Geomagnetically trapped electrons from cosmic ray albedo neutrons

Lenchek, A. M.; Singer, S. Fred; Wentworth, R. C.

doi:10.1029/jz066i012p04027

Cited by 117 publications

(115 citation statements)

References 34 publications

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“…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.…”

Section: Pure Pitch Angle Diffusion Simulations and Electron Loss Timmentioning

confidence: 99%

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

et al. 2015

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To improve our understanding of the role of electromagnetic ion cyclotron (EMIC) waves in radiation belt electron dynamics, we perform a comprehensive analysis of EMIC wave‐induced resonant scattering of outer zone relativistic (>0.5 MeV) electrons and resultant electron loss time scales with respect to EMIC wave band, L shell, and wave normal angle model. The results demonstrate that while H+‐band EMIC waves dominate the scattering losses of ~1–4 MeV outer zone relativistic electrons, it is He+‐band and O+‐band waves that prevail over the pitch angle diffusion of ultrarelativistic electrons at higher energies. Given the wave amplitude, EMIC waves at higher L shells tend to resonantly interact with a larger population of outer zone relativistic electrons and drive their pitch angle scattering more efficiently. Obliquity of EMIC waves can reduce the efficiency of wave‐induced relativistic electron pitch angle scattering. Compared to the frequently adopted parallel or quasi‐parallel model, use of the latitudinally varying wave normal angle model produces the largest decrease in H+‐band EMIC wave scattering rates at pitch angles < ~40° for electrons > ~5 MeV. At a representative nominal amplitude of 1 nT, EMIC wave scattering produces the equilibrium state (i.e., the lowest normal mode under which electrons at the same energy but different pitch angles decay exponentially on the same time scale) of outer belt relativistic electrons within several to tens of minutes and the following exponential decay extending to higher pitch angles on time scales from <1 min to ~1 h. The electron loss cone can be either empty as a result of the weak diffusion or heavily/fully filled due to approaching the strong diffusion limit, while the trapped electron population at high pitch angles close to 90° remains intact because of no resonant scattering. In this manner, EMIC wave scattering has the potential to deepen the anisotropic distribution of outer zone relativistic electrons by reshaping their pitch angle profiles to “top‐hat.” Overall, H+‐band and He+‐band EMIC waves are most efficient in producing the pitch angle scattering loss of relativistic electrons at ~1–2 MeV. In contrast, the presence of O+‐band EMIC waves, while at a smaller occurrence rate, can dominate the scattering loss of 5–10 MeV electrons in the entire region of the outer zone, which should be considered in future modeling of the outer zone relativistic electron dynamics.

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Section: Pure Pitch Angle Diffusion Simulations and Electron Loss Timmentioning

confidence: 99%

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

et al. 2015

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“…(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…”

Section: Bounce Period Related Term Smentioning

confidence: 99%

“…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 ,…”

Section: Bounce Period Related Term Smentioning

confidence: 99%

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

Thorne

2012

Ann. Geophys.

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Abstract. We perform a detailed derivation of the bounceaveraged relativistic Fokker-Planck diffusion equation applicable to arbitrary magnetic field at a constant Roederer L. The form of the bounce-averaged diffusion equation is found regardless of details of the mirror geometry, suggesting that the numerical schemes developed for solving the modified two-dimensional (2-D) Fokker-Planck equation in a magnetic dipole should be feasible for similar computation efforts on modeling wave-induced particle diffusion processes in any non-dipolar magnetic field. However, bounce period related terms and bounce-averaged diffusion coefficients are required to be computed in realistic magnetic fields. With the application to the Dungey magnetosphere that is controlled by the intensity of southward interplanetary magnetic field (IMF), we show that with enhanced southward IMF the normalized bounce period related term decreases accordingly, and bounce-averaged diffusion coefficients cover a broader range of electron energy and equatorial pitch angle with a tendency of increased magnitude and peaking at lower energies. The compression of the Dungey magnetosphere can generally produce scattering loss of plasma sheet electrons <∼4 keV and radiation belt electrons >∼100 keV on a timescale shorter than that in a dipolar field, and induce momentum diffusion at high pitch angles closer to 90 • . Correspondingly, the strong diffusion rate drops considerably as a product of changes in both the equatorial loss cone and the bounce period. The extent of differences in all the parameters introduced by the southward IMF intensification also becomes larger for a field line with higher equatorial crossing. With the derived general formulism of bounce-averaged diffusion equation for arbitrary 2-D magnetic field, our results confirm the need for the adoption of realistic magnetic fields to perform accurate determination of electron resonant scattering rates and precise multi-dimensional diffusion simulations of magnetospheric electron dynamics.

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“…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:…”

Section: Bounce Averaged Diffusion Coefficients and Fokkerplanck Diffmentioning

confidence: 99%

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

Tao

et al. 2012

Ann. Geophys.

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Abstract. We present a detailed numerical study on the effects of a non-dipole magnetic field on the Earth's plasma sheet electron distribution and its implication for diffuse auroral precipitation. Use of the modified bounce-averaged Fokker-Planck equation developed in the companion paper by Ni et al. (2012) for 2-D non-dipole magnetic fields suggests that we can adopt a numerical scheme similar to that used for a dipole field, but should evaluate bounce-averaged diffusion coefficients and bounce period related terms in nondipole magnetic fields. Focusing on nightside whistler-mode chorus waves at L = 6, and using various Dungey magnetic models, we calculate and compare of the bounce-averaged diffusion coefficients in each case. Using the Alternative Direction Implicit (ADI) scheme to numerically solve the 2-D Fokker-Planck diffusion equation, we demonstrate that chorus driven resonant scattering causes plasma sheet electrons to be scattered much faster into loss cone in a non-dipole field than a dipole. The electrons subject to such scattering extends to lower energies and higher equatorial pitch angles when the southward interplanetary magnetic field (IMF) increases in the Dungey magnetic model. Furthermore, we find that changes in the diffusion coefficients are the dominant factor responsible for variations in the modeled temporal evolution of plasma sheet electron distribution. Our study demonstrates that the effects of realistic ambient magnetic fields need to be incorporated into both the evaluation of resonant diffusion coefficients and the calculation of FokkerPlanck diffusion equation to understand quantitatively the evolution of plasma sheet electron distribution and the occurrence of diffuse aurora, in particular at L > 5 during geomagnetically disturbed periods when the ambient magnetic field considerably deviates from a magnetic dipole.

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Geomagnetically trapped electrons from cosmic ray albedo neutrons

Cited by 117 publications

References 34 publications

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

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

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

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

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