A novel technique for rapid L^* calculation using UBK coordinates

Abstract

[1] The magnetic drift invariant (L * ) is an important quantity used for tracking and organizing particle dynamics in the radiation belts, but its accurate calculation has been computationally expensive in the past, thus making it difficult to employ this quantity in real-time space weather applications. In this paper, we propose a new, efficient method to calculate L * using the principle of energy conservation. This method uses Whipple's (U, B, K) coordinates to quickly and accurately determine trajectories of particles at the magnetic mirror point from two-dimensional isoenergy contours. The method works for any magnetic field configuration and is able to accommodate constant electric potential along field lines. We compare the result of this method with those of International Radiation Belt Environment Modeling library (IRBEM-LIB) to demonstrate the performance of this new method. The method requires a preparation step, and thus may not be the optimal method for a single trajectory calculation; however, it presents a huge performance gain when adiabatically propagating a large population of particles in a given magnetic field configuration.

An Energetic Electron Flux Dropout Due to Magnetopause Shadowing on 1 June 2013

“…To examine possible magnetopause shadowing, we investigate drift shells using CIMI with the TS04 model. Drift shells are calculated finding the iso‐contours of the Hamiltonian H at a given time as done by Min et al (, ) using where Φ is the electrostatic potential that we omit as done in Kang et al (). This approximation is valid because convective potentials are much less than 226 keV for this particular event and therefore do not change drift shells significantly; this results in drift shells that are simply a function of B m only.…”

“…To examine possible magnetopause shadowing, we investigate drift shells using CIMI with the TS04 model. Drift shells are calculated finding the iso-contours of the Hamiltonian H at a given time as done by Min et al (2013aMin et al ( , 2013b using…”

A novel technique for rapid L∗ calculation: Algorithm and implementation

“…Second, the functional relationship between B m and K is approximated before the L ∗ calculation (Sheldon and Gaffey [] used a polynomial expression and Min et al . [] used spline interpolation), where B m is the magnitude of the magnetic field at a mirror point s m and K is the modified invariant [ Roederer , ] In this expression, s m′ denotes the conjugate mirror point to s m so that B ( s m′)= B ( s m )≡ B m , and the integration is made along the guiding field line s . Once the model coefficients are known, B m ( K ) or K ( B m ) is approximated from the functional form whenever they are needed, avoiding the repeated expensive field line tracing.…”

“…This approach ensures that the calculated trajectory is closed if the particle's drift shell is so, regardless of the grid resolution. Second, the functional relationship between B m and K is approximated before the L calculation (Sheldon and Gaffey [1993] used a polynomial expression and Min et al [2013] used spline interpolation), where B m is the magnitude of the magnetic field at a mirror point s m and K is the modified invariant [Roederer, 1970]…”

“…

1] Computing the magnetic drift invariant, L , rapidly and accurately has always been a challenge to magnetospheric modelers, especially given the importance of this quantity in the radiation belt community. Min et al (2013) proposed a new method of calculating L using the principle of energy conservation. Continuing with the approach outlined therein, the present paper focuses on the technical details of the algorithm to outline the implementation, systematic analysis of accuracy, and verification of the speed of the new method.

…”