency point. The observed loss cone distribution is a salient feature of these backstreaming electrons as the phase space density peaks on a ring centered along the magnetic field direction. Moreover, the data show no evidence of any effect due to a hypothetical cross‐shock electric potential on the observed angular distributions. Although similar distributions are seen at the terrestrial bow shock, the quantitative analysis of the measurements strongly indicates that the electrons are produced at the shock foot and escape upstream before exploring the entire shock structure.

Cosmic ray acceleration in hydromagnetic flux tubes

We find that hydromagnetic flux tubes in back-flows in the lobes of radio galaxies offer a suitable environment for the acceleration of cosmic rays (CR) to ultra-high energies. We show that CR can reach the Hillas (1984) energy even if the magnetised turbulence in the flux tube is not sufficiently strong for Bohm diffusion to apply. First-order Fermi acceleration by successive weak shocks in a hydromagnetic flux tube is shown to be equivalent to second-order Fermi acceleration by strong turbulence.

Extremely High energy peaked BL Lac nature of the TeV blazar Mrk 501

Extremely High energy peaked BL Lac (EHBL) objects are a special class of blazars with peculiar observational properties at X-ray and γ–ray energies. The observations of these sources indicate hard X-ray and γ–ray spectra and absence of rapid flux variations in the multi-wavelength light curves. These observational features challenge the leptonic models for blazars due to unusually hard particle spectrum in the emission region of the blazar jet and provide a strong motivation for exploring alternative scenarios to interpret the broad-band emission from blazars. At present, only few TeV blazars have been observed as EHBL objects in the extragalactic Universe. Due to their hard γ–ray spectra and long term variability, the observations of EHBL type of blazars at different redshifts help in probing the cosmic magnetic field and extragalactic background light in the Universe. Such objects also provide astrophysical sites to explore the particle acceleration mechanisms like magnetic reconnection and second order Fermi acceleration. Therefore, it has become important to identify more objects as EHBL using the observations available in the literature. Recent studies on the blazar Mrk 501 indicate that this source may exhibit an EHBL behaviour. In this paper, we use long term observations of Mrk 501 to explore its nature. Two sets of data, related to low and high/flaring activity states of Mrk 501, have been presented and compared with the observed features of a few well known EHBL type of blazars. We find that the spectral features of the blazar Mrk 501 indicate an EHBL nature of the source. Whereas, the temporal characteristics with fast variability during the high activity state of the source in X-ray and γ–ray energy bands are not compatible with the behaviour of EHBL type of blazars. However, Mrk 501 can be considered as an EHBL candidate in its low emission state. We also discuss the implications of identifying more EHBL objects using present and future ground-based γ-ray observatories.

Trapped and Accelerated Electrons Within a Magnetic Mirror Behind a Flux Rope on the Magnetopause

AbstractOn 6 December 2015, the Magnetospheric Multiscale satellites traversed the southward outflow of a magnetic reconnection on the magnetopause from the outside in. The magnetic structures or the geometries of the field lines inside this outflow are distinguished in detail by using the plasma and magnetic field observations. A flux rope and the magnetic flux piling‐up against this flux rope are found embedding in this outflow. The strong magnetosheath magnetic field allows the formation of a magnetic mirror in the flux pileup region. As the Magnetospheric Multiscale satellites approached the flux rope inside this mirror, the pitch angles of electrons converge toward 90°, indicating that the electrons are trapped inside the mirror. The local loss cones of these electrons along the satellite trajectory are estimated. It is found that the triangle‐like pitch angle distribution is well embraced by the curves of the estimated local loss cones. The energy spectra inside the mirror show that the electrons are accelerated in the direction perpendicular to the magnetic field. A test particle method is used to reproduce the acceleration process in a fitted 3‐D magnetic field model. The results show that the quasi‐perpendicular electrons experience the betatron acceleration when drifting into the stronger field region and that the electrons may also experience the Fermi acceleration when their pitch angles enlarge. The mirror structure on the magnetopause provides a unique opportunity to explore the behaviors of the magnetic reconnection associated electrons.

Generalized Fermi acceleration

In highly conducting astrophysical plasmas, charged particles are generically accelerated through Fermi-type processes involving repeated interactions with moving magnetized scattering centers. The present paper proposes a generalized description of these acceleration processes, by following the momentum of the particle through a continuous sequence of accelerated frames, defined in such a way that the electric field vanishes at each point along the particle trajectory. In each locally inertial frame, the Lorentz force affects the direction of motion of the particle, but the energy changes solely as a result of inertial corrections. This unified description of Fermi acceleration applies equally well in sub- and ultrarelativistic settings, in Cartesian or non-Cartesian geometries, flat or nonflat space-time. Known results are recovered in a variety of regimes -- shock, turbulent and shear acceleration -- and new results are derived in lieu of applications, e.g. nonresonant acceleration in relativistic turbulence, stochastic unipolar inductive acceleration and centrifugo-shear acceleration close to the horizon of a black hole.

Three Regimes and Four Modes for the Resonant Saturation of Parallel Ion-beam Instabilities

Abstract Motivated by recent advances in laboratory experiments on parallel ion-beam instabilities, we present a theoretical framework for—and simulations of—their evolution toward shock formation and Fermi acceleration. After reviewing the linear theory of beam instabilities, with an emphasis on how magnetic helicity and polarization depend on properties of the beam, we compare the evolution and saturation of three distinct parameter regimes: (I) the left-handed “non-resonant” regime; (II) the right-handed beam-gyroresonant regime; (III) the balanced, mixed-turbulence regime.

A Fokker–Planck Framework for Studying the Diffusion of Radio Burst Waves in the Solar Corona

Abstract Electromagnetic wave scattering off density inhomogeneities in the solar corona is an important process that determines both the apparent source size and the time profile of radio bursts observed at 1 au. Here we model the scattering process using a Fokker–Planck equation and apply this formalism to several regimes of interest. In the first regime the density fluctuations are considered quasi-static and diffusion in wavevector space is dominated by angular diffusion on the surface of a constant energy sphere. In the small-angle (“pencil-beam”) approximation, this diffusion further occurs over a small solid angle in wavevector space. The second regime corresponds to a much later time, by which scattering has rendered the photon distribution near-isotropic, resulting in a spatial diffusion of the radiation. The third regime involves time-dependent fluctuations and, therefore, Fermi acceleration of photons. Combined, these results provide a comprehensive theoretical framework within which to understand several important features of propagation of radio burst waves in the solar corona: emitted photons are accelerated in a relatively small inner region and then diffuse outward to larger distances. En route, angular diffusion results both in source sizes that are substantially larger than the intrinsic source and in observed intensity-versus-time profiles that are asymmetric, with a sharp rise and an exponential decay. Both of these features are consistent with observations of solar radio bursts.

Can a cosmic ray carrot explain the ionization level in diffuse molecular clouds?

Low energy cosmic rays are the major ionization agents of molecular clouds. However, it has been shown that, if the cosmic ray spectrum measured by Voyager 1 is representative of the whole Galaxy, the predicted ionization rate in diffuse clouds fails to reproduce data by 1-2 orders of magnitude, implying that an additional source of ionization must exist. One of the solutions proposed to explain this discrepancy is based on the existence of an unknown low energy (in the range 1 keV-1 MeV, not probed by Voyager) cosmic ray component, called carrot when first hypothesized by Reeves and collaborators in the seventies. Here we investigate the energetic required by such scenario. We show that the power needed to maintain such low energy component is comparable of even larger than that needed to explain the entire observed cosmic ray spectrum. Moreover, if the interstellar turbulent magnetic field has to sustain a carrot, through second-order Fermi acceleration, the required turbulence level would be definitely too large compared to the one expected at the scale resonant with such low energy particles. Our study basically rules out all the plausible sources of a cosmic ray carrot, thus making such hidden component unlikely to be an appealing and viable source of ionization in molecular clouds.

Electron Distribution Functions Around a Reconnection X‐Line Resolved by the FOTE Method

AbstractUsing data from the MMS mission and the First‐Order Taylor Expansion (FOTE) method, here we reveal electron distribution functions around a reconnection X‐line at the Earth's magnetopause. We find cigar distribution of electrons in both the magnetosphere‐side and magnetosheath‐side inflow regions, isotropic distribution of electrons at the separatrix, and loss of high‐energy electrons in the antiparallel direction in the magnetosheath‐side inflow region. We interpret the formation of cigar distribution in the inflow regions using the Fermi mechanism—as suggested in previous simulations, the loss of high‐energy electrons in the magnetosheath side using the parallel electric fields—which evacuate electrons to escape the diffusion region along the antiparallel direction, and the isotropic distribution at the separatrix using the pitch angle scattering by whistler waves—which exist frequently at the separatrix. We also find that the electron distribution functions can change rapidly (within 60 ms) from isotropic to cigar as the spacecraft moves slightly away from the separatrix.

BL Lacertae Objects: A Short Review

BL Lacertae objects (BLLs) constitute a class of active galactic nuclei (AGNs) with extreme observational features explained by non-thermal radiation from a relativistic jet nearly pointed along the observer’s line-of-sight. Their spectral energy distribution (SED), extending over 17-19 orders of the frequency, is of non-thermal origin and shows a typical two-humped structure. The lower-energy component, ranging from the radio to X-rays, is explained via synchrotron radiation emitted by ultra-relativistic electrons/positrons/protons, to be initially accelerated via the Blandford-Znajek mechanism or magneto-hydrodynamic processes in the vicinity of a central supermassive black hole. Afterwards, the particles should undergo further acceleration to ultra-relativistic energies by means of different mechanisms (first and second-order Fermi processes, relativistic magnetic reconnection, shear acceleration, jet-star interaction etc.) locally, in the jet emission zone. Our intensive X-ray spectral study of TeV-detected, high-energy-peaked BLLs (HBLs) often show the signatures of an effective second-order Fermi (stochastic) acceleration close to the shock front, while the processes related to the first-order Fermi acceleration are relatively rarely presented. The TeV-undetected HBLs and low-energy-peaked BLLs (LBLs) mostly do not show the signatures of efficient stochastic acceleration in their jets. Concerning the higher-energy component, the most frequently considered scenario incorporates an inverse Compton (IC) scattering of synchrotron photons by their ”parent” electron-positron population (synchrotron self-Compton model, SSC). However, this simple scenario sometimes is challenged by uncorrelated X-ray and TeV variability, more easily explained by multizone SSC, external Compton (EC) and hadronic scenarios.

Electron acceleration in interaction of magnetic islands in large temporal-spatial turbulent magnetic reconnection

A new combined Fermi, betatron, and turbulent electron acceleration mechanism is proposed in interaction of magnetic islands during turbulent magnetic reconnection evolution in explosive astrophysical phenomena at large temporal-spatial scale (LTSTMR), the ratio of observed current sheets thickness to electron characteristic length, electron Larmor radius for low-β and electron inertial length for high-β, is on the order of 1010–1011; the ratio of observed evolution time to electron gyroperiod is on the order of 107–109). The original combined acceleration model is known to be one of greatest importance in the interaction of magnetic islands; it assumes that the continuous kinetic-dynamic temporal-spatial scale evolution occurs as two separate independent processes. In this paper, we reconsider the combined acceleration mechanism by introducing a kinetic-dynamic-hydro full-coupled model instead of the original micro-kinetic or macro-dynamic model. We investigate different acceleration mechanisms in the vicinity of neutral points in magnetic islands evolution, from the stage of shrink and breakup into smaller islands (kinetic scale), to the stage of coalescence and growth into larger islands (dynamic scale), to the stages of constant and quasi-constant (contracting-expanding) islands (hydro scale). As a result, we give for the first time the acceleration efficiencies of different types of acceleration mechanisms in magnetic islands’ interactions in solar atmosphere LTSTMR activities (pico-, 10–2–105 m; nano-, 105–106 m; micro-, 106–107 m; macro-, 107–108 m; large-, 108–109 m).

The First- and Second-Order Fermi Acceleration Processes in BL Lacertae Objects

BL Lacertae objects constitute a rare class of active galactic nuclei with extreme observational features attributed to the Doppler-boosted emission from a relativistic jet, closely aligned to our line-of-sight. Their spectral energy distribution, extending over 17–19 orders of frequency from radio to the TeV energy range, is of non-thermal origin and shows a typical two-component structure. The lower-energy component, ranging from the radio to X-rays in the high-energy peaked BL Lacertae sources, is widely accepted to be a synchrotron radiation emitted by ultra-relativistic charged particles, to be initially accelerated via the Blandford–Znajek mechanism or magneto-hydrodynamic processes in the vicinity of the central super-massive black hole. However, the accelerated particles should lose the energy, sufficient for the emission of the keV-GeV photons, very quickly and the source can maintain its flaring state on the daily-weekly timescales only if some additional acceleration mechanisms are continuously at work. According to different studies and simulations,the particles can gain tremendous energies due to the propagation of relativistic shocks through the jet: By means of first-order Fermi mechanism at the shock front, or they undergo an efficient stochastic (second-order Fermi) acceleration close to the shock front, in the turbulent jet medium. Our intensive X-ray spectral study of TeV-detected, bright BL Lacertae objects (Mrk 421, 1ES 1959+650, Mrk 501) often show the signatures of the stochastic acceleration, while those related to the first-order Fermi process arefound relatively rarely. The TeV-undetected sources (1H 1516+660, BZB J1341+3959, BZB J1237+6258) mostly do not show the signatures of the efficient stochastic acceleration in their jets.

Particle acceleration and heating in a turbulent solar corona

Turbulence, magnetic reconnection, and shocks can be present in explosively unstable plasmas, forming a new electromagnetic environment, which we call here turbulent reconnection, and where spontaneous formation of current sheets takes place. We will show that the heating and the acceleration of particles is the result of the synergy of stochastic (second order Fermi) and systematic (first order Fermi) acceleration inside fully developed turbulence. The solar atmosphere is magnetically coupled to a turbulent driver (the convection zone), therefore the appearance of turbulent reconnection in the solar atmosphere is externally driven. Turbulent reconnection, once it is established in the solar corona, drives the coronal heating and particle acceleration.

Analytical estimates of proton acceleration in laser-produced turbulent plasmas

With the advent of high power lasers, new opportunities have opened up for simulating astrophysical processes in the laboratory. We show that second-order Fermi acceleration can be directly investigated at the National Ignition Facility, Livermore. This requires measuring the momentum-space diffusion of 3 MeV protons produced within a turbulent plasma generated by a laser. Treating Fermi acceleration as a biased diffusion process, we show analytically that a measurable broadening of the initial proton distribution is then expected for particles exiting the plasma.

System-size Convergence of Nonthermal Particle Acceleration in Relativistic Plasma Turbulence

Abstract We apply collisionless particle-in-cell simulations of relativistic pair plasmas to explore whether driven turbulence is a viable high-energy astrophysical particle accelerator. We characterize nonthermal particle distributions for varying system sizes up to L/2πρ e0 = 163, where L/2π is the driving scale and ρ e0 is the initial characteristic Larmor radius. We show that turbulent particle acceleration produces power-law energy distributions that, when compared at a fixed number of large-scale dynamical times, slowly steepen with increasing system size. We demonstrate, however, that convergence is obtained by comparing the distributions at different times that increase with system size (approximately logarithmically). We suggest that the system-size dependence arises from the time required for particles to reach the highest accessible energies via Fermi acceleration. The converged power-law index of the energy distribution, α ≈ 3.0 for magnetization σ = 3/8, makes turbulence a possible explanation for nonthermal spectra observed in systems such as the Crab Nebula.

Betatron Cooling of Suprathermal Electrons in the Terrestrial Magnetotail

Abstract The cigar distribution of suprathermal electrons (40–200 keV), showing electron pitch angles primarily in the parallel and anti-parallel directions, has been frequently observed in the terrestrial magnetotail. The formation of such a distribution is typically attributed to Fermi acceleration, betatron cooling, or a combination of these. To date, Fermi acceleration has been well studied via both observations and simulations, while betatron cooling has not been verified directly. In this study, we focus on the betatron cooling of suprathermal electrons. By analyzing a unique case observed by the Cluster spacecraft in the Earth's magnetotail (X GSM ≈ −15 R E ), we find a significant drop of electron flux in association with the decrease of magnetic field strength, i.e., a magnetic dip. This magnetic dip is formed due to the expansion of flux tubes driven by two opposite flows. The drop in electron flux, primarily in the perpendicular direction, is therefore strong evidence of betatron cooling. We successfully reproduce these processes using an analytical model.

Exclusion of standard ℏω gravitons by LIGO observation

Dyson (2013 Int. J. Phys. 28 1330041) argued that the extraordinarily large number of gravitons in a gravitational wave makes them impossible to be resolved as individual particles. While true, it is shown in this paper that a LIGO interferometric detector also undergoes frequent and discrete quantum interactions with an incident gravitational wave, in such a way as to allow the exchange of energy and momentum between the wave and the detector. This opens the door to another way of finding gravitons. The most basic form of an interaction is the first order Fermi acceleration (deceleration) of a laser photon as it is reflected by a test mass mirror oscillating in the gravitational wave, resulting in a frequency blueshift (redshift) of the photon depending on whether the mirror is advancing towards (receding from) the photon before the reflection. If e.g. a blueshift occurred, wave energy is absorbed and the oscillation will be damped. It is suggested that such energy exchanging interactions are responsible for the observed radiation reaction noise of LIGO (although the more common way of calculating the same amplitude for this noise is based on momentum considerations). Most importantly, in each interaction the detector absorbs or emits wave energy in amounts far smaller than the standard graviton energy where is the angular frequency of the gravitational wave. This sets a very tight upper limit on the quantization of the wave energy, viz. it must be at least 1011 times below , independently of the value of itself.

Disentangling multiple high-energy emission components in the Vela X pulsar wind nebula with the Fermi Large Area Telescope

Context. Vela X is a pulsar wind nebula in which two relativistic particle populations with distinct spatial and spectral distributions dominate the emission at different wavelengths. An extended 2° × 3° nebula is seen in radio and GeV gamma rays. An elongated cocoon prevails in X-rays and TeV gamma rays. Aims. We use ~9.5 yr of data from the Fermi Large Area Telescope (LAT) to disentangle gamma-ray emission from the two components in the energy range from 10 GeV to 2 TeV, bridging the gap between previous measurements at GeV and TeV energies. Methods. We determine the morphology of emission associated to Vela X separately at energies <100 and >100 GeV, and compare it to the morphology seen at other wavelengths. Then, we derive the spectral energy distribution of the two gamma-ray components over the full energy range. Results. The best overall fit to the LAT data is provided by the combination of the two components derived at energies <100 and >100 GeV. The first component has a soft spectrum, spectral index 2.19 ± 0.16−0.22+0.05, and extends over a region of radius 1.°36±0.°04, consistent with the size of the radio nebula. The second component has a harder spectrum, spectral index 0.9 ± 0.3−0.1+0.3, and is concentrated over an area of radius 0.°63±0.°03, coincident with the X-ray cocoon that had already been established as accounting for the bulk of the emission at TeV energies. Conclusions. The spectrum measured for the low-energy component corroborates previous evidence for a roll-over of the electron spectrum in the extended radio nebula at energies of a few tens of GeV possibly due to diffusive escape. The high-energy component has a very hard spectrum: if the emission is produced by electrons with a power-law spectrum, the electrons must be uncooled, and there is a hint that their spectrum may be harder than predictions by standard models of Fermi acceleration at relativistic shocks.