In an attempt to understand the source and propagation of Galactic cosmic rays, we have employed the modiÐed weighted slab technique along with recent values of the relevant cross sections to compute primary to secondary ratios including B/C and sub-Fe/Fe for di †erent Galactic propagation models. The models that we have considered are the disk-halo di †usion model, the dynamical halo wind model, the turbulent di †usion model, and a model with minimal reacceleration. The modiÐed weighted slab technique will be brieÑy discussed and a more detailed description of the models will be given. We will also discuss the impact that the various models have on the problem of anisotropy at high energy and discuss what properties of a particular model bear on this issue. Subject headings : cosmic rays È di †usion È magnetic Ðelds È shock waves THE APPLICATION OF THE MODIFIED WEIGHTED SLAB TECHNIQUE TO SIMPLIFIED MODELSThe weighted slab technique has long been used in studying the propagation of cosmic rays in the Galaxy from their points of origin to their observation points near the Earth (Davis 1960 ;Ginzburg & Syrovatskii 1964 ;Ginzburg & Ptuskin 1976 ;Lezniak 1979 ; also see Webber 1997). Several approximations are used in deriving this technique, among them the assumption that energy loss and/or gain is not signiÐcant and that the propagation in, and loss from, the Galaxy may be described by a function of energy per nucleon alone. Both of these simpliÐcations are known to be untrue : for low energies, ionization energy loss can be signiÐcant and rigidity, or energy per charge, is believed to be the parameter that best describes propagation.Ptuskin, Jones, & Ormes (1996) showed how the weighted slab technique could be made exact for Galactic propagation models in which energy gains and losses were proportional to the same mass density that determined nuclear fragmentation and time-dependent processes, e.g., radioactive decay, do not play a role. This modiÐcation allows for the fact that particles had di †erent (usually higher) energies in the past, and hence di †erent propagation properties, and that propagation is considered to be a function of rigidity, although energy per nucleon is the proper parameter for nuclear fragmentation calculations. Strictly, this technique is rigorous only for models in which the particle propagation parameters are proportional to a single function of energy for each particle species, and hence does not apply to Galactic wind models or turbulent di †usion models. However, most of these models may be closely approximated by simpliÐed homogeneous models in which the mean path length has an exponential distribution with a mean path length that is a particular function of rigidity. It is models of this type and approximation that we discuss in this study. In this paper we present some results of the numerical simulations where the most recent set of spallation cross sections were used.It should be noted that these models bear a similarity to the well-known leaky-box model in that they a...

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We have made a new analysis of cosmic-ray data from the CRS experiment on the Voyager 2 (V2) spacecraft. This analysis, which includes both penetrating and stopping particles in the HET telescope, extends the energy range from an upper energy limit of 100-300 MeV nucleon À1 for stopping particles to over 1 GeV nucleon À1 . This analysis provides almost continuous spectra over this broad energy range, including the peak in the differential spectra of the various nuclei. This enables us to obtain the relationship between the shape of the low-energy interstellar differential spectrum and the amount of solar modulation. Measurements at V2 at the modulation minimum in 1987 and again in 1997-1998 give nearly the same intensities and therefore the same solar modulation parameter, ¼ 260 MV, which is much lower than the value of 400 MV at the Earth. most of the modulation was occurring beyond 54 AU and also that the interplanetary part of the solar modulation out to $54 AU in the two time periods of opposite solar magnetic polarity was greatly different. The measured secondary/ primary ratios B/C and N/O can be fitted equally well using a simple leaky-box Galactic propagation model with an escape length $ P À0:5 either with a break in the escape dependence at 1 GeV nucleon À1 or with no break in the escape-length dependence to the accuracy of the experimental data itself, AE3%, over the entire energy range from less than 100 MeV nucleon À1 to over 10 GeV nucleon À1 using a combination of both V2 data at the lower energies and HEAO data at the higher energies. This same escape-length dependence also predicts the measured higher Z secondary/primary ratio Z ¼ 21-23/Fe well at all energies.