Advancements in ISR Spectra Modeling with Coulomb Collision Effects

The effect of Coulomb collisions produces a significant contribution to the ISR spectra for small aspect angles relative to the magnetic field. Based on single-particle statistics, Milla and Kudeki (2011) developed a model employing a nonlinear Langevin equation that captures this effect on the plasma and calculates the autocorrelation function based on the particle displacements. However, the computational limitations were encountered due to the very short time discretization needed to maintain the stability of the numerical solution. In this work, we present an improved numerical framework for solving the Langevin by using higher-order solvers for stochastic differential equations (SDE). Our approach enhances both the precision of moment estimations and computational efficiency, as shown through weak convergence analysis. Finally, we describe the preliminary results of plasma parameter estimation from this improved numerical framework and its possible extension toward a complete ISR library incorporating the Coulomb Collision effect.