Interplanetary acceleration of energetic particles at 1 and 5 AU

Energetic particle (0.1 to 100 MeV protons) acceleration is studied by using high resolution interplanetary magnetic field and plasma measurements at 1 AU (HEOS-2) and at 5 AU (Pioneer 10). Energy changes of a particle population are followed by computing test particle trajectories and the energy changes through the particle interaction with the time varying magnetic field. The results show that considerable particle acceleration takes place throughout the interplanetary medium, both in the corotating interaction regions (CIR) (5 AU), and in quiet regions (1 AU). Although shocks may contribute to acceleration we suggest statistical acceleration within the CIRs is sufficient to explain most energetic particle observations (e.g., McDonaldet al., 1975; Barnes and Simpson, 1976).The first and second order statistical acceleration coefficients which include transit time damping and Alfvén resonance interactions, are found to be well represented byD _T 8.5×10^–6 T ^0.5 MeV s^–1 andD _TT 4×10^–6 T ^1.5 MeV² s^–1 at 5 AU.By comparison, Fisk's estimates (1976), based on quasi-linear theory for transit-time damping, gaveD _TT 5×10^–7 T MeV² s^–1 at 1 AU.     

Study of parallel diffusion of energetic particles in the interplanetary medium using spacecraft data at 1 and 5 AU

Energetic particle (1–100 MeV) pitch angle scattering in the Interplanetary Magnetic Field (IMF) is studied using spacecraft magnetometer data at 1 AU (IMP 7 and HEOS 2) and at 5 AU (Pioneer 10). Particle trajectories are followed by a computer simulation of their movement in a realistic model of the IMF. Determination of the pitch angle diffusion coefficient at 1 AU (D ) leads to a parallel mean free path which is roughly independent of particle energy, 0.03 AU. At the lowest energy our result is at least a factor of 3 larger than the predictions of quasi linear theory. Results at 5 AU lead to a radial mean free path which is between 2 to 6 times smaller than at 1 AU, probably indicating a greater importance for perpendicular diffusion at large heliodistances. In fact a roughly constant radial mean free path ( _r 0.01 AU) is obtained when the contribution of perpendicular diffusion at 5 AU is taken into account (Moussaset al., 1981).     

The effect of interplanetary acceleration on the propagation of energetic solar particles in prompt events

Crank-Nicholson solutions are obtained to the time-dependent Fokker-Planck equation for propagation in the interplanetary medium following a point in time injection of energetic solar particles and including the acceleration terms $$\frac{\partial }{{\partial T}}\left( {D_{TT} \frac{{\partial U}}{{\partial T}}} \right) - \frac{\partial }{{\partial T}}\left( {\frac{{D_{TT} U}}{{2T}}} \right)$$ . The diffusion coefficient in kinetic energyD _TT is allowed to be either independent of radial distance,R(AU), or follow the lawD _TT=D₀T²R ₀ ² /(A²+R²) in either case with the 1 AU value ofD _TT at 10 MeV ranging between 10^?4 (MeV)² s^?1 and zero. The spatial diffusion mean free path at the Earth's orbit is fixed at λ_‖ AU at 10 MeV according to numerical estimates made by Moussas and Quenby. However, a variety ofR dependences are allowed. Reasonable agreement with experimental data out to 4 AU is obtained with the above values ofD _TT and the spatial diffusion coefficientK _r=K₀R^?2 forR«1 andK _r=K₀R^0.4 forR»1 AU. It is only in the decay phases of prompt events as seen at 2–4 AU that significant differences in the temporal behaviour of the events can be distinguished, depending on the value ofD _TT chosen within the above range. Experimental determination of the decay constant is difficult.     

Relatively stable,large-amplitude Alfvénic waves seen at 2.5 and 5.0 AU

Pioneer 11 and 10 observations of the wave structure seen in a corotating interaction region at 2.5 AU on day 284 of 1973 and 8 days later at 5 AU reveal large-amplitude Alfvénic structures with many detailed correlations seen between their features at the two radial distances. Hodogram analysis suggests the dominance of near plane polarized, transverse Alfvénic mode fluctuations with periods between 2 min and one hour or more. Some wave evolution close to the Corotating Interaction Region (CIR) shock is noticed, but waves towards the centre of the compression seem to propagate with little damping between the spacecraft observation positions.     

The evaluation of the interplanetary diffusion coefficient for energetic particles employing real magnetic field data

A numerical simulation of energetic particle motion in the interplanetary medium is carried out using HEOS-2 magnetometer data in order to computeD(), the pitch angle diffusion coefficient, where is cosine of pitch angle defined with respect to the local field. WhileD() exceeds that given by quasi-linear theory near 90° pitch angle, it is significantly less at higher values of , leading to a parallel transport coefficient in good accord with that given by experimental studies of solar proton propagation. In particular, =0.031 AU at a particle magnetic rigidity of 455 MV, while experimental results range from 0.05 to 0.07 AU (+100%, –50%) in this rigidity region. Furthermore, observed approximately -dependent solar proton pitch angle distributions are consistent with the computed findingD()/(1 – ²)² ~ constant.The validity of various analytical corrections to quasi-linear theory as 0 are also investigated numerically.     

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.     

Mean free paths of energetic particles at very large heliodistances (Pioneer 11 at 20 AU)

Pioneer 11 magnetic field data at 20 AU are analysed by the computational method of Moussas, Quenby, and Webb (1975), Moussas and Quenby (1978), and Moussas, Quenby, and Valdes-Galicia (1982a, b) to obtain the parallel mean free path , and the diffusion coefficient parallel to the magnetic field line K . This method is the most appropriate for the mean free path calculation at large heliodistances since the alternative method which is based on fitting of energetic particle intensities cannot be easily and accurately be used because the association of energetic particles with their parent flares is not precise. The results show that the mean free path has values between 0.85 and 0.98 AU, linearly increasing with energy according to (T_kinetic) = + MT, where = 0.846 AU and M = 4.44 × 10 ^–5 AU MeV^–1 for energies between 10 MeV and 3 GeV for protons. These values of the parallel mean free path are much larger than the values estimated by previous studies up to 6 AU. The diffusion coefficient dependence upon energy follows a relation which simply reflects an almost constant mean free path and a linear dependence on the velocity of the particle, so that at 20 AU heliodistance K (T _kin) = K _{, 1 MeV}(T _kin)T _kinetic , with = 1/2. The distance dependence of the parallel diffusion mean free path follows a power law, (R) = _{, 1 AU} R , where is 1 ± 0.1. While the parallel diffusion coefficient obeys a power-law relation with heliodistance R, K (R, T _kin) = K _{, 1 AU}(T _kin)R , with = 1 ± 0.1. The radial diffusion coefficient of cosmic rays is not expected to strongly depend upon the parallel diffusion coefficient because the nominal magnetic field at these large heliodistances (20 AU) is almost perpendicular to the radial direction and the contribution of the diffusion coefficient perpendicular to the magnetic field is expected to play a dominant role. However, the actual garden hose angle varies drastically and for long time periods and hence the contribution of the diffusion parallel to the field may continue to be important for the small scale structure of intensity gradients.     

The structure of the interplanetary medium during the first stip interval (September–October 1975) and prerelease of energetic solar particles

An analysis of the interplanetary medium structure is made during STIP 1. (September–October, 1975). Using a simple extrapolation method a reconstruction of the stream lines is made which shows that the interplanetary space during this time period was very quiet. Such a behaviour is expected because this interval is close to the minimum of the solar cycle activity.The evolution of two fast solar wind streams, which dominated the interplanetary medium for very long time periods, is studied.A peculiar solar proton event, with onset time before the optical flare, is explained according to Elliot mechanism — i.e., that energetic particles are stored for a long time and released, sometimes, before the optical flare.These particles can be seen only when the interplanetary medium is very quiet, (without shock waves) and the flare very isolated.     

Mean free paths of energetic charged particles parallel and antiparallel to the interplanetary magnetic field

A new method to calculate the mean free paths of energetic particles propagating parallel and anti-parallel to the interplanetary magnetic field, based on quasi-linear theory and the complex spectral polarization analysis of the field, is developed and presented. Applications of the method using HEOS 2 (1 AU), Pioneer 10 (5 AU), Pioneer 11 (20 AU), ICE (Giacobini-Zinner's comet) data have been made, showing that: (a) The mean free paths parallel and anti-parallel to the field can be completely different in various regions of the interplanetary medium and different time periods. (b) Particles are preferentially scattered in one direction. (c) The parallel and anti-parallel mean free paths become equal at certain energy. Comparisons with the results from another computational method are made.     

Drift motion and perpendicular diffusion of energetic particles in interplanetary space based on spacecraft data

A realistic model of the interplanetary magnetic field (IMF) is constructed based on measurements taken by Pioneer 10 magnetometer at 5 AU. Energetic particle (0.1–100 MeV) propagation in this field is studied by a computer simulation of its motion in order to calculateK , the perpendicular diffusion coefficient, and V _D the average drift velocity of an ensemble of particles. Determinations ofK lie in the range 3×10¹⁹–8×10²⁰ cm² s^–1 for the energies considered and they show that perpendicular diffusion may be an important process at these heliodistances when compared with parallel diffusion results obtained by similar techniques, contrary to what was previously thought. Drift velocity calculations are very close to predictions of guiding centre theory (within 30%) suggesting that this theory can be applied in the IMF. This result shows that gradient and curvature drifts can be present even in a highly perturbed field and thus they can have some influence in cosmic ray modulation.     

Noble gases in interplanetary dust particles,I: The excess helium‐3 problem and estimates of the relative fluxes of solar wind and solar energetic particles in interplanetary space

Abstract— We report mass‐spectrometric measurements of light noble gases pyrolytically extracted from 28 interplanetary dust particles (IDPs) and discuss these new data in the context of earlier analyses of 44 IDPs at the University of Minnesota. The noble gas database for IDPs is still very sparse, especially given their wide mineralogic and chemical variability, but two intriguing differences from isotopic distributions observed in lunar and meteoritic regolith grains are already apparent. First are puzzling overabundances of ³He, manifested as often strikingly elevated ³He/⁴He ratios—up to >40x the solar‐wind value—‐and found primarily but not exclusively in shards of some of the larger IDPs (“cluster particles”) that fragmented on impact with the collectors carried by high‐altitude aircraft. It is difficult to attribute these high ratios to ³He production by cosmic‐ray‐induced spallation during estimated space residence times of IDPs, or by direct implantation of solar‐flare He. Minimum exposure ages inferred from the ³He excesses range from ～50 Ma to an impossible >10 Ga, compared to Poynting‐Robertson drag lifetimes for low‐density 20–30 μm particles on the order of ～0.1 Ma for an asteroidal source and ～10 Ma for origin in the Kuiper belt. The second difference is a dominant contribution of solar‐energetic‐particle (SEP) gases, to the virtual exclusion of solar‐wind (SW) components, in several particles scattered throughout the various datasets but most clearly and consistently observed in recent measurements of a group of individual and cluster IDPs from three different collectors. Values of the SEP/SW fluence ratio in interplanetary space from a simple model utilizing these data are ～1% of the relative SEP/SW abundances observed in lunar regolith grains, but still factors of approximately 10–100 above estimates for this ratio in low‐energy solar particle emission.     

14 July 2000, a near-global coronal event and its association with energetic electron events detected in the interplanetary medium

On 14 July 2000, the LASCO coronagraphs showed a very fast halo coronal mass ejection in association with the radio bursts seen shortly after 10:00 UT. Radio imaging observations by the Nançay radioheliograph (NRH) of these bursts showed a very complex event that can be regarded as global: the sources encompassed all the visible range in longitude and a huge span in latitude. Another interesting feature of the radio event is its recurrent nature: after the most intense phase shortly after 10:00 UT, two other strong outbursts are detected, one at about 12:50 UT and another at about 13:48 UT. All of these sub-events showed similar development and likely evidence for CMEs. The launch of a CME in association with the 14:00 UT sub-event is inferred from WIND/WAVES, with interplanetary type II signatures in the hectometric wavelength range at that time. These later events were not detected by LASCO due to energetic particles hitting the CCD. During the Bastille Day event, energetic particle observations measured in situ by ACE/EPAM are dominated by energetic electrons. Changes in anisotropy and energy spectrum of the ～38–350 keV electrons suggest a good correlation with the coronal radio observations. In addition to the three main radio events and particle observations, the NRH data reveal moving features in the southern hemisphere. These moving features, located at about 45 deg south and with an angular extent of about 45 deg, are illuminated by non-thermal electrons and are seen at distances up to 2.5 solar radii from the Sun center. More generally, we interpret the global and recurrent coronal activity, revealed by the radio data, as responsible for populating the interplanetary medium with energetic electrons.     

Radiative losses and cut-offs of energetic particles at relativistic shocks

We investigate the acceleration and simultaneous radiative losses of electrons in the vicinity of relativistic shocks. Particles undergo pitch angle diffusion, gaining energy as they cross the shock by the Fermi mechanism and also emitting synchrotron radiation in the ambient magnetic field. A semi-analytic approach is developed which allows us to consider the behaviour of the shape of the spectral cut-off and the variation of that cut-off with the particle pitch angle. The implications for the synchrotron emission of relativistic jets, such as those in gamma-ray burst sources and blazars, are discussed.     

Numerical simulations of high-speed solar wind streams within 1 AU and their signatures at 1 AU

A parametric study of the evolution within, and signatures at, 1 AU of high-speed streams is performed with the use of a MHD, 21/2-D, time-dependent model. This study is an extension of an earlier one by Smith and Dryer (1990) who examined the ecliptic plane consequences of relatively short-duration, energetic solar disturbances. The present study examines both the erupting and corotating parts of long-duration, high-speed streams characteristic of coronal hole flows. By examining the variation of the simulated plasma velocity, density, temperature, and magnetic field at 1 AU, as well as the location of the solar coronal hole sources relative to the observer at 1 AU, we are able to provide some insight into the identification of the solar sources of interplanetary disturbances. We present and discuss two definitions for angle locating the solar source of interplanetary disturbances at 1 AU.We apply our results to the suggestion by Hewish (1988) that low-latitude coronal holes are suitably positioned to be the sources of major geomagnetic storms when the holes are in the eastern half of the solar hemisphere at the time of the commencement of the storm. Our results indicate that, for these cases, the streams emanating from within the hole must be very fast, greater than 1000 km s^–1, or very wide, greater than 60°, at the inner boundary of 18 solar radii in our simulation.     

Observations of energetic water-group ions at comet giacobini-zinner: Implications for ion acceleration processes

Observations of energetic water-group pick-up ions made by the EPAS instrument during the ICE fly-by of comet P/Giacobini-Zinner are investigated for evidence concerning the processes which accelerate the ions from initial pick-up energies of around 10 keV up to energies of a few hundred kilo-electronvolts. The form of the ion spectrum in the ion rest frame is first investigated and compared with theoretical suggestions that exponential energy distributions might be produced by either first or second order Fermi acceleration in the cometary environment. It is shown that such distributions do not fit the data at all well, but that rather (over the EPAS ion bulk rest frame energy range of ∼30 to <300 keV) the observed distribution functions closely approximate an exponential in ion speed. The higher energy (> 50 keV) data also fit a power law distribution very well, but at lower energies the data tend to show a flattening below the power law form. It is also shown that the observed spectra are much softer than those calculated by Ip and Axford (1986, Planet. Space Sci. 34, 1061) for the G-Z ion pick-up region upstream of the bow shock, indicating that if these distributions are indeed due to second order Fermi acceleration as they propose, then the ion mean free path must be rather larger than used in their calculations (i.e. rather larger than 5 water-group ion gyroradii). Overall, it is concluded that at the present stage of theoretical development it is premature to draw firm conclusions about acceleration mechanisms from studies of the ion spectrum alone. However, from the general spectral analysis it is also possible to investigate the variations of ion intensity and spectral hardness which take place during the comet encounter, and to gain an indication of the degree of isotropy of the ion distribution in the rest frame of the flow. We find that a ∼.5 × 10⁴km-wide region (∼ 35 min along the spacecraft trajectory) of rapid ion intensification and spectral hardening occurs immediately upstream from the turbulent mass-loaded region, suggestive of a first order Fermi process in which ions are successively reflected between the outer layer of the slowed, turbulent region and waves in the faster upstream flow. It is shown that within the turbulent region the ion distribution becomes rapidly isotropized in its own bulk rest frame, indicative of a sudden reduction in ion mean free path. Additional processes (possibly second order Fermi acceleration) must also occur in order to account for the further modest intensifications of the energetic ion fluxes observed within the turbulent mass-loaded region, as well as the presence of ions in the outer pick-up region which have energies well in excess of the local pick-up energy.     

On the equation of transport for cosmic-ray particles in the interplanetary region

In this paper we provide two new alternative derivations of the equation of transport for cosmic-ray particles in the interplanetary region. Both derivations are carried out by using particle positionr and timet in a frame of reference fixed in the solar system, and the particle momentump is specified relative to a local frame of reference moving with the solar wind. The first derivation is carried out by writing down a continuity equation for the cosmic rays, taking into account particle streaming and energy changes, and subsequently deriving the streaming and energy change terms in this equation. The momentum change term in the continuity equation, previously considered to be due to the adiabatic deceleration of particles in the expanding magnetic fields carried by the solar wind, appears in the present analysis as a dynamic effect in which the Lorentz force on the particle does not appear explicitly. An alternative derivation based on the ensemble averaged Liouville equation for charged particles in the stochastic interplanetary magnetic field using (r, p,t) as independent coordinates is also given. The latter derivation confirms the momentum change interpretation of the first derivation. We also provide a new derivation of the adiabatic rate as a combination of inverse-Fermi and betatron deceleration processes.     

Deflection of coronal mass ejection in the interplanetary medium

A solar coronal mass ejection (CME) is a large-scale eruption of plasma and magnetic fields from the Sun. It is believed to be the main source of strong interplanetary disturbances that may cause intense geomagnetic storms. However, not all front-side halo CMEs can encounter the Earth and produce geomagnetic storms. The longitude distribution of the Earth-encountered front-side halo CMEs (EFHCMEs) has not only an east–west (E–W) asymmetry  (Wang et al., 2002), but also depends on the EFHCMEs' transit speeds from the Sun to 1 AU. The faster the EFHCMEs are, the more westward does their distribution shift, and as a whole, the distribution shifts to the west. Combining the observational results and a simple kinetic analysis, we believe that such E–W asymmetry appearing in the source longitude distribution is due to the deflection of CMEs' propagation in the interplanetary medium. Under the effect of the Parker spiral magnetic field, a fast CME will be blocked by the background solar wind ahead and deflected to the east, whereas a slow CME will be pushed by the following background solar wind and deflected to the west. The deflection angle may be estimated according to the CMEs' transit speed by using a kinetic model. It is shown that slow CMEs can be deflected more easily than fast ones. This is consistent with the observational results obtained by Zhang et al. (2003), that all four Earth-encountered limb CMEs originated from the east. On the other hand, since the most of the EFHCMEs are fast events, the range of the longitude distribution given by the theoretical model is E40°,W70°, which is well consistent with the observational results (E40°,W75°).     

On the relative magnitude of streaming velocities of alpha particles and protons at 1 AU

The occurrence at a heliocentric distance of 1 AU of alpha particle streaming velocities larger than proton streaming velocities,v /v _p >1 (Ogilvie, 1975) is investigated on the basis of the theory suggesting the existence in the solar wind of an accelerating force acting preferentially on the alpha particles.Accurate solution of the three-fluid model equations for the quiet solar wind indicates that anecessary andsufficient condition for (v /v _p )_{1 AU}>1 is the presence of a relativelyweak accelerating forceacting in a limited region in the vicinity of 1 AU. If the force is effectiveonly at small heliocentric distances, the alpha particle streaming velocity excess vanishes at distances less than 1 AU, because of the (equalization) action of the dynamical friction force.     

Observation of saturnian stream particles in the interplanetary space

In January 2004 the dust instrument on the Cassini spacecraft detected the first high-velocity grain expelled from Saturn - a so-called stream particle. Prior to Cassini’s arrival at Saturn in July 2004 the instrument registered 801 faint impacts, whose impact signals showed the characteristic features of a high-velocity impact by a tiny grain. The impact rates as well as the directionality of the stream particles clearly correlate with the sector structure of the interplanetary magnetic field (IMF). The Cosmic Dust Analyser (CDA) registered stream particles dominantly during periods when the IMF direction was tangential to the solar wind flow and in the prograde direction. This finding provides clear evidence for a continuous outflow of tiny dust grains with similar properties from the saturnian system. Within the compressed part of co-rotating interaction regions (CIRs) of the IMF, characterized by enhanced magnetic field strength and compressed solar wind plasma, CDA observed impact bursts of faster stream particles. We find that the bursts result from the stream particles being sped up inside the compressed CIR regions. Our analysis of the stream-particle dynamics inside rarefaction regions of the IMF implies that saturnian stream particles have sizes between 2 and 9 nm and exit the saturnian systems closely aligned with the planet’s ring plane with speeds in excess of 70 km s⁻¹.     

Shock waves and type II radiobursts in the interplanetary medium

The planetary radio astronomy experiment on the Voyager spacecraft observed several type II solar radiobursts at frequencies below 1.3 MHz; these correspond to shock waves at distances between 20R and 1 AU from the Sun. We study the characteristics of these bursts and discuss the information that they give on shock waves in the interplanetary medium and on the origin of the high energy electrons which give rise to the radioemission. The relatively frequent occurence of type II bursts at large distances from the Sun favors the hypothesis of the emission by a longitudinal shockwave. The observed spectral characteristics reveal that the source of emission is restricted to only a small portion of the shock. From the relation between type II bursts, type III bursts and optical flares, we suggest that some of the type II bursts could be excited by type III burst fast electrons which catch up the shock and are then trapped.