Modelling He and H Isotopes in the Radiation Belts

Nuclear interactions between inner zone protons and atoms in the upper atmosphere produce energetic H and He nuclei that are an additional radiation belt source. We calculate production rates of these isotopes from models of the inner zone proton intensity, the upper atmosphere drift averaged composition and densities, and cross-sections for the various interaction processes. For comparison with observations of radiation belt H and He isotopes, the production rates are combined with a model of the energy loss rate in the residual atmosphere to calculate particle intensities. Although the calculations are in principle straightforward, they depend on a detailed knowledge of the various model inputs, including models for radiation belt protons, and may also depend on the phase of the solar cycle. On the other hand, the results of the calculations, when compared with the observational data, can provide useful tests of the model inputs. Preliminary results show that the atmosphere is a significant source for inner zone ^4He, ^3He, and d

Anomalous Cosmic Rays: The Principal Source of High Energy Heavy Ions in the Radiation Belts

Recent observations from SAMPEX have shown that "anomalous cosmic rays" are the principal source of high energy (> 10MeV/nuc) heavy ions trapped in the radiation belts. This component of interplanetary particles is known to originate from interstellar atoms that has been accelerated to high energies in the outer heliosphere. The mechanism by which anomalous cosmic rays with ~1 to ~50 Me V/nuc are trapped in a radiation belt at L ≈ 2 has now been verified. We discuss models for accelerating and trapping anomalous cosmic rays and review observations of their composition, energy spectra, pitch angle distribution, and time variations. Extrapolation of the fluxes observed at ~600 km to higher altitude and other time periods is also discussed

A Convex-Nonconvex variational method for the additive decomposition of functions on surfaces

We present a Convex-NonConvex variational approach for the additive decomposition of noisy scalar f ields defined over triangulated surfaces into piecewise constant and smooth components. The energy functional to be minimized is defined by the weighted sum of three terms, namely an L2 fidelity term for the noise component, a Tikhonov regularization term for the smooth component and a Total Variation (TV)-like non-convex term for the piecewise constant component. The last term is parametrized such that the free scalar parameter allows to tune its degree of non- convexity and, hence, to separate the piecewise constant component more effectively than by using a classical convex TV regularizer without renouncing to convexity of the total energy functional. A method is also presented for selecting the two regularization parameters. The unique solution of the proposed variational model is determined by means of an efficient ADMM-based minimization algorithm. Numerical experiments show a nearly perfect separation of the different components

A model of the secondary radiation belt

Products of nuclear reactions between primary radiation belt protons and constituents of the tenuous upper atmosphere form a collocated secondary radiation belt. A calculation of the time-dependent secondary intensity provides a model specification of this environmental component for low- and medium-altitude satellite orbits. It is based on an earlier model of the radiation belt protons, the novel feature being a determination of the secondary source function from nuclear reaction cross sections. All long-lived secondary products are included, isotopes of H and He being dominant while the heavier Li to O isotopes are present at relatively low levels. Secondary protons are shown to be a minor correction to the primary radiation belt

Multiply Charged Anomalous Cosmic Rays Above 15 MeV/nucleon

Ionic charge states of anomalous cosmic ray nitrogen, oxygen, and neon with kinetic energies above 15 MeV /nucleon have been measured using the geomagnetic field as a rigidity filter. Data from the MAST instrument on the polar-orbiting SAMPEX satellite taken during the period from 1992 to 1996 show that all three elements are predominantly multiply charged at high energies, confirming the earlier result for oxygen alone based on a smaller data set. Energy spectra of the singly charged and multiply charged components of each element are compared with model predictions

Observations of Geomagnetically Trapped Anomalous Cosmic Rays by SAMPEX

he first detailed measurements of a belt of geomagnetically trapped heavy ions that originated as interplanetary anomalous cosmic rays (ACRs) are being made by the polar orbiting satellite SAMPEX. The singly ionized interplanetary ACRs are trapped after losing electrons in the upper atmosphere. Their subsequent lifetime against energy loss by ionization of the atmosphere allows them to reach a substantially higher intensity than in interplanetary space. The ACR composition, which includes only elements with high first ionization potentials, is reflected in the trapped ACRs with some bias due to the trapping mechanism. The elements O, N, and Ne are present, while the lower atomic number elements, He and C, are either absent or substantially depleted relative to their interplanetary abundances. The trapping mechanism also determines the location of the ACR belt, which is confined to a narrow region near L=2, and the pitch‐angle distribution of the trapped ACRs, which is nearly isotropic except for the well‐defined loss cones. The intensities of the trapped and interplanetary ACRs have been measured by SAMPEX since its July, 1992 launch. Both have been steadily increasing with the approach of the minimum of the solar sunspot cycle

Geomagnetically Trapped Anomalous Cosmic Rays at Solar Minimum

The geomagnetically trapped a...r10malous cosmic rays have been monitored continuously by instrumentation on the SAMPEX satellite since its launch in mid-1992. With the approach of solar mimmum the intensity has been increasing along with that of the interplanetary anomalous cosmic ray source. We compare the time variations of the two components using data from the MAST instrument: describe improved measurements of the spatiaJ distribution of the trapped component, and discuss implications for the trapping and lifetime of the trapped component