Evolution Of Phase Space Density Research Articles

Diffusion Simulation of Outer Radiation Belt Electron Dynamics Induced by Superluminous L-O Mode Waves

Temporal evolution of outer radiation belt electron dynamics resulting from superluminous L-O mode waves is simulated at L=6.5. Diffusion rates are evaluated and then used as inputs to solve a 2D momentum-pitch-angle diffusion equation, particularly with and without cross diffusion terms. Simulated results demonstrate that phase space density (PSD) of energetic electrons due to L-O mode waves can enhance significantly within 24 h, covering a broader pitch-angle range in the absence of cross terms than that in the presence of cross terms. PSD evolution is also determined by the peak wave frequency, particularly at high kinetic energies. This result indicates that superluminous waves can be a potential candidate responsible for outer radiation belt electron dynamics.

A parametric study on outer radiation belt electron evolution by superluminous R‐X mode waves

A parametric study is presented on the temporal evolution of the phase space density (PSD) of the outer radiation belt energetic electrons driven by the superluminous right‐hand extraordinary (R‐X) mode waves at the location L = 4.5. Bounce‐averaged diffusion rates in pitch angle and momentum are calculated by varying the peak wave frequency, the wave normal angle distribution, and the wave latitudinal distribution. Those diffusion rates are used as inputs to solve a 2‐D momentum‐pitch angle diffusion equation. In particular, three cases are considered: momentum diffusion rates alone, momentum +pitch angle diffusion rates, and momentum +pitch angle +cross diffusion rates. Numerical results show that at 24 h, electron PSDs can enhance substantially for 1 MeV energy at higher pitch angles. Momentum diffusion dominates the dynamic evolution of energetic electrons, whereas the contribution of pitch angle or cross‐diffusion rates is insignificant using the specified wave model. In addition, PSD evolutions are sensitively dependent on the assumed different wave normal angle distributions and tend to be located in lower pitch angles when wave normal angles move to smaller regions. Diffusion coefficients and PSD evolution are largely determined by the wave latitudinal distributions. High‐latitude R‐X mode waves primarily contribute to pitch angle scattering of energetic electrons, whereas equatorial (or lower latitude) R‐X mode waves yield efficient acceleration of electrons. This result supports the previous findings that superluminous R‐X mode waves potentially contribute to dramatic variation in the outer radiation belt electron dynamics under appropriate conditions.

Three‐dimensional simulations of outer radiation belt electron dynamics including cross‐diffusion terms

Using our recently introduced hybrid finite difference method, we develop a three‐dimensional (3‐D) code to solve a fully bounce‐averaged pitch‐angle and energy diffusion equation, including radial diffusion and particularly the cross‐diffusion terms. We show that our 3‐D code can successfully prevent the unstable numerical problems resulting from the large and rapidly varying cross diffusion coefficients. We present one of the first simulations to examine the effects of radial diffusion and chorus‐electron interaction with/without cross diffusion terms on the radiation belt electron dynamics. Simulated results demonstrate that chorus waves may yield significant accelerations of energetic (∼MeV) electrons, leading to peaks in phase space density (PSD), which are subsequently smoothed by inward and outward radial diffusion. Moreover, neglecting cross‐diffusion rates generally produces relatively large overestimates in the PSD evolution, implying that cross diffusion terms are very critical in the 3‐D modeling of radiation belts dynamics. However, test case simulations show that such overestimates are sensitively dependent on the initial conditions together with wave models, deserving further thorough investigations.

Latest progress on interactions between VLF/ELF waves and energetic electrons in the inner magnetosphere

Interactions between very/extremely low frequency (VLF/ELF) waves and energetic electrons play a fundamental role in dynamics occurring in the inner magnetosphere. Here, we briefly discuss global properties of VLF/ELF waves, along with the variability of the electron radiation belts associated with wave-particle interactions and radial diffusion. We provide cases of electron loss and acceleration as a result of wave-particle interactions primarily due to such waves, and particularly some preliminary results of 3D evolution of phase space density from our currently developing 3D code. We comment on the existing mechanisms responsible for acceleration and loss, and identify several critical issues that need to be addressed. We review latest progress and suggest open questions for future investigation.

Collisionless Dynamical Friction and Relaxation in a Simple Drift Wave-Zonal Flow Turbulence

We present a study of the role of zonal flows in relaxation and transport in a reduced model of collisionless ITG turbulence. A fundamentally new constituent in the relaxation dynamics is revealed, namely that ion and electron guiding center motion togather necessitate a radial flux of polarization charge, which in turn exerts a dynamical friction on phase space density evolution. This effect then enters the evolution of 〈δ f 2〉 and the transport dynamics, as described by a Lenard-Balescu type equation. The underlying physics is similar to that which follows from conservation of potential vorticity, albeit now for a phase space fluid, and is not simple shearing or wave packet modulation. Consequences for zonal flow momentum balance are discussed.

Dynamic Evolution of Outer Radiation Belt Electrons due to Whistler-Mode Chorus

Following our preceding work, we perform a further study on dynamic evolution of energetic electrons in the outer radiation belt L = 4.5 due to a band of whistler-mode chorus frequency distributed over a standard Gaussian spectrum. We solve the 2D bounce-averaged Fokker–Planck equation by allowing incorporation of cross diffusion rates. Numerical results show that whistler-mode chorus can be effective in acceleration of electrons at large pitch angles, and enhance the phase space density for energies of about 1 MeV by a factor of 102 or above in about one day, consistent with observation of significant enhancement in flux of energetic electrons during the recovery phase of a geomagnetic storm. Moreover, neglecting cross diffusion often leads to overestimates of the phase space density evolution at large pitch angle by a factor of 5–10 after one day, with larger errors at smaller pitch angle, suggesting that cross diffusion also plays an important role in wave—particle interaction.

Tomographic measurements of longitudinal phase space density

Tomography — the reconstruction of a two-dimensional image from a series of its one-dimensional projections — is now a very broad topic with a wealth of algorithms for the reconstructions of both qualitative and quantitative images. One of the simplest algorithms has been modified to take into account the nonlinearity of large-amplitude synchrotron motion in a particle accelerator. This permits the accurate reconstruction of longitudinal phase space density from one-dimensional bunch profile data. The algorithm was developed in Mathematica™ in order to exploit the extensive built-in functions and graphics. Subsequently, it has been recoded in Fortran 90 with the aim of reducing the execution time by at least a factor of one hundred. The choice of Fortran 90 was governed by the desire ultimately to exploit parallel architectures, but sequential compilation and execution have already largely yielded the required gain in speed. The use of the method to produce longitudinal phase space plots, animated sequences of the evolution of phase space density and to estimate accelerator parameters is presented. More generally, the new algorithm constitutes an extension of computerized tomography which carers for nonrigid bodies whose projections cannot be measured simultaneously.