Adiabatic Deceleration Effects on the Formation of Heavy Ion Charge Spectra in Interplanetary Space

We investigate the effects of interplanetary propagation on the energy dependence of the mean ionic charge of ~0.1–1 MeV/n iron observed during impulsive solar particle events at 1 AU. A Monte-Carlo approach is applied to solve the transport equation which takes into account spatial diffusion as well as convection and adiabatic deceleration. We find that interplanetary propagation results in a shift of charge spectra observed at 1 AU towards lower energies due to adiabatic deceleration. Taking the above effect into account, we compare predictions of our model of charge-consistent stochastic acceleration with recent ACE observations. A detailed analysis of two particle events shows that our model can give a consistent explanation of the observed iron charge and energy spectra, and allows one to put constraints on the temperature, density, and the acceleration and escape time scales in the acceleration region.     

Interaction of interstellar pick-up ions with the solar wind

The interaction of interstellar pick-up ions with the solar wind is studied by comparing a model for the velocity distribution function of pick-up ions with actual measurements of He⁺ ions in the solar wind. The model includes the effects of pitch-ang'e diffusion due to interplanetary Alfvén waves, adiabatic deceleration in the expanding solar wind and the radial variation of the source function. It is demonstrated that the scattering mean free path is in the range 0.1 AU and that energy diffusion can be neglected as compared with adiabatic deceleration. The effects of adiabatic focusing, of the radial variation of the neutral density and of a variation of the solar wind velocity with distance from the Sun are investigated. With the correct choice of these parameters we can model the measured energy spectra of the pick-up ions reasonably well. It is shown that the measured differential energy density of the pick-up ions does not vary with the solar wind velocity and the direction of the interplanetary magnetic field for a given local neutral gas density and ionization rate. Therefore, the comparison of the model distributions with the measurements leads to a quantitative determination of the local interstellar gas density.Paper dedicated to Professor Hannes Alfvén on the occasion of his 80th birthday, 30 May 1988.     

Galactic cosmic ray modulation from 1965–1970

Numerical solutions of the cosmic-ray equation of transport within the solar cavity and including the effects of diffusion, convection, and energy losses due to adiabatic deceleration, have been used to reproduce the modulation of galactic electrons, protons and helium nuclei observed during the period 1965–1970. Kinetic energies between 10 and 10⁴ MeV/nucleon are considered. Computed and observed spectra (where data is available) are given for the years 1965, 1968, 1969 and 1970 together with the diffusion coefficients. These diffusion coefficients are assumed to be of separable form in rigidity and radial dependence, and are consistent with the available magneticfield power spectra. The force-field solutions are given for these diffusion coefficients and galactic spectra and compared with the numerical solutions. For each of the above years we have (i) determined the radial density gradients near Earth; (ii) found the mean energy losses suffered by galactic particles as they diffuse to the vicinity of the Earth's orbit; (iii) shown quantitatively the exclusion of low-energy galactic protons and helium nuclei from near Earth by convective effects; and (iv), for nuclei of a given energy near Earth, obtained their distribution in energy before entering the solar cavity. It is shown that the energy losses and convection lead to near-Earth nuclei spectra at kinetic energies ≤100 MeV/nucleon in which the differential intensity is proportional to the kinetic energy with little dependence on the form of the galactic spectrum. This dependence is in agreement with the observed spectra of all species of atomic nuclei and we argue that this provides strong observational evidence for the presence of energy losses in the propagation process; and for the exclusion of low energy galactic nuclei from near Earth.     

Implications of Proton Anisotropy Development Observed by the Erne Instrument During the 9 July 1996 Solar Particle Event

We analysed the solar particle event following the 9 July 1996 solar flare. High-energy protons were detected by the ERNE instrument on board SOHO. Anisotropy of arriving protons revealed very peculiar non-monotonic development. A short period of almost isotropic distribution was imbedded into the prolonged period of beam-like distribution of 14–17 MeV protons. This implies the existence of a narrow magnetic channel with a much smaller mean free path than in the surrounding quiet solar wind plasma. We used Monte Carlo simulations of interplanetary transport to fit the observed anisotropies and intensity–time profiles. Proton injection and transport parameters are estimated. The injection scenario is found to be very close to the scenario of the 24 May 1990 event, but the intensity and the interplanetary transport parameters are different. The extreme anisotropy observed implies prolonged injection of high-energy protons at the Sun and at the interplanetary shock front, and either a very large mean free path (≥ 5 AU) outside the slow transport channel, or alternatively, a somewhat smaller mean free path (≈2 AU) and enhanced focusing between the Sun and the Earth.     

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.     

Simulation of solar flare particle interaction with interplanetary shock waves

In order to study the propagation of solar cosmic rays in interplanetary space a computer program has been developed using a Monte-Carlo technique, which traces the histories of particles released impulsively at the Sun. The particle propagation model considers the adiabatic deceleration during the convective and diffusive transport of the particles, and the model of the interplanetary medium incorporates a radially expanding blast wave which exerts a sweeping action on the particles and accelerates them through the first-order Fermi process. It is shown that energetic storm particle events cannot be simulated by assuming a pure sweeping action of the interplanetary blast wave, but that energization of the particles while reflected at the shock can explain many observed features of such events.     

Monte Carlo model of the highly anisotropic solar proton event of 20 April 1971

The anisotropy of the particle distribution and its variation with time at 1 AU early in a solar cosmic ray event can provide information on the pitch-angle scattering of the particles in the interplanetary medium. The proton event of 20 April 1971 is described in which the anisotropy of the 7.6–55 MeV energy channel remained large (? 100%) and field-aligned well into the decay phase of the event. A Monte Carlo technique, which gives the pitch-angle distribution, is employed to investigate two models put forward to explain this sustained anisotropy. It is shown that the observed event is consistent with one model in which the injection of particles at the Sun decayed with ane-folding time of 7 hr. In this model the parallel propagation is determined by small-angle scattering in a diverging field equivalent to a uniform diffusion coefficient of 2.1 × 10²² cm² s^?1 (the corresponding classical mean free path is 0.90 AU). A model with impulsive injection and in whichκ(r) increases strongly with distance from the Sun cannot satisfactorily explain the observations.     

Interplanetary propagation of relativistic solar protons

Particle fluxes and pitch angle distributions of relativistic solar protons at Earth's orbit have been determined by Monte Carlo calculations. The analysis covers two hours after the release of the particles from the Sun and total of 8 × 10⁶ particle trajectories were simulated. The pitch angle scattering was assumed to be isotropic and the scattering mean free path was varied from 0.1 to 4 AU.The intensity-time profiles after a delta-like injection from the Sun show that the interplanetary propagation is clearly non-diffusive at scattering mean-free paths above 0.5 AU. All pitch angle distributions have a steady minimum at 90 °, and they become similar about 20 min after the arrival of first particles.As an application, the solar injection profile and the interplanetary scattering mean-free path of particles that gave rise to the GLE on 7 May, 1978 were determined. In contrast to the values of 3–5 AU published by other authors, the average scattering mean-free path was found to be about 1 AU.     

Study of the Geoeffectiveness and Galactic Cosmic-Ray Response of VarSITI-ISEST Campaign Events in Solar Cycle 24

We analyze and compare the geomagnetic and galactic cosmic-ray (GCR) response of selected solar events, particularly the campaign events of the group International Study of Earth-affecting Solar Transients (ISEST) of the program Variability of the Sun and Its Terrestrial Impact (VarSITI). These selected events correspond to Solar Cycle 24, and we identified various of their features during their near-Earth passage. We evaluated the hourly data of geomagnetic indices and ground-based neutron monitors and the concurrent data of interplanetary plasma and field parameters. We recognized distinct features of these events and solar wind parameters when the geomagnetic disturbance was at its peak and when the cosmic-ray intensity was most affected. We also discuss the similarities and differences in the geoeffectiveness and GCR response of the solar and interplanetary structures in the light of plasma and field variations and physical mechanism(s), which play a crucial role in influencing the geomagnetic activity and GCR intensity.     

Simulation of the temporal variations of the galactic cosmic-ray intensity at neutron monitor energies

We show that the temporal variations of the integrated galactic cosmic-ray intensity at neutron monitor energies (approximately above 3 GeV) can be reproduced applying a semi-empirical 1-D diffusion-convection model for the cosmic-ray transport in interplanetary space. We divide the interplanetary region into `magnetic shells' and find the relative reduction that each shell causes to the cosmic-ray intensity. Then the cosmic-ray intensity at the Earth is reproduced by the successive influence of all shells between the Earth and the heliospheric termination shock. We find that the position of the termination shock does not significantly affect the cosmic-ray intensity although there are some differences between the results for a constant and a variable termination shock radius. We also reproduce the cosmic-ray intensity applying the analytical solution of the force-field approximation (Perko, 1987) and find that the results cannot fit the observed data. Our results are compared with the Climax (geomagnetic cut-off 3 GV) and Huancayo (geomagnetic cut-off 13 GV) neutron monitor measurements for almost two solar cycles (1976–1996).     

On the Interplanetary Coronal Mass Ejection Shocks in the Vicinity of the Earth

We studied the relation between the near-Earth signatures of the interplanetary coronal mass ejections (ICMEs) shocks such as sudden storms commencement (SSC), and their counterparts of coronal mass ejections (CMEs) observed near-Sun by solar and heliospheric observatory (SOHO)/large angle and spectrometric coronagraph (LASCO) coronagraph during 1996?C2008. Our result showed that there is a good correlation between the travel time of the ICMEs shocks and their associated radial speeds. Also we have separated the ICME shocks into two groups according to their effective acceleration and deceleration. The results showed that the faster ICME shocks (with negative accelerations which decelerated by solar wind plasma) are more correlated to their associated travel time than those with positive accelerations.     

Energy changes of cosmic rays in the interplanetary region

A clarification and discussion of the energy changes experienced by cosmic rays in the interplanetary region is presented. It is shown that the mean time rate of change of momentum of cosmic rays reckoned for a fixed volume in a reference frame fixed in the solar system is 〈p〉 =p V·G/3 (p=momentum,V is the solar wind velocity andG=cosmic-ray density gradient). This result is obtained in three ways:

1. by a rearrangement and reinterpretation of the cosmic-ray continuity equation;
2. by using a scattering analysis based on that of Gleeson and Axford (1967);
3. by using a special scattering model in which cosmic-rays are trapped in ‘magnetic boxes’ moving with the solar wind.

The third method also gives the rate of change of momentum of particles within a moving ‘magnetic box’ as 〈p〉_ad = ?p ?·V/3, which is the adiabatic deceleration rate of Parker (1965). We conclude that ‘turnaround’ energy change effects previously considered separately are already included in the equation of transport for cosmic rays.     

Evidence for the existence of adiabatic energy loss in interplanetary space from observations of the decay of the February 25–March 2, 1969 series of solar cosmic ray events

The integral flux of low energy protons (> 10 MeV) observed by the University of New Hampshire cosmic ray detector aboard the Pioneer 9 spaceprobe has been compared with similar measurements of the near-Earth spacecraft Explorer 34 during the decay phase of the February 25–March 2, 1969 series of solar cosmic ray events. At this time the Pioneer 9 spaceprobe was 0.8 AU from the Sun and close to the Sun-Earth radial line. The ratio of integral fluxes as measured by the separated spacecraft can be calculated theoretically during the convective phase of the decay of these events and will depend on whether energy loss processes are operative. A comparison of the observed and theoretically calculated ratios suggests that the adiabatic energy loss process is operative.     

Energy losses of solar cosmic rays in interplanetary space

A simple model of solar cosmic ray propagation which includes diffusion, convection, and energy loss by adiabatic deceleration is studied. A Monte Carlo technique is employed to investigate the variation of mean particle energy in the interplanetary medium after the impulsive release of mono-energetic particles at the Sun. At 1 AU typical energy losses are 43% at 20 h and 64% at 60 h after particle release for a diffusion coefficient (r)= ₀r with =+1/2 and ₀=1.33 × 10²¹ cm² s^–1. When ₀ in this model is reduced by a factor of 4, the energy loss is greater by a factor of 2 at 60 h after particle release. When is increased, the energy losses are greater. Using the model parameters above, an increase in solar wind speed from 300 to 600 km s^–-1 gives rise to energy losses that are greater again by factor of 2 at a time of 60 h. Results are compared with an observation by Murray et al. (1971) of a knee in the energy spectrum of solar protons. It is not considered likely that the change in the energy of the knee with time requires, in addition to adiabatic deceleration, another energy change process which acts to increase the energy of particles.Part of this work was performed while the author was at CSIRO, Division of Radiophysics, Epping, NSW, Australia; also supported in part by the U.S. Atomic Energy Commission.     

An empirical model for the 11-year cosmic-ray modulation

An analysis of monthly data from nine world-wide neutron monitoring stations over the period 1965–1975 is carried out for the study of the long-term cosmic-ray modulation. In an attempt to gain insight into the relationships which exist between solar activity, high-speed solar wind streams and various terrestrial phenomena an empirical relation for the cosmic-ray modulation has been found. Accordingly the modulated cosmic-ray intensity is equal to the galactic cosmic-ray intensity corrected by a few appropriate solar, interplanetary and terrestrial activity indices which causes the disturbances in interplanetary space, multiplying with the corresponding time-lag of cosmic-ray intensity from each of these indices. This relation is well explained by a generalization of the Simpson solar wind model which has been proved by the spherically symmetric diffusion-convection theory.     

Multidimensional simulations of radiative transfer in Type Ia supernovae

A three-dimensional Monte Carlo code for modelling radiation transport in Type Ia supernovae is described. In addition to tracking Monte Carlo quanta to follow the emission, scattering and deposition of radiative energy, a scheme involving volume-based Monte Carlo estimators is used to allow properties of the emergent radiation field to be extracted for specific viewing angles in a multidimensional structure. This eliminates the need to compute spectra or light curves by angular binning of emergent quanta. The code is applied to two test problems to illustrate consequences of multidimensional structure on the modelling of light curves. First, elliptical models are used to quantify how large-scale asphericity can introduce angular dependence to light curves. Secondly, a model which incorporates complex structural inhomogeneity, as predicted by modern explosion models, is used to investigate how such structure may affect light-curve properties.     

On reproduction of long-term cosmic-ray modulation as seen by neutron monitor stations

The dependence of cosmic-ray intensity on 21st solar cycle phenomena has been studied using monthly cosmic-ray values from nine world wide Neutron Monitoring Stations.For this purpose the long-term cosmic-ray modulation is modelled by treating the most appropriate source functions among various solar, interplanetary and terrestrial activity indices as the input and the cosmic-ray intensity as the output of a linear system taking into account the corresponding time-lag. In this way the modulated galactic cosmic-ray intensity has been reproduced to a certain degree as the cosmic-ray variations follow the observations with a standard deviation of ~ 10%. Still remaining short-term variations in all stations with periods of 2.7 and 3.7 months can possibly be related to the galactic origin of cosmic-rays.The Simpson solar wind model improved by the spherically symmetric diffusion-convection theory can describe our proposed method.     

Design optimization and background modeling of the HEX experiment on Chandrayaan-I

Spacecraft and their subsystem components are subject to a very hazardous radiation environment in both near-Earth and deep space orbits. Knowledge of the effects of this high energy particle and electromagnetic radiation is essential in designing sensors, electronic circuits and living habitats for humans in near Earth orbit, en route to and on the Moon and Mars. This paper discusses the use of Monte Carlo simulations to optimize system design, radiation source modeling, and determination of background in sensors due to galactic cosmic rays and radiation from the Moon. The results demonstrate the use of Monte Carlo particle transport toolkits to predict secondary production, determine dose rates in space and design required shielding geometry.     

SCR Distribution Function in the Radial IMF Approximation

The transport of cosmic rays in the interplanetary medium is considered in terms of the kinetic equation describing the energetic particle scattering by magnetic irregularities and their focusing by the regular interplanetary magnetic field. The analytical expression for solar cosmic ray distribution function in the approximation of radial regular magnetic field is obtained and the evolution of energetic particle angular distribution is analyzed. The obtained results can be used for the analysis of ground-level enhancements of cosmic ray intensity.     

Shock waves propagation in the turbulent interplanetary plasma

Effect of turbulence on interplanetary shock waves propagation is considered. It is shown that background turbulence results in the additional shock wave deceleration which may be comparable with the deceleration due to plasma sweeping. The turbulent deceleration is connected with the energy losses due to the strong turbulence amplification behind the moving shock front.