Three-dimensional plasma measurements within the earth's magnetosphere

First magnetospheric measurements of the three-dimensional velocity distributions for positive ions and electrons within the energy range 1 eV E/Q 45keV are reported. These velocity distributions are gained with quadrispherical Lepedeas on board the spacecraft ISEE-1 and -2. Three-dimensional bulk flows of protons in the vicinity of the magnetopause and within the dayside magnetosphere and dawn sector of the magnetotail are presented. Proton drift velocities within the magnetosphere and magnetotail can be directly determined and employed to calculate the corresponding quasi-static perpendicular electric fields and to provide quantitative analyses of kinematical models for plasma motions. Nonmonotonic features in the electron velocity distributions are found simultaneously with the presence of electron cyclotron harmonic electrostatic waves in the dayside magnetosphere. The relationship of the observed electron velocity distributions to expectations for resonant pitch-angle and energy diffusion is discussed, as well as the possibility of the existence of proton cyclotron harmonic instabilities. Examples of the signature of field-aligned acceleration of protons into the magnetosphere and the presence of low-energy ionospheric ions in the near-earth magnetotail are also presented. Perpendicular electrostatic fields can be calculated from the observed three-dimensional velocity distributions and are found to have typical magnitudes of 1 mV m^-1.     

Wave-particle interactions between the ring current particles and micropulsations associated with the plasmapause

In this paper the drift-wave instabilities likely to occur at and near the plasmapause during the period of magnetospheric disturbances are described. The analysis predicts that the proton cyclotron drift loss-cone wave (non-flute electrostatic mode) grows at and near the plasmapause through the drift cyclotron resonant interactions of the ring current protons. The wave is particularly effective for the turbulent loss of the ring current protons just beyond the plasmapause. In a region just inside the plasmapause, the wave is likely to be stabilized by the Landau interaction of the plasmaspheric particles. The unstable wave propagates in opposite directions inside and outside the plasmapause. Accordingly, the proton precipitation pattern would be different in respective regions. The unified loss mechanism of the ring current protons is presented.It is suggested that an ordinary mode instability occurs through the drift resonant interactions with the ring current electrons far beyond the plasmapause. This wave is excited only in a high- plasma with the conditions that the electron temperature perpendicular to the magnetic field is greater than the parallel temperature and that the temperature gradient has an opposite sign to that of the number density and magnetic field. The frequency and wavelength of the fastest growing wave depend sharply on the temperature anisotropy as well as the strength of the inhomogeneities (in temperature, magnetic field and number density). The fastest growing wave has a period of 36.9 s under certain conditions. This wave is likely to be an origin of the pitch-angle diffusion of the ring current electrons.     

Determination of the characteristics of the gamma-ray telescope Gamma-1

The Gamma-1 telescope has been developed through a collaboration of scientists in the USSR and France in order to conduct -ray astronomical observations within the energy range from 50 to 5000 MeV. The major characteristics of the telescope were established by Monte-Carlo simulations and calibrations made with the aid of electron and tagged -ray beams produced by an accelerator, and these have been found to be as follows: the effective area for photons coming along the instrument's axis varies from about 50 cm² at E = 50 MeV to approximately 230 cm² at E 300 MeV; the angular resolution (half opening of the cone embracing 68% events) is equal to 2.7° at E = 100 MeV, and 1.8° at E = 300 MeV; the energy resolution (FWHM) varies from 70% to 35% as the energy of the detected photons increases from 100 to 550 MeV; the telescope's field-of-view at the half-sensitivity level is 300–450 square degrees depending upon the spectrum of the detected radiation, and the event selection logic. Proceeding from the thus obtained characteristics it is demonstrated that a point source producing a photon flux J (E 100 MeV) = 3 × 10^-7 cm^-2 s^-1, can be detected with a 5 significance by observing it during 10⁶ s at the level of the Cygnus background, and a source having intensity J (E 100 MeV) = 10^-6 cm^-2 s^-1 can be detected to within a mean square positional accuracy of about 15.     

Theoretical studies of the flux and energy spectrum of gamma radiation from the Sun

The purpose of this work is to study the various -ray-production mechanisms in solar flares and to calculate the flux, the spectrum, and the decay curves of radiation. Using the continuity equation and taking into account the energy losses for solar-flare-accelerated particles, we obtain the time-dependent particle distribution and thus the time behavior of the resulting rays. The important processes for producing rays in solar flares are found to be nonthermal electron bremsstrahlung, decay of neutral mesons, positron annihilation, neutron capture, and decay of excited nuclei. The results are applied to several known solar flares. For a large flare such as the class 3⁺ on February 23, 1956, continuous rays with energies up to 100 MeV from electron bremsstrahlung and neutral meson decays are observable at the orbit of the Earth by existing -ray detectors. Line rays from positron annihilation (0.51 MeV), neutron capture (2.23 MeV), and deexcitation of excited nuclei O¹⁶ (6.14 and 7.12 MeV) and C¹² (4.43 MeV) are particularly strong and well above the continuous -ray background due to electron bremsstrahlung. These lines can be detected at the Earth.NASA-NRC Resident Research Associate.     

Anomalous Cosmic Rays and Solar Modulation

We review aspects of anomalous cosmic rays (ACRs) that bear on the solar modulation of energetic particles in the heliosphere. We show that the latitudinal and radial gradients of these particles exhibit a 22-year periodicity in concert with the reversal of the Sun's magnetic field. The power-law index of the low energy portion of the energy spectrum of ACRs at the shock in 1996 appears to be -1.3, suggesting that the strength of the solar wind termination shock at the helioequatorial plane is relatively weak, with s 2.8. The rigidity dependence of the perpendicular interplanetary mean free path in the outer heliosphere for particles with rigidities between 0.2 and 0.7 GV varies approximately as R2, where R is particle rigidity. There is evidence that ACR oxygen is primarily multiply charged above 20 MeV/nuc and primarily singly-charged below 16 MeV/nuc. The location of the termination shock was at 65 AU in 1987 and 85 AU in 1994.     

Voyager energetic particle observations at interplanetary shocks and upstream of planetary bow shocks: 1977–1990

The Voyager 1 and 2 spacecraft include instrumentation that makes comprehensive ion (E 28 keV) and electron (E 22 keV) measurements in several energy channels with good temporal, energy, and compositional resolution. Data collected over the past decade (1977–1988), including observations upstream and downstream of four planetary bow shocks (Earth, Jupiter, Saturn, Uranus) and numerous interplanetary shocks to 30 AU, are reviewed and analyzed in the context of the Fermi and shock drift acceleration (SDA) models. Principal findings upstream of planetary bow shocks include the simultaneous presence of ions and electrons, detection of tracer ions characteristic of the parent magnetosphere (O, S, O⁺), power-law energy spectra extending to 5 MeV, and large (up to 100:1) anisotropies. Results from interplanetary shocks include observation of acceleration to the highest energies ever seen in a shock ( 22 MeV for protons, 220 MeV for oxygen), the saturation in energy gain to 300 keV at quasi-parallel shocks, the observation of shock-accelerated relativistic electrons, and separation of high-energy (upstream) from low-energy (downstream) populations to within 1 particle gyroradius in a near-perpendicular shock. The overall results suggest that ions and electrons observed upstream of planetary bow shocks have their source inside the parent magnetosphere, with first order Fermi acceleration playing a secondary role at best. Further, that quasi-perpendicular interplanetary shocks accelerate ions and electrons most efficiently to high energies through the shock-drift process. These findings suggest that great care must be exercised in the application of concepts developed for heliosphere shocks to cosmic ray acceleration through shocks at supernova remnants.     

Probing the solar wind acceleration region using spectroscopic techniques

Measurements of the intensities and profiles of UV and EUV spectral lines can provide a powerful tool for probing the physical conditions in the solar corona out to 8 R and beyond. We discuss here how measurements of spectral line radiation in conjunction with measurements of the white light K-corona can provide information on electron, proton and ion temperatures and velocity distribution functions; densities; chemical abundances and mass flow velocities. Because of the fundamental importance of such information, we provide a comprehensive review of the formation of coronal resonance line radiation, with particular emphasis on the H i L line, and discuss observational considerations such as requirements for rejection of stray light and effects of emission from the geocorona and interplanetary dust. Finally, we summarize some results of coronal H i L and white light observations acquired on sounding rocket flights.Paper presented at the IX-th Lindau Workshop The Source Region of the Solar Wind.     

Energetic particles at high latitudes

We review work on diffusion coefficients of energetic particles with an attempt to extract implications on their behaviour at high latitudes. In the ecliptic plane results from solar energetic particle propagation between the Sun and about 5 AU can be described by an effective radial mean free path _r which is approximately constant as a function of distancer. When particle propagation in three dimensions in the heliosphere is considered it is not sufficient to consider _r only. Jovian electrons can be used as probes to determine the parameters of three-dimensional diffusion. In the polar regions diffusion is dominated by its parallel component. Some predictions how should vary with latitude are discussed. For different choices of this variation we present expectations for intensity-time profiles of solar particle events during the Ulysses polar passages.     

The Edison infrared space observatory

For five years, theEdison program has had the goal of developing new designs for infrared space observatories which will break the cost curve by permitting more capable missions at lower cost. Most notably, this has produced a series of models for purely radiative and radiative/mechanical (hybrid) cooling which do not use cryogens and optical designs which are not constrained by the coolant tanks. Purely radiatively-cooled models achieve equilibrium temperatures as low as about 20 K at a distance of 1 AU from the sun. More advancedEdison designs include mechanical cooling systems attached to the telescope assembly which lower the optical system temperature to 5 K or less. Via these designs, near-cryogenic temperatures appear achievable without the limitations of cryogenic cooling. OneEdison model has been proposed to the European Space Agency as the next generation infrared space observatory and is presently under consideration as a candidate ESA Cornerstone mission. The basic design is also the starting point for elements of future infrared space interferometers.     

Latitude and solar-cycle dependence of radial IMF intensity

I describe a simple procedure for extrapolating the observed solar magnetic field into the heliosphere, which averages the asymptotic fields computed using the standard source surface and current sheet models. The resultant field is characterized by strong latitudinal gradients (maintained by volume currents outside the source surface) and by abrupt reversals in direction at the current sheets. The model yields good agreement with the observed long-term variation of the radial IMF component in the ecliptic, and is used to predict the variation of |B _r | along the latitudinal trajectory of Ulysses during 1990–1994. As found in earlier studies, the magnitude ofB _r at any latitude is determined largely by the strength and relative orientation of the Sun's dipole moment.     

Some problems of gamma-astronomy

The modern state of gamma-ray astronomy is reviewed, the paper being mainly devoted to the theoretical models that describe generation of gamma-ray emission under astrophysical conditions. Basic information on the processes of generation and absorption of gamma-rays, as well as the results of observations for various gamma-ray photon energies are reported.In the region of soft gamma-ray emission (i.e., for energies less than tens of MeV), where emission in gamma-ray lines dominates, we also discuss the nature of gamma-ray bursts, the origin of gamma-ray emission from the galactic centre, etc.Discrete sources and, in particular, the mysterious source Cyg X-3 are discussed in the region of very high (E > 10¹² eV) and ultra-high (E > 10¹⁵ eV) energy gamma-ray emission.A larger portion of the review is devoted to the analysis of cosmic-ray origin on the basis of the available gamma-ray data in the region from several tens of MeV to several GeV. The peculiarity of this energy range is, in particular, in the fact that the diffuse galactic emission was observed mainly there. We also discuss the problem of determination of the cosmic-ray density gradient from the gamma-ray data.The origin of high-latitude gamma-ray emission, the problem of galactic gamma-ray halo, etc., are discussed.The theoretical models explaining the nature of unidentified gamma-ray sources, as well as the results of measurements and theoretical estimations of a gamma-ray flux from SN1987A are analysed.List of Notations m electron mass, m = 9.108 × 10^–28 g, - M proton mass, M = 1.672 × 10^–24 g, - e electron charge, e = 4.803 × 10^–10 CGS - c velocity of light, c = 2.9979 × 10¹⁰ cm s^–1, - k Boltzmann constant, k = 1.380 × 10^–16 erg grad^–1, - e electron - p proton - gamma-ray photon - p antiproton - ^{0 0}-meson - -lepton - e ⁺ positron - r, , x radio-frequency, gamma-ray, and X-ray emission bands - E total energy of a particle - E _k kinetic energy - p particle momentum - spectral index for particles - spectral index for emission - n particle density (concentration) - H magnetic field strength - T temperature - _ph energy of low-energy photons - emission frequency - r _H Larmor radius of relativistic particles - k wave number - , z cylindric coordinates, in this case the coordinate (radius) along the galactic disk, z perpendicular to the galactic disk - M solar mass, M = 1.99 × 10³³ g.     

IMF connection for energetic protons observed at Ulysses via mid-latitude solar wind rarefaction regions

As Ulysses moved inward and southward from mid-1992 to early 1994 we noticed the occasional occurrence of inter-events, lasting about 10 days and falling between the recurrent events, observed at proton energies of 0.48–97 MeV, associated with Corotating Interaction Regions (CIR). These inter-events were present for several sequences of two or more solar rotations at intensity levels around 1% of those of the neighbouring main events. When we compared the Ulysses events with those measured on IMP-8 at 1 AU we saw that the inter-events appeared at Ulysses after the extended emission (>10 days) of large fluxes of solar protons of the same energy that lasted at least one solar rotation at 1 AU. The inter-events fell completely within the rarefaction regions (dv/dt<0) of the recurrent solar wind streams. The interplanetary magnetic field (IMF) lines in the rarefactions map back to the narrow range of longitudes at the Sun which mark the eastern edge of the source region of the high speed stream. Thus the inter-events are propagating at mid-latitudes to Ulysses along field lines free from stream-stream interactions. They are seen in the 0.39–1.28 MeV/nucleon He, which exhibit a faster decay, but almost never in the 38–53 keV electrons. We show that the inter-events are unlikely to be accelerated by reverse shocks associated with the CIRs and that they are more likely to be accelerated by sequences of solar events and transported along the IMF in the rarefactions of the solar wind streams.     

A three-dimensional plasma and energetic particle investigation for the wind spacecraft

This instrument is designed to make measurements of the full three-dimensional distribution of suprathermal electrons and ions from solar wind plasma to low energy cosmic rays, with high sensitivity, wide dynamic range, good energy and angular resolution, and high time resolution. The primary scientific goals are to explore the suprathermal particle population between the solar wind and low energy cosmic rays, to study particle accleration and transport and wave-particle interactions, and to monitor particle input to and output from the Earth's magnetosphere.Three arrays, each consisting of a pair of double-ended semi-conductor telescopes each with two or three closely sandwiched passivated ion implanted silicon detectors, measure electrons and ions above 20 keV. One side of each telescope is covered with a thin foil which absorbs ions below 400 keV, while on the other side the incoming <400 keV electrons are swept away by a magnet so electrons and ions are cleanly separated. Higher energy electrons (up to 1 MeV) and ions (up to 11 MeV) are identified by the two double-ended telescopes which have a third detector. The telescopes provide energy resolution of E/E0.3 and angular resolution of 22.5°×36°, and full 4 steradian coverage in one spin (3 s).Top-hat symmetrical spherical section electrostatic analyzers with microchannel plate detectors are used to measure ions and electrons from 3 eV to 30 keV. All these analyzers have either 180° or 360° fields of view in a plane, E/E0.2, and angular resolution varying from 5.6° (near the ecliptic) to 22.5°. Full 4 steradian coverage can be obtained in one-half or one spin. A large and a small geometric factor analyzer measure ions over the wide flux range from quiet-time suprathermal levels to intense solar wind fluxes. Similarly two analyzers are used to cover the wide range of electron fluxes. Moments of the electron and ion distributions are computed on board.In addition, a Fast Particle Correlator combines electron data from the high sensitivity electron analyzer with plasma wave data from the WAVE experiment (Bougeretet al., in this volume) to study wave-particle interactions on fast time scales. The large geometric factor electron analyzer has electrostatic deflectors to steer the field of view and follow the magnetic field to enhance the correlation measurements.     

Observations of substorm-associated particle-flux variations at 6⩽L⩽8 with GEOS-1

Measurements made with the charged particle spectrometer of the Max-Planck-Institut für Aeronomie onboard GEOS-1 were used to investigate the behaviour of energetic electrons and ions in the dusk sector of the magnetosphere. During substorms the integral ion flux ( 24 KeV) increased whereas the integral electron flux ( 20 KeV) first decreased and later on also increased. The dependences of these flux variations on pitch-angle and particle energy are described and discussed in terms of particle drift in the geomagnetic and geoelectric fields and adiabatic energy variations. The results also provide some information on the source region of the drifting particles.     

Relativistic solar proton events

Energetic solar flare particles contain rich information concerning mechanisms of particle acceleration on the Sun and subsequent transport through turbulent interplanetary space. Even the most energetic particles, in particular protons with kinetic energy above 500 MeV, may undergo coronal and interplanetary propagation effects, disturbing their accelerated injection spectrum after release from the solar flare. Relativistic solar proton events are recorded by neutron monitors at ground level. A detailed knowledge of the response of these ground-based detectors to the impact by a beam of protons on the top of the atmosphere is required to analyze these observations. The spectral index of arriving protons can be obtained from the response of the world-wide network of neutron monitors provided their directional anisotropy is known. The spectral index may also by determined from the relative enhancements in count rates of two similar detectors at different altitudes but similar asymptotic cones of acceptances, or from the relative enhancements of two detectors with different spectral sensitivities but at the same location of high latitude. Ground level enhancements from solar flare protons have been recorded at Sanae, Antarctica, since 1971 by two neutron monitors with different sensitivities to primary protons in the rigidity range from 1 GV to 5 GV. Spectral indexes of about 20 of these more energetic solar flare proton events have been determined from the two detector enhancements recorded at Sanae. These indexes do not show any increase (softening of the relativistic proton spectra) with increasing heliolongitude away from the preferred IMF connection region as was obtained for 20–80 MeV protons. Furthermore, most of the enhanced count rates show fluctuations larger than statistical, indicative of propagation in a mostly turbulent interplanetary magnetic field.     

Dynamics of magnetospheric ion Composition as observed by the GEOS mass spectrometer

After one year of operation the GEOS-1 Ion Composition Experiment has surveyed plasma composition at all local times in the L range 3 8 and the energy per charge range from thermal to 16 keV/e. From measurements made in the keV range during eleven magnetic storms we find that the percentage of heavy (M/Q > 1) ions present in the outer magnetosphere increases by a factor of 3 to 10 during disturbances. We conclude that two independent sources (solar wind, characterized by ⁴He²⁺, and ionosphere, characterized by O⁺) give on the average comparable contributions to injected populations, although in a single event one or the other source may dominate. However, in magnetically quiet periods protons are the dominant species with a few percent of heavy ions. With the help of special satellite manoeuvres magnetic field aligned fluxes of 0.05-3 keV/e H⁺, He⁺, O⁺ with traces of O²⁺ have been observed which may be related to ion beams found previously at lower altitudes in the auroral zone. At still lower energies ( 1 eV/e) the thermal plasma population is found to be made up of six ion species, three of which, D⁺, He²⁺ and O²⁺, were unknown in the magnetosphere prior to the GEOS-1 measurements. We present here a study of the evolution of doubly charged ions and their parent populations over four consecutive days. Various production mechanisms for doubly charged ions are discussed. We argue that ionization of singly charged ions by UV and energetic electrons and protons is the dominant process for plasmasphere production. Furthermore, the observed high concentrations of O²⁺ at high altitudes are a result of production in the upper ionosphere and plasmasphere combined with upward transport by thermal diffusion. Throughout the 1 year lifetime of GEOS-1 the ICE functioned perfectly and, because of its novel design, a short review of technical performance is included here.     

Some results of ionospheric investigations by means of coherent radiowaves emitted by satellites

In this paper we discuss theoretical expressions, determining the difference of Doppler shifts of various coherent radiowave frequencies emitted by a radiator moving in the ionosphere or interplanetary medium. The rotating Doppler effect (Faraday effect) caused by the Doppler shifts ±H of the ordinary and extraordinary waves is also considered. In a three-dimensional inhomogeneous ionosphere, stationary in time (N/t = 0), is determined in the general case, by an equation with three variables. The equation for proper depends only on the local value of the electron concentration N _c around the radiator and on integral values, determining, by means of additional calculations, the angle of refraction or its components, the horizontal gradients of electron concentration N/x and N/y, and in some cases, the integral electron concentration ₀ ^zcN dz. We describe the analysis of the measurements, made with the satellites Cosmos I, II and partially XI, assuming that N/t = N/y = 0, with a two variables equation. The expected errors are considered. The results coincide well for different points (Moscow, The Crimea, Sverdlovsk) and thus agree with the measurements of _H and with height-frequency ionospheric characteristics. The curve giving electron concentration versus height N (z) in the outer ionosphere (above the maximum of F2), shows a new maximum higher than the main maximum of the ionosphere N _MF2 at 120–140 km. At this maximum the value of N (z) is (0.9–0.95) N _MF2. The new data on the large-scale horizontal inhomogeneities of the ionosphere, exceed the previous ones by about a factor 10. By means of the irregular variations of the spectrum W() of the inhomogenous formation is determined. Three unknown constant maxima with values 16 to 18 km, 28 to 32 km and 100 to 120 km are found. The spectrum W () mainly characterizes the local properties of the ionosphere along the orbit of the satellite.     

Presupernova models and supernovae

Present status of the theories for presupernova evolution and triggering mechanisms of supernova explosions are summarized and discussed from the standpoint of the theory of stellar structure and evolution. It is not intended to collect every detail of numerical results thus far obtained, but to extract physically clear-cut understanding from complexities of the numerical stellar models. For this purpose the evolution of stellar cores is discussed in a generalized fashion. The following types of the supernova explosions are discussed. The carbon deflagration supernova of intermediate mass star which results in the total disruption of the star. Massive star evolves into a supernova triggered by photo-dissociation of iron nuclei which results in a formation of a neutron star or a black hole depending on its mass. These two are typical types of the sueprnovae. Between them there remains a range of mass for which collapse of the stellar core is triggered by electron captures, which has been recently shown to leave a neutron star despite oxygen deflagration competing with the electron captures. Also discussed are combustion and detonation of helium or carbon which take place in accreting white dwarfs, and the collapse which is triggered by electron-pair creation in very massive stars.Appendix: Notations A mass number of atomic nucleus - B _v(a, b) incomplete beta function - c _p specific heat at constant pressure - c _p sound velocity - c(sub) center of the star - E _e mean energy of an electron captured by nucleus - E _n nuclear energy release from unit mass of the nuclear fuel specified by n - E _thr threshold energy (9.3) - E _thr,0 energy difference between the ground states of daughter nucleus and parent nucleus (9.1) - E energy of gamma ray emitted from daughter nucleus (9.1) - E _v mean energy of a neutrino emitted by electron capture (9.1) - f flatness parameter (2.17) - g local gravitational acceleration (2.16) - H atomic mass unit - H _p scale height of pressure (2.22) - H (sub) hydrogen-burning shell - k Boltzmann constant - l mixing length of convection - L _cr(M _r ) local Eddington's critical luminosity (4.3) - L _n integrated nuclear energy generation rate by nuclear fuel specified by n - L _v neutrino luminosity - L _{v, cr}(M _r ) local Eddington's critical neutrino luminosity (11.2) - M (current) mass of a star - m _M core mass contained interior to the carbon-burning shell - M _Ch Chandrasekhar's limiting mass (9.6) - M _H core mass contained interior to the hydrogen-burning shell - M _He core mass contained interior to the helium-burning shell - M _ms mass of a star at its zero-age min-sequence - M _O core mass contained interior to the oxygen-burning shell - M _r mass contained interior to a shell at r - M _Si core mass contained interior to the silicon-burning shell - M _WD mass of white dwarf (7.1) - M ₀ normalization factor to the non-dimensional mass (3.3) - M ₁ core mass (3.6) - N polytropic index between pressure and density (2.3) - n polytropic index between pressure and temperature (10.1) - N _A Avogadro number - N _ad adiabatic polytropic index - N _e number of electrons in unit mass of matter - NSE nuclear statistical equilibrium - P pressure - ph (sub) photosphere - Q _e mass fraction of the envelope exterior of the shell e (2.14) - R stellar radius - r radial distance of a shell - r ₀ normalization factor to the non-dimensional radius (3.2) - s specific entropy - S _i specific entropy of ions - T temperature - U homology invariant defined by (2.1) - u _gas specific internal energy of gas - u _rad energy of the radiation field per volume in which unit mass of gas is contained (6.4) - V homology invariant defined by (2.2) - _def velocity of deflagration front (6.10) - X concentration by weight of hydrogen - Y concentration by weight of helium - Y _e mole number of electrons in one gram of matter (9.7) - Y _v mole number of neutrinos in one gram of matter - Z concentration by weight of the elements other than hydrogen and helium - z shock strength (6.6) - 1 (sub) usually denotes the core edge (2.13) - ratio of the mixing length to the scale height of pressure (l/H _p ) - ratio of gas pressure to the total pressure - ratio of the specific heats - gD locus of singularity in U-V plane (2.5) - M(H _p ) mass contained within unit scale height of pressure (4.4) - _ec energy rate by electron captures (9.5) - _n nuclear energy generation rate by the nuclear fuel specified by n - _v neutrino loss rate - L _v ^(D) neutrino loss rate excluding the neutrinos from the electron captures (9.4) - non-dimensional density (3.1) - P/, not the non-dimensional temperature (2.7) - _W Weinberg's angle (5.8) - opacity - _v neutrino opacity (11.2) - describes the effect of electron degeneracy in equation of state (2.19) - _ec rate of electron capture - mean molecular weight - _e mean molecular weight of electrons - _e chemical potential of an electron excluding the rest mass (8.1) - _i mean molecular weight of ions - non-dimensional radius (3.1) - non-dimensional pressure (3.1) - matter density - _cr ^GR critical density above which the general relativistic instability sets in - _cr critical density for reimplosion of the core by beta processes (Section 5) - _ign density at the ignition - _nse density above which the deflagrated matter results in NSE composition - _e non-dimensional entropy of electron-per one electron in units of k(9.2) - _ff timescale of free fall (6.2) - _h (H _p ) timescale of heat transport over unit scale height of pressure (4.4) - _n nuclear timescale for a change in temperature (6.1) - non-dimensional mass (3.1) - _e chemical potential of an electron in units of kT (8.1)     

Finite Larmor radius effects in the magnetosphere

This article reviews theories and observations related to effects produced by finite (and large) Larmor radii of charged particles in the magnetosphere. The FLR effects depend on =r _H /L, wherer _H is the Larmor radius andL is the spatial scale for field/plasma inhomogeneity. The parameter is a basic expansion parameter for most equations describing plasma dynamics in the magnetosphere. The FLR effects enter naturally the drift approximation for particle motion and represent also non-ideal MHD terms in the fluid formalism. The linear and higher order terms in lead to charge separation, energization of particles, and produce viscosity without collisions. The FLR effects introduce also important corrections to the dispersion relations for MHD waves and drift instabilities. Expansion of plasma into magnetic field leads to filamentation of the plasma boundary and to creation of structures with thickness less than an ion gyroradius. Large Larmor radius effects (1) in curved magnetic field geometry lead to stochastic behaviour of particle trajectories and to deterministic chaos. The tiny scale of the electron and ion gyroradii does not necessarily mean that FLR/LLR phenomena have negligible effect on the macroscopic dynamics and energetics of the whole magnetosphere. On the contrary, the small scale gyro-effects may provide the physical mechanism for gyroviscous coupling between the solar wind and the magnetosphere, the mechanism for triggering disruption of the magnetotail current layer, and the mechanism for parallel electric field that accelerate auroral particles.     

Cosmic ray investigation for the Voyager missions; energetic particle studies in the outer heliosphere—And beyond

A cosmic-ray detector system (CRS) has been developed for the Voyager mission which will measure the energy spectrum of electrons from 3–110 MeV and the energy spectra and elemental composition of all cosmic-ray nuclei from hydrogen through iron over an energy range from 1–500 MeV/nuc. Isotopes of hydrogen through sulfur will be resolved from 2–75 MeV/nuc. Studies with CRS data will provide information on the energy content, origin and acceleration process, life history, and dynamics of cosmic rays in the galaxy, and contribute to an understanding of the nucleosynthesis of elements in the cosmic-ray sources. Particular emphasis will be placed on low-energy phenomena that are expected to exist in interstellar space and are known to be present in the outer Solar System. This investigation will also add to our understanding of the transport of cosmic rays, Jovian electrons, and low-energy interplanetary particles over an extended region of interplanetary space. A major contribution to these areas of study will be the measurement of three-dimensional streaming patterns of nuclei from H through Fe and electrons over an extended energy range, with a precision that will allow determination of anisotropies down to 1%. The required combination of charge resolution, reliability and redundance has been achieved with systems consisting entirely of solid-state charged-particle detectors.Principal Investigator of the Voyager Cosmic Ray Experiment.