ISR Spectra Estimates via Higher-Order Stochastic Modeling of Coulomb Collisions

The Incoherent Scatter Radar (ISR) technique is a widely used diagnostic method in ionospheric research, providing quantitative estimates of plasma state parameters. However, measurements at the Jicamarca Radio Observatory (JRO) have exhibited a documented discrepancy between radar-derived electron-to-ion temperature ratio and in situ measurements. This gap is attributed to Coulomb collisions affecting the spectrum at small aspect angles relative to the geomagnetic field. Based on single-particle statistics, Milla and Kudeki (2011) developed a model that employs a nonlinear Langevin equation to capture this effect in the plasma. Incorporating these collisions into theoretical plasma models has been computationally expensive because the Langevin equation framework requires a very short time discretization required to maintain the stability of the numerical solution. This work optimizes the numerical foundations 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. We present a first version of an ISR spectral library for JRO that successfully incorporates Coulomb collision effects within this high-performance numerical framework.