About

Anthony Chan is a Professor of Physics and Astronomy at Rice University and a member of the Ken Kennedy Institute. His primary research area is theoretical space plasma physics, with a particular focus on the acceleration and transport of radiation belt electrons, which are relativistic electrons trapped in Earth's magnetospheric fields. His work involves the theory and simulation of the dynamics of relativistic charged particles in electromagnetic fields, including their motion in large-scale magnetospheric fields and turbulent wave fields. Professor Chan is actively involved in developing a comprehensive large-scale computational model called K2 to simulate the dynamics of Earth's radiation belts, in collaboration with Dr. Scot Elkington from the University of Colorado. This model development is coordinated with data analysis from the NASA Van Allen Probes twin spacecraft mission, where Professor Chan serves as a Co-Investigator on the RBSP-ECT Instrument Team. He holds a PhD from Princeton University, earned in 1991, and also obtained his BS and MS degrees from the University of Auckland, New Zealand, in 1981 and 1983 respectively.

Research topics

• Physics
• Computer Science
• Geophysics
• Computational physics
• Classical mechanics
• Nuclear physics
• Applied mathematics
• Mathematical optimization
• Mathematics
• Mechanics
• Quantum mechanics
• Mathematical analysis

Selected publications

• Sayram: A Positivity‐Preserving Open Source 3D Radiation Belt Modeling Code

  Journal of Geophysical Research Space Physics · 2025-06-28 · 4 citations

  articleOpen accessSenior author

  Abstract Radiation belt dynamics is typically modeled using a quasilinear diffusion equation. However, standard numerical methods often produce non‐physical negative or oscillatory solutions due to cross‐diffusion terms. Here, we present Sayram, an open‐source 3D radiation belt modeling code that employs a positivity‐preserving finite volume method to address this decades‐old numerical challenge. Sayram incorporates key physical processes of the radiation belts, including local wave–particle interactions, radial diffusion, and losses due to precipitation and magnetopause shadowing. We validate Sayram using 1D radial diffusion, 2D pitch‐angle and momentum diffusion, and a 3D model diffusion problem. Additionally, we apply it to a GEM challenge storm‐time radiation belt event, demonstrating consistency with previous results. Compared to other 3D radiation belt codes, Sayram employs an implicit time integration scheme, preserves positivity, and ensures conservation properties. The code is developed in C++ with a highly modular design, allowing for easy adaptation to similar tasks. By making Sayram open source, we aim to provide the radiation belt community with a robust tool to improve radiation belt modeling and forecasting.

  PublisherOA PDFDOI

• Sayram: A Positivity-Preserving Open Source 3D Radiation Belt Modeling Code

  2025-03-14

  preprintOpen accessSenior author

  Standard numerical solutions of multi-dimensional diffusion equations often yield negative, unphysical phase space densities. To address this, we present Sayram, an open-source 3D code for modeling electron flux evolution in Earth’s radiation belts. Using a recently proposed positivity-preserving finite volume method, Sayram ensures physically realistic solutions across a variety of 1D, 2D, and 3D test cases. Its implicit formulation removes constraints from the CFL condition, enabling efficient time stepping. Importantly, the computational overhead associated with ensuring positivity preservation is negligibly small, making Sayram as efficient as other non-positivity-preserving codes based on standard finite difference methods under the same simulation parameters. While developed for radiation belt studies and forecasting, Sayram can also be applied to study general multi-dimensional diffusion processes in other areas, such as wave-particle interactions in planetary magnetospheres and the solar wind. By combining positivity preservation, efficiency, and openness, Sayram provides a robust tool for research across multiple disciplines.

  PublisherDOI

• Estimating quasi-linear diffusion coefficients for varying values of density ratio

  Frontiers in Astronomy and Space Sciences · 2024-12-09 · 1 citations

  articleOpen accessSenior author

  This paper considers a method for estimating bounce-averaged quasi-linear diffusion coefficients due to whistler-mode waves for a specified ratio of plasma frequency to gyrofrequency, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m1"><mml:mrow><mml:msub><mml:mrow><mml:mi>ω</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant="normal">Ω</mml:mi></mml:mrow><mml:mrow><mml:mi>e</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> , using values precomputed for a different value of that ratio. This approach was recently introduced to facilitate calculations associated with the “POES technique,” generalized to infer both wave intensity and cold plasma density from measurements of particle fluxes near the loss cone. The original derivation was justified on the basis of parallel-propagating waves but applied to calculations with much more general models of the waves. Here, we justify the estimates, which are based on equating resonant frequencies for differing values of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m2"><mml:mrow><mml:msub><mml:mrow><mml:mi>ω</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant="normal">Ω</mml:mi></mml:mrow><mml:mrow><mml:mi>e</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> and energy, for wide ranges of wave normal angle, resonance number, energy, and equatorial pitch angle. Refinements of the original estimates are obtained and tested numerically against full calculations of the diffusion coefficients for representative wave models. The estimated diffusion coefficients can be calculated rapidly and generally give useful estimates for energies in the 30-keV–300-keV range, especially when both relevant values of the ratio <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m3"><mml:mrow><mml:msub><mml:mrow><mml:mi>ω</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant="normal">Ω</mml:mi></mml:mrow><mml:mrow><mml:mi>e</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> are large.

  PublisherOA PDFDOI

• Modeling Radiation Belt Dynamics Using a Positivity‐Preserving Finite Volume Method on General Meshes

  Journal of Geophysical Research Space Physics · 2024-09-01 · 5 citations

  articleSenior author

  Abstract Standard finite volume or finite difference methods may produce unphysical negative solutions of phase space density when applied to radiation belt diffusion equation with cross diffusion terms. In this work, we apply a recently proposed positivity‐preserving finite volume (PPFV) method to a 2D diffusion problem of radiation belt electrons with both structured and unstructured meshes. Our test using a model problem shows that the new method does not produce unphysical negative solutions with both types of meshes even with strong cross‐diffusion terms. By applying the method to the 2D pitch angle and energy diffusion problem, we demonstrate that the method achieves positivity of solutions without requiring excessive number of grid points and shows good agreement with previous results obtained using a layer method. The ability of preserving positivity of the solution with unstructured meshes allows the method to handle complex boundary configurations. Our results suggest that the new PPFV method could be useful in modeling radiation belt diffusion processes or in building a physics‐based forecast model.

  PublisherDOI

• Numerical Calculations of Adiabatic Invariants from MHD-Driven Magnetic Fields

  2024-05-02

  preprintOpen accessSenior author

  The adiabatic invariants (M, J, Φ) and the related invariants (M, K, L∗) have been established as effective coordinate systems for describing radiation belt dynamics at a theoretical level, and through numerical techniques, can be paired with in-situ observations to order phase-space density. To date, methods for numerical techniques to calculate adiabatic invariants have focused on empirical models such the Tsyganenko models TS05, T96, and T89. In this work, we develop methods based on numerical integration and variable step size iteration for the calculation of adiabatic invariants, applying the method to the Lyon-Fedder-Mobarry (LFM) global magnetohydrodynamics (MHD) simulation code, with optional coupling to the Rice Convection Model (RCM). By opening the door to adiabatic invariant modeling with MHD magnetic fields, the opportunity for exploratory modeling work of radiation belt dynamics is enabled. Calculations performed using LFM are cross-referenced with the same code applied to the T96 and TS05 Tsyganenko models evaluated on the LFM grid. Important aspects of the adiabatic invariant calculation are reviewed and discussed, including (a) sensitivity to magnetic field model used, (b) differences in the problem between quiet and disturbed geomagnetic states, and (c) the selection of key parameters, such as the magnetic local time step size for drift shell determination. The rigorous development and documentation of this algorithm additionally acts as preliminary step for future thorough reassessment of in-situ phase-space density results using alternative magnetic field models.

  PublisherOA PDFDOI

• Numerical Calculations of Adiabatic Invariants From MHD‐Driven Magnetic Fields

  Journal of Geophysical Research Space Physics · 2024-06-01 · 2 citations

  articleOpen accessSenior author

  Abstract The adiabatic invariants ( M , J , Φ) and the related invariants ( M , K , L *) have been established as effective coordinate systems for describing radiation belt dynamics at a theoretical level, and through numerical techniques, can be paired with in situ observations to order phase‐space density. To date, methods for numerical techniques to calculate adiabatic invariants have focused on empirical models such the Tsyganenko models TS05, T96, and T89. In this work, we develop methods based on numerical integration and variable step size iteration for the calculation of adiabatic invariants, applying the method to the Lyon‐Fedder‐Mobarry (LFM) global magnetohydrodynamics (MHD) simulation code, with optional coupling to the Rice Convection Model (RCM). By opening the door to adiabatic invariant modeling with MHD magnetic fields, the opportunity for exploratory modeling work of radiation belt dynamics is enabled. Calculations performed using LFM are cross‐referenced with the same code applied to the T96 and TS05 Tsyganenko models evaluated on the LFM grid. Important aspects of the adiabatic invariant calculation are reviewed and discussed, including (a) sensitivity to magnetic field model used, (b) differences in the problem between quiet and disturbed geomagnetic states, and (c) the selection of key parameters, such as the magnetic local time step size for drift shell determination. The rigorous development and documentation of this algorithm additionally acts as preliminary step for future thorough reassessment of in situ phase‐space density results using alternative magnetic field models.

  PublisherDOI

• Simulation of radiation belt wave-particle interactions in an MHD-particle framework

  Frontiers in Astronomy and Space Sciences · 2023 · 20 citations

  1st authorCorresponding
  • Physics
  • Computational physics
  • Geophysics

  In 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.

  PublisherOA PDFDOI

• Hamiltonian Formulations of Quasilinear Theory for Magnetized Plasmas

  arXiv (Cornell University) · 2022-08-19

  preprintOpen accessSenior author

  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 (1966) 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_Chan (2001,2004). The resulting quasilinear theory for nonuniform magnetized plasmas yields a $3\times 3$ 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).

  PublisherOA PDFDOI

• Using MEPED observations to infer plasma density and chorus intensity in the radiation belts

  Frontiers in Astronomy and Space Sciences · 2022-11-21 · 8 citations

  articleOpen access

  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.

  PublisherDOI

• Hamiltonian formulations of quasilinear theory for magnetized plasmas

  Frontiers in Astronomy and Space Sciences · 2022-10-06 · 12 citations

  articleOpen accessSenior author

  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).

  PublisherOA PDFDOI

Recent grants

• Collaborative Research: Diffusive Transport of Relativistic Electrons in Earth's Magnetosphere

  NSF · $220k · 2003–2007

Frequent coauthors

• S. R. Elkington

  Laboratory for Atmospheric and Space Physics

  69 shared

• J. M. Albert

  United States Air Force Research Laboratory

  23 shared

• Liheng Zheng

  16 shared

• M. Wiltberger

  15 shared

• Alain J. Brizard

  14 shared

• Liu Chen

  13 shared

• Xin Tao

  University of Science and Technology of China

  13 shared

• A. N. Jaynes

  University of Iowa

  12 shared

Education

• Ph.D., Astrophysical Sciences

  Princeton University

  1989