Determination of equilibrium electron temperature and times using an electron swarm model with BOLSIG+ calculated collision frequencies and rate coefficients

Abstract

Electromagnetic pulse (EMP) events produce low‐energy conduction electrons from Compton electron or photoelectron ionizations with air. It is important to understand how conduction electrons interact with air in order to accurately predict EMP evolution and propagation. An electron swarm model can be used to monitor the time evolution of conduction electrons in an environment characterized by electric field and pressure. Here a swarm model is developed that is based on the coupled ordinary differential equations (ODEs) described by Higgins et al. (1973), hereinafter HLO. The ODEs characterize the swarm electric field, electron temperature, electron number density, and drift velocity. Important swarm parameters, the momentum transfer collision frequency, energy transfer collision frequency, and ionization rate, are calculated and compared to the previously reported fitted functions given in HLO. These swarm parameters are found using BOLSIG+, a two term Boltzmann solver developed by Hagelaar and Pitchford (2005), which utilizes updated cross sections from the LXcat website created by Pancheshnyi et al. (2012). We validate the swarm model by comparing to experimental effective ionization coefficient data in Dutton (1975) and drift velocity data in Ruiz‐Vargas et al. (2010). In addition, we report on electron equilibrium temperatures and times for a uniform electric field of 1 StatV/cm for atmospheric heights from 0 to 40 km. It is shown that the equilibrium temperature and time are sensitive to the modifications in the collision frequencies and ionization rate based on the updated electron interaction cross sections.

Comparison of equilibrium ohmic and nonequilibrium swarm models for monitoring conduction electron evolution in high‐altitude EMP calculations

“…It has been shown previously that the equilibrium electron temperature, U eq , increases appreciably with increasing height for a given electric field, E [ Longmire and Longley , ; Pusateri et al , ]. This means that there is a direct relationship between the equilibrium U eq and the reduced electric field, E / N , where N is the atmospheric number density [ Pusateri et al , ]. It has also been reported that the ionization rate increases significantly with increasing U eq [ Higgins et al , ; Pusateri et al , ].…”

“…Here it is important to consider a complete description of the time‐dependent conduction electron distribution for the conduction current calculation. Thus, we focus on calculating the conduction current density through the use of a nonequilibrium electron swarm model as presented in Pusateri et al []. We present the final form of the equations solved in the CHAP‐LA code as well as the procedure for integrating the ohmic and swarm conduction electron model into CHAP‐LA in sections 2.1 and 2.2, respectively.…”

“…The electron swarm model from Pusateri et al [] is the swarm conduction current model used for this analysis. The electron swarm model evaluates the conduction current as a function of time using .…”

“…The electron swarm model evaluates the conduction current as a function of time using . A few modifications were made to the set of ODEs presented in Pusateri et al [] in order to properly integrate the swarm model code into CHAP‐LA. The primary current density J p was included in the time derivative of the electric field.…”

“…v d , r , v d , θ , and v d , ϕ are the r , θ , and ϕ components of the drift velocity, respectively. Including the equations to track N + and N − , as well as including the other additional terms, has no effect on the equilibrium calculations used for validation in Pusateri et al [].…”