Browsing by Author "Chan, Anthony A."
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Item Eigenmode analysis of compressional poloidal modes in a self‐consistent magnetic field(Wiley, 2017) Xia, Zhiyang; Chen, Lunjin; Zheng, Liheng; Chan, Anthony A.In this study, we simulate a self‐consistent magnetic field that satisfies force balance with a model ring current that is radially localized, axisymmetric, and has anisotropic plasma pressure. We find that the magnetic field dip forms near the high plasma pressure region with plasma β >∼ 0.6, and the formed magnetic dip becomes deeper for larger plasma βand also slightly deeper for larger anisotropy. We perform linear analysis on a ppol of self‐consistent equilibria for second harmonic compressional poloidal modes of sufficiently high azimuthal wave number. We investigate the effect of anisotropic pressure on the eigenfrequency of the poloidal modes and the characteristics of the compressional magnetic field component. We find that the eigenfrequency is reduced at the outer edge of the thermal pressure peak and increased at the inner edge. The compressional magnetic field component occurs primarily within 10° of the equator on both the inner and outer edges, with stronger compressional magnetic field component on the outer edge. Larger β and smaller anisotropy can increase the change of eigenfrequency and the strength of the compressional magnetic field component. The critical condition on plasma β and pressure anisotropy of an Alfvén ballooning instability is also identified.Item Electric and magnetic radial diffusion coefficients using the Van Allen probes data(Wiley, 2016) Ali, Ashar F.; Malaspina, David M.; Elkington, Scot R.; Jaynes, Allison N.; Chan, Anthony A.; Wygant, John; Kletzing, Craig A.ULF waves are a common occurrence in the inner magnetosphere and they contribute to particle motion, significantly, at times. We used the magnetic and the electric field data from the Electric and Magnetic Field Instrument Suite and Integrated Sciences (EMFISIS) and the Electric Field and Waves instruments (EFW) on board the Van Allen Probes to estimate the ULF wave power in the compressional component of the magnetic field and the azimuthal component of the electric field, respectively. Using L∗, Kp, and magnetic local time (MLT) as parameters, we conclude that the noon sector contains higher ULF Pc-5 wave power compared with the other MLT sectors. The dawn, dusk, and midnight sectors have no statistically significant difference between them. The drift-averaged power spectral densities are used to derive the magnetic and the electric component of the radial diffusion coefficient. Both components exhibit little to no energy dependence, resulting in simple analytic models for both components. More importantly, the electric component is larger than the magnetic component by one to two orders of magnitude for almost all L∗ and Kp; thus, the electric field perturbations are more effective in driving radial diffusion of charged particles in the inner magnetosphere. We also present a comparison of the Van Allen Probes radial diffusion coefficients, including the error estimates, with some of the previous published results. This allows us to gauge the large amount of uncertainty present in such estimates.Item Ground-based magnetometer determination of in situ Pc4–5 ULF electric field wave spectra as a function of solar wind speed(2012) Rae, I. Jonathan; Mann, Ian R.; Murphy, Kyle R.; Ozeke, Louis G.; Milling, David K.; Chan, Anthony A.; Elkington, Scot R.; Honary, Farideh; American Geophysical UnionWe present a statistical characterization of ground-based ultra-low-frequency ( 1–15 mHz) magnetic wave power spectral densities (PSDs) as a function of latitude (corresponding to dipole L-shells from L 2.5–8), local time, and solar wind speed. We show a clear latitudinal dependence on the PSD profiles, with PSDs increasing monotonically from low- to auroral zone latitudes, where PSDs are peaked before decay in amplitude at higher latitudes. In general, ULF wave powers are highest on the nightside, followed by the local morning, noon, and finally dusk sectors, and are well-characterized and well-ordered by solar wind speed at all MLTs spanning L 2.5–8. A distinct peak in PSD in the 2–8 mHz frequency range above a background power law is evident at most stations studied in this paper, demonstrating a significant non power law like component in the ULF wave power spectrum, in particular at high solar wind speeds. We conclude that field line resonance (FLR) behavior in the magnetosphere is most likely responsible for the peak in PSD, and that such peaks should be included in any radiation belt radial diffusion model addressing radiation belt dynamics. Furthermore, we utilize a model in order to map the ground-based magnetic ULF wave power measurements into electric fields in the equatorial plane of an assumed dipole magnetic field, and find excellent agreement with the in situ CRRES electric fields shown by Brautigam et al. [2005], clearly demonstrating the utility of ground-based measurements in providing reliable estimates of ULF electric field PSD for nowcast input into radiation belt radial diffusion models.Item Hamiltonian formulations of quasilinear theory for magnetized plasmas(Frontiers Media S.A., 2022) Brizard, Alain J.; Chan, Anthony A.Hamiltonian formulations of quasilinear theory are presented for the cases of uniform and nonuniform magnetized plasmas. First, the standard quasilinear theory of Kennel and Engelmann (Kennel, Phys. Fluids, 1966, 9, 2377) is reviewed and reinterpreted in terms of a general Hamiltonian formulation. Within this Hamiltonian representation, we present the transition from two-dimensional quasilinear diffusion in a spatially uniform magnetized background plasma to three-dimensional quasilinear diffusion in a spatially nonuniform magnetized background plasma based on our previous work (Brizard and Chan, Phys. Plasmas, 2001, 8, 4762–4771; Brizard and Chan, Phys. Plasmas, 2004, 11, 4220–4229). The resulting quasilinear theory for nonuniform magnetized plasmas yields a 3 × 3 diffusion tensor that naturally incorporates quasilinear radial diffusion as well as its synergistic connections to diffusion in two-dimensional invariant velocity space (e.g., energy and pitch angle).Item Magnetic field power spectra and magnetic radial diffusion coefficients using CRRES magnetometer data(Wiley, 2015) Ali, Ashar F.; Elkington, Scot R.; Tu, Weichao; Ozeke, Louis G.; Chan, Anthony A.; Friedel, Reiner H.W.We used the fluxgate magnetometer data from Combined Release and Radiation Effects Satellite (CRRES) to estimate the power spectral density (PSD) of the compressional component of the geomagnetic field in the ∼1 mHz to ∼8 mHz range. We conclude that magnetic wave power is generally higher in the noon sector for quiet times with no significant difference between the dawn, dusk, and the midnight sectors. However, during high Kp activity, the noon sector is not necessarily dominant anymore. The magnetic PSDs have a very distinct dependence on Kp. In addition, the PSDs appear to have a weak dependence on McIlwain parameter L with power slightly increasing as L increases. The magnetic wave PSDs are used along with the Fei et al. (2006) formulation to compute DBLL[CRRES] as a function of L and Kp. The L dependence of DBLL[CRRES] is systematically studied and is shown to depend on Kp. More significantly, we conclude that DELL is the dominant term driving radial diffusion, typically exceeding DBLL by 1–2 orders of magnitude.Item Modulation of chorus intensity by ULF waves deep in the inner magnetosphere(Wiley, 2016) Xia, Zhiyang; Chen, Lunjin; Dai, Lei; Claudepierre, Seth G.; Chan, Anthony A.; Soto-Chavez, A.R.; Reeves, G.D.Previous studies have shown that chorus wave intensity can be modulated by Pc4-Pc5 compressional ULF waves. In this study, we present Van Allen Probes observation of ULF wave modulating chorus wave intensity, which occurred deep in the magnetosphere. The ULF wave shows fundamental poloidal mode signature and mirror mode compressional nature. The observed ULF wave can modulate not only the chorus wave intensity but also the distribution of both protons and electrons. Linear growth rate analysis shows consistence with observed chorus intensity variation at low frequency (f <∼ 0.3fce), but cannot account for the observed higher-frequency chorus waves, including the upper band chorus waves. This suggests the chorus waves at higher-frequency ranges require nonlinear mechanisms. In addition, we use combined observations of Radiation Belt Storm Probes (RBSP) A and B to verify that the ULF wave event is spatially local and does not last long.Item Simulation of radiation belt wave-particle interactions in an MHD-particle framework(Frontiers Media S.A., 2023) Chan, Anthony A.; Elkington, Scot R.; Longley, William J.; Aldhurais, Suhail A.; Alam, Shah S.; Albert, Jay M.; Jaynes, Allison N.; Malaspina, David M.; Ma, Qianli; Li, WenIn this paper we describe K2, a comprehensive simulation model of Earth’s radiation belts that includes a wide range of relevant physical processes. Global MHD simulations are combined with guiding-center test-particle methods to model interactions with ultra low-frequency (ULF) waves, substorm injections, convective transport, drift-shell splitting, drift-orbit bifurcations, and magnetopause shadowing, all in self-consistent MHD fields. Simulation of local acceleration and pitch-angle scattering due to cyclotron-scale interactions is incorporated by including stochastic differential equation (SDE) methods in the MHD-particle framework. The SDEs are driven by event-specific bounce-averaged energy and pitch-angle diffusion coefficients. We present simulations of electron phase-space densities during a simplified particle acceleration event based on the 17 March 2013 event observed by the Van Allen Probes, with a focus on demonstrating the capabilities of the K2 model. The relative wave-particle effects of global scale ULF waves and very-low frequency (VLF) whistler-mode chorus waves are compared, and we show that the primary acceleration appears to be from the latter. We also show that the enhancement with both ULF and VLF processes included exceeds that of VLF waves alone, indicating a synergistic combination of energization and transport processes may be important.Item UBER v1.0: a universal kinetic equation solver for radiation belts(European Geosciences Union, 2021) Zheng, Liheng; Chen, Lunjin; Chan, Anthony A.; Wang, Peng; Xia, Zhiyang; Liu, XuRecent proceedings in radiation belt studies have proposed new requirements for numerical methods to solve the kinetic equations involved. In this article, we present a numerical solver that can solve the general form of the radiation belt Fokker–Planck equation and Boltzmann equation in arbitrarily provided coordinate systems and with user-specified boundary geometry, boundary conditions, and equation terms. The solver is based upon the mathematical theory of stochastic differential equations, whose computational accuracy and efficiency are greatly enhanced by specially designed adaptive algorithms and a variance reduction technique. The versatility and robustness of the solver are exhibited in four example problems. The solver applies to a wide spectrum of radiation belt modeling problems, including the ones featuring non-diffusive particle transport such as that arising from nonlinear wave–particle interactions.Item ULF wave derived radiation belt radial diffusion coefficients(2012) Ozeke, Louis G.; Mann, Ian R.; Murphy, Kyle R.; Rae, I. Jonathan; Milling, David K.; Elkington, Scot R.; Chan, Anthony A.; Singer, Howard J.; National Aeronautics and Space Administration; American Geophysical UnionWaves in the ultra-low-frequency (ULF) band have frequencies which can be drift resonant with electrons in the outer radiation belt, suggesting the potential for strong interactions and enhanced radial diffusion. Previous radial diffusion coefficient models such as those presented by Brautigam and Albert (2000) have typically used semiempirical representations for both the ULF wave’s electric and magnetic field power spectral densities (PSD) in space in the magnetic equatorial plane. In contrast, here we use ground- and space-based observations of ULF wave power to characterize the electric and magnetic diffusion coefficients. Expressions for the electric field power spectral densities are derived from ground-based magnetometer measurements of the magnetic field PSD, and in situ AMPTE and GOES spacecraft measurements are used to derive expressions for the compressional magnetic field PSD as functions of Kp, solar wind speed, and L-shell. Magnetic PSD results measured on the ground are mapped along the field line to give the electric field PSD in the equatorial plane assuming a guided Alfvén wave solution and a thin sheet ionosphere. The ULF wave PSDs are then used to derive a set of new ULF-wave driven diffusion coefficients. These new diffusion coefficients are compared to estimates of the electric and magnetic field diffusion coefficients made by Brautigam and Albert (2000) and Brautigam et al. (2005). Significantly, our results, derived explicitly from ULF wave observations, indicate that electric field diffusion is much more important than magnetic field diffusion in the transport and energization of the radiation belt electrons.Item Using MEPED observations to infer plasma density and chorus intensity in the radiation belts(Frontiers Media S.A., 2022) Longley, William J.; Chan, Anthony A.; Jaynes, Allison N.; Elkington, Scot R.; Pettit, Joshua M.; Ross, Johnathan P. J.; Glauert, Sarah A.; Horne, Richard B.Efforts to model and predict energetic electron fluxes in the radiation belts are highly sensitive to local wave-particle interactions. In this study, we use multi-point measurements of precipitating and trapped electron fluxes to investigate the dynamic variation of chorus wave-particle interactions during the 17 March 2013 storm. Quasilinear theory characterizes the chorus wave-particle interaction as a diffusive process, with the diffusion coefficients depending on the particle energy and pitch angle, as well as the background plasma parameters such as the wave intensity and plasma density. These plasma parameters in the radiation belts are spatially localized and time-varying, so we construct event-specific diffusion coefficients using MEPED (onboard POES/MetOp) measurements of electron fluxes at low Earth orbit. This new method provides realistic diffusion coefficients for chorus waves that account for changes in the wave intensity, the plasma density, and the magnetic field strength in the outer radiation belt. We show that the inferred chorus intensity is significantly lower than previous estimates that use MEPED observations since the same amount of increased precipitation by 30–300 keV electrons can be explained by a change in the plasma density. This technique therefore allows for us to create time varying, global maps of the plasma-gyrofrequency ratio (fpe/fce), and therefore plasma density, in the outer radiation belts using the MEPED measurements. The global density estimates compare reasonably well to in situ density measurements from RBSP-B.