Modeling radiation belt radial diffusion in ULF wave fields: 2. Estimating rates of radial diffusion using combined MHD and particle codes

[1] Quantifying radial transport of radiation belt electrons in ULF wave fields is essential for understanding the variability of the trapped relativistic electrons. To estimate the radial diffusion coefficients (DLL), we follow MeV electrons in realistic magnetospheric configurations and wave fields calculated from a global MHD code. We create idealized pressure-driven MHD simulations for controlled solar wind velocities (hereafter referred to as pressure-driven Vx simulations) with ULF waves that are comparable to GOES data under similar conditions, by driving the MHD code with synthetic pressure profiles that mimic the pressure variations of a particular solar wind velocity. The ULF wave amplitude, in both magnetic and electric fields, increases at larger radial distance and during intervals with higher solar wind velocity and pressure fluctuations. To calculate DLL as a function of solar wind velocity (Vx = 400 and 600 km/s), we follow 90 degree pitch angle electrons in magnetic and electric fields of the pressure-driven Vx simulations. DLL is higher at larger radial distance and for the case with higher solar wind velocity and pressure variations. Our simulated DLL values are relatively small compared to previous studies which used larger wave fields in their estimations. For comparison, we scale our DLL values to match the wave amplitudes of the previous studies with those of the idealized MHD simulations. After the scaling, our DLL values for Vx = 600 km/s are comparable to theDLL values derived from Polar measurements during nonstorm intervals. This demonstrates the use of MHD models to quantify the effect of pressure-driven ULF waves on radiation belt electrons and thus to differentiate the radial diffusive process from other mechanisms

EMIC Waves in the Earth\u27s Inner Magnetosphere as a Function of Solar Wind Structures During Solar Maximum

Here we analyze the statistics of electromagnetic ion cyclotron (EMIC) waves observed in the Earth\u27s inner magnetosphere during coronal mass ejection (CME), high-speed stream (HSS), and quiet solar wind (QSW) conditions in the upstream solar wind (SW). For our analysis we use the EMIC wave observations by the two Van Allen Probes during their first magnetic local time (MLT) revolution. The major results of our analysis are as follows: (1) Criteria to identify the HSS, CME, and QSW conditions in the SW are formulated. (2) 54%, 36%, and 10% of EMIC wave events are observed during CME, HSS, and QSW, respectively. (3) 12% of events are closely associated with the fast growth of magnetospheric compression, among which 76%, 24%, and 0% are observed during CME, HSS, and QSW, respectively. (4) A majority of the QSW, HSS-driven, and CME-driven events is observed in the 9–12, 12–24, and 8–24 hr MLT sectors, respectively. (5) CME-driven events are distributed along all L shells, whereas the majority of the HSS-driven and QSW events are confined to L \u3e 3.5. (6) The fractions of events during CME and HSS have a maximum in the near-equatorial region, whereas the fractions of the QSW events have a minimum there. (7) Independent of the SW driver, no strong events are observed below the local O+ gyrofrequency, whereas 65–70% and 30–35% of events are observed between the O+ and He+ gyrofrequencies and above the He+ gyrofrequency, respectively

Electric and magnetic radial diffusion coefficients using the Van Allen probes data

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

ULF wave derived radiation belt radial diffusion coefficients

Waves 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

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

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

EMIC Waves in the Earth's Inner Magnetosphere as a Function of Solar Wind Structures During Solar Maximum

Here we analyze the statistics of electromagnetic ion cyclotron (EMIC) waves observed in the Earth\u27s inner magnetosphere during coronal mass ejection (CME), high-speed stream (HSS), and quiet solar wind (QSW) conditions in the upstream solar wind (SW). For our analysis we use the EMIC wave observations by the two Van Allen Probes during their first magnetic local time (MLT) revolution. The major results of our analysis are as follows: (1) Criteria to identify the HSS, CME, and QSW conditions in the SW are formulated. (2) 54%, 36%, and 10% of EMIC wave events are observed during CME, HSS, and QSW, respectively. (3) 12% of events are closely associated with the fast growth of magnetospheric compression, among which 76%, 24%, and 0% are observed during CME, HSS, and QSW, respectively. (4) A majority of the QSW, HSS-driven, and CME-driven events is observed in the 9–12, 12–24, and 8–24 hr MLT sectors, respectively. (5) CME-driven events are distributed along all L shells, whereas the majority of the HSS-driven and QSW events are confined to L \u3e 3.5. (6) The fractions of events during CME and HSS have a maximum in the near-equatorial region, whereas the fractions of the QSW events have a minimum there. (7) Independent of the SW driver, no strong events are observed below the local O+ gyrofrequency, whereas 65–70% and 30–35% of events are observed between the O+ and He+ gyrofrequencies and above the He+ gyrofrequency, respectively

Review of modeling of losses and sources of relativistic electrons in the outer radiation belt I: Radial transport

In this paper, we focus on the modeling of radial transport in the Earth's outer radiation belt. A historical overview of the first observations of the radiation belts is presented, followed by a brief description of radial diffusion. We describe how resonant interactions with poloidal and toroidal components of the ULF waves can change the electron's energy and provide radial displacements. We also present radial diffusion and guiding center simulations that show the importance of radial transport in redistributing relativistic electron fluxes and also in accelerating and decelerating radiation belt electrons. We conclude by presenting guiding center simulations of the coupled particle tracing and magnetohydrodynamic (MHD) codes and by discussing the origin of relativistic electrons at geosynchronous orbit. Local acceleration and losses and 3D simulations of the dynamics of the radiation belt fluxes are discussed in the companion paper

Review of modeling of losses and sources of relativistic electrons in the outer radiation belt II: Local acceleration and loss

This paper focuses on the modeling of local acceleration and loss processes in the outer radiation belt. We begin by reviewing the statistical properties of waves that violate the first and second adiabatic invariants, leading to the loss and acceleration of high energy electrons in the outer radiation belt. After a brief description of the most commonly accepted methodology for computing quasi-linear diffusion coefficients, we present pitch-angle scattering simulations by (i) plasmaspheric hiss, (ii) a combination of plasmaspheric hiss and electromagnetic ion cyclotron (EMIC) waves, (iii) chorus waves, and (iv) a combination of chorus and EMIC waves. Simulations of the local acceleration and loss processes show that statistically, the net effect of chorus waves is acceleration at MeV energies and loss at hundreds of keV energies. The combination of three-dimensional (3D) simulations of the local processes and radial transport show that the complexity of the behavior of the radiation belts is due to a number of competing processes of acceleration and loss, and depends on the dynamics of the plasmasphere, ring current, and solar wind conditions

Ground-based magnetometer determination of in situ Pc4–5 ULF electric field wave spectra as a function of solar wind speed

We 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 L2.5–8), 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 L2.5–8. 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