Browsing by Author "Zheng, Liheng"

Now showing 1 - 5 of 5
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    A Method to Compute Three Dimensional Magnetospheric Equilibria with Dipole Tilt and its Application in Estimating Magnetic Flux Tube Volume
    (2011) Zheng, Liheng; Tofforetto, Grank
    In this thesis we describe a new version of a magneto-friction model, which was developed for computing the magnetospheric equilibrium that includes an arbitrary Earth's dipole tilt and interplanetary magnetic field. We also describe the algorithms of this new friction code that trace magnetic field lines, locate the neutral sheet, and identify the magnetopause In addition, we present a generalized theory for calculating magnetic flux tube volume in the magnetotail, in an attempt to generalize the Wolf [2006] empirical formula, and describe a method for estimating flux tube volume from measurements at geosynchronous orbit. This new method has been tested against various equilibrated magnetospheres generated by the new friction code. Although still incomplete, the method exhibits promising features, and is to be completed in the future.
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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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    Effects of magnetic drift shell splitting on electron diffusion in the radiation belts
    (Wiley, 2016) Zheng, Liheng; Chan, A.A.; O’Brien, T.P.; Tu, W.; Cunningham, G.S.; Albert, J.M.; Elkington, S.R.
    Drift shell splitting in the presence of pitch angle scattering breaks all three adiabatic invariants of radiation belt electron motion and produces new diffusion terms that fully populate the diffusion tensor in the Fokker-Planck equation. The Radbelt Electron Model (REM) solves such a Fokker-Planck equation and is used to investigate the phase space density sources. Our simulation results and theoretical arguments suggest that drift shell splitting changes the phase space location of the source to smaller L shells, which typically reduces outer zone phase space density enhancements, and this reduction has a limit corresponding to two-dimensional local diffusion on a curved surface in the phase space.
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    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.
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    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, Xu
    Recent 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.