The year 2019 marks the 60th anniversary of the concept of radial diffusion in magnetospheric research. This makes it one of the oldest research topics in radiation belt science. While first introduced to account for the existence of the Earth’s outer belt, radial diffusion is now applied to the radiation belts of all strongly magnetized planets. But for all its study and application, radial diffusion remains an elusive process. As the theoretical picture evolved over time, so, too, did the definitions of various related concepts, such as the notion of radial transport. Whether data is scarce or not, doubts in the efficacy of the process remain due to the use of various unchecked assumptions. As a result, quantifying radial diffusion still represents a major challenge to tackle in order to advance our understanding of and ability to model radiation belt dynamics. The core objective of this review is to address the confusion that emerges from the coexistence of various definitions of radial diffusion, and to highlight the complexity and subtleties of the problem. To contextualize, we provide a historical perspective on radial diffusion research: why and how the concept of radial diffusion was introduced at Earth, how it evolved, and how it was transposed to the radiation belts of the giant planets. Then, we discuss the necessary theoretical tools to unify the evolving image of radial diffusion, describe radiation belt drift dynamics, and carry out contemporary radial diffusion research.

Diffusion-driven radiation belt models require multiple physics-based inputs to specify the radiation environment through which spacecraft travel, including diffusion coefficients. Even though event-specific coefficients are necessary for model accuracy, their routine integration in operational models has not yet been achieved. In fact, one of the key inputs, the radial diffusion coefficient, is still commonly determined by a Kp-driven parameterization. This work presents a method to determine continuous time series of time-varying radial diffusion coefficients. A theoretical model is developed in which electromagnetic radial diffusion is controlled by the magnetopause immediate time history. Specifically, radial diffusion is described as a function of the average, variance, and autocorrelation time of the geocentric stand-off distance to the subsolar point on the magnetopause. Because the magnitudes of these three magnetopause parameters vary with time and magnetic activity, so does radial diffusion. To a lesser extent, radial diffusion is also controlled by the drift frequency of the radiation belt population. Moreover, radial diffusion is quantified using a standard model in which the magnetopause is controlled by the solar wind. Although the resulting diffusion coefficients span several orders of magnitude per Kp index, the median magnitudes are remarkably similar to the ones provided by the standard Kp-driven statistical parameterization.

The “zebra stripes” are peaks and valleys commonly present in the spectrograms of energetic particles trapped in the Earth’s inner belt. Several theories have been proposed over the years to explain their generation, structure and evolution. Yet, the plausibility of various theories has not been tested due to a historical lack of ground-truth, including in-situ electric field measurements. In this work, we leverage the new visibility offered by the database of NASA Van Allen Probes electric drift measurements to reveal the conditions associated with the generation of zebra stripe patterns. Energetic electron flux measurements by the Radiation Belt Storm Probes Ion Composition Experiment between January 1, 2013 and December 31, 2015 are systematically analyzed to determine 370 start times associated with the generation of zebra stripes. Statistical analyses of these events reveal that the zebra stripes are usually created during substorm onset, a time at which prompt penetration electric fields are present in the plasmasphere. All the pieces of experimental evidence collected are consistent with a scenario in which the prompt penetration electric field associated with substorm onset leads to a sudden perturbation of the trapped particle drift motion. Subsequent inner belt drift echoes constitute the zebra stripes. This study exemplifies how the analysis of trapped particle dynamics in the inner belt and slot region provides complimentary information on the dynamics of plasmaspheric electric fields. It is the first time that the signature of prompt penetration electric fields is detected in near‐equatorial electric field measurements below L=3.

No existing instrument is capable of consistently measuring all three components of the DC and low frequency electric field (E-field) throughout the heliosphere with sufficient accuracy to determine the smallest, and most geophysically relevant component: the E-field component parallel to the background magnetic field. E-field measurements in the heliosphere are usually made on spinning spacecraft equipped with two disparate types of double probe antennas: (1) long wire booms in the spin plane, and (2) ~10 times shorter rigid booms along the spin axis. On such systems, the potential difference (signal + noise) is divided by the boom length to produce a resultant E-field component. Because the spacecraft-associated errors are larger nearer the spacecraft, the spin plane components of the E-field are well measured while the spin axis component are poorly measured. As a result, uncertainty in the parallel E-field is usually greater than its measured value. Grotifer leverages more than fifty years of expertise in delivering highly accurate spin plane E-field measurements, while overcoming inaccuracies generated by spin axis E-field measurements. Its design consists of mounting detectors on two rotating plates, oriented at 90° with respect to each other, on a non-rotating central body. Each rotating plate has two component measurements of the E-field such that the Twin Orthogonal Rotating Platforms (TORPs) provide four instantaneous measurements of the E-field, and the three E-field components are well-measured by the rotating detectors. Grotifer (Giant rotifer) is a reference to the rotifer, also known as the “wheel animalcule”, which has twin crowns of antenna-like cilia that appear to rotate in all directions. Grotifer marks a profound change in E-field instrument design that represents the best path forward to close the observational gap that currently hampers resolution of significant science questions at the forefront of space plasma physics research. Here, we present the Grotifer design concept implemented as a 27-U CubeSat, discuss the important features in the design and operation of Grotifer, and demonstrate the feasibility of implementing Grotifer using existing sub-systems and technologies.

Specifying radial diffusion magnitude is one of the main requirements for physics-based radiation belt models. Yet, radial diffusion quantification remains uncertain. The most commonly used parameterization for the logarithm of radial diffusion magnitude is a linear function of a magnetic index, Kp, with a coarse time resolution of three hours. This work presents alternate linear parameterizations of similar quality for the logarithm of radial diffusion magnitude, considering other magnetic indices and solar wind parameters. Using a time series for the logarithm of electromagnetic radial diffusion magnitude with a 1-minute time resolution, we investigate linear relationships with magnetic indices such as Kp, Hp60, Hp30, AE, SymH, and Dst and solar wind parameters such as solar wind dynamic pressure, solar wind speed and the north‐south component of the interplanetary magnetic field. We find that Kp, Hp60, Hp30, and solar dynamical pressure yield the strongest linear correlation with the logarithm of radial diffusion magnitude. We also provide simple, linear models of the logarithm of radial diffusion magnitude that best fit the time series. This work contributes to improving the time resolution for radial diffusion parameterization and radiation belt models. In particular, it suggests that Hp60 and Hp30 could also be used in place of Kp in the most commonly used Kp‐driven parameterization for radiation belt radial diffusion.