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NASA NTRS1985

Acceleration of energetic particles

Acceleration of some particles from the background plasma to highly superthermal energies is a common feature of collisionless shocks in interplanetary space. The complete in situ measurements of bulk flows, thermal plasma, electromagnetic waves and energetic particles available for interplanetary shocks both suggest and test the models of shock acceleration in the solar system and the rest of the universe. This tutorial will review the present state of shock acceleration theory. Scatter-free acceleration by grad B drift in the plasma electric field E = -V x B/c, and diffusive acceleration resulting from scattering by Alfven waves in the plasma on both sides of the shock are discussed. The diffusive theory in simple steady state gives power-law spectra, but also shows the effects of time-dependent shocks and injection rates, escape and other losses, the self-consistent Alfven wave spectra, and plasma flow fields affected by diffusive energetic particle acceleration.

Forman, M. A.↗
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.↗
NASA NTRS1986

The origin of cosmic rays

Data related to the development of cosmic rays are discussed. The relationship between cosmic ray production and the steady-state Boltzmann equation is analyzed. The importance of the power-law spectrum, the scattering rate, the theory of shock acceleration, anisotropic instabilities, and cosmic ray diffusion in the formation of cosmic rays is described. It is noted that spacecraft observations at the earth's bow shock are useful for studying cosmic rays and that the data support the collisionless shock-wave theory of cosmic ray origin.

Eichler, D.↗
NASA NTRS1985

The cosmic-ray shock structure problem for relativistic shocks

The time asymptotic behaviour of a relativistic (parallel) shock wave significantly modified by the diffusive acceleration of cosmic-rays is investigated by means of relativistic hydrodynamical equations for both the cosmic-rays and thermal gas. The form of the shock structure equation and the dispersion relation for both long and short wavelength waves in the system are obtained. The dependence of the shock acceleration efficiency on the upstream fluid spped, long wavelength Mach number and the ratio N = P sub co/cP sub co+P sub go)(Psub co and P sub go are the upstream cosmic-ray and thermal gas pressures respectively) are studied.

Webb, G. M.↗
NASA NTRS1993

Simulations of particle acceleration in parallel shocks: Direct comparison between Monte Carlo and one-dimensional hybrid codes

We have made a direct comparison between two different computer simulations of a plane, parallel, collisionless shock including particle acceleration to energies typical of those of diffuse ions observed at the earth bow shock. Despite the fact that the one-dimensional hybrid and Monte Carlo techniques employ entirely different algorithms, they give surprisingly close agreement in the overall shapes of the complete distribution functions for protons as well as heavier ions. Both methods show that energetic ions emerge smoothly from the background thermal plasma with approximately the same relative injection rate and that the fraction of the incoming plasma's energy flux that is converted into downstream enthalpy flux of the accelerated population (i.e., the acceleration efficiency) is similar in the two cases. The fraction of the downstream proton distribution made up of superthermal particles is quite large, with at least 10% of the energy flux going into protons with energies above 10 keV. In addition, an upstream precursor, produced by backstreaming energetic particles, is present in both shocks, although the Monte Carlo precursor is considerably longer than that produced in the hybrid shock. These results offer convincing evidence that, at least in these ways, the two simulations are consistent in their description of parallel shock structure and particle acceleration, and they lay the groundwork for development of shock models employing a combination of both methods.

Ellison, Donald C.↗
NASA NTRS1982

Cosmic-ray acceleration by stellar winds. II - The spectrum of accelerated particles

Consideration is given to the spectrum of particles accelerated at a stellar wind terminal shock and, at the same time, modulated by convection and diffusion in the stellar wind and decelerated by adiabatic expansion of the unshocked wind. It is noted that a proper study of this problem combines the whole of the cosmic-ray modulation problem with first-order Fermi acceleration at the shock due to repeated diffusive scattering across the shock. The modulation aspect of the model described here is much simpler than modern models of modulation alone; this makes it possible to derive illustrative analytical expressions for the accelerated spectra. Particular cases of monoenergetic and truncated power laws are computed. Energy losses and convective modulation compete with acceleration at the shock so effectively in this model that enhancement of the background cosmic-ray flux by a factor of more than 2 is extremely unlikely.

Forman, M. A.↗
NASA NTRS1991

Oblique MHD cosmic-ray modified shocks: Two-fluid numerical simulations

We present the first results of time dependent, two-fluid, cosmic-ray (CR) modified, MHD shock simulations. The calculations were carried out with a new numerical code for 1-D ideal MHD. By coupling this code with the CR energy transport equation we can simulate the time-dependent evolution of MHD shocks including the acceleration of the CR and their feedback on the shock structures. We report tests of the combined numerical method including comparisons with analytical steady state results published earlier by Webb, as well as internal consistency checks for more general MHD CR shock structures after they appear to have converged to dynamical steady states. We also present results from an initial time dependent simulation which extend the parameter space domain of previous analytical models. These new results support Webb's suggestion that equilibrium oblique shocks are less effective than parallel shocks in the acceleration of CR. However, for realistic models of anisotropic CR diffusion, oblique shocks may achieve dynamical equilibrium on shorter timescale than parallel shocks.

Frank, Adam↗
NASA NTRS1994

Oblique magnetohydrodynamic cosmic-ray-modified shocks: Two-fluid numerical simulations

We present the first results of time-dependent two-fluid cosmic-ray (CR) modified magnetohydrodynamic (MHD) shock simulations. The calculations were carried out with a new numerical code for one-dimensional ideal MHD. By coupling this code with the CR energy transport equation we can simulate the time-dependent evolution of MHD shocks, including the acceleration of the CR and their feedback on the shock structures. We report tests of the combined numerical method including comparisons with analytical steady state results published earlier by Webb, as well as internal consistency checks for more general MHD CR shock structures after they apppear to have converged to dynamical steady states. We also present results from an initial time-dependent simulation which extends the parameter space domain of previous analytical models. These new results support Webb's suggestion that equilibrium oblique shocks are less effective than parallel shocks in the acceleration of CR. However, for realistic models of anisotropic CR diffusion, oblique shocks may achieve dynamical equilibrium on shorter timescales than parallel shocks.

Frank, Adam↗
NASA NTRS1981

On the origin of the MeV energy nucleon flux associated with CIRs

Measurements of recurrent enhancements of interplanetary nucleon flux in the MeV energy range are presented and interpreted. The features recur at the solar rotation period in association with stream-stream plasma interaction regions corotating with the sun. At distances from the sun less than 1 AU, the maximum intensities of the hydrogen and helium components increase with increasing distance between 300%/AU and 600%/AU. A model is proposed which predicts the acceleration of nuclei from keV plasma energies to MeV energies by means of transit time damping of magnetosonic waves as solar wind plasma flows from the sun. Numerical solutions of the transport equation are derived to demonstrate that the model does not reproduce radial variations of hydrogen and helium fluxes, and estimates are made of the radial diffusive mean free path. Finally, the observations are found to be consistent with nucleon acceleration at the CIR shocks beyond 1 AU with subsequent diffusion toward the sun.

Christon, S. P.↗
NASA NTRS1985

Cosmic ray secondary nuclei and the structure of the galaxy

The consequencies of diffusive acceleration of cosmic rays in supernova shocks propagation through an inhomogeneous interstellar medium are explored. The acceleration takes place in the hot, tenuous, intercloud gas, while nuclear collisions, leading to the production of cosmic ray secondaries, predominantly occur in those regions where the supernova shocks collide with interstellar clouds. A simple model is used to calculate the interaction of a (cosmic ray + gas) shock with a cloud, and thus determine the gross topology. Extending this to the whole system, using mean cloud sizes and space densities, allows us to calculate the secondary/primary cosmic ray abundance ratios for light and heavy nuclei.

Morfill, G. E.↗
NASA NTRS1985

Spatial dependence of the local diffusion coefficient measured upstream of the November 12, 1978 interplanetary traveling shock

Characteristics of wuprathermal particles accelerated by quasi-parallel interplanetary traveling shocks have been generally explained in terms of a first order Fermi mechanism. Such models require diffusive scattering of particles upstream of the shock. This scattering is characterized by a local diffusion coefficient, kappa, which is determined by the local power density of waves in the upstream region. The dependence of the diffusion coefficient of suprathermal upstream protons on distance from the November 12, 1978 interplanetary traveling shock using a different approach is studied. Unlike previous studies this method, which is based on measurements of particle streaming and intensity gradients, does not rely on predictions. The local spatial variations of Kappa upstream of the November 12, 1978 shock have been chosen for study because the characteristics of this quasi-parallel shock have been extensively studied, and also because of its favorable geometry (i.e. B field nearly radial).

Gloeckler, G.↗
NASA NTRS1983

Temporal development of diffuse ion events upstream of the earth's bow shock - The October 31, 1977, event

The origin of the intensity-time profile characteristic of diffuse ion events upstream of the earth's bow shock is investigated. It is believed that the profile results from a rotation of the interplanetary magnetic field that produces as a systematic variation in the connection time of field lines with the bow shock. If the connection time exceeds the time needed to reach equilibrium between the shock acceleration and ion loss processes, a plateau in the ion intensity is formed. The upstream diffusion ion event of October 31, 1977, for which simultaneous magnetic field and ion intensity data have been published is used to test this scenario. This event is analyzed using a two-dimensional Gleeson-Axford equation to describe the shock acceleration process and a model bow shock whose nose serves as a uniform source of ions injected into the acceleration process. Intensity-time profiles are calculated for 30-keV and 120-keV protons for a range of diffusion coefficients using connection times that are based on the shock geometry and the magnetic field data.

Skadron, G.↗
NASA NTRS1981

Acceleration of energetic ions at the earth's bow shock

A simple analytical solution is presented which incorporates many of the processes believed to be important in the acceleration of the 'diffuse' component of energetic ions at the earth's bow shock, and which can account for many of the characteristics observed for these events. The solution can account for the observed spectral shape, the observed spatial dependence of the intensity, and the observed magnitude and spatial dependence of the anisotropy.

Lee, M. A.↗
NASA NTRS1992

Numerical simulations of time-dependent cosmic ray mediated shocks

Recent research in unsteady shocks that are influenced by nonlinear aspects of diffusive particle acceleration and that involve multidimensional flows is outlined, and some of the difficulties in making further progress are discussed. It is suggested that in many situations it is probably not appropriate to assume steady states for astrophysical CR shocks. This results both from the need to be concerned about the finite rate at which CR pressure builds and modifies a shock and from the existence of instabilities. Even so, it seems likely that CR-modified shocks can develop to a state with substantial CR pressure. The overall acceleration efficiency and the CR particle momentum distribution produced in time-dependent flows typically depend on several details such as the ratio of various time scales and the initial proportion of relativistic to nonrelativistic particles in the CR populations.

Jones, T. W.↗
NASA NTRS1987

Particle acceleration at shocks - A Monte Carlo method

A Monte Carlo method is presented for the problem of acceleration of test particles at relativistic shocks. The particles are assumed to diffuse in pitch angle as a result of scattering off magnetic irregularities frozen into the fluid. Several tests are performed using the analytic results available for both relativistic and nonrelativistic shock speeds. The acceleration at relativistic shocks under the influence of radiation losses is investigated, including the effects of a momentum dependence in the diffusion coefficient. The results demonstrate the usefulness of the technique in those situations in which the diffusion approximation cannot be employed, such as when relativistic bulk motion is considered, when particles are permitted to escape at the boundaries, and when the effects of the finite length of the particle mean free path are important.

Kirk, J. G.↗
NASA NTRS1977

Wave-particle interaction phenomena associated with shocks in the solar wind

Microscopic wave-particle interaction phenomena must generally affect the evolution of a traveling interplanetary discontinuity such as a collisionless shock, and solar wind plasma instabilities should also be associated with interplanetary acceleration, diffusion, and dissipation. Recent local measurements from diagnostics on widely separated spacecraft illustrate some examples of these interaction phenomena, and two bounding cases are considered in detail here. It is shown that the interplanetary shock of September 14, 1974 (detected on IMP-7, 8, Hawkeye-1, and Pioneer 11) was associated with intense local electrostatic noise and ion acceleration, while the shock of January 6, 1975 (detected on IMP-7 and Helios-1) had no detectable electrostatic turbulence.

Scarf, F. L.↗
NASA NTRS1982

Starprobe - The science opportunities

The scientific objectives of the NASA Starprobe mission for an unmanned spacecraft to pass within three solar radii of the sun's surface are reviewed. Fundamental observations of gravitation, relativity, and factors related to the solar interior, measurements of the static and dynamic electromagnetic fields and the particle populations close to the sun, and observations of the solar atmosphere from the photosphere to the corona with high spatial resolution would be possible with the Starprobe. A determination of the quadrupole coefficient in the expansion of the gravitational potential field of the sun is noted to be possible by measuring the departure from a Keplerian orbit of the Starprobe as it passes perihelion, yielding data on the rate of revolution of the interior of the sun. Further information on shock acceleration, energy losses, radio bursts, interplanetary propagation, and diffusion will be available at 10-60 solar radii.

Underwood, J. H.↗
NASA NTRS1984

A detailed X-ray and radio comparison of Kepler's supernova remnant

High-resolution radio images of Kepler's SNR (SNR (SN 1604) at 6 and 21 cm have been obtained using the VLA. The orientation of linear polarization in the SNR implies a substantial nonrandom radial component for the magnetic field of the remnant. Based on a new X-ray picture of the SNR, obtained using the Einstein Observatory, a detailed comparison of the X-ray and radio morphology is carried out. There is a good correlation between rotation measure, obtained from the radio maps, and emission measure, an X-ray-derived quantity in the SNR shell. From the mean electron density value infered from an analysis of X-ray fluxes, a mean radial magnetic field of 14 micro G and a total magnetic field of 70 microG are estimated. The energy density of relativistic electrons in Kepler's SNR in the shell comparable to the energy density in the magnetic field; the relativistic electron-pressure is 2 percent of the thermal gas pressure. The strong correlation between radio emissivity and X-ray emissivity found over the SNR in somewhat large scale can be ascribed to acceleration of thermal electrons at the shock wave and insignificant diffusion of resultant relativistic electrons.

Matsui, Y.↗