Pitch-angle dependence of first-order Fermi acceleration at shock fronts.
Pitch-angle dependence of first-order Fermi acceleration of particles trapped between shock front and moving magnetic mirror
PARTICLE ACCELERATION↗
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A new path for the electron bulk energization in solar flares: Fermi acceleration by magnetohydrodynamic turbulence in reconnection outflows
We recently proposed that a magnetohydrodynamic (MHD) turbulent cascade produces the bulk energization of electrons to approximately 25 keV in the impulsive phase of solar flares (LaRosa & Moore 1993). In that scenario, (1) the cascading MHD turbulence is fed by shear-unstable Alfvenic outflows from sites of strongly driven reconnection in the low corona, and (2) the electrons are energized by absorbing the energy that flows down through the cascade. We did not specify the physical mechanism by which the cascading energy is ultimately transferred to the electrons. Here we propose that Fermi acceleration is this mechanism, the process by which the electrons are energized and by which the cascading MHD turbulence is dissipated. We point out that in the expected cascade MHD fluctuations of scale 1 km can Fermi-accelerate electrons from 0.1 keV to approximately 25 keV on the subsecond timescales observed in impulsive flares, provided there is sufficient trapping and scattering of electrons in the MHD turbulence. We show that these same fluctuations provide the required trapping; they confine the electrons within the turbulent region until the turbulence eis dissipated. This results in the energization of all of the lectrons in each large-scale (5 x 10(exp 7)cm) turbulent eddy to 25 keV. The Fermi process also requires efficient scattering so that the pitch-angle distribution of the accelerating electrons remains isotropic. We propose that the electrons undergo resonant scattering by high-frequency plasma R-waves that, as suggested by others (Hamilton & Petrosian 1992), are generated by the reconnection. Ions are not scattered by R-waves. Provided that there is negligible generation of ion-scattering plasma turbulence (e.g., L-waves) by the reconnection or the MHD turbulence, the ions will not Fermi-accelerate and the cascading energy is transferred only to the electrons. We conclude that, given this situation, electron Fermi acceleration can plausibly account for the electron bulk energization in impulsive solar flares.
Larosa, T. N.↗
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.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Fermi acceleration of charged particles in transition region beyond magnetosphere.
Fermi acceleration of charged particles in shock transition region beyond magnetosphere
CHARGED PARTICLE↗
The fermi acceleration of charged particles in the transition region beyond the magnetosphere
Fermi acceleration of charged particles in transition region
FERMI SURFACE↗
Fermi acceleration of Lyman-alpha photons by shocks
The repeated scattering of Ly-alpha radiation across a shock front results in a systematic blueshift which may greatly exceed the shock velocity vs and is proportional to cube root of (Nvs), where N is the column density of hydrogen atoms on either side of the shock front. The blueshifting process is similar to the Fermi acceleration of cosmic rays and may be responsible for the blue asymmetric line profiles that have been observed in high-redshift Ly-alpha galaxies. The Ly-alpha line profile in 3C 326.1 is accounted for by a model in which shocks, driven into a population of interstellar clouds by a radio lobe, trigger the formation of ionizing stars and Fermi accelerate the Ly-alpha radiation emitted by H II regions surrounding those stars. Galaxy mergers, particularly between galaxies with low dust content, should produce Ly-alpha lines with strong blue wings.
Neufeld, David A.↗
Fermi acceleration and the structure of interstellar turbulence
Recent observations at length scales of at least about 10 to the 18th cm and about 10 to the 11th cm suggest the possibility of a generally turbulent interstellar gas with a Kolmogorov spectrum. The total r.m.s. fluctuation in fluid properties is of the same order as the mean. The consequences of such a turbulence spectrum for cosmic rays are discussed. If the turbulence is composed of Alfven waves propagating in both directions along the average magnetic field, the rate of Fermi acceleration is found to be significant. Consequences of the turbulence for spatial transport and the general dynamics of the interstellar gas, as well as possible energy sources for the turbulence, are discussed. It is concluded that Fermi acceleration by interstellar turbulence is a possible acceleration mechanism for galactic cosmic rays.
Jokipii, J. R.↗
A model of Fermi acceleration at shock fronts with an application to the earth's bow shock.
Model of Fermi acceleration at shock front developed and applied to Earth bow shock
BOW SHOCK↗
Stochastic Fermi acceleration in solar flares
Proton spectra, valid from non- to ultra-relativistic energies, resulting from stochastic Fermi acceleration in solar flares are calculated. These spectra were obtained by numerically solving the Fokker-Planck equation, in which the escape of the particles from the acceleration region is characterized by an energy-independent escape time. In addition to equilibrium spectra, time-dependent energy spectra showing the approach to equilibrium are also presented. These numerical equilibrium spectra are compared with previous results which were obtained either by Monte Carlo simulations or approximate analytical treatments. There are no analytic solutions valid in the transrelativistic regime, which is very important for the production of pions and neutrons in solar flares. The acceleration efficiency is related to physical parameters, in particular the energy density in either magnetosonic or Alfven waves, and a lower limit is placed on either of these energy densities from acceleration times implied by gamma-ray observations. Also discussed is the physical interpretation of the escape time.
Miller, James A.↗
Explanation of the secondary to primary ratio within the continuous Fermi accelerator model
The secondary to primary ratio in galactic cosmic radiation at relativistic momenta is calculated in a model, where the primaries are continuously accelerated from the thermal galactic background medium by 1st and 2nd order Fermi acceleration. It is shown that the measured decrease with momentum does not exclude that cosmic rays are accelerated in the interstellar medium as a whole. Once a momentum dependence of the mean lifetime and the different spatial source distributions are adequately taken into account, the measured decreasing ratio can be explained.
Lerche, I.↗
Fast Fermi acceleration in the plasma sheet boundary layer
A longstanding question in the field of magnetospheric physics is the source of the energetic particles which are commonly observed along the plasma-sheet boundary layer (PSBL). Several models have been suggested for the acceleration of these particles. Here, a means is suggested by which the fast Fermi acceleration mechanism (Wu, 1984) can accelerate electrons at the plasma sheet and perhaps account for some of the observations. In this scheme, a localized hydromagnetic disturbance propagating through the tail lobe region impinges upon the PSBL, deforming it and displacing it in toward the central plasma sheet. The boundary layer can then act like a moving magnetic mirror. If the disturbance is propagating nearly perpendicular to the layer, then its velocity projected parallel to the layer (and the magnetic field) can be very large, resulting in significant acceleration of reflected particles.
Wu, C. S.↗
Combined first and second order Fermi acceleration at comets
Two-dimensional, time-dependent model calculations indicate that an interplay between velocity and spatial diffusion may be responsible for the acceleration of implanted heavy ions in the cometary preshock region. Velocity diffusion (second order Fermi acceleration) accelerates the pickup ions to moderate energies thus creating a seed population for the more efficient diffusive-compressive shock acceleration. Solar wind convection limits the time available for diffusive-compressive acceleration, therefore the resulting energy spectrum above 100 keV is a power law with a spectral index of 5 - 6, a value which is in reasonably good agreement with observations.
Gombosi, T. I.↗
Combined first- and second-order Fermi acceleration in cometary environments
Two-dimensional (one velocity space and one spatial dimension), time-dependent model calculations indicate that an interplay between velocity and spatial diffusion may be responsible for the acceleration of implanted heavy ions in the cometary preshock region. Velocity diffusion (second-order Fermi acceleration) accelerates the pickup ions to moderate energies, thus creating a seed population for the more efficient diffusive-compressive shock acceleration. Solar wind convection limits the time available for diffusive-compressive acceleration. Therefore, the resulting energy spectrum above the pickup energy is a combination of an exponential decrease at lower energies (up to about 100 keV) and a power law spectrum at higher energies. The calculated energy spectra constitute a surprisingly good fit to the published Vega and Giotto energy spectra above the pickup energy.
Gombosi, T. I.↗
Energetic ions upstream of planetary bow shocks - Fermi acceleration or leakage?
Observations of energetic ions upstream of earth, Jupiter, and Saturn are examined. The velocity dispersions, energy spectra, and ion compositions for the three planets are described. Fermi acceleration and leakage are analyzed as the potential mechanism for the presence of energetic particles upstream of planetary bow shocks. It is noted that energetic ions upstream of planetary bow shock originate from within the planetary magnetosphere, and leakage is the mechanism for the energetic particles.
Krimigis, S. M.↗
Fermi acceleration of auroral particles.
Review of a number of nighttime acceleration mechanisms proposed in the literature for the role of producing the keV nighttime auroral-particle fluxes. Parallel electric fields are rejected for several reasons, but particularly because of the observed simultaneous precipitation of electrons and protons. Acceleration in the neutral sheet is inadequate for producing the particle energies, the observed field-aligned pitch-angle distribution at high latitudes, and the spectral hardening toward lower latitudes. Neutral point mechanisms, although often suggested in principle, have never been demonstrated satisfactorily in theory or in practice. Pitch-angle scattering from a trapped population produced by transverse adiabatic compression is also incapable of producing the field-aligned distribution. It is therefore suggested that longitudinal or Fermi acceleration, which results from the known magnetospheric convection, is the main nighttime auroral acceleration mechanism. The argument is supported by data obtained with the soft-particle spectrometer on Isis 1.
Sharber, J. R.↗
First-order Fermi acceleration in the two-stream limit
A study of the first-order Fermi mechanism for accelerating cosmic-rays at relativistic and nonrelativistic shocks is carried out by using the two-stream approximation. Exact steady-state analytic solutions illustrating the shock acceleration process in the test-particle limit in which monoenergetic (relativistic) seed particles enter the shock through an upstream free-escape boundary are obtained. The momentum spectrum of the shock accelerated particles consists of a series of Dirac delta distributions corresponding to particles that have undergone an integral number of acceleration cycles. Since particles in the model have a finite fixed escape probability from the shock and the particle momenta p are equally spaced in log p, the envelope of the delta functions series is a power law in momentum. The solutions are used to discuss time-dependent aspects of the shock acceleration process in terms of the finite cycle time, escape probability, and momentum change per cycle that can be deduced from the steady-state model. The length-scale over which the accelerated particles extend upstream of the shock is shown to depend upon the particle energy, with the higher energy particles extending further upstream. This effect is shown to be intimately related to the kinematic threshold requirement that the particle speed exceed the fluid speed in order for particles to swim upstream of the shock and participate in the shock acceleration process.
Bogdan, T. J.↗
First-order Fermi acceleration in solar flares as a mechanism for the second-step acceleration of prompt protons and relativistic electrons
Solar flare data from June 27, 1980 balloon-based observations were studied in terms of the hard X ray component. A temporal delay of 3 sec was observed for the X ray emissions above 235 keV. The delay occurred relative to the low-energy electrons and indicated a second acceleration stage. An estimation of the acceleration rate of the first-order Fermi process operating in a closed flare loop was found to be in agreement with the resulting data, including the acceleration of both protons and relativistic electrons. Additional support for the first-order Fermi process is noted in the fact that flares generally occur in magnetic loops, a condition which allows energetic particles to continually interact with the upward moving shock fronts. A correlation has also been observed between the delay times and the H-alpha areas, encouraging the interpretation that the delay times are the shock transit times.
Bai, T.↗
First-order Fermi acceleration of the diffuse ion population near the earth's bow shock
The flux of 30-65 keV particles observed by the ISEE-3 200 earth radii upstream is shown to be an upstream escape of the energetic ions in the earth's bow shock. A formal solution to the transport equation for the distribution function of energetic particles upstream from an isotropic monoenergetic source of particles/sq cm at a plane shock where the plasma changes speed is found, and escape conditions are defined. The efficiency of the acceleration is calculated to depend on the charge/particle, and fluxes near and far upstream of the shock are described analytically. Any model which takes into account shock acceleration by diffusive scattering with significant escape losses produces the observed spectrum close to the shock. The escape loss upstream is demonstrated to control the spectrum and the variation of flux and anisotropy with distance from the shock.
Forman, M. A.↗