Browsing by Author "Chan, Anthony A"

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    Development and Application of Stochastic Methods for Radiation Belt Simulations
    (2015-09-04) Zheng, Liheng; Chan, Anthony A; Wolf, Richard A; Dugan, Brandon
    This thesis describes a method for modeling radiation belt electron diffusion, which solves the radiation belt Fokker-Planck equation using its equivalent stochastic differential equations, and presents applications of this method to investigating drift shell splitting effects on radiation belt electron phase space density. The theory of the stochastic differential equation method of solving Fokker-Planck equations is formulated in this thesis, in the context of the radiation belt electron diffusion problem, and is generalized to curvilinear coordinates to enable calculation of the electron phase space density as a function of adiabatic invariants M, K and L. Based on this theory, a three-dimensional radiation belt electron model in adiabatic invariant coordinates, named REM (for Radbelt Electron Model), is constructed and validated against both known results from other methods and spacecraft measurements. Mathematical derivations and the essential numerical algorithms that constitute REM are presented in this thesis. As the only model to date that can solve the fully three-dimensional diffusion problem, REM is used to study the effects of drift shell splitting, which gives rise to M-L and K-L off-diagonal terms in the radiation belt diffusion tensor. REM simulation results suggest that drift shell splitting reduces outer radiation belt electron phase space density enhancements during electron injection events. Plots of the phase space density sources, which are unique products of the stochastic differential equation method, and theoretical analysis further reveal that this reduction effect is caused by a change of the phase space location of the source to smaller $L$ shells, and has a limit corresponding to two-dimensional local diffusion on a curved surface in the (M,K,L) phase space.
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    Multiscale Stochastic Simulations of Radiation Belt Dynamics
    (2024-04-05) Aldhurais, Suhail Adel; Chan, Anthony A
    A quantitative evaluation of the main physical processes in Earth's radiation belts has been difficult because of the broad-spectrum of timescales of the physical processes (milliseconds to several minutes). This thesis presents the K2 model, which incorporates a wide spectrum of timescales by combining Stochastic Differential Equation (SDE) methods into an otherwise Magnetohydrodynamics (MHD)-particle framework. We present the simulation results of March 17, 2013 event and show the capabilities of the K2 model. Additionally, an important spacecraft under-sampling of the simulation results is observed using NASA Van Allen Probes spacecraft orbits. A separate guiding-center code is constructed to investigate the quasilinear diffusion limit of the radial transport produced by ultra low-frequency waves contained in the MHD fields. We show that given sufficient phase randomization, the particle motion is diffusive. It is observed numerically that the addition of the electric and electromagnetic diffusion coefficients is equal to the combined diffusion coefficient.
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    Pair Creation Transparency in Gamma-Ray Pulsars
    (2014-07-30) Story, Sarah A; Baring, Matthew G; Chan, Anthony A; Damjanovic, Danijela
    Pulsars are rapidly rotating, highly magnetized neutron stars that produce photon pulses in energies from radio to gamma-rays. The population of known gamma-ray pulsars has been increased nearly twenty-fold in the past six years since the launch of the Fermi Gamma-Ray Space Telescope; it now exceeds 145 sources and has defined an important part of Fermi's science legacy. In order to understand the detectability of pulsars in gamma-rays, it is important to consider not only the radiative mechanisms that produce gamma-rays, but the processes that can attenuate photons before they can leave the pulsar magnetosphere. Here I explore two such processes, one-photon magnetic pair creation and two-photon pair creation. Magnetic pair creation has been at the core of radio pulsar paradigms and central to polar cap models of gamma-ray pulsars for over three decades. Among the population characteristics well established for Fermi pulsars is the common occurrence of exponential turnovers in the spectra in the 1-10 GeV range. These turnovers are too gradual to arise from magnetic pair creation in the strong magnetic fields of pulsar inner magnetospheres. By demanding insignificant photon attenuation precipitated by such single-photon pair creation, the energies of these turnovers for Fermi pulsars can be used to compute lower bounds for the typical altitude of GeV band emission. In this thesis, I explore such pair transparency constraints below the turnover energy and update earlier altitude bound determinations that have been deployed in various gamma-ray pulsar papers by the Fermi-LAT collaboration. For low altitude emission locales, general relativistic influences are found to be important, increasing cumulative opacity, shortening the photon attenuation lengths, and also reducing the maximum energy that permits escape of photons from a neutron star magnetosphere. Rotational aberration influences are also explored, and are found to be small at low altitudes, except near the magnetic pole. Our analysis clearly demonstrates that including near-threshold physics in the pair creation rate is essential to deriving accurate attenuation lengths and escape energies. The altitude bounds we compute for Fermi pulsars are typically in the range of 2-7 stellar radii and provide key information on the emission altitude in radio quiet pulsars that do not possess double peaked pulse profiles. The bound for the Crab pulsar is at a much higher altitude, with the detection by the atmospheric Cherenkov telescope MAGIC out to 350-400 GeV implying a lower bound of 310 km to the emission region, i.e., approximately 20% of the light cylinder radius. These results are also extended to the super-critical field domain, where it is found that emission in magnetars originating below around 10 stellar radii will not appear in the Fermi-LAT band. Two-photon pair creation becomes important at high altitudes and for photons produced by curvature radiation from charges flowing downward along magnetic field lines. Because the efficiency of two-photon pair creation does not depend on the local magnetic field strength, it can continue to be active in the weak-field regions far from the neutron star. It is found that two-photon pair creation can strongly attenuate photons emitted from downward-traveling charges except at very high altitudes of emission, but in the absence of rotational aberration, it is unable to produce significant opacity for upward-traveling charges unless unrealistically high neutron star surface temperatures are assumed.