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.     

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.     

Spectral polarization analysis of the interplanetary magnetic field fluctuations

A new computational method and algorithm, based on complex Fourier analysis, is used to derive the spectral density of plane and circularly polarized fluctuation components of the interplanetary magnetic field. Applications of the method have been made using HEOS 2 (1 AU), Pioneer 10 (5 AU), Pioneer 11 (20 AU), and ICE (Giocabini-Zinner's comet) data sets. The results show the existence of circularly polarized MHD waves in all cases.     

A ‘Ulysses’ cosmic-ray latitude gradient observation and modulation models

The EPAC instrument on Ulysses is sensitive to relativistic cosmic rays when far from Jupiter and in the absence of energetic solar particles. Measurement of the latitude gradient of these particles, after correction for time variations, has been made for the 1993–1994 south polar pass. The average magnitude of the gradient is about the same or smaller than predicted by a model which includes full gradient drift. However, the latitude dependence of the solar plasma output into interplanetary space (including fast-stream and magnetic turbulence effects) seems to be important in determining the magnitude of modulation.     

Cosmic-ray perpendicular diffusion coefficient computed using Voyager data at 15 AU

Perpendicular diffusion due to either field line wandering or random gradient and curvature effects makes a substantial contribution to the radial transport of particles at distances of about 5 AU and beyond when lines of the interplanetary magnetic field (IMF) become almost azimuthal. Here test particle trajectories are followed in a field model which uses a magnetic field sample taken by Voyager 2 at 14.8 AU. Techniques previously developed (Moussas et al., 1982a) are employed to calculate the perpendicular diffusion coefficient for 100 MeV protons and arising from random gradient and curvature effects. The result K=(2.8±0.9)×10²¹ cm² s^–1 shows a substantial increase above the value determined previously at 5 AU and, assuming a power law radial dependence Kr , implies 0.8–1.1. This result is consistent with observations of the cosmic-ray radial gradient.     

Ambiguity in Determining the Diffusion Coefficient from Shock-Associated Energetic Particle Increases

A numerical solution to the Fisk and Lee (1980) equations for the particle intensity upstream of a corotating interplanetary shock is considered for the November 1991 event observed at Ulysses. A numerically derived parallel diffusion coefficient is available for this region (Quenby et al., 1993), based upon in-situ magnetometer data. Fitting the transport equations solution to the upstream energetic particle distribution function, employing a radial diffusion coefficient = ₀ r, where r and are, respectively, radial distance from the Sun and particle velocity, and with ₀ fixed from the magnetometer derived coefficient yielded a range of statistically acceptable values of (, ). These ran from (0.5, 0.0) to (1.8, 1.6) along a thin strip of — space, hence demonstrating the improbability that the velocity and radial dependence of the particle diffusion can be fixed from such particle and magnetic field data alone.     

The shape of the diffuse cosmic X-ray spectrum

Recent work by Dyer and Morfill has shown that satellite measurements of the diffuse cosmic X-ray spectrum made with crystal scintillators may include errors due to radioactive spallation products formed in the detector by inner belt and cosmic ray protons.

An estimate is made of the magnitude of this source of background for the various experimental situations and it is shown that apparent features at 40 keV and 1 MeV are likely to be due to radioactive decays in the instruments. A review is made of experiments covering the range 1 keV-100 MeV in order to ascertain whether a single exponent spectrum is capable of fitting the experimental results. The astrophysical implications of such a spectrum are briefly considered.

Suggestions are made for the location and correction for background of future experiments.

     

Anomalous He Acceleration,the Particle Source and the Transport Coefficient

Anomalous He⁺component acceleration at the heliospheric termination shock is modelled numerically via a steady-state solution to the combined cosmic-ray transport equation and shock boundary condition via a matrix inversion technique. This numerical solution automatically provides a no-drift modulation solution for the He⁺. Consistency with experimental data on the anomalous component is obtained for injection at 10 keV nucl^-1, at 120 AU, with a distribution function f(v)=2.75 × 10^-24 m^-6 s³ and a radial diffusion coefficient k=2.24× 10²² cm² s^-1 at 20 AU and for 100 MeV nucl^-1 particles but which varied proportional to v r where v and r are, respectively, particle velocity and solar distance,=1.3 and =0.5. However, a range of values of (,) between (1,0) and (2.4,1.4) were found to yield acceptable fits to the data. Pre-acceleration of ionised He at CIRs is possible as a source, although there is sufficient quiet-solar-wind-associated He⁺ for the required injection flux and the constraints on the injection efficiency are less at the terminal shock. These conclusions are insensitive to the terminal shock position and to the value of the injection energy.     

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).