Dipole representations of the earth's magnetic field have been found to have insufficient accuracy for the study of magnetically trapped particles. A coordinate system consisting of the magnitude of the magnetic field B, and the integral invariant I has been found to adequately organize, measurements made at different geographic locations. It is shown in the present paper, that a parameter L = f(B,I) can be defined which retains most of the desirable properties of I and which has the additional property of organizing measurements along lines of force. Since the parameter L is the analog of a physical distance in a dipole field (the equatorial radius of a magnetic shell), it is usually found to present fewer conceptual difficulties than the integral invariant I.

/pdf/coordinates-for-mapping-the-distribution-of-magnetically-2llokep7yc.pdf

Coordinates for Mapping the Distribution of Magnetically Trapped Particles

https://ams.cern.ch/AMS/Publications/AMS-06_PREP_vol366.pdf

The Alpha Magnetic Spectrometer (AMS)on the International Space Station : Part I - results from the test flight on the space shuttle

Energetic Ion and Electron Irradiation of the Icy Galilean Satellites

Molecular dynamics simulations were performed on series of gold nanoclusters comprised of 459, 1157, and 3943 atoms, to study their structures and properties during heating and cooling. The increased depression of melting point as particle size decreases has been interpreted in terms of Pawlow's triple point theory, the liquid shell model, and extensions of the two. The solid−liquid interfacial free energy σsl of ∼0.15 J/m2 inferred from the liquid shell model was close to the values predicted by several empirical relations. When molten particles in a given series were frozen, several different final structures were obtained even though conditions had been identical. Most of the frozen clusters attained an icosahedral structure, a structure found to be stable to mild annealing. Other structures observed were imperfect truncated decahedra, twinned truncated octahedra, and hexagonal close packed structures. The rate of crystal nucleation in liquid clusters was analyzed in terms of classical nucleation theor...

Melting and Freezing of Gold Nanoclusters

The ability of the cosmic-ray neutron albedo mechanism to account for geomagnetically trapped electrons is investigated quantitatively. Injection as a function of energy, pitch angle, and altitude is computed from a reasonable neutron albedo model. Loss mechanisms (slowing down and pitch-angle diffusion) based on Coulomb interactions with the residual atmosphere are considered to act both independently and simultaneously. It is found that slowing down is generally dominant. The resulting electron belt has the following features: (a) an intensity whose energy spectrum shows a peak at ∼200 kev; (b) an angular distribution that is approximately ‘isotropic’ up to the loss cone; and (c) an omnidirectional, integral intensity in the geomagnetic equatorial plane that is approximately constant vs. altitude. The absolute intensities depend directly on the atmospheric model used in the calculation; namely, rv−2.7, where atmospheric density is taken as ρ0r−v. These results agree only poorly with spectrometer observations which show an energy spectrum with a peak at a much lower energy. However, the quantitative agreement as to intensity is good at energies ≳400 kev. It is concluded that only a small fraction of the trapped electrons can be accounted for in terms of neutron albedo, essentially all trapped electrons >400 kev. An ‘auroral’ component of low-energy electrons is also present. The energy of this low-energy component probably derives from local acceleration, and ultimately from the sun. The effect of the Capetown magnetic anomaly is investigated and shown to produce a ‘slot’ of only 2 per cent in the equatorial plane in the vicinity of 2.7 earth radii.

Geomagnetically trapped electrons from cosmic ray albedo neutrons

On the motion of charged particles in the geomagnetic field

A differential equation of transport is written for protons losing energy in an atmosphere but not scattering. It is solved under the approximation that a proton loses a negligible amount of energy while it drifts once around the earth in longitude. Three cases are treated: the equilibrium, solution with input and loss rates equal; the solution for impulsive injection at t = 0, the intensity then dying away; and the solution for the intensity zero initially, the input mechanism being turned on at t = 0. No numerical work bearing on the geometry of the source function is included. The treatment is an improvement over previous ones in that it adequately treats the particles as moving along their actual trajectories. A detailed comparison with observations over South Africa shows that the altitude dependence of intensity is roughly consistent with the view that the particles seen by the unshielded Geiger tube on 1958e are protons supplied by a weak source (for example, by decay of albedo neutrons) which are lost to the detector when their energy is reduced below the detection threshold by absorption. The atmosphere required has a temperature of about 2000°K at 400 km if it is pure dissociated nitrogen. At some height between about 1100 and 1300 km the scale height sharply increases in a way consistent with the view that at this height the composition changes to pure dissociated hydrogen. Only relative intensities are used in these comparisons.

On the Theory of Protons Trapped in the Earth's Magnetic Field

Secondary products of the interaction of cosmic rays with the earth's atmosphere, when projected upward and when of an energy below the Stormer cutoff, are trapped by the earth's magnetic field and guided to an impact with the atmosphere in the hemisphere opposite that of their formation. These particles are called the re-entrant albedo. In the present paper we derive an expression for their intensity and make a simplified computation of a particular case where data are available for comparison.

Re-entrant cosmic-ray albedo

On cosmic ray cutoffs

Several people have computed numerically the magnetic field caused by an axially symmetric body of plasma imbedded in a dipole magnetic field. In the present paper we derive an approximate formula for this magnetic field, without first choosing a particular functional form for the plasma density. This has the consequence that we can easily discuss any particular case without recourse to a computer, whereas previous treatments resulted in a tabulation of an answer for a particular case only, and new cases required new computer runs. The method used avoids the usual fine net required by the singularity in the integrand. We achieve this by constructing a new quadrature formula which treats this singularity exactly. The then permitted coarse net makes possible an algebraic treatment rather than a numerical one.

Ernest C. Ray

Papers

On the motion of charged particles in the geomagnetic field

On the Theory of Protons Trapped in the Earth's Magnetic Field

Re-entrant cosmic-ray albedo

On cosmic ray cutoffs

The terrestrial ring current