Anthony A. Chan

Space Weather Modeling Framework: A new tool for the space science community

[1] The Space Weather Modeling Framework (SWMF) provides a high-performance flexible framework for physics-based space weather simulations, as well as for various space physics applications. The SWMF integrates numerical models of the Solar Corona, Eruptive Event Generator, Inner Heliosphere, Solar Energetic Particles, Global Magnetosphere, Inner Magnetosphere, Radiation Belt, Ionosphere Electrodynamics, and Upper Atmosphere into a high-performance coupled model. The components can be represented with alternative physics models, and any physically meaningful subset of the components can be used. The components are coupled to the control module via standardized interfaces, and an efficient parallel coupling toolkit is used for the pairwise coupling of the components. The execution and parallel layout of the components is controlled by the SWMF. Both sequential and concurrent execution models are supported. The SWMF enables simulations that were not possible with the individual physics models. Using reasonably high spatial and temporal resolutions in all of the coupled components, the SWMF runs significantly faster than real time on massively parallel supercomputers. This paper presents the design and implementation of the SWMF and some demonstrative tests. Future papers will describe validation (comparison of model results with measurements) and applications to challenging space weather events. The SWMF is publicly available to the scientific community for doing geophysical research. We also intend to expand the SWMF in collaboration with other model developers.

Acceleration of relativistic electrons via drift‐resonant interaction with toroidal‐mode Pc‐5 ULF oscillations

There has been increasing evidence that Pc-5 ULF oscillations play a fundamental role in the dynamics of outer zone electrons. In this work we examine the adiabatic response of electrons to toroidal-mode Pc-5 field line resonances using a simplified magnetic field model. We find that electrons can be adiabatically accelerated through a drift-resonant interaction with the waves, and present expressions describing the resonance condition and half-width for resonant interaction. The presence of magnetospheric convection electric fields is seen to increase the rate of resonant energization, and allow bulk acceleration of radiation belt electrons. Conditions leading to the greatest rate of acceleration in the proposed mechanism, a nonaxisymmetric magnetic field, superimposed toroidal oscillations, and strong convection electric fields, are likely to prevail during storms associated with high solar wind speeds.

Fully adiabatic changes in storm time relativistic electron fluxes

It has been suggested that much of the drop and subsequent recovery of storm time relativistic electron fluxes at geosynchronous orbit can be explained in terms of a fully adiabatic response (all three adiabatic invariants conserved) to magnetic field changes. To calculate this effect, we assume a prestorm electron flux distribution constructed from CRRES satellite data, we use modular magnetospheric magnetic field models to represent the magnetic field configuration before and during the storm, and we use Liouvilles theorem to evolve the prestorm electron flux. In this work we focus on the important special case of equatorially mirroring electrons. During the main phase of a storm with a Dst minimum of -100 nT we find that the fully adiabatic effect can cause a flux decrease of up to 2 orders of magnitude, consistent with observed flux decreases. We also find that the magnitude of the fully adiabatic flux decrease is larger for lower energies, again in agreement with observations. The contribution of prestorm electron fluxes to the recovery phase flux increase at synchronous orbit is expected to be small because of losses to the dawnside magnetopause. A comparison of fully adiabatic fluxes with measured electron fluxes for the November 2-5, 1993, storm indicates that for this event the fully adiabatic effect may be contributing to the observed decrease but that nonadiabatic effects are clearly important. Overall we conclude that the fully adiabatic effect can account for a significant fraction of observed flux decreases and that differences between the observed and the fully adiabatic fluxes help to clarify when and where additional loss and source mechanisms exist.

Stochastic modeling of multidimensional diffusion in the radiation belts

Abstract : A new code for solving radiation belt diffusion equations has been developed and applied to the 2-D bounce-averaged energy pitch angle quasi-linear diffusion equation. The code uses Monte Carlo methods to solve Ito stochastic differential equations (SDEs) which are mathematically equivalent to radiation belt diffusion equations. We show that our SDE code solves the diffusion equation with off-diagonal diffusion coefficients in contrast to standard finite difference codes which are generally unstable when off-diagonal diffusion coefficients are included. Our results are in excellent agreement with previous results. We have also investigated effects of assuming purely parallel propagating electromagnetic waves when calculating the diffusion coefficients and find that this assumption leads to errors of more than an order of magnitude in flux at some equatorial pitch angles for the specific chorus wave model we use. Further work is needed to investigate the sensitivity of our results to the wave model parameters. Generalization of the method to 3-D is straight-forward, thus making this model a very promising new way to investigate the relative roles of pitch angle, energy, and radial diffusion in radiation belt dynamics.

Anisotropic Alfvén‐ballooning modes in Earth's magnetosphere

We have carried out a theoretical analysis of the stability and parallel structure of coupled shear Alfven and slow magnetosonic waves in Earths inner magnetosphere (i.e., at equatorial distances between about five and ten Earth radii) including effects of finite anisotropic plasma pressure. Multiscale perturbation analysis of the anisotropic Grad-Shafranov equation yields an approximate self-consistent magnetohydrodynamic (MHD) equilibrium. This MHD equilibrium is used in the numerical solution of a set of eigenmode equations which describe the field line eigenfrequency, linear stability, and parallel eigenmode structure. We call these modes anisotropic Alfven-ballooning modes. The main results are: (1) The field line eigenfrequency can be significantly lowered by finite pressure effects. (2) The parallel mode structure of the transverse wave components is fairly insensitive to changes in the plasma pressure, but the compressional magnetic component can become highly peaked near the magnetic equator as a result of increased pressure, especially when P⊥ > P∥ (here P⊥ and P∥ are the perpendicular and parallel plasma pressure). (3) For the isotropic (P∥ = P⊥ = P) case ballooning instability can occur when the ratio of the plasma pressure to the magnetic pressure, β = P/(B²/8π), exceeds a critical value β0B ≈ 3.5 at the equator. (4) Compared to the isotropic case the critical beta value is lowered by anisotropy, either due to decreased field line bending stabilization when P∥ > P⊥ or due to increased ballooning-mirror destabilization when P⊥ > P∥ (5) We use a β-δ stability diagram to display the regions of instability with respect to the equatorial values of the parameters β and δ, where β¯=(1/3)(β∥+2β⊥) is an average beta value and δ = 1 − P∥/P⊥ is a measure of the plasma anisotropy. The diagram is divided into regions corresponding to the firehose, mirror and ballooning instabilities. It appears that observed values of the plasma pressure are below the critical value for the isotropic ballooning instability but it may be possible to approach a ballooning-mirror instability when P⊥/P∥ ≳ 2.

Can substorms produce relativistic outer belt electrons

In an effort to explain how magnetic storms can cause strong enhancements in outer belt MeV electrons, we have studied the substorm-associated acceleration of energetic (tens of keV) plasma sheet electrons and their injection into the outer-trapped region of the magnetosphere. The study is based on tracing test particles in three-dimensional MHD simulations of substorm dipolarization. The simulation-based electric and magnetic fields [Birn and Hesse, 1996] exhibit a strong earthward collapse around local midnight, leading to magnetic field dipolarization along with a corresponding induction electric field. The test particle traces show that tens of keV plasma sheet electrons can be transported from about x ≈ −20 RE to x ≈ −10 RE and can gain about a factor of 10 in energy. If these particles are further transported inward to L ∼ 6 while conserving the first adiabatic invariant, they will have energies of an MeV or more. In the substorm acceleration process the dominant energy gain occurs during the earthward radial transport by E × B drift in the strong dipolarization region. In our calculations the electrons that gain the most energy are ones that circle a local maximum in the equatorial magnetic field strength and thus spend a relatively long time in the region of collapsing field. The first adiabatic invariant is broken at the beginning of the particle trajectory, near the neutral line, where the magnetic curvature radius can be comparable to the particle gyroradius. The second adiabatic invariant is also broken later in the process, when particles can be temporarily trapped in off-equatorial magnetic minima associated with MHD waves on the dipolarizing field lines. Estimation of the number of accelerated plasma sheet electrons indicates that the Birn-Hesse substorm, which is not particularly large, produces only ∼ 2% of the number of MeV electrons observed in a typical post storm outer belt electron enhancement. A series of substorms, some of them large, might produce a large enough enhancement, but it should be noted that this is an order of magnitude estimate, and it is rather sensitive to plasma sheet and substorm parameters.

Nonlinear relativistic gyrokinetic Vlasov-Maxwell equations

A set of self-consistent nonlinear gyrokinetic equations is derived for relativistic charged particles in a general nonuniform magnetized plasma. Full electromagnetic-field fluctuations are considered with spatial and temporal scales given by the low-frequency gyrokinetic ordering. Self-consistency is obtained by combining the nonlinear relativistic gyrokinetic Vlasov equation with the low-frequency Maxwell equations in which charge densities and current densities are expressed in terms of moments of the gyrokinetic Vlasov distribution. For these self-consistent gyrokinetic equations, a low-frequency energy conservation law is also derived.

Loss of ring current O(+) ions due to interaction with Pc 5 waves

The behavior of ring current ions in low-frequency geomagnetic pulsations is investigated analytically and numerically. We focus primarily on ring current O+ ions, whose flux increases dramatically during geomagnetic storms and decays at a rate which is not fully explained by collisional processes. This paper presents a new loss mechanism for the O+ ions due to the combined effects of convection and corotation electric fields and interaction with Pc 5 waves (wave period: 150–600 s) via a magnetic drift-bounce resonance. A test particle code has been developed to calculate the motion of the ring current O+ ions in a time-independent dipole magnetic field, and convection and corotation electric fields, plus Pc 5 wave fields, for which a simple analytical model has been formulated based on spacecraft observations. For given fields, whether a particle gains or loses energy depends on its initial kinetic energy, pitch angle at the equatorial plane, and the position of its guiding center with respect to the azimuthal phase of the wave. The ring current O+ ions show a dispersion in energies and L values with decreasing local time across the day side, and a bulk shift to lower energies and higher L values. The former is due to the wave-particle interaction causing the ion to gain or lose energy, while the latter is due to the convection electric field. Our simulations show that, due to interaction with the Pc 5 waves, the particles kinetic energy can drop below that required to overcome the convection potential and the particle will be lost to the dayside magnetopause by a sunward E × B drift. This may contribute to the loss of O+ ions at intermediate energies (tens of keV) observed during the recovery phase of geomagnetic storms.

Relativistic bounce-averaged quasilinear diffusion equation for low-frequency electromagnetic fluctuations

A relativistic bounce-averaged quasilinear diffusion equation is derived to describe stochastic particle transport associated with low-frequency electromagnetic fluctuations in a nonuniform magnetized plasma. Expressions for the relativistic quasilinear diffusion coefficients are calculated explicitly for magnetically-trapped particle distributions in axisymmetric magnetic geometry in terms of drift-bounce resonant contributions associated with low-frequency fluctuations which conserve the first adiabatic invariant.

Energetic electrons at geostationary orbit during the November 3–4, 1993 storm: Spatial/temporal morphology, characterization by a power law spectrum and, representation by an artificial neural network

Electrons of energy several MeV or greater have been implicated in the failure and malfunction of geostationary spacecraft. It is therefore important to be able to specify and even forecast the fluxes of these particles during and following geomagnetic storms. A first step is the understanding of their relationship to lower-energy electrons that can already be well modeled. It is therefore the goal of this paper to examine the relative time, spatial, and spectral relationships between 1.5 MeV electrons and intermediate energy electrons down to about 100 keV. For the November 1993 geomagnetic storm we find that electrons from about 100 keV to 1.5 MeV at GEO can be conveniently characterized by a power law spectrum and that the slope and intercept of this spectrum vary in systematic ways during the storm. This suggests the possibility of developing prediction filters or artificial neural networks, driven by a storm activity indicator (such as Dst), local time and a lower-energy electron flux, to specify the energetic electron spectral characteristics. We further find that local time diurnal effects are an important contributor to the apparent time delay of the recovery of energetic electrons and when these effects are considered the recovery phase enhancement is nearly uniform across the spectrum. This paper will report the spatial and temporal morphology of these intermediate to energetic electrons, their characterization by a power law and the variations of the power law slope and intercept throughout the November 1993 storm. These temporal, spatial, and spectral properties suggest that the recovery phase enhancement is due to the entry of the intermediate energy electrons from the geomagnetic tail as part of the storm injection process. We also discuss our success at building an Artificial Neural Network system to specify the storm time energetic electron flux spectra.