Geomagnetically trapped electrons from cosmic ray albedo neutrons

Abstract

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.

Resonant scattering of outer zone relativistic electrons by multiband EMIC waves and resultant electron loss time scales

“…In order to investigate the temporal evolution of outer zone relativistic electron pitch angle distribution due to EMIC wave scattering, we perform the 1-D pure pitch angle diffusion simulations [e.g., Meredith et al, 2006;Thorne et al, 2013;Ni et al, 2013Ni et al, , 2014aNi et al, , 2014b by numerically solving the equation where f is the phase space density (PSD), t is the time, and the electron bounce period is approximated as Lenchek et al, 1961]. The upper boundary condition for PSD in a eq space is set as ∂f ∂α eq α eq ¼ 90°À Á ¼ 0, and the corresponding lower boundary condition is set as ∂f ∂α eq α eq ¼ 0°À Á ¼ 0 for the strong diffusion and as f(α eq ≤ α LC ) = 0 (where α LC is the equatorial loss cone angle) for the weak diffusion.…”

Bounce-averaged Fokker-Planck diffusion equation in non-dipolar magnetic fields with applications to the Dungey magnetosphere

“…(17). In a dipolar field, the normalized S 0 , as a quarter-bounce integral, has been investigated in detail by Lenchek et al (1961) and Davidson (1976) and recently revisited by Orlova and Shprits (2011). Two good empirical approximations of S 0 in terms of sin α eq , S 0 ≈ 1.30 − 0.56 sin α eq (29) with an error within 4.5 % and…”

“…Compared to the results in a dipolar field, the degree of decrease in S 0 increases considerably with equatorial pitch angle, varying from ∼1 % at α eq ≈ 0 • to >50 % at α eq ≈ 90 • . Based upon the previous studies (e.g., Lenchek et al, 1961;Schulz and Lanzerotti, 1974;Davidson, 1976;Orlova and Shprits, 2011), we have adopted a fifthorder polynomial of sin α eq , S 0 α eq = a 5 sin α eq 5 +a 4 sin α eq 4 +a 3 sin α eq 3 +a 2 sin α eq 2 +a 1 sin α eq +a 0 ,…”

Evolution of the plasma sheet electron pitch angle distribution by whistler-mode chorus waves in non-dipole magnetic fields

“…In a dipole field, S(α eq ) can be approximated by S(α eq ) = 1.38 − 0.32sinα eq −0.32 sinα eq (e.g., Lenchek et al, 1961;Orlova and Shprits, 2011). In general, S(α eq ) is given as:…”