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NASA NTRS1988

Collisionless shock formation and the prompt acceleration of solar flare ions

The formation mechanisms of collisionless shocks in solar flare plasmas are investigated. The priamry flare energy release is assumed to arise in the coronal portion of a flare loop as many small regions or 'hot spots' where the plasma beta locally exceeds unity. One dimensional hybrid numerical simulations show that the expansion of these 'hot spots' in a direction either perpendicular or oblique to the ambient magnetic field gives rise to collisionless shocks in a few Omega(i), where Omega(i) is the local ion cyclotron frequency. For solar parameters, this is less than 1 second. The local shocks are then subsequently able to accelerate particles to 10 MeV in less than 1 second by a combined drift-diffusive process. The formation mechanism may also give rise to energetic ions of 100 keV in the shock vicinity. The presence of these energetic ions is due either to ion heating or ion beam instabilities and they may act as a seed population for further acceleration. The prompt acceleration of ions inferred from the Gamma Ray Spectrometer on the Solar Maximum Mission can thus be explained by this mechanism.

Cargill, P. J.↗
NASA NTRS1983

Acceleration of low-energy protons and alpha particles at interplanetary shock waves

The low-energy protons and alpha particles in the energy range 30 keV/charge to 150 keV/charge associated with three different interplanetary shock waves in the immediate preshock and postshock region are studied using data obtained by the ISEE 3. The spatial distributions in the preshock and postshock medium are presented, and the dependence of the phase space density at different energies on the distance from the shock and on the form of the distribution function of both species immediately at the shock is examined. It is found that in the preshock region the particles are flowing in the solar wind frame of reference away from the shock and in the postshock medium the distribution is more or less isotropic in this frame of reference. The distribution function in the postshock region can be represented by a power law in energy which has the same spectral exponent for both protons and alpha particles. It is concluded that the first-order Fermi acceleration process can consistently explain the data, although the spectra of diffuse bow shock associated particles are different from the spectra of the interplanetary shock-associated particles in the immediate vicinity of the shock. In addition, the mean free path of the low energy ions in the preshock medium is found to be considerably smaller than the mean free path determined by the turbulence of the background interplanetary medium.

Scholer, M.↗
NASA NTRS1983

Acceleration and transport processes - Verification and observations

The general problem of diffusive transport and acceleration of energetic charged particles is considered. The transport of solar-flare particles, solar modulation of galactic cosmic rays and shock acceleration processes on the solar wind are examined and observational tests are summarized. It is concluded that the basic diffusive transport equation is a useful approximation in situations like the solar wind, where turbulent scattering by magnetic irregularities is sufficient to maintain near isotropy. The application of this equation to the interstellar medium andd other, more distant astrophysical regimes is then discussed and implications for gamma-ray astrophysics are outlined. Finally the evidence for interstellar turbulence is reviewed and its consequences briefly discussed.

Jokipii, J. R.↗
NASA NTRS1985

Stochastic particle acceleration in solar flares

It is proposed that particles during the second phase of solar flares are accelerated by stochastic resonant scattering off hydromagnetic waves and first order Fermi acceleration in shock waves generated in the impulsive phase of the flare. Solutions allow arbitrary power law momentum dependences of the momentum diffusion coefficient as well as the momentum diffusion coefficient as well as the momentum loss time. The acceleration time scale to a characteristic energy approximately 100 keV for protons can be as short as 5s. The resulting electron spectra show a characteristic double power law with a transition around 200 keV and are correlated to the proton spectra evaluated under equal boundary conditions, indicating that electrons and protons are accelerated by the same mechanism. The correlation between the different spectral indices in the electron double power law and between electron and proton spectra are governed by the ratio of first to second order acceleration and therefore allow a determination of the Alfven Mach number of the shock wave.

Droege, W.↗
NASA NTRS1995

Magnetic reconnection in the presence of sheared flow and density asymmetry: Applications to the Earth's magnetopause

Classical models of magnetic reconnection consist of a small diffusion region bounded by two symmetric slow shocks, across which the plasma is accelerated. Asymmetries often present in space plasmas are sheared plasma flow and dissimilar plasma densities on the two sides of current sheets. In this paper, we investigate magnetic reconnection in the presence of a shear flow and an asymmetric density across the current sheet using two-dimensional magnetohydrodynamic (MHD) simulations. The results demonstrate that magnetic reconnection can occur only for a plasma flow velocity (in the frame of the X line) which is below the Alfven speed in each inflow region. This limits the velocity of the X line to a certain range for a given flow shear and provides an upper limit to the total velocity shear at which reconnection ceases to operate. Depending on the direction of the flow in the adjacent inflow region, the effects from the sheared flow and from the density asymmetry will compete with or enhance each other in respect to the magnitude and location of the currents which bound the outflow regions. The results are applied to the dayside and flank regions of the magnetosphere. For the dayside region where the magnetosheath flow is slow, the magnetic field transition region is thin and the accelerated flow is earthward of the sharp current layer (magnetopause). At the flanks tailward of the X line, shear flow and density asymmetry effects compete making the magnetic field transition layer broad with the high-speed flow contained within the transition region which explains corresponding observations. At the flanks sunward of the X line, shear flow and density asymmetry effects enhance each other and lead to a strong current sheet on the magnetosheath side of the accelerated flow. The total volume affected by magnetic reconnection is much larger than the steady state region. A large bulge region precedes the steady state region. Qualitatively, the bulge and the steady state region have similar signatures and both can explain observations. We provide criteria in order to distinguish between the bulge and the steady state region in observations.

La Belle-Hamer, A. L.↗
NASA NTRS1994

Electron injection and acceleration at nonlinear shocks: Results of numerical simulations

We present results of numerical simulations of electron injection and acceleration at nonlinear high Mach number shocks. The electrons are assumed to be heated at the thermal subshock to an energy E(sub inj), which is treated as a free parameter, above which they are injected by self-generated whistlers to momentum m(sub p) x V(sub A). This injection mechanism requires Mach numbers greater than (43/(beta(sub -)))(((k T(sub e))/(E(sub inj)))(exp 1/2)), where T(sub e) and beta (sub -) are the upstream electron temperature and plasma beta parameter. Above m(sub p) x V(sub A) electrons are trapped in the shock by Alfven waves. In the proton precursor region the Alfven waves are assumed to be generated by protons accelerated at the shock, and have nonlinear intensities. Below GeV, however, electrons of a given rigidity propagate faster than protons with a similar rigidity and therefore diffuse to regions ahead of the proton precursor. In those regions the Alfven waves are generated by the electrons themselves. The diffusion coefficient appears to increase with decreasing acceleration efficiency. As a result, the number of electrons accelerated to energies GeV and above and, hence, the electron to proton ratio, depend only weakly on the extent of electron heating at the subshock. The negative feedback also renders the electron spectra insensitive to shock compression ratio and smoothing length scale. The estimated e/p ratio at GeV is between approximately 1%-10%.

Levinson, Amir↗
NASA NTRS1998

Direct Acceleration of Pickup Ions at The Solar Wind Termination Shock: The Production of Anomalous Cosmic Rays

We have modeled the injection and acceleration of pickup ions at the solar wind termination shock and investigated the parameters needed to produce the observed Anomalous Cosmic Ray (ACR) fluxes. A non-linear Monte Carlo technique was employed, which in effect solves the Boltzmann equation and is not restricted to near-isotropic particle distribution functions. This technique models the injection of thermal and pickup ions, the acceleration of these ions, and the determination of the shock structure under the influence of the accelerated ions. The essential effects of injection are treated in a mostly self-consistent manner, including effects from shock obliquity, cross- field diffusion, and pitch-angle scattering. Using recent determinations of pickup ion densities, we are able to match the absolute flux of hydrogen in the ACRs by assuming that pickup ion scattering mean free paths, at the termination shock, are much less than an AU and that modestly strong cross-field diffusion occurs. Simultaneously, we match the flux ratios He(+)/H(+) or O(+)/H(+) to within a factor approx. 5. If the conditions of strong scattering apply, no pre-termination-shock injection phase is required and the injection and acceleration of pickup ions at the termination shock is totally analogous to the injection and acceleration of ions at highly oblique interplanetary shocks recently observed by the Ulysses spacecraft. The fact that ACR fluxes can be modeled with standard shock assumptions suggests that the much-discussed "injection problem" for highly oblique shocks stems from incomplete (either mathematical or computer) modeling of these shocks rather than from any actual difficulty shocks may have in injecting and accelerating thermal or quasi-thermal particles.

Ellison, Donald C.↗
NASA NTRS1987

Energetic particle acceleration in spherically symmetric accretion flows and shocks

Steady state, spherically symmetric solutions of the cosmic-ray transport equation describing the acceleration of energetic particles in galactic accretion flows onto neutron stars, black holes, white dwarfs, and protostars are studied. The results indicate that astrophysical accretion flows can be partitioned into distinct classes depending upon whether the accretion rate lies above or below a critical value of a few times 10 to the -7th stellar masses/yr. When the particle transport is convection-dominated, both classes of accretion flows exhibit a spectral index appropriate for first-order Fermi acceleration at a plane shock in the absence of losses. As the particle transport becomes diffusion-dominated, both classes show a break and precipitous falloff in the particle spectrum due to the escape of these particles from the accretion flow. The precise nature of the spectrum depends on the relationship between the particle momentum and the spatial diffusion coefficient.

Webb, G. M.↗
NASA NTRS1994

Enhanced cosmic-ray acceleration rates in highly inclined astrophysical shocks

The theory of cosmic-ray acceleration by subluminal magnetohydrodynamics (MHD) astrophysical shocks according to the test particle approximation is extended to highly oblique shocks where flow speeds which appear nonrelativistic in the shock rest frame appear on transformation to the de Hoffmann-Teller or E identically equal to 0 frame to have upstream flow speeds approaching c. Monte Carlo simulation shows that relative to the predictions of diffusion theory, as the upstream E identically equal to 0 frame velocity approaches c, flatter spectra and faster acceleration rates occur. These spectral and acceleration time changes are similar to those found for relativistic, parallel MHD shocks and may affect all nonthermal active galactic nuclei emission from relativistic electrons. Also there is an additional means of increasing the upper limit of the cosmic-ray spectrum expected from active galactic nuclei, although the approximation used may not accurately reproduce the spectral shape.

Lieu, R.↗
NASA NTRS1994

Model images of radio halos around supernova remnants

I present model calculations of profiles and two-dimensional images of the radio synchrotron emission of young supernova remnants, concentrating on observable effects of relativistic eletrons diffusing upstream of the shock wave. If the preshock electron scattering mean free path is sufficiently long, observable synchrotron halos outside the bulk of the radio emission can potentially result; their absence can constrain the mean free path from above. If scattering is primarily due, as expected, to Alfven waves with amplitude detla(B), the halo is expected to extend a distance of order r(sub g)c(delta(B)/B)(exp 2)/v(sub s) beyond the shock, where r(sub g) is the gyroradius of the electrons emitting at the observed frequency, B is the upstream magnetic field strength, v(sub s) is the shock velocity, and the amplitude delta(B) refers to wave with wavelength comparable to r(sub g), of order 10(exp 13) cm for typical supernova-remnant parameters. However, the detailed geometry of the halo varies with the assumptions about particle acceleration in the shock wave. I present an atlas of model profiles and images as a function of preshock diffusion length, of aspect angle between the magnetic field and the line of sight, and of other relevant parameters.

Reynolds, Stephen P.↗
NASA NTRS1981

Energetic particle spectra in finite shocks - The earth's bow shock

Particle acceleration and escape at the earth's bow shock wave are discussed in order to account for reported exponential fast particle spectra. A model is presented of particle acceleration in a finite two-dimensional shock perpendicular to the magnetic field, with particle parallel and perpendicular diffusion coefficients inversely proportional to each other. It is shown that the exponential particle energy per unit charge spectra observed by Ipavich et al. (1979) for the case of a radial solar wind magnetic field may be obtained if the fast particles escape the shock by means of resonant diffusion to unconnected field lines. The calculated e-folding value of the energy/charge ratio is found to be independent of the level of turbulence near the shock and in good agreement with observations. For the case of a nonradial solar wind magnetic field, the model is noted to predict that convection may be the dominant means of escape. It is also pointed out that the parallel and perpendicular diffusion coefficients may be measured indirectly at the bow shock.

Eichler, D.↗
NASA NTRS1994

Ion injection and acceleration at quasi-perpendicular shocks

We present and discuss results of a new model for ion injections and acceleration at quasi-perpendicular collisionless shocks. We use the one-dimensional hybrid simulation (kinetic ions/fluid electrons) and impose an assumption on the ion motion so that diffusion across the magnetic field (normal to the shock front) is possible. These motions are otherwise suppressed by both one- and two-dimensional simulations. We find that, even in strictly perpendicular shocks, when scattering normal to the field is included, a fraction of the incident ions are accelerated to suprathermal energies. When reasonable scattering times are considered, only pickup ions are injected, whereas thermal solar wind ions are not. The acceleration of these ions is very rapid. We have found that a few of the initially low-energy pickup ions can reach many tens to a few hundred times the plasma ramming energy in less than 100 gyroperiods. Furthermore, highly field aligned energetic ions are found to exist upstream of the slightly oblique shock. The most direct applications of this study is toward the interpretation of observations of both solar wind and interstellar pickup ion distributions in the vicinity of interplanetary shocks which are most often quasi-perpendicular. This work also directly addresses a fundamental issue with regard to our current understanding of the anomalous component of cosmic rays.

Giacalone, J.↗
NASA NTRS1986

Coupled hydromagnetic wave excitation and ion acceleration upstream of the Jovian bow shock

We extend the Lee (1982) self-consistent theory of upstream wave excitation and particle energization to address observations by Voyager 2 of sunward propagating MHD waves and diffuse suprathermal particle populations upstream of the Jovian bow shock. Two new ideas are incorporated into the theory. First, the interplanetary seed wave population is taken to be an equal admixture of waves propagating both toward and away from the shock parallel to the interplanetary magnetic field. Second, finite connection times are incorporated approximately into the theory in an effort to understand whether the particle spectra at high energy are limited by particle escape or finite connection time. It is found that finite connection times dominate the particle distribution at energies above 40 keV. In this manner the suprathermal proton distributions can be accounted for by a multiple reflection, shock acceleration theory. We find that the theory can also account for the low-frequency waves observed upstream of the shock in conjunction with the suprathermal ions.

Smith, C. W.↗
NASA NTRS1981

Monte Carlo simulation of charged particles upstream of the earth's bow shock

A simple model of the earth's bow shock is presented and compared with ISEE-1 observations of diffuse ions upstream of the shock. Ion behavior is modeled in a test particle simulation using Monte Carlo techniques for a plane parallel shock at which cold solar wind ions are heated sufficiently to allow diffusion back upstream. Fitting of the model to the observations indicates that the diffusion coefficient must increase faster than linearly with velocity, and provides an upper limit to the acceleration efficiency defined as the proportion of incoming solar wind ions accelerated and observed upstream. Results suggest that astrophysical shocks are capable of accelerating ions directly from the thermal plasma without the need for a distinct preenergizing injection stage.

Ellison, D. C.↗
NASA NTRS1987

Voyager 2 plasma wave observations at Uranus

At Uranus, the Voyager 2 plasma wave investigation observed very significant phenomena related to radio emissions, dust impacts, and magnetospheric wave-particle interactions. On January 19, 1986 (R = 270 R-sub U) the plasma wave investigation detected an intense radio burst at 31 and 56 kHz, and this provided the first indication that Uranus had a magnetosphere. During the encounter, more of these sporadic bursts were observed along with relatively continuous radio emissions extending down to 10 kHz, and a sporadic narrowband radio signal with f near 5 kHz. As Voyager passed through the ring plane, the plasma wave investigation recorded a large number of dust impacts. The Voyager 2 plasma wave instrument also detected many strong electromagnetic and electrostatic plasma waves, with intensity peaks in the region within 12 Uranus radii. These waves have characteristics that can interact strongly with the local plasma and with the trapped energetic particles, leading to precipitation into the atmosphere, charged particle acceleration, and charged particle diffusion. In addition, strong wave activity was detected in the region of the bow and shock and moderate levels in the magnetic tail.

Scarf, F. L.↗
NASA NTRS1994

Statistical analysis of diffuse ion events upstream of the Earth's bow shock

A statistical study of diffuse energetic ion events and their related waves upstream of the Earth's bow shock was performed using data from the Active Magnetospheric Particle Tracer Explorers/Ion Release Module (AMPTE/IRM) satellite over two 5-month periods in 1984 and 1985. The data set was used to test the assumption in the self-consistent model of the upstream wave and particle populations by Lee (1982) that the particle acceleration through hydromagnetic waves and the wave generation are directly coupled. The comparison between the observed wave power and the wave power predicted on the observed energetic particle energy density and solar wind parameters results in a high correlation coefficient of about 0.89. The intensity of diffuse ions falls off approximately exponentially with the distance upstream from the bow shock parallel to the magnetic field with e-folding distances which vary from approximately 3.3 R(sub E) to approximately 11.7 R(sub E) over the energy range from 10 keV/e to 67.3 keV/e for both protons and alpha particles. After normalizing the upstream particle densities to zero bow shock distance by using these exponential variations, a good correlation (0.7) of the density of the diffuse ions with the solar wind density was found. This supports the suggestion that the solar wind is the source of the diffuse ions. Furthermore, the spectral slope of the diffuse ions correlates well with the solar wind velocity component in the direction of the interplanetary magnetic field (0.68 and 0.66 for protons and alpha particles) which concurs with the notion that the solar wind plays an important role in the acceleration of the upstream particles.

Trattner, K. J.↗
NASA NTRS1989

Seed population for about 1 MeV per nucleon heavy ions accelerated by interplanetary shocks

Data obtained between 1977 and 1982 by the ISEE 1 and ISEE 3 satellites on the composition of heavy ions of about 1 MeV per nucleon, accelerated in interplanetary shock events which followed solar flare events, are examined. It was found that the average relative abundances for C, O, and Fe in the shock events were very close to those found for energetic ions in the solar flares, suggesting that, at these energies, the shock accelerated particles have the solar energetic particles as their seed population. This hypothesis is supported by the fact that the Fe/O ratio in the solar particle events is very strongly correlated with the Fe/O ratio in associated diffusive shock events.

Tan, L. C.↗
NASA NTRS1985

Time-dependent nonlinear cosmic ray shocks confirming abstract

Numerical studies of time dependent cosmic ray shock structures in planar geometry are interesting because analytical time-independent solutions are available which include the non-linear reactions on the plasma flow. A feature of these time asymptotic solutions is that for higher Mach numbers (M approximately 5) and for a low cosmic ray upstream pressure the solution is not uniquely determined by the usual conservation laws of mass, momentum and energy. These numerical solutions clearly indicate that much work needs to be done before we understand shock acceleration as a time dependent process. The slowness of the process is possibly due to the fact that there is a diffusive flux into the downstream region in addition to the usual advective losses. Analytic investigations of thie phenomenon are required.

Dorfi, E. A.↗