Radial Diffusion of Planetary Radiation Belts' Particles by Fluctuations with Finite Correlation Time

Radial diffusion in planetary radiation belts is a dominant transport mechanism resulting in the energization and losses of charged particles by large-scale electromagnetic fluctuations. In this study, we revisit the radial diffusion formalism by relaxing the assumption of zero correlation time in the spectrum of fluctuations responsible for the transport of charged particles. We derive a diffusion coefficient by assuming fluctuations that (1) are time homogeneous, (2) too small to trap the particles, and (3) can decorrelate on timescales comparable to the transit time of the particles. We demonstrate through self-similar solutions of the Fokker-Planck equation that autocorrelation time tc much larger than the linear transit time/particle drift period tau(L) = WL D1 results in characteristic time for transport independent of the drift frequency and faster than for short correlation time. In both instances, that is for short (t(L)>> t(c)) and long (t(L) similar to t(s), with s <1. However, in the absence of sources and sinks, particle transport for both short and long autocorrelation times result in equilibrium distribution along L* with differences of less than 10% across lower magnetic drift shells. The main consequence of incorporating finite correlation time appears in intermediate times much longer than the drift period but before the distribution function reaches equilibrium and indicates the importance of quantifying observationally the spectral properties of fluctuations for the modeling of planetary radiation belts.Peer reviewe

On the threshold energization of radiation belt electrons by double layers

Using a Hamiltonian approach, we quantify the energization threshold of electrons interacting with radiation belts' double layers discovered by Mozer et al. (2013). We find that double layers with electric field amplitude E0 ranging between 10 and 100 mV/m and spatial scales of the order of few Debye lengths are very efficient in energizing electrons with initial velocities v∥ ≤ vth to 1 keV levels but are unable to energize electrons with E ≥ 100 keV. Our results indicate that the localized electric field associated with the double layers are unlikely to generate a seed population of 100 keV necessary for a plethora of relativistic acceleration mechanisms and additional transport to higher energetic levels.Peer reviewe

Compacting the description of a time-dependent multivariable system and its multivariable driver by reducing the state vectors to aggregate scalars : the Earth's solar-wind-driven magnetosphere

Using the solar-wind-driven magnetosphere-ionosphere-thermosphere system, a methodology is developed to reduce a state-vector description of a time-dependent driven system to a composite scalar picture of the activity in the system. The technique uses canonical correlation analysis to reduce the time-dependent system and driver state vectors to time-dependent system and driver scalars, with the scalars describing the response in the system that is most-closely related to the driver. This reduced description has advantages: low noise, high prediction efficiency, linearity in the described system response to the driver, and compactness. The methodology identifies independent modes of reaction of a system to its driver. The analysis of the magnetospheric system is demonstrated. Using autocorrelation analysis, Jensen- Shannon complexity analysis, and permutation-entropy analysis the properties of the derived aggregate scalars are assessed and a new mode of reaction of the magnetosphere to the solar wind is found. This state-vector-reduction technique may be useful for other multivariable systems driven by multiple inputs.Peer reviewe

Radial Transport in the Earth’s Radiation Belts: Linear, Quasi-linear, and Higher-order Processes

Observational studies of the Earth’s radiation belts indicate that Alfvénic fluctuations in the frequency range of 2–25 mHz accelerate electrons to relativistic energies. For decades, statistical models of radiation belts have quantified the impact of Alfvénic waves in terms of quasi-linear diffusion. However, quasi-linear models are inadequate to quantify Alfvénic radial transport occurring on timescales comparable to the azimuthal drift period of 0.1–10 MeV electrons. With recent advances in observational methodologies offering coverage of the Earth’s radiation belts on fast timescales, a theoretical framework that distinguishes between fast and diffusive radial transport can be tested for the first time in situ. In this report, we present a drift-kinetic description of radial transport for planetary radiation belts. We characterize fast linear processes and determine the conditions under which higher-order effects become dynamically significant. In the linear regime, wave–particle interactions are categorized in terms of resonant and nonresonant responses. We demonstrate that the phenomenon of zebra stripes is nonresonant and can originate from injection events in the inner radiation belts. We derive a radial diffusion coefficient for a field model that satisfies Faraday’s law and that contains two terms: one scaling as L ^10 independent of the azimuthal number m , and a second scaling as m ^2 L ^6 . In the higher-order regime, azimuthally symmetric waves with properties consistent with in situ measurements can energize 10–100 keV electrons in less than a drift period. This process provides new evidence that acceleration by Alfvénic waves in radiation belts cannot be fully contained within diffusive models

Formation of Foreshock Transients and Associated Secondary Shocks

Upstream of shocks, the foreshock is filled with hot ions. When these ions are concentrated and thermalized around a discontinuity, a diamagnetic cavity bounded by compressional boundaries, referred to as a foreshock transient, forms. Sometimes, the upstream compressional boundary can further steepen into a secondary shock, which has been observed to accelerate particles and contribute to the primary shock acceleration. However, secondary shock formation conditions and processes are not fully understood. Using particle-in-cell simulations, we reveal how secondary shocks are formed. From 1D simulations, we show that electric fields play a critical role in shaping the shock's magnetic field structure, as well as in coupling the energy of hot ions to that of the shock. We demonstrate that larger thermal speed and concentration ratio of hot ions favor the formation of a secondary shock. From a more realistic 2D simulation, we examine how a discontinuity interacts with foreshock ions leading to the formation of a foreshock transient and a secondary shock. Our results imply that secondary shocks are more likely to occur at primary shocks with higher Mach number. With the secondary shock's previously proven ability to accelerate particles in cooperation with a planetary bow shock, it is even more appealing to consider them in particle acceleration of high Mach number astrophysical shocks.Peer reviewe

Quantifying the non-linear dependence of energetic electron fluxes in the Earth's radiation belts with radial diffusion drivers

In this study, we use mutual information to characterise statistical dependencies of seed and relativistic electron fluxes in the Earth's radiation belts on ultra-low-frequency (ULF) wave power measured on the ground and at geostationary orbit. The benefit of mutual information, in comparison to measures such as the Pearson correlation, lies in the capacity to distinguish non-linear dependencies from linear ones. After reviewing the property of mutual information and its relationship with the Pearson correlation for Gaussian bivariates, we present a methodology to quantify and distinguish linear and non-linear statistical dependencies that can be generalised to a wide range of solar wind drivers and magnetospheric responses. We present an application of the methodology by revisiting the case events studied by Rostoker et al. (1998). Our results corroborate the conclusions of Rostoker et al. (1998) that ULF wave power and relativistic electron fluxes are statistically dependent upon one another. We also estimate that the Pearson correlation is missing between 20 % and 30 % of the statistical dependency between ULF wave power and relativistic electron fluxes. Thus, the Pearson correlation underestimates the impact of ULF waves on energetic electron fluxes. However, we find that observed enhancements in relativistic electron fluxes correlate modestly, both linearly and non-linearly, with the ULF power spectrum when compared with values found in previous studies (Simms et al., 2014) and with correlational values found between seed electrons and ULF wave power for the same case events. Our results are indicative of the importance of incorporating data analysis tools that can quantify linear and non-linear interdependencies of various solar wind drivers.In this study, we use mutual information to characterise statistical dependencies of seed and relativistic electron fluxes in the Earth's radiation belts on ultra-low-frequency (ULF) wave power measured on the ground and at geostationary orbit. The benefit of mutual information, in comparison to measures such as the Pearson correlation, lies in the capacity to distinguish non-linear dependencies from linear ones. After reviewing the property of mutual information and its relationship with the Pearson correlation for Gaussian bivariates, we present a methodology to quantify and distinguish linear and non-linear statistical dependencies that can be generalised to a wide range of solar wind drivers and magnetospheric responses. We present an application of the methodology by revisiting the case events studied by Rostoker et al. (1998). Our results corroborate the conclusions of Rostoker et al. (1998) that ULF wave power and relativistic electron fluxes are statistically dependent upon one another. We also estimate that the Pearson correlation is missing between 20 % and 30 % of the statistical dependency between ULF wave power and relativistic electron fluxes. Thus, the Pearson correlation underestimates the impact of ULF waves on energetic electron fluxes. However, we find that observed enhancements in relativistic electron fluxes correlate modestly, both linearly and non-linearly, with the ULF power spectrum when compared with values found in previous studies (Simms et al., 2014) and with correlational values found between seed electrons and ULF wave power for the same case events. Our results are indicative of the importance of incorporating data analysis tools that can quantify linear and non-linear interdependencies of various solar wind drivers.Peer reviewe

The impact on global magnetohydrodynamic simulations from varying initialisation methods : results from GUMICS-4

We investigate the effects of different initialisation methods of the GUMICS-4 global magnetohydrodynamic (MHD) simulation to the dynamics in different parts of the Earth's magnetosphere and hence compare five 12 h simulation runs that were initiated by 3 h of synthetic data and followed by 9 h of solar wind measurements using the OMNI data as input. As a reference, we use a simulation run that includes nearly 60 h of OMNI data as input prior to the 9 h interval examined with different initialisations. The selected interval is a high-speed stream event during a 10-day interval (12-22 June 2007). The synthetic initialisations include stepwise, linear and sinusoidal functions of the interplanetary magnetic field with constant density and velocity values. The results show that the solutions converge within 1 h to give a good agreement in both the bow shock and the magnetopause position. However, the different initialisation methods lead to local differences which should be taken into consideration when comparing model results to satellite measurements.Peer reviewe