Quasi-linear simulations of inner radiation belt electron pitch angle and energy distributions

“Peculiar” or “butterfly” electron pitch angle distributions (PADs), with minima near 90°, have recently been observed in the inner radiation belt. These electrons are traditionally treated by pure pitch angle diffusion, driven by plasmaspheric hiss, lightning-generated whistlers, and VLF transmitter signals. Since this leads to monotonic PADs, energy diffusion by magnetosonic waves has been proposed to account for the observations. We show that the observed PADs arise readily from two-dimensional diffusion at L = 2, with or without magnetosonic waves. It is necessary to include cross diffusion, which accounts for the relationship between pitch angle and energy changes. The distribution of flux with energy is also in good agreement with observations between 200 keV and 1 MeV, dropping to very low levels at higher energy. Thus, at this location radial diffusion may be negligible at subrelativistic as well as ultrarelativistic energy

The origin of Jupiter's outer radiation belt

The intense inner radiation belt at Jupiter (>50 MeV at 1.5 RJ) is generally accepted to be created by radial diffusion of electrons from further away from the planet. However, this requires a source with energies that exceed 1 MeV outside the orbit of the moon Io at 5.9 RJ, which has never been explained satisfactorily. Here we test the hypothesis that this source population could be formed from a very soft energy spectrum, by particle injection processes and resonant electron acceleration via whistler mode chorus waves. We use the British Antarctic Survey Radiation Belt Model to calculate the change in the electron flux between 6.5 and 15 RJ; these are the first simulations at Jupiter combining wave particle interactions and radial diffusion. The resulting electron flux at 100 keV and 1 MeV lies very close to the Galileo Interim Radiation Electron model spectrum after 1 and 10 days, respectively. The primary driver for the increase in the flux is cyclotron resonant acceleration by chorus waves. A peak in phase space density forms such that inside L≈9 radial diffusion transports electrons toward Jupiter, but outside L≈9 radial diffusion acts away from the planet. The results are insensitive to the softness of the initial energy spectrum but do depend on the value of the flux at the minimum energy boundary. We conclude by suggesting that the source population for the inner radiation belt at Jupiter could indeed be formed by wave-particle interactions

Electron losses from the radiation belts caused by EMIC waves

Electromagnetic Ion Cyclotron (EMIC) waves cause electron loss in the radiation belts by resonating with high energy electrons at energies greater than about 500 keV. However, their effectiveness has not been fully quantified. Here we determine the effectiveness of EMIC waves by using wave data from the fluxgate magnetometer on CRRES to calculate bounce averaged pitch angle and energy diffusion rates for L* =3.5 - 7 for five levels of Kp between 12 - 18 MLT. To determine the electron loss EMIC diffusion rates were included in the BAS Radiation Belt Model together with whistler mode chorus, plasmaspheric hiss and radial diffusion. By simulating a 100 day period in 1990 we show that EMIC waves caused a significant reduction in the electron flux for energies greater than 2 MeV but only for pitch angles lower than about 60°.The simulations show that the distribution of electrons left behind in space looks like a pancake distribution. Since EMIC waves cannot remove electrons at all pitch angles even at 30 MeV, our results suggest that EMIC waves are unlikely to set an upper limit on the energy of the flux of radiation belt electrons

Quantifying hiss-driven energetic electron precipitation: A detailed conjunction event analysis

Abstract We analyze a conjunction event between the Van Allen Probes and the low-altitude Polar Orbiting Environmental Satellite (POES) to quantify hiss-driven energetic electron precipitation. A physics-based technique based on quasi-linear diffusion theory is used to estimate the ratio of precipitated and trapped electron fluxes (R), which could be measured by the two-directional POES particle detectors, using wave and plasma parameters observed by the Van Allen Probes. The remarkable agreement between modeling and observations suggests that this technique is applicable for quantifying hiss-driven electron scattering near the bounce loss cone. More importantly, R in the 100-300 keV energy channel measured by multiple POES satellites over a broad L magnetic local time region can potentially provide the spatiotemporal evolution of global hiss wave intensity, which is essential in evaluating radiation belt electron dynamics, but cannot be obtained by in situ equatorial satellites alone. Key Points Measured and calculated hiss Bw from POES electron measurements agree well Electron ratio measured by POES is able to estimate hiss wave intensity This technique can be used to provide global hiss wave distributio

Electron acceleration at Jupiter: input from cyclotron-resonant interaction with whistler-mode chorus waves

Jupiter has the most intense radiation belts of all the outer planets. It is not yet known how electrons can be accelerated to energies of 10 MeV or more. It has been suggested that cyclotron-resonant wave-particle interactions by chorus waves could accelerate electrons to a few MeV near the orbit of Io. Here we use the chorus wave intensities observed by the Galileo spacecraft to calculate the changes in electron flux as a result of pitch angle and energy diffusion. We show that, when the bandwidth of the waves and its variation with L are taken into account, pitch angle and energy diffusion due to chorus waves is a factor of 8 larger at L-shells greater than 10 than previously shown. We have used the latitudinal wave intensity profile from Galileo data to model the time evolution of the electron flux using the British Antarctic Survey Radiation Belt (BAS) model. This profile confines intense chorus waves near the magnetic equator with a peak intensity at ∼5° latitude. Electron fluxes in the BAS model increase by an order of magnitude for energies around 3 MeV. Extending our results to L = 14 shows that cyclotron-resonant interactions with chorus waves are equally important for electron acceleration beyond L = 10. These results suggest that there is significant electron acceleration by cyclotron-resonant interactions at Jupiter contributing to the creation of Jupiter's radiation belts and also increasing the range of L-shells over which this mechanism should be considered

Minimum Induced Drag for Tapered Wings Including Structural Constraints

For a wing in steady level flight, the lift distribution that minimizes induced drag depends on a tradeoff between wingspan and wing-structure weight. In 1933, Prandtl suggested that tapered wings have an advantage over rectangular wings due to this tradeoff. However, Prandtl’s solutions were obtained using assumptions that correspond to rectangular wings. Therefore, his claim was not analytically proven by his 1933 publication. Here, an approach similar to Prandtl’s is taken with more general approximations that apply to wings of arbitrary planform. This more general development is used to study Prandtl’s claim about tapered wings. Closed-form solutions for the optimum wingspan and corresponding induced drag are presented for wings having elliptic and linearly-tapered planforms with constraints of fixed wing loading and maximum stress. It is shown that induced drag is minimized with a triangular planform, which gives a reduction in induced drag of up to 24.44% over the rectangular planform and up to 11.71% over the elliptic planform. Numerical solutions for the lift distributions that minimize induced drag for each planform are also presented. It is shown that the optimum lift distribution produces up to 5.94% less induced drag than the elliptic lift distribution when the triangular planform is used

Chorus acceleration of radiation belt relativistic electrons during March 2013 geomagnetic storm

Abstract The recent launching of Van Allen probes provides an unprecedent opportunity to investigate variations of the radiation belt relativistic electrons. During the 17-19 March 2013 storm, the Van Allen probes simultaneously detected strong chorus waves and substantial increases in fluxes of relativistic (2 - 4.5 MeV) electrons around L = 4.5. Chorus waves occurred within the lower band 0.1-0.5fce (theelectron equatorial gyrofrequency), with a peak spectral density ∼10-4 nT 2/Hz. Correspondingly, relativistic electron fluxes increased by a factor of 102-103 during the recovery phase compared to the main phase levels. By means of a Gaussian fit to the observed chorus spectra, the drift and bounce-averaged diffusion coefficients are calculated and then used to solve a 2-D Fokker-Planck diffusion equation. Numerical simulations demonstrate that the lower-band chorus waves indeed produce such huge enhancements in relativistic electron fluxes within 15 h, fitting well with the observation. Key Points Initial RBSP correlated data of chorus waves and relativistic electron fluxes A realistic simulation to examine effect of chorus on relativistic electron flux Chorus yields huge increases inelectron flux rapidly, consistent with data

Event-specific chorus wave and electron seed population models in DREAM3D using the Van Allen Probes

Abstract The DREAM3D diffusion model is applied to Van Allen Probes observations of the fast dropout and strong enhancement of MeV electrons during the October 2012 double-dip storm. We show that in order to explain the very different behavior in the two dips, diffusion in all three dimensions (energy, pitch angle, and Lo) coupled with data-driven, event-specific inputs, and boundary conditions is required. Specifically, we find that outward radial diffusion to the solar wind-driven magnetopause, an event-specific chorus wave model, and a dynamic lower-energy seed population are critical for modeling the dynamics. In contrast, models that include only a subset of processes, use statistical wave amplitudes, or rely on inward radial diffusion of a seed population, perform poorly. The results illustrate the utility of the high resolution, comprehensive set of Van Allen Probes\u27 measurements in studying the balance between source and loss in the radiation belt, a principal goal of the mission. Key Points DREAM3D uses event-specific driving conditions measured by Van Allen Probes Electron dropout is due to outward radial diffusion to compressed magnetopause Event-specific chorus and seed electrons are necessary for the enhancement