Terms Of Adiabatic Invariants Research Articles

An Empirical Model of the Equatorial Electron Pitch Angle Distributions in Earth's Outer Radiation Belt

AbstractIn this study, we present an empirical model of the equatorial electron pitch angle distributions (PADs) in the outer radiation belt based on the full data set collected by the Magnetic Electron Ion Spectrometer (MagEIS) instrument onboard the Van Allen Probes in 2012–2019. The PADs are fitted with a combination of the first, third and fifth sine harmonics. The resulting equation resolves all PAD types found in the outer radiation belt (pancake, flat‐top, butterfly and cap PADs) and can be analytically integrated to derive omnidirectional flux. We introduce a two‐step modeling procedure that for the first time ensures a continuous dependence on L, magnetic local time and activity, parametrized by the solar wind dynamic pressure. We propose two methods to reconstruct equatorial electron flux using the model. The first approach requires two uni‐directional flux observations and is applicable to low‐PA data. The second method can be used to reconstruct the full equatorial PADs from a single uni‐ or omnidirectional measurement at off‐equatorial latitudes. The model can be used for converting the long‐term data sets of electron fluxes to phase space density in terms of adiabatic invariants, for physics‐based modeling in the form of boundary conditions, and for data assimilation purposes.

Calculation of Last Closed Drift Shells for the 2013 GEM Radiation Belt Challenge Events

AbstractRadiation belt behavior is often analyzed in terms of adiabatic invariants, of which the third roughly characterizes the radial distance of particle drift shells. The outermost, or last closed drift shell, can be an important boundary for numerical modeling, especially for drift‐averaged treatments such as three‐dimensional diffusion codes. Here we discuss calculation of the last closed drift shell, using the widely used International Radiation Belt Environment Modeling (IRBEM) Library, the LanlGeoMag code, and a guiding center code named AFRL‐Shell, in conjunction with a variety of current magnetic field models. We present results for the four events in 2013, comprising the radiation belt challenge organized by the Quantitative Assessment of Radiation Belt Modeling focus group of the Geospace Environment Modeling (GEM) program.

Three‐dimensional radiation belt simulations in terms of adiabatic invariants using a single numerical grid

The dynamics of electrons in the Earth's radiation belts can be described by the Fokker‐Planck equation, which includes radial diffusion, and local energy and pitch angle diffusion. Previously, the Versatile Electron Radiation Belt (VERB) code utilized two grids to solve the Fokker‐Planck equation; one grid, which keeps the first and second adiabatic invariants constant, was used for the computation of the radial diffusion, and the other grid, orthogonal in energy and pitch angle at each fixed radial distance, was used for the computation of energy diffusion, pitch angle diffusion, and mixed energy and pitch angle diffusion. At each time step, the results were interpolated between the two grids. In the current work, we present a new method for numerical solution of the Fokker‐Planck diffusion equation written in terms of adiabatic invariants using a single numerical grid. The one‐grid solution allows us to eliminate the time‐consuming interpolation. The solution in terms of adiabatic invariants implicitly accounts for conservation of phase space density during adiabatic magnetic field fluctuations. The Fokker‐Planck equation written in terms of adiabatic invariants is easier to solve with a realistic magnetic field configuration, compared to the Fokker‐Planck equation written in terms of energy and pitch angle. To validate the approach, we compare a 2‐D simulation at fixed L* in terms of the adiabatic invariants (μ, K) with a simulation on a grid orthogonal in energy and pitch angle. Both simulations produce essentially the same result. Accurate simulations on the (μ, K) grid require resolution of 601 × 601 points, while only 101 × 101 grid points are sufficient for performing an accurate simulation on the grid orthogonal in energy and pitch angle. We propose a new invariant V ≡ μ ⋅ (K + 0.5)2 with the new grid orthogonal in (V, K, L*), that is more convenient for 2‐D and 3‐D simulations. The 2‐D and 3‐D simulations on the (V, K, L*) grid produce the same result as the two‐grid method with a grid resolution of only 101 × 101 points in V and K.

The radial gradient of relativistic electrons at geosynchronous orbit

Earth's outer electron radiation belt is a highly dynamic region, driven externally by the solar wind and controlled within the magnetosphere by numerous source and loss processes. Critical to assessing the importance of the different source and loss processes and to developing accurate physics‐based models of the radiation belts is knowing phase space density and its radial gradient in terms of adiabatic invariants. In this paper, we demonstrate a new technique for determining the radial gradient of relativistic electron phase space density at geosynchronous orbit. This technique utilizes the fact that the GOES geosynchronous satellites are located at different geomagnetic latitudes because of their separation in longitude, even though both are located on the geographic equator. From simultaneous measurements at different geomagnetic latitudes, and therefore in different L shells, we are able to obtain the local radial gradient of phase space density. We have restricted these initial calculations to a single value of magnetic moment (M = 6000 MeV/G) and to equatorially mirroring particles. In order to minimize the sensitivity of our results to the magnetic field model used, we have analyzed data from a time period with quiet geomagnetic conditions, when the relativistic electron flux was elevated and steady. We find that during this time period the radial gradient of phase space density was positive. This indicates that the direction of radial diffusion was inward, transporting electrons from outside to within geosynchronous orbit.

Regular and chaotic aspects of charged particle motion in a magnetotail‐like field with a neutral line

The motion of charged particles is studied numerically and analytically using a test particle approach. Acceleration near the X‐type neutral line is described in terms of adiabatic invariants and separatrix crossings. The relation between regular and chaotic properties of the process is discussed for a realistic source in the plasma mantle.