The EMFISIS wave and magnetic field observations will address several key science objectives for the RBSP mission. Specifically, EMFISIS addresses the three overarching Level 1 Science questions:
1.1 Which physical processes produce radiation belt enhancement events?
An essential unanswered question of inner magnetospheric dynamics is how electrons are accelerated to relativistic (MeV) energies following some magnetic storms. Comprehensive studies at geosynchronous orbit have indicated that acceleration in that region is correlated with enhanced ULF waves [Mathie and Mann, 2000; O’Brien et al., 2001; Green and Kivelson, 2001]. However, the heart of the radiation belts lies well inside geosynchronous orbit, in the region near 3-5 RE. Theoretical calculations suggest that ULF acceleration mechanisms should be substantially reduced in efficiency at lower L, compared to geosynchronous orbit [Falthammar, 1969; Elkington, 2003]. On the other hand, local acceleration involving VLF waves, particularly lower-band chorus, becomes most efficient in the region just outside the plasmapause, which corresponds to the radial range 3-5 RE for storm conditions [Summers et al. 1998; Meredith, 2003a].
Radial Transport and Acceleration by ULF waves. The global distribution and variability of low frequency Pc4 and Pc5 waves can be monitored by ground-based magnetometers and by satellites [Liu et al., 2009], and the observed wave spectral characteristics have been used to evaluate radial diffusion coefficients [Brautigan et al., 2005; Perry et al., 2005; Ukhorskiy et al., 2005; Huang et al., 2010] and employed in dynamic modeling of the outer radiation belt [Loto’aniu et al., 2006a; Ukhorskiy et al., 2009; Chu et al., 2010]. The properties of magnetospheric ULF waves, excited in response to solar wind variability, have also been obtained from global MHD simulations and used to study the dynamic variability of radiation belt electrons [Fei et al., 2006; Kress et al., 2007]. Although radial diffusion transport is able to simulate several important features of radiation belt dynamics, it fails to describe the rapid flux variation and the prolonged duration of electron acceleration observed during individual storms [Miyoshi et al., 2006; Subbotin and Shprits , 2009]. The ability of ULF waves to cause effective radial diffusion depends on the amplitude and the poloidal or toroidal properties of the waves and their modal structure [Perry et al., 2005]. The azimuthal mode structure of ULF waves in space will be determined by multi-point EMFISIS measurements of magnetic fields on the two RBSP spacecraft.
Local Acceleration by Whistler-Mode Waves. Persistent peaks in energetic electron phase space density have been identified in the heart of the outer radiation zone (L~5) [Green and Kivelson, 2004; Chen et al., 2006b, 2007], which support earlier theoretical studies of the importance of local stochastic acceleration [Summers et al., 1998; Horne and Thorne, 1998]. Potential mechanisms responsible for the local acceleration to relativistic energies during the recovery phase of a storm include cyclotron resonant interactions with VLF chorus in the low-density region just outside the plasmapause [Horne et al., 2005] and Landau resonance with equatorial magnetosonic waves [Horne et al., 2007]. The rate of acceleration is strongly dependent on plasma density, specifically, on the ratio between the electron gyro-frequency and the plasma frequency.
The EMFISIS wave instruments provide measurements of the power spectral density of VLF waves every 6s, and a full 3D spectral matrix with the same cadence along with a selection of burst modes which include full waveforms from all three axes of the electric and magnetic field sensors. This information, together with our measurements of plasma density, are critical for understanding the effectiveness of local acceleration. Our observations, in conjunction with RBSP electron observations and detailed theoretical modeling, will allow us to determine whether the electron distribution evolves in a manner consistent with local acceleration or by inward radial diffusion.
Prompt Acceleration by Drift Resonance. New radiation belts have been observed to be created on time-scales of minutes, as interplanetary shocks compress the magnetosphere and resonantly accelerate energetic seed populations in the inner magnetosphere [Vampola and Korth, 1992; Blake, 1992; Wygant, 1994]. The new belts can persist from months to years after their formation. The mechanism involved is compression of the magnetosphere by an interplanetary shock, which drives a compressional wave deep into the inner magnetosphere. The azimuthal electric fields associated with this shock can be tens to hundreds of mV/m, on timescales of seconds to minutes. As these compressional waves propagate through the inner magnetosphere, they resonantly accelerate high-energy electrons and protons whose drift periods are commensurate with the wave period [Hudson, 1997; Li, et al., 1993].
The magnetic field variations in the compressional wave are the direct drivers that energize the seed populations to form the new radiation belt. These quantities must be measured on timescales appropriate to the wave propagation, which requires at least one-second resolution in order to resolve the fast rise time of the initial compressional pulse. At present we have only a basic understanding of this type of event, but with the RBSP mission having two well-instrumented spacecraft at different local times and/or radial distances, we will be able to measure the magnetic and electric field variations at two spatial locations for the first time, and better understand the propagation of the compressional wave.
1.2 What are the dominant mechanisms for relativistic electron loss?
Nearly every magnetic storm begins with a dramatic decrease in relativistic electron fluxes over much of the inner magnetosphere. Some of this drop is the result of reversible adiabatic effects [Kim and Chan, 1997], while the remainder represents real loss through wave scattering into the atmosphere, magnetopause shadowing, and demagnetization on highly stretched field lines.
Pitch-angle Scattering and Loss to the Atmosphere. Energetic radiation belt electrons can be scattered into the loss cone and lost by collisions in the atmosphere during resonant interactions with whistler-mode chorus emissions [Thorne et al., 2005], plasmaspheric hiss [Lyons et al., 1972; Abel and Thorne, 1998] and electromagnetic ion cyclotron waves [Albert, 2003; Summers and Thorne, 2003; Jordanova et al., 2008]. Although significant advances have been made recently in the theory and modeling of wave-particle scattering [Millan and Thorne, 2010], the theoretical calculations need to be thoroughly tested against in situ observations. Our proposed measurements of local electric and magnetic fields and wave power spectral intensity and angular distribution will enable unprecedented progress in our physical understanding of relativistic electron losses from the inner magnetosphere.
Magnetopause Shadowing and Current Sheet Scattering. Electrons can be lost from the radiation belts as they drift through the magnetopause or as they get scattered into the loss cone by current sheet scattering. Both these processes are important at larger L-shells during disturbed geomagnetic conditions, when the magnetosphere is compressed on the dayside and stretched on the nightside. During the main phase of the storm a strong ring current will distort the magnetic field and allow current sheet scattering to move to lower L-shells. Similarly, the outward motion of the radiation belt particles due to the adiabatic effect causes electrons to move to larger L, thus increasing the losses through the magnetopause [Shprits et al., 2006; Jordanova et al., 2008]. Accurate measurements of magnetic field distortions during geomagnetic storms are required to compute the effectiveness of such loss.
1.3 How do ring current and other geomagnetic processes affect radiation belt behavior?
There are several aspects in which the temporal and spatial evolution of the ring current influences radiation belt dynamics that will be investigated using EMFISIS data. The development of a strong ring current during the main phase of a geomagnetic storm inflates the magnetic field at near-Earth distances. This changes the adiabatic drifts of the charged particles as well as the losses through the magnetopause. Large magnetic field depressions have been measured at distances as small as 3–4 Earth radii (RE) during major geomagnetic storms (Dst < − 250 nT) and have been associated with the storm time ring current enhancement [e.g., Cahill, 1966; Tsyganenko et al., 2003]. Sophisticated physics-based models [e.g., Chen et al., 2006a; Jordanova et al., 2006, 2010b; Zaharia et al., 2006, 2010] have been developed to investigate the effect of plasma pressure on the magnetic field in the inner magnetosphere during magnetic storms. The computed magnetic field and electric currents showed that plasma pressure strongly affects the B-field, even very close to Earth, and large field depressions develop near Earth at the storm peak. Magnetic field data from EMFISIS will be used to verify these computations and validate the models.
Ring current dynamics are also closely related to the development of intense sub-auroral electric fields involved in the magnetosphere-ionosphere (MI) coupling phenomenon known as sub-auroral polarization streams (SAPS). The asymmetric ring current closes via field-aligned currents through the ionosphere and may be responsible for the penetrating electric fields at mid-latitudes. While the general characteristics of SAPS are well-documented and understood from ionospheric and low-altitude observations [e.g., Foster and Vo, 2002; Mishin et al., 2003], the magnetospheric signature has not been as extensively investigated.
During geomagnetic storms ring current distributions are anisotropic and become unstable to excitation of plasma waves which cause the further acceleration or loss of radiation belt particles (see discussion of RBSP objectives in sections 2.1 and 2.2). The ion distributions can generate electromagnetic ion cyclotron (EMIC) waves [e.g., Cornwall et al., 1970; Jordanova et al., 1997, 2001] and magnetosonic waves [e.g., Horne et al., 2000, Chen et al., 2010b], while the electron distributions can excite whistler-mode waves [e.g., Kennel and Thorne, 1967; Horne et al., 2003]. The wave distributions during various storms will depend on storm strength and ion composition; for example, Thorne and Horne  have shown that increased O+ content favors the generation of waves below the O+ gyrofrequency and damps waves above it. Using theoretical modeling (described in section 2.4) together with EMFISIS wave and field observations and RBSP particle measurements, we will identify the evolution of the storm-time ring current and quantify its effects on the radiation belt particles.
EMFISIS will provide measurements of the large-scale magnetic field to place in context the EFW measurements of the convection electric field, an essential quantity for studying ring current evolution during a magnetic storm. Enhanced convection transports moderately energetic particles (ions and electrons) into the inner magnetosphere and accelerates them to form a strong storm-time ring current [e.g., Lyons and Williams, 1980; Wolf et al., 1997], while time-dependent variations in the large-scale electric field traps particles on closed drift trajectories [e.g., Ejiri, 1978]. Kinetic model simulations [Jordanova et al., 2001, 2003; Liemohn et al., 2001; Zaharia et al., 2010] of ring current development during storms have shown reasonable agreement with the Dst index, indicating the dominant role of magnetospheric convection in ring current energization and trapping. Detailed comparison of modeled ring current distributions, however, showed significant differences at low L, depending on the electric field model being used [Jordanova et al., 2003; Yu et al., 2012] and highlight the importance of measuring the large-scale electric field.
Other mechanisms that contribute to ring current flux intensification during the main phase of the storm are radial diffusion [e.g., Chen et al., 1994, Jordanova and Miyoshi, 2005] and substorm-induced electric fields [e.g., Wolf et al., 1997; Fok et al., 1999]. Radial diffusion affects mostly the local time variations of higher energy (>100 keV) particles, which have drift periods shorter than those of the typical storm main phase and thus drift several times around the Earth during the period of enhanced electric field. Ganushkina et al.  found that plasma sheet ions rapidly penetrate deep into the inner magnetosphere, well inside L=4, due to short-lived intense electric fields that are formed in connection with substorm onset. Detailed measurements and simulations are needed to clarify the extent to which these two processes contribute to ring current buildup. EMFISIS measurements of VLF wave properties combined with EFW electric field measurements will clarify the effect of wave-particle interactions and time-varying electric fields on ring current dynamics during geomagnetic storms.
1.4 Theory and Modeling
Radiation belt particles are influenced by the global distribution of magnetospheric plasma waves, as well as the global magnetospheric electric and magnetic fields, but the properties of such waves and fields will only be monitored along the orbit of the two RBSP satellites. Theory and modeling must be employed to place the spatially-limited observations in a global context. Below, we describe how the EMFISIS theory and modeling team will utilize the available observations to address the primary RSBP science objectives.
Quantifying the Effects of Diffusion on the Radiation Belt Population. Measurements made by the proposed wave instruments can only be used to evaluate local rates of radial, pitch-angle and energy diffusion. However, over the two-year duration of the mission, statistical models for the global distribution of all relevant waves will be constructed, as a function of MLT, L-shell, latitude, and geomagnetic activity. This unique RBSP data source will allow us to develop statistical models for the global distribution of particle scattering, which can be used in a Fokker Planck equation to solve for the temporal variability of phase space density.
Ring Current and Radiation Belt Modeling. A newly-developed coupled ring current-radiation belt model [Jordanova and Miyoshi, 2005; Jordanova et al., 2006, 2010a,b; Zaharia et al., 2006, 2010] will be used as a powerful tool to understand the dynamics of energetic electrons and ions in the inner magnetosphere. This model represents an extension of our ring current-atmosphere interactions model (RAM) to relativistic energies and electrons. RAM solves numerically the bounce-averaged kinetic equation for H+, O+, and He+ ions and electrons in the Solar Magnetic (SM) equatorial plane and is two-way coupled with a 3-D equilibrium code (SCB) that calculates the magnetic field in force balance with the anisotropic ring current distributions. The electric field model represents the gradient of an ionospheric convection potential (mapped to the SM equatorial plane along SCB field lines) and a corotation potential. The RAM-SCB model can be driven either by empirical electric fields [e.g., Weimer, 2001] and boundary conditions or by those provided from a global magnetohydrodynamics (MHD) model, e.g. BATSRUS [Powell et al., 1999] self-consistently coupled with an electric field model (RIM) [Ridley and Liemohn, 2002] and driven by dynamic solar wind input. Figure 3shows RAM-SCB simulations during the 22 April 2001 storm indicating significant depressions in the magnetic field intensity on the nightside during the storm main phase when the ring current pressure intensifies. The location of the pressure peak, as well as the peak magnitude depends strongly on the strength of the convection and the magnetic field morphology. The EMFISIS measurements of the large-scale electric and magnetic fields will be used to test and improve the physics-based models.
The RAM-SCB model is coupled with a time-dependent 2-D plasmasphere model [Rasmussen et al., 1993]. Initially, electron losses due to scattering by plasma waves inside and outside the plasmasphere were included using a simplified loss term (F/twp) with an appropriate timescale twp. Pitch angle scattering by EMIC waves was incorporated, within regions of EMIC instability predicted by the anisotropic ring current ion populations, using quasi-linear diffusion coefficients [Jordanova et al., 2008]. The diffusion properties of the model will be updated as RBSP data become available. We will perform simulations of geomagnetic storms and compute the electron scattering within the spatial regions of EMIC, magnetosonic, and whistler mode waves using quasi-linear theory. This global modeling will allow us to differentiate among the changes of the phase space density from transport and those from local acceleration and loss of energetic particles (RBSP science objectives 1 and 2 discussed in sections 2.1 and 2.2).
Figure 3. (top) Dst index during the April 2001storm; (middle) ring current pressure calculations in the SM equatorial plane with RAM-SCB; (bottom) difference between the self-consistently calculated magnetic field intensity and the Earth dipolar field (after Zaharia et al., 2006).
To assess the changes of the radiation belts due to scattering by various plasma waves, knowledge of the global wave distributions is needed. One of our approaches will be to simulate the wave excitation by the anisotropic ring current distributions using our RAM-SCB model [Jordanova et al., 2012] and to compare the wave growth predicted by our model with EMFISIS observations to estimate the wave amplitudes. Another approach will be to use the statistical models for the global distribution of all relevant waves constructed from RBSP data as a function of geomagnetic activity. A valuable test to our model will be provided by comparisons of ion and electron fluxes predicted by RAM-SCB with the pitch-angle distributions measured by the RBSP particle instruments.
Physical Understanding of Wave Excitation. To develop a physics-based predictive model of the radiation belts, physical understanding of the most important transport, acceleration, and loss processes is required. Our kinetic ring current model (RAM-SCB) will provide global simulations of the equatorial distribution of all plasma waves important for radiation belt dynamics.
Figure 4. . (a) Proton ring current anisotropy obtained with RAM-SCB at 20 UT 20 November 2002 using W01 electric field and either dipolar (DIP), self-consistent (SCB), or T04 magnetic field, and (b) the corresponding convective growth rate of EMIC waves (after Jordanova et al., 2010b).
We will calculate EMIC and magnetosonic wave excitation by the anisotropic ring current ion distributions during storm time. Figure 4shows the equatorial growth rate of EMIC waves with frequencies between the oxygen and helium gyrofrequencies obtained with three different model formulations during the November 2002 storm. Intense EMIC waves are generated in the postnoon high-density plasmaspheric drainage plumes by the anisotropic ring current distributions that develop due to drift-shell splitting in realistic non-dipolar magnetic fields [Jordanova et al., 2010b]. We will perform similar simulations and compare the regions of large wave growth with EMFISIS observations. The global patterns of intense ion and electron precipitation will be compared to energetic particle data from the RBSP mission.
In addition, we will simulate with our kinetic model the injection of plasma sheet electrons into the inner magnetosphere by enhanced convection electric fields; this will provide a seed population of electrons. We will calculate the growth rate of whistler-mode waves due to the anisotropic ring current electron population using the dispersion relation for whistler waves and plasmaspheric densities from the coupled plasmasphere model. Global simulations of whistler instability during a geomagnetic storm were performed for the first time by Jordanova et al. [2010a] indicating significant wave growth in the dawnside MLT region outside the plasmasphere. Detailed comparisons with the EMFISIS wave data will be made to verify the location of whistler-mode growth and estimate the wave amplitudes. We will investigate the effect of these waves on the local acceleration and loss of radiation belt electrons and compare it to the effects of inward radiation belt transport and acceleration.
Non-linear Wave-Particle Interactions Extremely intense chorus emissions are occasionally observed [Cattell et al., 2008; Tsurutani et al, 2009] with amplitudes (> 100 mV/m) far in excess of those where quasi-linear scattering is valid. Non-linear test particle scattering of resonant electrons in such large amplitude waves [Bortnik et al. 2008a] indicates that resonant electrons tend to exhibit advective transport towards the loss cone rather than the stochastic diffusive behavior. Such advective scattering could dramatically increase the average rate of resonant electron loss, and may thus be related to the observed electron dropouts [Onsager et al., 2007; Morley et al., 2010] during the main phase of magnetic storms. Non-linear phase trapping of electrons in large amplitude chorus can also lead to non-diffusive acceleration at relativistic energies [Albert, 2002; Furuya et al., 2008; Summers and Omura, 2007]. Such processes will be treated with test particle scattering codes and the effects will be incorporated into the RAM code simulations.