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.     

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.     

Galactic and Anomalous Cosmic Rays in the Heliosphere

We discuss the present status of our understanding of the transport and acceleration of anomalous cosmic rays and the transport of galactic and CIR-accelerated particles in the heliosphere. Currently, two- and three-dimensional numerical codes can accurately model many of the observed phenomena – with the major current uncertainties being the values of the parameters such as the diffusion coefficients and the effects of the poorly understood structure beyond the termination shock. We illustrate the nature of the phenomena by discussing in detail the response of energetic particles to co-rotating interaction regions, the acceleration of singly- and multiply-charged anomalous cosmic rays, and the effects of galactic cosmic rays on the structure of the solar wind and its termination shock. This revised version was published online in July 2006 with corrections to the Cover Date.     

The physics of particle acceleration at the heliospheric termination shock

Cosmic rays are ubiquitous in space, and the essential similarity of their energy spectra in many different regions places significant general constraints on the mechanisms for their acceleration and confinement. Diffusive shock acceleration is at present the most successful acceleration mechanism proposed, and, together with transport in Kolmogorov turbulence, can account for the universal specta. A unique laboratory for studying the acceleration and transport of charged particles is the outer heliosphere, including the solar wind termination shock and heliosheath.

A widely accepted paradigm for the transport and acceleration of energetic particles in the heliosphere has evolved over the last few decades. This picture has successfully explained many features of the modulation of galactic cosmic rays and the transport and acceleration of anomalous cosmic rays at the solar-wind termination shock. Recent Voyager observations near and beyond the termination shock have revealed new, and in some cases, unexpected phenomena which have led to questions concerning the established paradigm. The physical interpretation of the observations requires a blunt termination shock, rapid inward motion of the shock and temporal variations over time scales ranging from hours to 22 years. Incorporation of these into the physics has promise of explaining most, if not, all of the observed phenomena while retaining the advantages of the termination shock paradigm for both galactic and anomalous cosmic rays.     

The Injection, Acceleration, and Dynamical Influence of Interstellar Pickup Ions at the Solar Wind Termination Shock

The interaction of interstellar pickup ions with the solar wind termination shock is reviewed and assessed. The pickup ions mass and momentum load the wind and increase its pressure, effects which decrease the strength of the shock and its distance from the Sun. The pickup hydrogen may contribute substantially to the "reflected" ion population, which should provide most of the dissipation at the supercritical quasi-perpendicular shock. A fraction of the pickup ions impinging on the shock is "injected" into the process of diffusive shock acceleration to form the anomalous cosmic ray component. An injection mechanism which accounts for the apparent absence of solar wind ions in the anomalous component is "shock surfing", in which pickup ions which approach the shock slowly may be trapped between the upstream Lorentz force and the shock potential and accelerated in the motional electric field beyond the energy threshold for diffusive shock acceleration. However, the simplest interpretation of shock surfing would favor less massive pickup ion species, in contradiction with Voyager observations of anomalous component composition. A possible extension of the shock surfing mechanism is considered, as well as other injection mechanisms. Finally, the pressure of the anomalous component may modify the structure of the termination shock, which in turn may influence injection rates. This revised version was published online in July 2006 with corrections to the Cover Date.     

Physics and Gasdynamics of the Heliospheric Interface

During 30 years, a big theoretical effort to understand the physical processes in the heliospheric interface has followed the pioneer papers by Parker (1961) and Baranov et al. (1971). The heliospheric interface is a shell formed by the solar wind interaction with the ionized component of the circumsolar local interstellar medium (LISM). For fully ionized supersonic interstellar plasma two-shocks (the termination shock and the bow shock) and a contact discontinuity (the heliopause) are formed in the solar wind/LISM interaction. However, LISM consists of at least of three components additional to plasma: H-atoms, galactic cosmic rays and magnetic field. The interstellar atoms that penetrate into the solar wind, are ionized there and form pickup ions. A part of the pickup ions is accelerated to high energies of anomalous cosmic rays (ACRs). ACRs may modify the plasma flow upstream the termination shock and in the heliosheath. In this short review I summarize current understanding of the physical and gasdynamical processes in the heliospheric interface, outline unresolved problems and future perspectives. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Multifluid Character of the `Baranov' Interface

Since about three decades now it is clearly recognized that the interaction of the solar system with the ambient interstellar medium flow mainly is characterized by its hydrodynamic nature invoking structures like the inner shock, the heliopause and the outer shock with plasma sheath regions in between. After the pioneering works by Eugene Parker and Vladimir Baranov the main outlines of this interaction scenario were established, while some discussion on location and geometry of these structures is still going on till now. Fundamentally new aspects of this interaction problem have meanwhile appeared calling for new and more consistent calculations. The revisions of the earlier interaction concept starts with the neutral LISM gas component passing through the solar system. At the occasion of ionizations of this component a medium-energetic plasma component in form of keV-energetic pick-up ions is created. This component changes the distant solar wind properties by mass-, momentum-, and energy-loading, by wave generation and lowering the solar wind Mach numbers. Furthermore pick-up ions serve as a seed population for a high-energetic plasma population with energies between 10 and 100 MeV/nuc called anomalous cosmic rays. This latter component by means of its pressure gradient not only modifies the solar wind flow but also modulates its termination shock. In this paper it is shown how the main features of the enlarged interaction scenario change if the above mentioned multifluid character of the scenario is taken into account. While now we present a `multicolour vision' of the interacting heliosphere, it should never be forgotten that these modern views only were possible due to the fundamental `black-and-white vision' already presented by Baranov in the seventieths. This revised version was published online in July 2006 with corrections to the Cover Date.     

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 anomalous cosmic rays at the heliospheric termination shock

Astronomy Letters - The acceleration of anomalous cosmic rays (ACRs) at the heliospheric termination shock and their influence on the shock structure and location are analyzed in terms of a...     

Interplanetary Pick-Up Ion Acceleration A Study of Anisotropic Phase-Space Diffusion

Interplanetary pick-up ions originate from ionizations of neutral interstellar atoms in the heliosphere. Over the past periods it was generally expected that after pick-up by the frozen-in solar wind magnetic fields these ions quickly isotropize in velocity space by strong pitch- angle scattering, they do, however, not assimilate to the ambient solar wind ions. Meanwhile careful investigations of pick-up ion data obtained with the plasma analyzers on AMPTE and ULYSSES could clearly reveal that, especially at periods of flow-aligned fields, noticeably anisotropic distributions must prevail. To better understand the evolutionary tracks of pick-up ions in interplanetary phase-space we carried out an injection study which takes into account all relevant convection and diffusion processes, i.e. describing pitch angle scattering, adiabatic cooling, drifts and energy diffusion. As demonstrated here particles injected at 1 AU establish a distribution function with substantial anisotropies up to distances beyond 6 AU. Only under the action of fairly strong isotropic turbulence levels a trend towards isotropy can be recognized. The bulk velocity of the injected pick-up ions turns out to be remarkably smaller than the solar wind velocity. It also is obvious that pick-ups are strongly spread out from that solar wind plasma parcel into which they were originally implanted. As one consequence it must be concluded that the derivation of interstellar He gas parameters, using He pick-up ion flux data, require appreciable caution. Due to anisotropic spatial diffusion the location of the LISM helium cone axis, i.e. the LISM wind vector, and the LISM helium temperature are hidden in the associated He⁺pick-up ion flux patterns. This revised version was published online in July 2006 with corrections to the Cover Date.     

The influence of the anomalous cosmic-ray component on the dynamics of the solar wind

It is well known that both the galactic and anomalous cosmic rays show positive intensity gradients in the outer heliosphere which are connected with corresponding pressure gradients. Due to an efficient dynamical coupling between the solar wind plasma and these highly energetic media by means of convected MHD turbulences, there exists a mutual interaction between these media. As one consequence of this scenario the enforced pressure gradients influence the distant solar wind expansion. Here we concentrate in our theoretical study on the interaction of the solar wind only with the anomalous cosmic-ray component. We use the standard two-fluid model in which the cosmic-ray fluid modifies the solar wind flow via the cosmic-ray pressure gradient. Then we derive numerical solutions in the following steps: first we calculate an aspherical pressure distribution for the anomalous cosmic rays, describing their diffusion in an unperturbed radial solar wind. Second, we then consider the perturbation of the solar wind flow due to these induced anomalous cosmic-ray pressure gradients. Within this context we especially take account of the action of a non-spherical geometry of the heliospheric shock which may lead to pronounced upwinddownwind asymmetries in the pressures and thereby in the resulting solar wind flows. As we can show in our model, which fits the available observational data, radial decelerations of the distant solar wind by between 5 to 11% are to be expected, however, the deviations of the bulk solar wind flow from the radialdirections are only slightly pronounced.     

On the escape of particles from cosmic ray modified shocks

Stationary solutions to the problem of particle acceleration at shock waves in the non-linear regime, when the dynamical reaction of the accelerated particles on the shock cannot be neglected, are known to show a prominent energy flux escaping from the shock towards upstream infinity. On physical grounds, the escape of particles from the upstream region of a shock has to be expected in all those situations in which the maximum momentum of accelerated particles,   p _max  , decreases with time, as is the case for the Sedov–Taylor phase of expansion of a shell supernova remnant, when both the shock velocity and the cosmic ray induced magnetization decrease. In this situation, at each time t , particles with momenta larger than   p _max( t )  leave the system from upstream, carrying away a large fraction of the energy if the shock is strongly modified by the presence of cosmic rays. This phenomenon is of crucial importance for explaining the cosmic ray spectrum detected at the Earth. In this paper, we discuss how this escape flux appears in the different approaches to non-linear diffusive shock acceleration, and especially in the quasi-stationary semi-analytical kinetic ones. We apply our calculations to the Sedov–Taylor phase of a typical supernova remnant, including in a self-consistent way particle acceleration, magnetic field amplification and the dynamical reaction on the shock structure of both particles and fields. Within this framework, we calculate the temporal evolution of the maximum energy reached by the accelerated particles and of the escape flux towards upstream infinity. The latter quantity is directly related to the cosmic ray spectrum detected at the Earth.     

On the Possible Detection of Evidence for the Approach of Voyager 1 to the Heliospheric Boundaries

Quite an unusual behavior of the low-energy ion fluxes measured with the LECP and CRS instruments onboard Voyager 1, which is located in the outer heliosphere at a distance of about 90 AU, has been observed since July 2002 until recently (February 2003). This behavior can be interpreted as a possible manifestation of a combination of the global heliospheric disturbance produced by solar activity and the precursor of the outer heliosphere with its termination shock. The extremely large variability of the enhanced ion fluxes since the second half of 2002 in several energy channels from 0.5 to several MeV/nucleon is presumed to be associated with the sources of their acceleration near the termination shock. The simultaneous increase in the flux of protons with energies above 70 MeV may result from the easier penetration of Galactic cosmic rays because of the reduction in modulation at the declining phase in the current solar cycle 23 after the maximum in 2000 and from an admixture of the anomalous component accelerated at the termination shock.     

Piston shock and Forbush effect

A model of a piston shock produced by a sharp jump in the velocity of the solar wind with a helical magnetic field is suggested to explain the origin of the Forbush decrease of cosmic rays with a hard energy spectrum at solar activity minimum and, in some cases, at solar activity maximum. The contact velocity, the compression ratio, the contact position, the ratio of the magnetic field near the contact to the seed field, the maximum momentum of the particles subjected to modulation, and the modulation depth for the neutron and muon cosmic ray components have been calculated. The theoretical calculations are compared with experimental data.     

Galactic cosmic ray distribution in the simplest model of termination shock near the heliospheric boundaries

The termination shock at the heliospheric boundary is simulated in terms of a two-layer turbulent medium for which the average radial component of solar wind velocity is nonzero inside the heliosphere and zero for external magnetic inhomogeneities. Galactic cosmic rays (GCRs) are scattered more strongly in the solar wind than in the interstellar medium. A boundary value problem for density is defined to describe GCR propagation in the given two-layer medium. The exact analytical solution of it is derived. The phase density and GCR fluxes in the whole range of the particle energies, as well as the degree of anisotropy of high-energy GCRs, are determined. The qualitative agreement of theoretical calculations and observed GCR distributions is obtained. In particular, in the region near the termination shock, an increase in the high-energy particle density and a decrease in the low-energy particle density are observed.     

Cosmic ray acceleration to very high energy through the non-linear amplification by cosmic rays of the seed magnetic field

The maximum energy for cosmic ray acceleration at supernova shock fronts is usually thought to be limited to around 10¹⁴–10¹⁵ eV by the size of the shock and the time for which it propagates at high velocity. We show that the magnetic field can be amplified non-linearly by the cosmic rays to many times the pre-shock value, thus increasing the acceleration rate and facilitating acceleration to energies well above 10¹⁵ eV. A supernova remnant expanding into a uniform circumstellar medium may accelerate protons to 10¹⁷ eV and heavy ions, with charge Ze , to Z ×10¹⁷ eV. Expansion into a pre-existing stellar wind may increase the maximum cosmic ray energy by a further factor of 10.     

Relationship between high-energy physical phenomena on the sun and in astrophysics

High energy phenomena on the surface of the Sun are manifestations of part of the solar dynamo cycle. Convection and magnetic field give rise to unstable, twisted flux loops that become solar flares when the resistive tearing mode proceeds to the nonlinear limit. If such twisted flux loops did not dissipate rapidly due to an enhanced resistivity, then the dynamo would not work. The act of dissipation leads to intense heating and acceleration leading to X-rays and accelerated particles. The particles in turn give rise to hard X-rays, gamma rays, neutrons, and solar cosmic rays. In high-energy astrophysics such phenomena occur in accretion disks around compact objects like black holes in quasars and SS433. The resulting acceleration may explain the observed extremely high-energy cosmic rays of up to 10²⁰ eV and the high-energy gamma rays of 10¹² to 10¹⁵ eV. These high energies are more readily explained by acceleration E parallel to B as opposed to stochastic shock acceleration. The anisotropy and localization of gamma rays from solar flares potentially may indicate which mechanism is prevalent.     

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”.     

Signatures of the Interplanetary Helium Cone Reflected by Pick-up Ions

As known for a long time, interstellar wind neutral helium atoms deeply penetrate into the inner heliosphere and, when passing through the solar gravity field, form a strongly pronounced helium density cone in the downwind direction. Helium atoms are photoionized and picked-up by the solar wind magnetic field, but as pick-up ions they are not simply convected outwards with the solar wind in radial directions as assumed in earlier publications. Rather they undergo a complicated diffusion-convection process described here by an appropriate kinetic transport equation taking into account adiabatic cooling and focusing, pitch angle scattering and energy diffusion. In this paper, we solve this equation for He⁺pick-up ions which are injected into the solar wind mainly in the region of the helium cone. We show the resulting He⁺pick-up ion density profile along the orbit of the Earth in many respects differs from the density profile of the neutral helium cone: depending on solar-wind-entrained Alfvénic turbulence levels, the density maximum when looking from the Earth to the Sun is shifted towards the right side of the cone, the ratio of peak-densities to wing-densities varies and a left-to-right asymmetry of the He⁺-density profile is pronounced. Derivation of interstellar helium parameters from these He⁺-structures, such as the local interstellar medium (LISM) wind direction, LISM velocity and LISM temperature, are very much impeded. In addition, the pitch-angle spectrum of He⁺pick-up ions systematically becomes more anisotropic when passing from the left to the right wing of the cone structure. All effects mentioned are more strongly pronounced in high velocity solar wind compared to the low velocity solar wind.     

Active galactic nuclei flow velocities and the highest energy cosmic rays

The dependence of the maximum energy cosmic rays can reach via diffusive shock acceleration in AGN jets on flow speeds is discussed. It is shown that in highly inclined termination shocks where the speed of the de Hoffman-Teller frame is crucial, a good independent knowledge of the jet speed is required to properly assess the extent of the cosmic ray spectrum.