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2019 
The past decade transformed our observational understanding of energetic particle processes in nearEarth space. An unprecedented suite of observational systems were in operation including the Van Allen Probes, Arase, MMS, THEMIS, Cluster, GPS, GOES, and LANLGEO magnetospheric missions. They were supported by conjugate lowaltitude measurements on spacecraft, balloons, and groundbased arrays. Together these significantly improved our ability to determine and quantify the mechanisms that control the buildup and subsequent variability of energetic particle intensities in the inner magnetosphere. The highquality data from NASA\textquoterights Van Allen Probes are the most comprehensive insitu measurements ever taken in the nearEarth space radiation environment. These observations, coupled with recent advances in radiation belt theory and modeling, including dramatic increases in computational power, has ushered in a new era, perhaps a \textquotedblleftgolden era,\textquotedblright in radiation belt research. We have edited a Journal of Geophysical Research: Space Science Special Collection dedicated to Particle Dynamics in the Earth\textquoterights Radiation Belts in which we gather the most recent scientific findings and understanding of this important region of geospace. This collection includes the results presented at the American Geophysical Union Chapman International Conference in Cascais, Portugal (03/2018) and many other recent and relevant contributions. The present article introduces and review the context, current research, and main questions that motivate modern radiation belt research divided into the following topics: (1) particle acceleration and transport, (2) particle loss, (3) the role of nonlinear processes, (4) new radiation belt modeling capabilities and the quantification of model uncertainties, and (5) laboratory plasma experiments. Ripoll, JeanFrancois; Claudepierre, Seth; Ukhorskiy, Sasha; Colpitts, Chris; Li, Xinlin; Fennell, Joe; Crabtree, Chris; Published by: Journal of Geophysical Research: Space Physics Published on: 12/2019 YEAR: 2019 DOI: 10.1029/2019JA026735 inner magnetosphere; laboratory plasma experiments; Particle acceleration; particle loss; Radiation belts; Van Allen Probes 
2017 
Bayesian Spectral Analysis of Chorus SubElements from the Van Allen Probes We develop a Bayesian spectral analysis technique that calculates the probability distribution functions of a superposition of wavemodes each described by a linear growth rate, a frequency and a chirp rate. The Bayesian framework has a number of advantages, including 1) reducing the parameter space by integrating over the amplitude and phase of the wave, 2) incorporating the data from each channel to determine the model parameters such as frequency which leads to high resolution results in frequency and time, 3) the ability to consider the superposition of waves where the waveparameters are closely spaced, 4) the ability to directly calculate the expectation value of wave parameters without resorting to ensemble averages, 5) the ability to calculate error bars on model parameters. We examine one risingtone chorus element in detail from a disturbed time on November 14, 2012 using burst mode waveform data of the three components of the electric and magnetic field from the EMFISIS instrument on board NASA\textquoterights Van Allen Probes. The results demonstrate that subelements are likely composed of almost linear waves that are nearly parallel propagating with continuously changing wave parameters such as frequency and wavevector. Between subelements the wave parameters of the dominant mode undergoes a discrete change in frequency and wavevector. Near the boundary of subelements multiple waves are observed such that the evolution of the waves is reminiscent of wavewave processes such as parametric decay or nonlinear induced scattering by particles. These nonlinear processes may affect the saturation of the whistlermode chorus instability. Crabtree, Chris; Tejero, Erik; Ganguli, Gurudas; Hospodarsky, George; Kletzing, Craig; Published by: Journal of Geophysical Research: Space Physics Published on: 04/2017 YEAR: 2017 DOI: 10.1002/2016JA023547 
Whistler mode chorus is one of the most important emissions affecting the energization of the radiation belts. Recent laboratory experiments that inject energetic electron beams into a cold plasma have revealed several spectral features in the nonlinear evolution of these instabilities that have also been observed in hightime resolution in situ waveform data. These features include (1) a subelement structure which consists of an amplitude modulation on timescales slower than the bounce time, (2) closely spaced discrete frequency hopping that results in a faster apparent frequency chirp rate, (3) fast frequency changes near the subelement boundaries, and (4) harmonic generation. In this paper, we develop a finite dimensional selfconsistent Hamiltonian model for the evolution of the resonant beam of electrons. We analyze a single wave case and demonstrate that the instability occurs due to a Krein collision, which manifests as a coupling between a negative and positive energy mode. This analysis revealed that the nonlinear evolution of the spectrally stable fixedpoints of the selfconsistent Hamiltonian develop a subpacket structure similar to that of space observations. We then analyze the case of two whistler waves to show that the model reproduces the nonlinear harmonic generation and leads to a hypothesis for the closely spaced frequency hopping observed in laboratory experiments and space data. Crabtree, Chris; Ganguli, Gurudas; Tejero, Erik; Published by: Physics of Plasmas Published on: 03/2017 YEAR: 2017 DOI: 10.1063/1.4977539 Dispersion relations; Electron beams; SingingEigenvalues; Van Allen Probes; Whistler waves 
2015 
Nonlinear Generation of Electromagnetic Waves through Induced Scattering by Thermal Plasma We demonstrate the conversion of electrostatic pump waves into electromagnetic waves through nonlinear induced scattering by thermal particles in a laboratory plasma. Electrostatic waves in the whistler branch are launched that propagate near the resonance cone. When the amplitude exceeds a threshold ~5 \texttimes 106 times the background magnetic field, wave power is scattered below the pump frequency with wave normal angles (~59\textdegree), where the scattered wavelength reaches the limits of the plasma column. The scattered wave has a perpendicular wavelength that is an order of magnitude larger than the pump wave and longer than the electron skin depth. The amplitude threshold, scattered frequency spectrum, and scattered wave normal angles are in good agreement with theory. The results may affect the analysis and interpretation of space observations and lead to a comprehensive understanding of the nature of the Earth\textquoterights plasma environment. Tejero, E.; Crabtree, C.; Blackwell, D.; Amatucci, W.; Mithaiwala, M.; Ganguli, G.; Rudakov, L.; Published by: Scientific Reports Published on: 12/2015 YEAR: 2015 DOI: 10.1038/srep17852 
Evolution of lower hybrid turbulence in the ionosphere Threedimensional evolution of the lower hybrid turbulence driven by a spatially localized ion ring beam perpendicular to the ambient magnetic field in space plasmas is analyzed. It is shown that the quasilinear saturation model breaks down when the nonlinear rate of scattering by thermal electron is larger than linear damping rates, which can occur even for low wave amplitudes. The evolution is found to be essentially a threedimensional phenomenon, which cannot be accurately explained by twodimensional simulations. An important feature missed in previous studies of this phenom enon is the nonlinear conversion of electrostatic lower hybrid waves into electromagnetic whistler and magnetosonic waves and the consequent energy loss due to radiation from the source region. This can result in unique lowamplitude saturation with extended saturation time. It is shown that when the nonlinear effects are considered the net energy that can be permanently extracted from the ring beam is larger. The results are applied to anticipate the outcome of a planned experiment that will seed lower hybrid turbulence in the ionosphere and monitor its evolution. Ganguli, G.; Crabtree, C.; Mithaiwala, M.; Rudakov, L.; Scales, W.; Published by: Physics of Plasmas Published on: 11/2015 YEAR: 2015 DOI: 10.1063/1.4936281 
Laboratory studies of nonlinear whistler wave processes in the Van Allen radiation belts Important nonlinear wavewave and waveparticle interactions that occur in the Earth\textquoterights Van Allen radiation belts are investigated in a laboratory experiment. Predominantly electrostatic waves in the whistler branch are launched that propagate near the resonance cone with measured wave normal angle greater than 85\textdegree . When the pump amplitude exceeds a threshold \~5\texttimes106 times the background magnetic field, wave power at frequencies below the pump frequency is observed at wave normal angles (\~55\textdegree) . The scattered wave has a perpendicular wavelength that is nearly an order of magnitude larger than that of the pump wave. Occasionally, the parametric decay of a lower hybrid wave into a magnetosonic wave and a whistler wave is simultaneously observed with a threshold of δB/B0\~7\texttimes107 . Tejero, E.; Crabtree, C.; Blackwell, D.; Amatucci, W.; Mithaiwala, M.; Ganguli, G.; Rudakov, L.; Published by: Physics of Plasmas Published on: 09/2015 YEAR: 2015 DOI: 10.1063/1.4928944 
Laboratory studies of nonlinear whistler wave processes in the Van Allen radiation belts Important nonlinear wavewave and waveparticle interactions that occur in the Earth\textquoterights Van Allen radiation belts are investigated in a laboratory experiment. Predominantly electrostatic waves in the whistler branch are launched that propagate near the resonance cone with measured wave normal angle greater than 85\textordmasculine. When the pump amplitude exceeds a threshold ~5 x10^6 times the back ground magnetic field, wave power at frequencies below the pump frequency is observed at wave normal angles (~55\textordmasculine). The scattered wave has a perpendicular wavelength that is nearly an order of magnitude larger than that of the pump wave. Occasionally, the parametric decay of a lower hybrid wave into a magnetosonic wave and a whistler wave is simultaneously observed with a Tejero, E.; Crabtree, C.; Blackwell, D.; Amatucci, W.; Mithaiwala, M.; Ganguli, G.; Rudakov, L.; Published by: Physics of Plasmas Published on: 08/2015 YEAR: 2015 DOI: 10.1063/1.4928944 Electrostatic Waves; magnetic fields; Nonlinear scattering; Plasma electromagnetic waves; Whistler waves 
2014 
Generation of electromagnetic waves in the very low frequency band by velocity gradient It is shown that a magnetized plasma layer with a velocity gradient in the flow perpendicular to the ambient magnetic field is unstable to waves in the Very Low Frequency band that spans the ion and electron gyrofrequencies. The waves are formally electromagnetic. However, depending on wave vector k⎯⎯=kc/ωpe (normalized by the electron skin depth) and the obliqueness, k⊥/k , where k⊥, are wave vectors perpendicular and parallel to the magnetic field, the waves are closer to electrostatic in nature when k⎯⎯>>1 and k⊥>>k and electromagnetic otherwise. Inhomogeneous transverse flows are generated in plasma that contains a static electric field perpendicular to the magnetic field, a configuration that may naturally arise in the boundary layer between plasmas of different characteristics. Ganguli, G.; Tejero, E.; Crabtree, C.; Amatucci, W.; Rudakov, L.; Published by: Physics of Plasmas Published on: 01/2014 YEAR: 2014 DOI: 10.1063/1.4862032 
2012 
Weak turbulence in the magnetosphere: Formation of whistler wave cavity by nonlinear scattering We consider the weak turbulence of whistler waves in the in lowβ inner magnetosphere of the earth. Whistler waves, originating in the ionosphere, propagate radially outward and can trigger nonlinear induced scattering by thermal electrons provided the wave energy density is large enough. Nonlinear scattering can substantially change the direction of the wave vector of whistler waves and hence the direction of energy flux with only a small change in the frequency. A portion of whistler waves return to the ionosphere with a smaller perpendicular wave vector resulting in diminished linear damping and enhanced ability to pitchangle scatter trapped electrons. In addition, a portion of the scatteredwave packets can be reflected near the ionosphere back into the magnetosphere. Through multiple nonlinear scatterings and ionospheric reflections a longlived wavecavity containing turbulent whistler waves can be formed with the appropriate properties to efficiently pitchangle scatter trapped electrons. The primary consequence on the earth\textquoterights radiation belts is to reduce the lifetime of the trapped electron population. Crabtree, C.; Rudakov, L.; Ganguli, G.; Mithaiwala, M.; Galinsky, V.; Shevchenko, V.; Published by: Physics of Plasmas Published on: 01/2012 YEAR: 2012 DOI: 10.1063/1.3692092 
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