Wave-particle interactions with parallel whistler waves: Nonlinear and time-dependent effects revealed by particle-in-cell simulations

Camporeale, Enrico; Zimbardo, G.

doi:10.1063/1.4929853

Cited by 22 publications

(35 citation statements)

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“…To explain the origin of the MeV electrons in the radiation belt, studies suggested that the storm and substorm injection process from plasma sheet into the inner magnetosphere accelerates low‐energy (e.g., a few keV) electrons to a few hundred keV. Once in the inner magnetosphere, electrons interact with ultra low frequency (ULF) waves [e.g., Elkington et al , ; Rostoker et al , ; Ukhorskiy et al , ; Mathie and Mann , , ], very low frequency (VLF) waves [e.g., Summers et al , ; Omura et al , ; Thorne , ; Simms et al , ; Camporeale , ; Camporeale and Zimbardo , ], or magnetosonic waves [e.g., Horne et al , ; Shprits et al , ], which can energize electrons to MeV energy range.…”

Section: Introductionmentioning

confidence: 99%

Information theoretical approach to discovering solar wind drivers of the outer radiation belt

et al. 2016

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The solar wind‐magnetosphere system is nonlinear. The solar wind drivers of geosynchronous electrons with energy range of 1.8–3.5 MeV are investigated using mutual information, conditional mutual information (CMI), and transfer entropy (TE). These information theoretical tools can establish linear and nonlinear relationships as well as information transfer. The information transfer from solar wind velocity (Vsw) to geosynchronous MeV electron flux (Je) peaks with a lag time of 2 days. As previously reported, Je is anticorrelated with solar wind density (nsw) with a lag of 1 day. However, this lag time and anticorrelation can be attributed at least partly to the Je(t + 2 days) correlation with Vsw(t) and nsw(t + 1 day) anticorrelation with Vsw(t). Analyses of solar wind driving of the magnetosphere need to consider the large lag times, up to 3 days, in the (Vsw, nsw) anticorrelation. Using CMI to remove the effects of Vsw, the response of Je to nsw is 30% smaller and has a lag time < 24 h, suggesting that the MeV electron loss mechanism due to nsw or solar wind dynamic pressure has to start operating in < 24 h. nsw transfers about 36% as much information as Vsw (the primary driver) to Je. Nonstationarity in the system dynamics is investigated using windowed TE. When the data are ordered according to transfer entropy value, it is possible to understand details of the triangle distribution that has been identified between Je(t + 2 days) versus Vsw(t).

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Section: Introductionmentioning

confidence: 99%

Information theoretical approach to discovering solar wind drivers of the outer radiation belt

et al. 2016

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“…Indeed, it is important to note that the particle dynamics is entirely determined by the specification of the diffusion coefficients, boundary conditions, and initial conditions, in equation . Some of the shortcomings of the quasi‐linear diffusion approach have been discussed, for instance, by [ Shalchi and Schlickeiser , ; Ragot , ; Lemons , ; Camporeale and Zimbardo , ; Camporeale , ].…”

Section: Introductionmentioning

confidence: 99%

On the propagation of uncertainties in radiation belt simulations

et al. 2016

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We present the first study of the uncertainties associated with radiation belt simulations, performed in the standard quasi‐linear diffusion framework. In particular, we estimate how uncertainties of some input parameters propagate through the nonlinear simulation, producing a distribution of outputs that can be quite broad. Here we restrict our focus on two‐dimensional simulations (in energy and pitch angle space) of parallel‐propagating chorus waves only, and we study as stochastic input parameters the geomagnetic index Kp (that characterizes the time dependency of an idealized storm), the latitudinal extent of waves, and the average electron density. We employ a collocation method, thus performing an ensemble of simulations. The results of this work point to the necessity of shifting to a probabilistic interpretation of radiation belt simulation results and suggest that an accurate specification of a time‐dependent density model is crucial for modeling the radiation environment.

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“…we excite specific wave modes at the boundary, as opposed to considering an initial-value problem in which one typically considers waves that grow from an initially unstable distribution (e.g. see Camporeale, 2015;Camporeale & Zimbardo, 2015;Silva et al, 2017;Hikishima et al, 2009;Katoh & Omura, 2006Katoh et al, 2018;Omura et al, 2008Omura et al, , 2009Omura et al, , 2010Omura et al, , 2011Ratcliffe & Watt, 2017); (ii) by considering the response of a distribution of electrons, we track the diffusion in energy and pitch angle space across the entire phase-space domain, in contrast to some previous similar studies of diffusion (e.g. see Camporeale & Zimbardo, 2015;Tao et al, 2011Tao et al, , 2012) that considered resonant particles only.…”

Section: Discussionmentioning

confidence: 99%

“…Specifically, they found this threshold to be

false| B_{w,rms}^{2} false/ B_{0}^{2} false| \geq 2 \times 1 0^{- 7}

for 10keV electrons, and

false| B_{w,rms}^{2} false/ B_{0}^{2} false| \geq 7 \times 1 0^{- 6}

for 1MeV electrons, where waves have root‐mean‐squared amplitudes of magnitude B w,rms in a background field B 0 . Camporeale and Zimbardo () used self‐consistent kinetic simulations to investigate diffusion during the linear growth phase and saturation of anisotropy‐driven instabilities that self‐consistently generate whistler‐mode waves. They found evidence of nonlinear and time‐dependent effects, with enhanced pitch angle diffusion during the linear growth phase.…”

Section: Introductionmentioning

confidence: 99%

“…There are a large number of theoretical calculations and numerical experiments relevant to the work presented in this paper and so it is not possible to discuss every one (e.g. a non-exhaustive list of such works on whistler-mode wave-particle interactions includes Albert, 2001Albert, , 2002Albert, , 2010Bortnik, Thorne, Inan, et al, 2008;Camporeale, 2015;Camporeale & Zimbardo, 2015;Silva et al, 2018;Mourenas et al, 2018;Omura et al, 2007;Tao & Bortnik, 2010;Tao et al, 2011Tao et al, , 2012Tao et al, , 2013. Instead, we focus on some of the works that -either with test-particle or particle-in-cell (PiC) codes -analyzed the statistical/diffusive response of the plasma, by directly extracting particle data.…”

Section: Introductionmentioning

confidence: 99%

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Particle‐in‐cell Experiments Examine Electron Diffusion by Whistler‐mode Waves: 1. Benchmarking With a Cold Plasma

et al. 2019

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Using a particle-in-cell code, we study the diffusive response of electrons due to wave-particle interactions with whistler-mode waves. The relatively simple configuration of field-aligned waves in a cold plasma is used in order to benchmark our novel method, and to compare with previous works that used a different modelling technique. In this boundary-value problem, incoherent whistler-mode waves are excited at the domain boundary, and then propagate through the ambient plasma. Electron diffusion characteristics are directly extracted from particle data across all available energy and pitch-angle space. The 'nature' of the diffusive response is itself a function of energy and pitch-angle, such that the rate of diffusion is not always constant in time. However, after an initial transient phase, the rate of diffusion tends to a constant, in a manner that is consistent with the assumptions of quasilinear diffusion theory. This work establishes a framework for future investigations on the nature of diffusion due to whistler-mode wave-particle interactions, using particle-in-cell numerical codes with driven waves as boundary value problems.Plain Language Summary 'Whistler-mode' plasma waves interact with electrons in the Earth's outer radiation belts. This wave-particle interaction plays a significant role in both electron acceleration, and in the loss of electrons to the atmosphere via 'pitch angle scattering'. Such processes are typically modelled using numerical diffusion codes, with electron diffusion coefficients that characterize the nature and the strength of the wave-particle interaction. These diffusion coefficients are calculated using a mixture of long-established theory and input parameters taken from data and/or empirical models. We present a novel method for the direct extraction of characteristics of the electron diffusion from particle-in-cell numerical experiments. Our results demonstrate that the rate of diffusion can be time-dependent at early times, but then tends to constant values in a manner that is consistent with quasilinear theory.

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Wave-particle interactions with parallel whistler waves: Nonlinear and time-dependent effects revealed by particle-in-cell simulations

Cited by 22 publications

References 62 publications

Information theoretical approach to discovering solar wind drivers of the outer radiation belt

Information theoretical approach to discovering solar wind drivers of the outer radiation belt

On the propagation of uncertainties in radiation belt simulations

Particle‐in‐cell Experiments Examine Electron Diffusion by Whistler‐mode Waves: 1. Benchmarking With a Cold Plasma

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