On a proper electron collision frequency for a Fokker–Planck collision model with Jicamarca applications

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Recently, Sulzer and Gonzalez (J. Geophys. Res. 104 (22) (1999) 22, 535) showed that the previously neglected effect of electron–electron and electron–ion Coulomb collisions has a significant impact on determining the incoherent scatter autocorrelation functions (IS-ACFs) observed at Jicamarca. Considering the physically and mathematically complicated nature of Coulomb collisions, they evaluated these effects with lengthy numerical computations which actually simulated the random electron trajectories for different possible electron velocities and for different state parameters of the medium, in a Monte Carlo-like simulation. Their conclusions have been readily accepted by the IS community for Jicamarca pointing angles very close to perpendicular to the magnetic field, but a controversy arose when the application of their results to angles around 3 ∘ off perpendicular to the magnetic field implied electron effective collision frequencies larger than the accepted values published in existing literature. Here we have taken a more analytical approach by using a simplified Fokker–Planck collision model with a velocity-independent collision frequency. We can reproduce the results of Sulzer and Gonzalez with this simplified analytical model, provided that an effective, velocity-independent collision frequency is used whose value depends upon the angle between the radar beam direction and the magnetic field. The physical reason for this seemingly strange result is that, for incoherent scatter, the relative importance of the Fokker–Planck friction and velocity diffusion terms changes with this angle. Furthermore, we estimated values for the electron frictional collision coefficient based on the more precise velocity-dependent one and found that, indeed, the large values are justified, supporting the previously controversial results of Sulzer and Gonzalez (1999).