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Radial diffusion coefficients quantify non-adiabatic transport of energetic particles by electromagnetic field fluctuations in planetary radiation belts. Theoretically, radial diffusion occurs for an ensemble of particles that experience irreversible violation of their third adiabatic invariant, which is equivalent to a change in their Roederer L* parameter. Thus, the Roederer L* coordinate is the fundamental quantity from which radial diffusion coefficients can be computed. In this study, we present a methodology to calculate the Lagrangian derivative of L* from global magnetospheric simulations, and test it with an application to Vlasiator, a hybrid-Vlasov model of near-Earth space. We use a Hamiltonian formalism for particles confined to closed drift shells with conserved first and second adiabatic invariants to compute changes in the guiding center drift paths due to electric and magnetic field fluctuations. We investigate the feasibility of this methodology by computing the time derivative of L* for an equatorial ultrarelativistic electron population travelling along four guiding center drift paths in the outer radiation belt during a 5 minute portion of a Vlasiator simulation. Radial diffusion in this simulation is primarily driven by ultralow frequency waves in the Pc3 range (10–45 s period range) that are generated in the foreshock and transmitted through the magnetopause to the outer radiation belt environment. Our results show that an alternative methodology to compute detailed radial diffusion transport is now available and could form the basis for comparison studies between numerical and observational measurements of radial transport in the Earth’s radiation belts.

I briefly review, compare and contrast two theoretical works that have significantly influenced radial diffusion research thus far, namely, the works of Fälthammar (1965, https://doi.org/10.1029/JZ070i011p02503) and the works of Fei et al. (2006, https://doi.org/10.1029/2005JA011211). Leveraging Fälthammar's model for magnetic field disturbances, I demonstrate that Fei et al's formulas are incorrect: they underestimate radial diffusion by a factor two in the presence of magnetic field disturbances. This underestimation comes from the erroneous assumption that radial displacements driven by magnetic field disturbances are statistically independent from radial displacements driven by induced electric fields while in fact both displacements are proportional to each other. Fei et al.'s approach is similar to Fälthammar's approach in that they both analyze radial diffusion by pieces, depending on the nature of the driver. Yet, the Fokker-Planck equation requires only one radial diffusion coefficient to characterize statistically a trapped radiation belt population cross drift shell motion. Thus, it is worth questioning the practice that consists of defining the coefficient as a sum of independent contributions. In addition, both theoretical models rely on the assumption that the background magnetic field is primarily dipolar, leading to flawed estimates. To overcome these limitations and to improve radial diffusion quantification, I use a general formulation for the variation of the third adiabatic invariant (1) to describe how to compute a radial diffusion coefficient in the most general way and (2) to highlight the assumptions that need to be questioned.

Satellite-based direct electric field measurements deliver crucial information for space science studies. Yet, they require meticulous design and calibration. In-flight calibration of double-probe instruments is usually presented in the most common case of tenuous plasmas, where the presence of an electrostatic structure surrounding the charged spacecraft alters the geophysical electric field measurements. To account for this effect and the uncertainty in the boom length, the measured electric field is multiplied by a parameter called the shorting factor (s f ). In the plasmasphere, the Debye length is very small in comparison with spacecraft dimension and there is no shorting of the electric field measurements (s f = 1). However, the electric field induced by spacecraft motion greatly exceeds any geophysical electric field of interest in the plasmasphere. Thus, the highest level of accuracy in calibration is required. The objective of this work is to discuss the accuracy of the setting S f =1 and therefore to examine the accuracy of Van Allen Probes electric field measurements below L = 2. We introduce a method to determine the shorting factor near perigee. It relies on the idea that the value of the geophysical electric field measured in the Earth's rotating frame of reference is independent of whether the spacecraft is approaching perigee or past perigee, i.e. it is independent of spacecraft velocity. We obtain that S f =0.994 ± 0.001. The resulting margins of errors in individual electric drift measurements are of the order of ± 0.1% of spacecraft velocity (a few meters per second).

The mechanisms for accelerating electrons from thermal to relativistic energies in the terrestrial magnetosphere, on the sun, and in many astrophysical environments have never been verified. We present the first direct observation of two processes that, in a chain, cause this acceleration in Earth's outer radiation belt. The two processes are parallel acceleration from electron-volt to kilovolt energies by parallel electric fields in time-domain structures (TDS), after which the parallel electron velocity becomes sufficiently large for Doppler-shifted upper band whistler frequencies to be in resonance with the electron gyration frequency, even though the electron energies are kilovolts and not hundreds of kilovolts. The electrons are then accelerated by the whistler perpendicular electric field to relativistic energies in several resonant interactions. TDS are packets of electric field spikes, each spike having duration of a few hundred microseconds and containing a local parallel electric field. The TDS of interest resulted from nonlinearity of the parallel electric field component in oblique whistlers and consisted of ∼ 0.1 msec pulses superposed on the whistler waveform with each such spike containing a net parallel potential the order of 50 V. Local magnetic field compression from remote activity provided the free energy to drive the two processes. The expected temporal correlations between the compressed magnetic field, the nonlinear whistlers with their parallel electric field spikes, the electron flux and the electron pitch angle distributions were all observed.