Electromagnetic Ion Cyclotron (EMIC) Waves for Radiation Belt Remediation Applications
Maria de SoriaSantacruz (PhD Candidate), Committee: Prof. Manuel MartinezSanchez (Professor), Dr. Gregory Ginet, Prof. David Miller, Prof. Jeffrey Hoffman and Prof. Kerri Cahoy
Motivation and Objectives
The high energy particles of the Van Allen belts coming from cosmic rays, solar storms, high altitude nuclear explosions (HANEs) and other processes represent a significant danger to humans and spacecraft operating in those regions, as well as an obstacle to exploration and development of space technologies. The "Radiation Belt Remediation" (RBR) concept has been proposed as a way to solve this problem through ULF/VLF transmissions in the magnetosphere, which will create a pitchangle scattering of these energetic particles. A portion of the particles would then fall into their loss cone, lowering the altitude of their mirror point to a level where they are absorbed by the atmosphere.
The possible utilization of Whistler waves for precipitation of highenergy trapped electrons has been studied extensively [e.g. Inan et al, 2003], and a space test of a linear antenna for this purpose is in preparation [Spangers et al, 2006]. The lower frequency EMIC band has also been studied in the context of electron precipitation [e.g. Albert and Bortnik, 2009], but much less study has been devoted to the use of the lefthand polarized branch of EMIC waves for ion precipitation.
The possible utilization of Whistler waves for precipitation of highenergy trapped electrons has been studied extensively [Inan et al., 2003], and a space test of a linear antenna for this purpose is in preparation [Ginet et al., 2009]. The lower frequency EMIC band has also been studied in the context of electron precipitation [Albert and Bortnik, 2009], but much less work has been devoted to the use of the lefthand polarized branch of EMIC waves for proton precipitation.
This study aims at characterizing the ability of Electromagnetic Ion Cyclotron (EMIC) waves to precipitate energetic protons and electrons trapped in the Van Allen belts, and to translate these findings into engineering specifications of a spaceborne RBR system able to significantly reduce this energetic radiation. In order to fulfill this goal, the following objectives have been defined:
1. Determine the type of antenna able to radiate EMIC waves in the magnetospheric plasma. This is a largely unexplored territory that should be addressed, given its potential practical importance. Linear fullwave models to calculate the radiation pattern and radiation impedance in the farfield region due to a spaceborne electric dipole have been developed [De SoriaSantacruz, 2011; Wang and Bell, 1969]. However, the sheath around a spacebased RBR antenna is very thick, and so its capacitance is almost the vacuum capacitance, which is nearly independent of the frequency and proportional to the transmitter length. The associated reactance is extremely high for the EMIC band to the point that it is not possible to use an electric dipole to radiate these waves without the help of any other device. On the other hand, in terms of the radiation resistance, a short antenna would be ideal, because the relevant wavelengths (those near the resonance cone) are indeed very short; unfortunately, short antennas suffer the most from the small capacitance problem, although even a multikm antenna would have too much reactance at the EMIC regime. This study deals with two innovative ways to emit these waves; the first option involves plasma contactors at both ends of a linear dipole, thus avoiding oscillatory charge accumulation. The second case under consideration consists of a magnetic dipole working as an EMIC transmitter.
2. Characterize the radiation impedance and radiation pattern of this antenna in the farfield region.
3. Study the cold plasma wavepropagation of the EMIC band radiated from the proposed transmitter. In order to do that we will need to modify previously developed raytracing codes, which are able to handle Whistler waves.
4. Characterize the interaction of EMIC waves with the energetic population of particles in the belts. The waves are considered monochromatic and propagating at an angle to the geomagnetic field. Similar studies have been previously developed for Whistlers interacting with electrons, but no attention has been paid to the lower frequency and its interaction with both highenergy protons and electrons. This model uses a Lagrangian formulation involving a test particle simulation of the nonlinear equations of motion [Inan et al., 1978] to reproduce the interaction between the distribution of energetic particles and EMIC waves. This formulation allows one to deal with coherent and narrowband waves, which are fundamentally different from those produced by incoherent signals. In the later case the particles perform a random walk in velocity space, whereas during the interaction with a coherent wave individual particles are not scattered randomly, but they stay in resonance long enough for the particle's pitch angle to be substantially changed through nonlinear interactions. This model takes into account the oblique propagation of coherent EMIC pulsed waves in a multiion plasma and their interaction with the energetic protons and electrons in the Van Allen belts.
i. Study the scattering of the magnetospheric energetic distribution using a test particle method.
ii. Study the scattering of a single particle. This analysis determines the region in velocity space that includes all particles that can resonantly interact with the waves, which is an input to the distribution function.
5. Characterize the feasibility in terms of power levels, frequencies, voltages, currents and mass of a potential spaceborne RBR antennae capable of significantly reduce the energetic radiation in the belts.
6. Estimate precipitated fluxes and compare them with the values of typical background precipitation.
EMIC Dispersion
EMIC waves propagate below the proton gyrofrequency Ωp. In this study we use cold plasma theory as a first approximation. The dispersion relation has two branches depending on its sign, which determines polarization (Lmode or Rmode). Figure 1 presents the different features of the oblique EMIC dispersion relation in the presence of heavy ions, which are:
Figure 1  Oblique (θ= 45°) EMIC dispersion in the presence of heavy ions 
Approach / Tools
Four models constitute the simulation of the interaction between energetic particles and EMIC waves:

1. Magnetospheric models
 2. Antenna radiation model
 3. Propagation model
 4. Waveparticle interaction model
The magnetospheric models of plasma density, composition and magnetic field are inputs to the rest of the code. The antenna radiation model generates inputs to the propagation model, which determines the characteristics of EMIC waves along the magnetic lines required for waveparticle interaction calculations. The magnetic lines are discretized in latitude, and for every time and latitude step the properties of the waves originated at the source antenna (radiation model) are updated using raytracing (propagation model). These properties are used to solve the nonlinear equations of motion of test energetic particles from given distribution function interacting with the wave (waveparticle interaction model). The process is repeated for every time step and every latitude and the precipitated flux is calculated as a result of this iteration. This procedure is illustrated in Figure 2. It must be noted that part of the complexity of this analysis resides in finding the right combination of antenna source location (antenna operations), wave characteristics (antenna design) and target particles (range of energies, pitch angles, etc.) that would provide the best result in terms of precipitation. This iteration links with the translation to engineering specifications of a spaceborne system able to perform this mission.
Figure 2  Algorithm Schematics 
Results
The first steps consisted of reproducing previous work of whistlers interacting with electrons, which allows one to validate the approach and methodology. Once the different aspects of this interaction have been checked with previous publications we could safely start changing the wave dispersion, propagation and target particles to address our problem. So far we have reproduced most of the work relative to whistlers interacting with electrons using a formulation based on nonlinear equations of motion, an we have started introducing the new EMIC regime and proton interaction. Some of the results obtained so far are presented next.
Figure 3 reproduces Chang and Inan, 1985 results for relativistic electrons interacting with a 0.5 seconds Whistler pulse which enters the magnetosphere at 1000 km of altitude and propagates along L=4 (neq=400 el/cm3). The wave magnetic field intensity and frequency at the equator are taken to be Bweq=5 pT and f=2.5 kHz. As the input pulse propagates toward the equator, it first interacts with higher energy electrons because the resonant electron energy decreases when approaching the equator. These electrons arrive first to the precipitation region near the wave injection point, and equatorial scattered particles arrive later. As the pulse travels past the equator, it interacts again with higher energy electrons and, although interacting with the wave at later times, they can overtake these electrons scattered earlier by the wave close to the equator. This explanation matches the results presented in the figure, where the dynamic spectra of the precipitated energy flux is presented versus the particles' energy and the time after transmission.
Figure 3  Dynamic spectra of the wave induced flux for Bw = 5 pT and E0 = 100 keV 
The analyses above relative to whistlerelectron interaction allowed us to validate the methodology being developed. We have most of the ingredients to start analyzing the case of EMICprotons. Next, we present our first steps in this direction, which address the implementation of the EMIC dispersion relation and the analysis of the resonance condition of protons and the EMIC wave band. This is an ongoing study that will result in the compatible range of frequencies, particles' energies and shells of operation input to the waveparticle interaction analysis. Figure 4 presents a specific case for L=2. The resonant energy required for cyclotron interaction with MeV protons is plotted as a function of resonant latitude and frequency. We observe that the required energy of the target particles increases with latitude and decreases with frequency, which means that compared to resonance at higher latitudes, interaction at the equator (longer resonance times, higher scattering) for a fixed target's energy would require lower frequencies.
Figure 4  Resonant energy of protons for EMIC interaction versus resonant latitude and frequency 
Similar to Inan's studies for the whistlerelectron case [Inan, 1977], we have analyzed the interaction of parallel propagating EMIC waves and a single sheet of protons uniformly distributed in Larmor phase. Figure 5 represents the RMS scattering referred to the equator versus the wave power flux for equatorial interaction between protons at the edge of the loss cone and parallel propagating EMIC waves at L=1.5. According to these results and for the given parameters, the wave field is proportional to the scattering for power fluxes < 104 W/m2; in the literature this regime is called “linear mode”, where we can neglect the wave term in the equation for the variation of the phase between the perpendicular momentum and the perpendicular lefthanded Bw. This linear mode is equivalent to assume that the wave effects are so small that the variation of that phase is very close to what it would have been without wave.
Figure 5  RMS pitchangle scattering versus power flux for parallel EMICproton resonant interaction at the equator (L=1.5) 
According to these results and neglecting the wave term in the phase equation, Figure 6 presents the pitchangle scattering referred to the equator versus latitude of a single equatorially (L=1.5) resonant sheet of protons interacting with an oblique EMIC wave with a wavenormal angle of ψ=80° and power flux of 8.1·106 W/m2. These protons have their velocity vector at the equator along the edge of the loss cone and are uniformly distributed in Larmor phase (each curve corresponds to a different phase). The RMS scattering for this case equals ΔαRMSeq=0.06°, which is one order of magnitude smaller than the scattering obtained for field aligned waves (ΔαRMSeq=0.5°) as shown in Figure 5. Finally, Figure 7 presents the maximum scattering of each of these protons in the sheet versus their initial Larmor phase. In this Figure we can perfectly observe the sinusoidal behavior of the scattering characteristic of this linear behavior. When neglecting the wave term from the phase equation, the variation in time of the parallel and perpendicular momentum depend sinusoidally on the phase, which is now nondependent on the wave field.
Figure 6  Total pitchangle scattering versus latitude for a oblique EMIC wave interacting with equatorially resonant protons (L=1.5) 
Figure 7  Maximum pitchangle scattering versus initial Larmor phase for a oblique EMIC wave interacting with equatorially resonant protons (L=1.5)] 
References
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