A Multiion, Flux‐Corrected Transport Based Hydrodynamic Model for the Plasmasphere Refilling Problem

Abstract

The objective of this paper is the application of a newly developed flux-corrected transport based hydrodynamic solution methodology to the plasmasphere refilling problem following a geomagnetic storm. The flux-corrected transport method is extremely well-suited to the solution of nonlinear partial differential equations with shocks and discontinuities. In this solution methodology, every ion species is modeled as two separate fluids originating from the northern and southern hemispheres. We present refilling results that include three ion (H + , He + , and O + ) species and two neutrals (H and O). We believe that with additional modifications, the model can be adapted to the solution of other ionosphere-magnetosphere coupling problems. Plain Language SummaryThe paper applies a newly developed multispecies hydrodynamic model to the plasmasphere refilling problem following geomagnetic storms. We believe that with additional development, the model can be applied to other ionosphere-magnetosphere coupling problems. Key Points:• Developed a hydrodynamic model for the plasmasphere refilling problem following geomagnetic storms • The model is based on the well-known flux-corrected transport method • The model is applied to the plasmasphere refilling problem for three ion species and two neutrals along the L = 4 line Figure 9. (a) Ambipolar electric field profile after 20 min. (b) Ambipolar electric field profile after 2 hr. (c) Ambipolar electric field profile after 15 hr. (d) Ambipolar electric field profile after 40 hr.

A Semikinetic Model of Plasmasphere Refilling Following Geomagnetic Storms and Comparison With Hydrodynamic Results

“…The Coulomb collision mean free paths shown in Tables 1 to 3 respectively during early to middle hours of refilling are significantly larger than the length scale of the hydrodynamic/electrostatic discontinuities in the ion concentration profiles observed during those hours (Chatterjee, 2018;Chatterjee & Schunk, 2019, 2020. As a result, the Coulomb collisions could not have played a thermalizing role, thus bringing to question the inherent assumption of Maxwellian velocity distribution function needed in the justification of the hydrodynamic model and presenting a rationale for kinetic modeling.…”

“…It was also seen (Chatterjee, 2018;Chatterjee & Schunk, 2019, 2020 that even 15 hr after the onset of the refilling process, that there were shocks and discontinuities in the solution profile, which were in part hydrodynamic and in part electrostatic (Chatterjee, 2018;Chatterjee & Schunk, 2019, 2020Rasmussen & Schunk, 1988;Singh et al, 1986). The Coulomb collision mean free paths, estimated at representative latitude points after 30 min, 2, 15, and 40 hr (the end of refilling), are presented in Tables 1 to 4, respectively.…”

“…Diffusion-dominated models, where the nonlinear inertial terms in the plasma transport equations are ignored and thus only low-speed, subsonic flow can be modeled (Bailey et al, 1997;Maruyuma et al, 2016;Schunk et al, 2004;Young et al, 1980). B. Hydrodynamic models, where the nonlinear inertial terms in the plasma transport equations are retained (Banks et al, 1971;Chatterjee, 2018;Chatterjee & Schunk, 2019, 2020Huba & Joyce, 2000;Khazanov et al, 1984;Krall & Huba, 2013Rasmussen & Schunk, 1988;Singh et al, 1986).…”

The development and validation of a ‘flux-corrected transport’ based solution methodology for the plasmasphere refilling problem following geomagnetic storms

“…These benchmarks are simplified versions of the plasmasphere refilling problem, but correctly predict high supersonic velocities at the onset of refilling and refilling times consistent with the literature (Singh et al 1986), along with correct analytical solution for the concentration and drift velocity in the steady-state. The model has been subsequently applied to the multi-ion refilling problem in Chatterjee (2018) and Chatterjee and Schunk (2019). The ultimate objective of this research is the development of a 3D multi-ion model for ionosphere-magnetosphere coupling problems in open and closed magnetic field line geometries.…”

“…In Chatterjee's doctoral dissertation (Chatterjee 2018), an FCT-based solution methodology was developed independently of Singh et al (1986) and Rasmussen and Schunk (1988), and this solution methodology has the capability of accommodating multiple ions and neutrals. The refilling results involving multiple ions and neutrals are presented in Chatterjee (2018) and Chatterjee and Schunk (2019), but here in this paper, the basic algorithmic details of the solution methodology developed in Chatterjee (2018) are provided along with the validating analytical benchmarks that are close approximations of the refilling problem. The validation benchmarks and results described in the following sections involve only H + ions.…”