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NASA NTRS1987

On the acceleration of charged particles at relativistic shock fronts

The diffusive acceleration of highly relativistic particles at a shock is reconsidered. Using the same physical assumptions as Blandford and Ostriker (1978), but dropping the restriction to nonrelativistic shock velocities, the authors find approximate solutions of the particle kinetic equation by generalizing the diffusion approximation to higher order terms in the anisotropy of the particle distribution. The general solution of the transport equation on either side of the shock is constructed, which involves the solution of an eigenvalue problem. By matching the two solutions at the shock, the spectral index of the resulting power law is found by taking into account a sufficiently large number of eigenfunctions. Low-order truncation corresponds to the standard diffusion approximation and to a somewhat more general method described by Peacock (1981). In addition to the energy spectrum, the method yields the angular distribution of the particles and its spatial dependence.

Kirk, J. G.↗
NASA NTRS1981

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.↗
NASA NTRS1987

Fermi acceleration at shocks with arbitrary velocity profiles

Diffusive particle acceleration in modified shock fronts is considered. A method by means of which to obtain the resulting particle spectrum for an arbitrary flow profile is outlined; this method is based on a reformulation of the transport equation as a nonlinear first-order equation. Besides the shape of the flow profile, the spectral index of particles depends on the Peclet number of the shock. Results are given for some sample profiles.

Schneider, Peter↗
NASA NTRS1986

Modeling of ion acceleration through drift and diffusion at interplanetary shocks

A test particle simulation designed to model ion acceleration through drift and diffusion at interplanetary shocks is described. The technique consists of integrating along exact particle orbits in a system where the angle between the shock normal and mean upstream magnetic field, the level of magnetic fluctuations, and the energy of injected particles can assume a range of values. The technique makes it possible to study time-dependent shock acceleration under conditions not amenable to analytical techniques. To illustrate the capability of the numerical model, proton acceleration was considered under conditions appropriate for interplanetary shocks at 1 AU, including large-amplitude transverse magnetic fluctuations derived from power spectra of both ambient and shock-associated MHD waves.

Decker, R. B.↗
NASA NTRS1986

Diffusive electron acceleration at SNR shock fronts and the observed SNR radio spectral indices

The radio synchrotron emission from relativistic electrons in shell supernova remnants (SNRs) provides a unique opportunity to probe the energy distribution of energetic electrons at their acceleration site (SNR shock fronts). This information provides insight into the acceleration mechanism(s). The implications of these observations for the diffusive (first-order Fermi) acceleration of electrons at the SNR shock fronts are discussed.

Bogdan, T. J.↗
NASA NTRS1989

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.↗
NASA NTRS1989

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.↗
NASA NTRS1983

Monte Carlo simulation of steady state shock structure including cosmic ray mediation and particle escape

Both hydrodynamic calculations (Drury and Volk, 1981, and Axford et al., 1982) and kinetic simulations imply the existence of thermal subshocks in high-Mach-number cosmic-ray-mediated shocks. The injection efficiency of particles from the thermal background into the diffusive shock-acceleration process is determined in part by the sharpness and compression ratio of these subshocks. Results are reported for a Monte Carlo simulation that includes both the back reaction of accelerated particles on the inflowing plasma, producing a smoothing of the shock transition, and the free escape of particles allowing arbitrarily large overall compression ratios in high-Mach-number steady-state shocks. Energy spectra and estimates of the proportion of thermal ions accelerated to high energy are obtained.

Ellison, D. C.↗
NASA NTRS1990

Injection and diffusive transport of suprathermal through energetic solar flare protons (35 keV to 20 MeV)

Consideration is given to the injection and interplanetary propagation of low-energy protons caused by the solar particle event of July 20, 1981, in which flare protons in the range from 35 keV to 20 MeV were observed by instruments on ISEE 3. The observed time-intensity and time-anisotropy profiles were fitted over the entire energy range using a model based on the spherically symmetric Fokker-Plank equation, including convection, diffusion, and adiabatic deceleration. The results are used to discuss the behavior of the radial interplanetary diffusion coefficient and the scattering mean free path for protons. Also, evidence is found for diffusive coronal shock acceleration of protons during the event.

Beeck, J.↗
NASA NTRS2000

Cosmic Rays and Their Radiative Processes in Numerical Cosmology

A cosmological hydrodynamic code is described, which includes a routine to compute cosmic ray acceleration and transport in a simplified way. The routine was designed to follow explicitly diffusive, acceleration at shocks, and second-order Fermi acceleration and adiabatic loss in smooth flows. Synchrotron cooling of the electron population can also be followed. The updated code is intended to be used to study the properties of nonthermal synchrotron emission and inverse Compton scattering from electron cosmic rays in clusters of galaxies, in addition to the properties of thermal bremsstrahlung emission from hot gas. The results of a test simulation using a grid of 128 (exp 3) cells are presented, where cosmic rays and magnetic field have been treated passively and synchrotron cooling of cosmic ray electrons has not been included.

Ryu, Dongsu↗
NASA NTRS1985

Collisionless shocks in the heliosphere: Reviews of current research

The present conference on heliospheric collisionless shocks considers such macrostructure-, microstructure-, and particle acceleration-related topics as interplanetary shock phenomena near and within 1 AU, as well as beyond, planetary bow shocks, shock formation and evolution in the solar atmosphere, MHD and gasdynamic theories for planetary bow waves, and subcritical collisionless shock waves. Also discussed are ion reflection, gyration, and dissipation at supercritical shocks, the numerical simulation of quasi-perpendicular collisionless shocks, electron distributions near collisionless shocks, the microtheory of collisionless shock current layers, plasma waves and instabilities, the electron foreshock, upstream suprathermal ions, and both diffusive and shock drift acceleration.

Tsurutani, Bruce T.↗
NASA NTRS1989

The radio signatures of a slow coronal mass ejection - Electron acceleration at slow-mode shocks?

The evolution of a coronal mass ejection (CME) event observed on February 17, 1985 is studied using two-dimensional radio imaging observations along with simultaneously obtained coronagraph observations. This event shows that a slow CME can be associated with type II and type IV radio bursts. The implications of the spatial association of the radio bursts with the CME are discussed. It is argued that the CME is due to an instability of the large-scale magnetic field in a helmet streamer and that the radio bursts are some of the responses to this instability. The new feature of this event is the clear association of the moving type IV burst with a CME traveling slower than the coronal Alfven speed. The structure of slow shocks driven by such a CME is discussed, and it is shown that shock drift and diffusive acceleration are ineffective. An acceleration mechanism involving current-driven lower hybrid waves is proposed.

Kundu, M.↗
NASA NTRS1994

Particle acceleration mechanisms

High-energy particle acceleration is observed to proceed in a diverse variety of astrophysical sites ranging from the terrestrial aurorae to the most distant quasars. Particle acceleration is a fairly common channel for the release of large-scale kinetic, rotational, and magnetic energy. Physical mechanisms include electrostatic acceleration, stochastic processes, and diffusive shock energization. Cosmic-ray energy spectra have shapes which reflect escape, collisional, and radiative losses. The overall acceleration efficiency is controlled by the low-energy particle injection which may, in turn, feed back into the energization. Recent observational developments, which illustrate these general principles and raise fresh questions, are briefly summarized.

Blandford, R. D.↗
NASA NTRSDate not supplied

Origin of High-Energy Protons Responsible for Late-Phase Pion-Decay Gamma-Ray Continuum from the Sun

Gamma-ray emission from solar eruptions can last far beyond the impulsive phase of the associated flares, and hence termed as sustained gamma-ray emission (SGRE). These gamma-rays result from the decay of neutral pions produced when >300 MeV protons collide with hydrogen and heavier elements in the solar photosphere. The source of protons producing SGRE has two possible origins: (i) particles accelerated in the associated flare are somehow trapped in magnetic structures and diffuse slowly to the chromosphere, and (ii) particles accelerated at the shock front that diffuse back to the Sun. In this presentation, we compile currently available observations and inferences that support these two possibilities. We use the gamma-ray data from the Fermi Large Area Telescope (Fermi/LAT) in conjunction with coronal mass ejection (CME) data from the Solar and Heliospheric Observatory (SOHO) and type II radio burst information from the Wind spacecraft. We also use the GOES soft X-ray flare information.

Nat Gopalswamy↗
NASA NTRS1982

Coupled hydromagnetic wave excitation and ion acceleration upstream of the earth's bow shock

A self-consistent theory is set forth for the excitation of hydromagnetic waves and the acceleration of 'diffuse' ions upstream of the earth's bow shock in the quasi-equilibrium that results when the solar wind velocity and the interplanetary magnetic field are nearly parallel. For the waves, the quasi-equilibrium derives from a balance between excitation by the ions, which stream relative to the solar wind plasma, and convective loss to the magnetosheath. For the diffuse ions, the quasi-equilibrium derives from a balance between injection at the shock front, confinement to the foreshock by pitch angle scattering on the waves, and acceleration by compression at the shock front. It also results from loss to the magnetosheath, loss due to escape upstream of the foreshock, and loss via diffusion perpendicular to the average magnetic field onto field lines that do not connect to the shock front. Diffusion equations describing the ion transport and wave kinetic equations describing the hydromagnetic wave transport are solved self-consistently to give analytical expressions. These describe (1) the differential wave intensity spectrum as a function of frequency and distance from the bow shock and (2) the ion omnidirectional distribution functions and anisotropies as functions of energy and distance from the bow shock.

Lee, M. A.↗
NASA NTRS1986

Interstellar scattering of compact radio sources near supernova remnants

A multifrequency VLBI search for interstellar scattering of extragalactic radio sources near supernova remnants is reported. VLBI observations at 610, 1663, and 4991 MHz were made of compact sources near the supernova remnants CTA 1, G33.6 + 0.1, G74.9 + 1.2, and HB 21, and 610 MHz observations were also made of a source near HB 9. These observations were motivated by the possibility of enhanced cosmic ray-induced turbulence in front of supernova remnants, as expected in 'diffusive' theories of shock wave acceleration. Angular broadening is definitely seen in the case of the source 2013 + 370, which lies within 4 arcmin of the supernova remnant G74.9 + 1.2. Present observations cannot unambiguously attribute the scattering material to the supernova remnant, as the line of sight also passes through the Cygnus OB1 association. The source 1849 + 005 appears to be highly scattered, as fringes were not detected even on short baselines at 5 GHz. This result may be due to the low galactic longitude of this source rather than its proximity to the supernova remnant G 33.6 + 0.1. Broadening was not detected for sources whose lines of sight pass close to the supernova remnants HB 9, HB 21, and CTA 1.

Spangler, S. R.↗
NASA NTRS1982

The two-dimensional structure of diffuse ions associated with the earth's bow shock

The lateral distribution of upstream, diffuse energetic ions resulting from shock acceleration at an idealized model bow shock is investigated, where the model consists of a uniform planar shock along which steady source ion injection takes place over a finite region of the shock. The solution exhibits growth toward a peak ion concentration whose location beneath the point of initial magnetic connection with the shock is sensitive to the model parameters. It is found that a plateau forms if the source size is large in comparison to the scale length of ion distribution function's growth, and that cross-field diffusion strongly enhances the diffuse ion concentration near the leading edge of the source.

Skadron, G.↗