Properties of energetic water-group ions in the extended pick-up region surrounding comet Giacobini-Zinner

The properties of energetic (65–95 keV) cometary water-group ions in the extended solar wind pick-up region surrounding comet Giacobini-Zinner are examined using data from the EPAS instrument on the ICE spacecraft. In the outer part of this region, extending from cometocentric distances of several hundred thousand to a few million kilometres (the limit of pick-up ion detectability), it is found that large modulations of the ion flux occur (with J_MAX/J_MIN 10²-10³) which are related to the direction of the magnetic field. It is also found that the ions stream in a direction which is intermediate between the directions of the solar wind flow and the E × B drift, and that ions are present at energies somewhat above the local pick-up energy. These properties indicate that the waves which are excited by the unstable “ring-beam” pick-up ion velocity distributions do result in significant scattering of the ions in this region, both in pitch angle and in energy, but that they have insufficient amplitude to scatter the ions into near isotropy in the solar wind frame. Closer to the comet (but still upstream from the bow shock), the ion flux modulations are considerably reduced in amplitude and the ions respond less to the E × B drift, indicating that the ions are scattered nearer to isotropy in this region. Inbound, this transition takes place relatively abruptly at a distance of 4 × 10⁵ km in association with an increase in the solar wind speed, after which the ion flux increases, and ceases to be modulated by the field direction, while the streaming direction is continuously antisolar and unmodulated by the direction of the E × B drift. Outbound, weak vestiges of the ring-beam ion anisotropy are present in the region immediately upstream from the bow shock (at −1 × 10⁵ km), but these become more marked at distances in excess of t4 × 10⁵ km, increasing gradually with increasing distance from the comet. It is shown that the evolution of the ion properties is qualitatively consistent with expectations based on quasi-linear diffusion of the ions by the magnetosonic waves observed during the encounter.     

Acceleration of Pick-up Ions at the Solar Wind Termination Shock

It is generally accepted that pick-up ions act as a seed population for anomalous cosmic rays originating at the solar wind termination shock. We believe that the ion pre-acceleration process operating in the heliosphere up to the termination shock can be very important to inject the ions into the shock acceleration process. The pick-up ions pre-accelerated by solar wind turbulences have already a pronounced high energy tail when they reach the shock. Some fraction of these ions can experience further acceleration up to energies of anomalous cosmic rays by means of shock drift and diffusive acceleration. In the present paper the shock drift acceleration of pick-up ions suffering multiple reflection due to abrupt changes in both the strength and direction of the magnetic field through the shock is considered. The reflection process operates for high velocity particles different from the reflection by the electric cross-shock potential. During the first reflection the mean kinetic energy of pick-up ions increases by approximately a factor of 10. Reflected particles have highly anisotropic velocity distribution. Subsequent excursion of the particles in the turbulent upstream flow leads to diffusion in pitch-angle space and, as a result, the particles can return to the shock again suffering, thus, multiple encounters. In order to describe the motion of particles in the upstream and down streamparts of the flow we solve the Fokker-Plank transport equation for anisotropic velocity distribution function. This revised version was published online in July 2006 with corrections to the Cover Date.     

Reflection of pre-accelerated pick-up ions at the solar wind termination shock: The seed for anomalous cosmic rays

It has been hypothesized for quite some time that interplanetary pick-up ions due to energization taking place in the region close to the solar wind termination shock, at some fraction and as an outcome of a complicated chain of processes, eventually are converted into species of the anomalous cosmic-ray particles. For the actual conversion efficiency it is of great importance to know the energy distribution of these pick-up ions upon their arrival at the shock. It turns out that pre-acceleration of these ions during their passage through the heliosphere shall substantially increase their chances to become reflected at the shock into the upstream direction which is a prerequisite for a further climb-up in energy by virtue of Fermi-1 acceleration processes. In this paper we start out from stochastically pre-accelerated pick-up ions and investigate their behaviour at the shock. With the use of adiabatic approaches in the de Hoffman-Teller frame of the shock, we calculate the energy distribution function of the reflected part of pick-up ions. From the calculated distribution functions it turns out that the reflected ions in the average suffer an energy increase by about a factor of 10, still not enough to let them move off the shock by spatial diffusion in the upstream direction. Thus, since converted back into the shock, they can undergo repeated reflections and energy gains till the diffusion-convection limit is reached. As we show in addition, the reflection probability for pick-up ions is about a factor of 10 higher than expected from the present literature and strongly varies with the off-axis angle, pointing to the fact that the termination shock represents a surface with a three-dimensionally varying source strength for the production of anomalous cosmic rays. The ACR source pattern is also expected to vary during the solar cycle and the relevant injection energies are expected to be larger by factors of 10 to 100 than the canonically adopted 1 keV nucl^–1.Institute for Problems of Mechanics of the Russian Academy of Sciences, Prospect Vernadskogo 101, 117526, Moscow, Russia.     

Shock surfing acceleration

Analytical and numerical analysis identify shock surfing acceleration as an ideal pre-energization mechanism for the slow pick-up ions at quasiperpendicular shocks. After gaining sufficient energy by shock surfing, pick-up ions undergo diffusive acceleration to reach their observed energies. Energetic ions upstream of the cometary bow shock, acceleration of solar energetic particles by magnetosonic waves in corona, ion enhancement in interplanetary shocks, generation of anomalous cosmic rays from interstellar pick-up ions at the termination shock are some of the cases where shock surfing acceleration apply. Inclusion of the lower-hybrid wave turbulence into the laminar model of shock surfing can explain the preferential acceleration of heavier particles as observed by Voyager at the termination shock. At relativistic energies, unlimited acceleration of ions is theoretically possible; because for sufficiently strong shocks main limitation of the mechanism, caused by the escape of accelerated particles downstream of the shock during acceleration no longer exists.     

Low energy ions in co-rotating interaction regions at 1 AU: Evidence for statistical ion acceleration

The possibility of the statistical acceleration of solar wind ions to energies above 10 keV in the vicinity of co-rotating high speed solar wind streams by scattering from hydromagnetic waves is considered. We find that this process may occur only in the compressed fast stream plasma within the interaction region between the stream interface and the trailing edge, and may account for the energetic ion enhancements observed in this region by Richardson and Zwickl (Planet. Space Sci. 32, 1179, 1984). When statistical acceleration occurs in the outer heliosphere, the accelerated ions may provide a source population for acceleration at the co-rotating reverse shock.     

Pick-up Ion Measurements in the Heliosphere – A Review

Measurements of the composition and spatial distribution of pick-up ions inside the heliosphere are reviewed. The first interstellar ⁴He⁺pick-up ions were detected with the SULEICA instrument on the AMPTE spacecraft near Earth's orbit. Most data on pick-up ions were taken in the solar-wind and suprathermal energy range of SWICS on Ulysses while the spacecraft cruised from 1.4 to 5.4 AU and explored the high-latitude heliosphere and solar wind from the ecliptic to ± 80^° heliolatitude. This includes the discovery of H⁺, ⁴He⁺⁺, ³He⁺, N⁺,O⁺, and Ne⁺ pick-up ions that originate from the interstellar neutralgas penetrating the heliosphere. From their fluxes properties of the interaction region between the heliosphere and the Local Interstellar Cloud such as the limits on filtration and the strength of the interstellar magnetic field have been revealed. Detailed analysis of the velocity distributions of pick-up ions led to 1) the discovery of a new distinct source, the so-called Inner Source, consisting of atoms released from interstellar and interplanetary dust inside the heliosphere, 2) the determination of pick-up ion transport parameters such as the long mean free path for pitch-angle scattering of order1 AU, and 3) detailed knowledge on the very preferential injection and acceleration of pick-up ions during interplanetary energetic particle events such as Co-rotating Interaction Regions and Coronal Mass Ejections. SWICS measurements have fully confirmed the theory of Fisk, Koslovsky, and Ramaty that pick-up ions derived from the interstellar gas are the dominant source of the Anomalous Cosmic Rays; they are pre-accelerated inside the heliosphere and re-accelerated at the solar-wind Termination Shock according to Pesses, Eichler, and Jokipii. The data indicate that the Inner Source of pick-up ionsis largely responsible for the occurence of C⁺ in the Anomalous Cosmic Rays. The abundances of recently discovered Inner-Source Mg⁺ and Si⁺ are solar-wind like and consistent with their abundances in the energetic particles associated with Co-rotating Interaction Regions. Knowledge on the injection and acceleration processes in Co-rotating Interaction Regions is applied to discuss the current observational evidence for the Interplanetary Focusing Cone of the interstellar neutral gas due to the Sun's gravitational force. The 25–150 keV/amu suprathermal ⁴He⁺ pick-up ion fluxes measured by CELIAS/STOF on board SOHO over 360^° of ecliptic longitude represent a `local' ionization and acceleration of interstellar atoms at 1 AU or smaller heliocentric distances. Completing the first limited data set of SULEICA/AMPTE on ⁴He⁺ pick-up ions they indicate a density enhancement in the Interplanetary Focusing Cone which is confirmed by recent SWICS/ACE data. Clear evidence for signatures in ecliptic longitude are found in the data on energetic neutral H fluxes observed with the CELIAS/HSTOF sensor on board SOHO. These fluxes are enhanced in the upstream and downstream directions of the interstellar wind. Detection of energetic H atoms, which propagate unaffected by the Heliospheric Magnetic Field, provided for the first time a diagnostic tool for observations near Earth to analyze the structure in ecliptic longitude of the interface region between the heliosphere and the Local Interstellar Cloud. This revised version was published online in July 2006 with corrections to the Cover Date.     

On the origin of energetic particles in the foreshock region of the Earth’s bow shock

We consider the processes related to the formation of the so-called foreshock region upstream of the Earth’s bow shock. We suggest a model based on the surfing of pick-up ions in the bow shock front in terms of which the ion acceleration mechanism in the front can be explained. We ascertain the physical conditions under which the accelerated ions lie upstream of the shock front and determine the direction of motion of the energetic ions. We conclude that it is this population of energetic ions (longitudinal beams) that plays a major role in forming the ion foreshock boundary.     

Observations of energetic ions in inverted V events

Simultaneous measurements of keV ions and electrons with the ESRO 1A satellite have shown the following ion characteristics among others. Ions of about 6 keV energy are strongly field-aligned on the flanks of the inverted V events (mainly through the disappearance of the ion flux near 90° pitch angle). Field-aligned electron fluxes are often found in the same regions of the inverted V events where the ions are field-aligned. At the centre of inverted V events isotropization occurs (except in some small events). The 1 keV ion flux at large pitch angles (80°) is generally not reduced very much when the 6 keV, 80° ion flux shows strongly decreased values. The ratio of the 1 to 6 keV ion flux has a maximum near the centre of an inverted V event where the electron spectrum is hardest and the 6 keV ions are isotropic (or nearly isotropic).The observations are interpreted in terms of a model with two oppositely directed field-aligned electrostatic potential drops: one upper accelerating electrons downward and one lower, produced by the electron influx, which accelerates ions downward. Ion scattering in turbulent wave fields is proposed to be responsible for the observation that the 1 keV ion flux at large pitch angles does not decrease strongly where the 6 keV ion flux does and as an explanation of the isotropization at the centre of the event. The source problem for the ions is eliminated by the precipitating electrons ionizing continuously the thin neutral atmosphere even at altitudes of a few thousand kilometers.     

Particle acceleration by ultrarelativistic shocks: theory and simulations

We consider the acceleration of charged particles near ultrarelativistic shocks, with Lorentz factor     . We present simulations of the acceleration process and compare these with results from semi-analytical calculations. We show that the spectrum that results from acceleration near ultrarelativistic shocks is a power law,     , with a nearly universal value     for the slope of this power law.
We confirm that the ultrarelativistic equivalent of the Fermi acceleration at a shock differs from its non-relativistic counterpart by the occurrence of large anisotropies in the distribution of the accelerated particles near the shock. In the rest frame of the upstream fluid, particles can only outrun the shock when their direction of motion lies within a small loss cone of opening angle     around the shock normal.
We also show that all physically plausible deflection or scattering mechanisms can change the upstream flight direction of relativistic particles originating from downstream by only a small amount:     . This limits the energy change per shock crossing cycle to     , except for the first cycle where particles originate upstream. In that case the upstream energy is boosted by a factor     for those particles that are scattered back across the shock into the upstream region.     

Resonant interactions between cometary ions and low frequency electromagnetic waves

We explore the conditions for resonance between cometary pick-up ions and parallel propagating electromagnetic waves. A model ring—beam distribution for the pick-up H₂O⁺ ions is adopted which allows a direct comparison of the source of free energy for growth from either the beam or the gyrating ring in the limit near marginal stability. Under average solar wind conditions in the inner solar system, the gyrating ring provides the dominant contribution to wave growth. The presence of a field-aligned beam is only important to allow resonance with R-mode waves which occur in two distinct frequency bands either well above or below the pick-up ion gyrofrequency. The most unstable mode is the low frequency R-mode or fast MHD wave, though higher frequency whistlers or low frequency L-mode waves may also be excited by the same source of free energy. The nature of the unstable waves is strongly influenced by the inclination of the interplanetary field. For 3° the rate of the low frequency R-mode growth is dramatically reduced and resonant L-mode waves should experience net ion beam damping. Conversely for 75°, the ion beam velocity will be insufficient to allow resonant R-mode instability; L-mode waves should therefore predominate. The low frequency fast MHD mode should experience the most rapid amplification for intermediate inclination; 30° 75°. In the frame of the solar wind such waves must propagate along the field in the direction upstream towards the Sun with a phase speed lower than the beaming velocity of the pick-up ions. The waves are consequently blown back away from the Sun and would thus be detected with a left-hand polarization by an observer in the cometary frame. We consider this the most likely mechanism to account for the interior MHD waves observed by satellites over an extended spatial region surrounding comets Giacobini-Zinner and Halley.     

Observations of outflowing ion beams on auroral field lines at altitudes of many earth radii

The composition, energy and angular characteristics of upward flowing ionospheric ions at altitudes greater than ～ 20,000 km have been studied by means of the PROGNOZ-7 ion composition experiment. Very narrow beams, having widths corresponding to a mirroring altitude of the order a few thousand kilometers or less, may be found up to altitudes exceeding 30,000 km on the nightside. At much higher altitudes and in regions connected to the dayside/flank boundary layer and plasma mantle, the beams are much broader than expected from adiabatic particle motions from an ionospheric source/acceleration region, suggesting that pitch angle scattering or transverse acceleration processes are present there. Considerable mass dispersion effects have also been observed in some upward flowing ionospheric ion beams. The peak energy for the O⁺ ions may differ by several keV compared to that for the H⁺ ions in one and the same ion beam at altitudes above ～ 20,000 km. The O⁺ ions in these beams have gained considerably more energy than H⁺ in the acceleration process. Many examples with a much higher O⁺ than H⁺ content in the beam have been observed. Possible mechanisms giving rise to the observed effects are discussed, one being several kV of potential drop below the neutral H, O-crossover altitude (500–1500 km). At altitudes where the upflowing ionospheric ions are intermixed with magnetosheath ions, mass dispersion effects are also observed. This dispersion often appears to be the result of a velocity filtering effect caused by the dawn-dusk electric field (earthward convection).     

Energization of positive ions in the cometary foreshock region

The energization of positive ions in front of a cometary bow shock is investigated. Ions produced by ionization of the cometary neutrals interact with the solar wind protons to produce, among other waves, large amplitude oscillations of the ambient magnetic field. Such oscillations are convected towards the comet at the unperturbed solar wind speed far from the shock and at a lower speed closer to the shock (due to the solar wind mass loading) ; hence, they can energize the suprathermal ions by Fermi acceleration. The spatial extension of the acceleration region is of the order of 10⁶ km and the resulting ion energy spectrum is harder than in the Earth's bow shock case. The energization of cometary ions produces an additional deceleration of the solar wind, such that the cometary bow shock of Halley-type comet may be regarded as a “cosmic ray shock”.     

A model of particle acceleration to high energies by multiple supernova explosions in OB associations

The possibility of cosmic-ray (CR) acceleration to energies above 10⁹ GeV per nucleus in extended Galactic OB associations is analyzed. A two-stage acceleration mechanism is justified: at the first stage, the acceleration by separate shock fronts from spatially and temporally correlated supernovae explosions takes place, and, at the second stage, the Fermi acceleration by supersonic turbulence in an extended, strongly perturbed region near the OB association takes place. We calculate the CR energy spectrum, the change in CR chemical composition with energy, and the energy dependence of the mean logarithm of atomic mass, ?lnA?, for the accelerated particles. The calculated values are compared with those observed near the break in the energy spectrum. We estimate the turbulence parameters, which allow the observed features of the energy spectrum and the CR enrichment with heavy elements to be explained.     

Transport,charge exchange and loss of energetic heavy ions in the earth's radiation belts: Applicability and limitations of theory

Ions in the trapping region of the earth's magnetosphere are subject to physical and chemical interactions which control their absolute and relative abundances. Charge exchange reactions act to establish a distribution of ionic states that is largely determined by the chemical properties of the individual species. Convection (“drift”) mechanisms and cross-L diffusion cause ions to be distributed over the entire trapping region with flux intensities determined by the nature and strength of the ion source, transport and loss mechanisms which in general are dependent on energy, mass and charge. Current theories describe ion transport through path tracing for individual particles or by radial diffusion for a population as a whole based on stochastic analysis; a comprehensive treatment of the combined convection and diffusion for trapped and non-trapped ions is yet to be developed. Even in studies where diffusion is the sole transport mechanism considered, only equatorially mirroring particles ($\text{α}{}_0\text{=}\text{π}\text{2}$) have been theoretically treated. There are clearly both upper and lower bounds on the ion energy beyond which diffusion theory ceases to be valid: at high energies where the ion gyroradius becomes too large for the adiabatic approximations to be valid and at low energies where convective drift is a dominant process. In spite of the known shortcomings of the diffusion theory and associated modeling, intriguing theoretical predictions of the relative ionic composition of the radiation belts have been made and some of them are now confirmed by direct observation. Among them is the predicted importance of ions heavier than protons at ring current energies of tens of keV which follows from the charge exchange chemistry.     

Energies of Electrons Accelerated in Turbulent Reconnecting Current Sheets in Solar Flares

Yohkoh observations strongly suggest that electron acceleration in solar flares occurs in magnetic reconnection regions in the corona above the soft X-ray flare loops. Unfortunately, models for particle acceleration in reconnecting current sheets predict electron energy gains in terms of the reconnection electric field and the thickness of the sheet, both of which are extremely difficult to measure. It can be shown, however, that application of Ohm's law in a turbulent current sheet, combined with energy and Maxwell's equations, leads to a formula for the electron energy gain in terms of the flare power output, the magnetic field strength, the plasma density and temperature in the sheet, and its area. Typical flare parameters correspond to electron energies between a few tens of keV and a few MeV. The calculation supports the viewpoint that electrons that generate the continuum gamma-ray and hard X-ray emissions in impulsive solar flares are accelerated in a large-scale turbulent current sheet above the soft X-ray flare loops.     

Comparison of the Fermi and betatron acceleration efficiencies in collapsing magnetic traps

The acceleration of charged particles in the solar corona during flares is investigated in terms of a model in which the electrons and ions preaccelerated in the magnetic reconnection region are injected into a collapsing magnetic trap. Here, the particle energy increases rapidly simultaneously through the Fermi and betatron mechanisms. Comparison of the efficiencies of the two mechanisms shows that the accelerated electrons in such a trap produce more intense hard X-ray (HXR) bursts than those in a trap where only the Fermi acceleration mechanism would be at work. This effect explains the Yohkoh and RHESSI satellite observations in which HXR sources more intense than the HXR emission from the chromosphere were detected in the corona.     

Origin of 30 ∼ 100 kev protons observed in the upstream region of the Earth's bow shock

a Fermi-type acceleration model is constructed to explain the origin of energetic protons (30 ～ 100 keV) which have been observed upstream of the bow shock. It is shown that the suprathermal protons (with energy of several keV) can be accelerated up to several tens of keV through the Fermi-type process in which the reflection at the shock front and the scattering in the upstream region are coupled. The efficiency of the scattering process is estimated by using the result of Barnes' quasilinear treatment of the wave excitation. The resultant energy spectrum and flux intensity ($\text{10}{}^3\text{～ 10}{}^4\text{protons}\text{(}\text{cm}{}^2\text{s ster keV}$) in 32 ～ 45.3keV) are consistent with the observation, and the softening of the energy spectrum observed in the dawn region can be explained by the decrease in the efficiency of the acceleration process in the dawn region due to the curvature of the bow shock and the reduction of shock strength. The spatial distribution of the flux predicted by the model is also consistent with the observation. In view of these consistencies the Fermi-type acceleration process is suggested as a possible candidate mechanism to explain the upstream protons although we do not intend to exclude other possibilities.     

Anisotropy of > 35keV ions in corotating particle events at 1 AU

The anisotropy of 35–1000 keV ions in two corotating particle events associated with high-speed solar wind streams at 1 AU is examined in terms of the diffusion-convection propagation model using data from the Energetic Proton Anisotropy Spectrometer on ISEE-3. The calculated diffusive anisotropy in the solar wind frame is found to be sunward and closely field-aligned, with a nearly energy-independent magnitude of ～ 40%. For one stream, using the Voyager 2 data of Decker et al. (1981), a positive gradient of ～ 100%/AU is found for ? 50 keV ions between 1 and 4 AU. The observations do not appear to support the scatter-free propagation model and indicate that ions with energies as low as a few tens of keV may be in diffusive equilibrium with the solar wind in this class of events.     

Dynamics of electrons and heavy ions in Mercury's magnetosphere

Several basic magnetospheric processes at Mercury have been investigated with simple models. These include the adiabatic acceleration and convection of equatorially mirroring charged particles, the current sheet acceleration effect, and the acceleration of Na⁺ and other exospheric ions by the magnetospheric electric and magnetic fields near the planetary surface. The current steady-state treatment of the magnetospheric drift and convection processes suggests that the region of the inner magnetosphere as explored by the Mariner 10 spacecraft during its encounter with Mercury should be largely devoid of energetic (>100 keV) electrons in equatorial mirroring motion. As for ion motion, the large gyroradii of the heavy ions permit surface reimpact as well as loss via intercepting the magnetopause. Because of the kinetic energy gained in the gyromotion, the first effect could lead to sputtering processes and hence generation of secondary ions and neutrals. The second effect could account for the loss of about 50% of Mercury's exospheric ions.     

Modeling of Proton Acceleration in a Magnetic Island Inside the Ripple of the Heliospheric Current Sheet

Crossings of the heliospheric current sheet (HCS) at the Earth’s orbit are often associated with observations of anisotropic beams of energetic protons accelerated to energies from hundreds of keV to several MeV and above. A connection between this phenomenon and the occurrence of small-scale magnetic islands (SMIs) near reconnecting current sheets has recently been found. This study shows how pre-accelerated protons can be energized additionally due to oscillations of multiple SMIs inside the ripple of the reconnecting HCS. A model of the electromagnetic field of an oscillating 3D SMI with a characteristic size of ~0.001 AU is developed. A SMI is supposed to be bombarded by protons accelerated by magnetic reconnection at the HCS to energies from ~1keV to tens of keV. Numerical simulations have demonstrated that the resulting longitudinal inductive electric fields can additionally reaccelerate protons injected into a SMI. It is shown that there is a local “acceleration” region within the island in which particles gain energy most effectively. As a result, their average escape energies range from hundreds of keV to 2 MeV and above. There is almost no particle acceleration outside the region. It is shown that energies gained by protons significantly depend on the initial phase and the place of their entry into a SMI but weakly depend on the initial energy. Therefore, low-energy particles can be accelerated more efficiently than high-energy particles, and all particles can reach the total energy limit upon their escape from a SMI. It is also found that the escape velocity possesses a strong directional anisotropy. The results are consistent with observations in the solar wind plasma.