Geoscience Reference
In-Depth Information
Fig. 9. Collisional incoherent scatter spectra as a function of magnetic aspect angle and
Doppler frequency for
λ
B
=
3 m (e.g., Jicamarca radar Bragg wavelength). An O+ plasma is
considered (from Milla & Kudeki, 2011).
In summary, the single-electron ACF's needed for ISR spectral calculations cannot be obtained
from Brownian motion model (45) at small aspect angles. This necessitates the construction
of a numerical “library” compiled from Monte Carlo simulations based on the Langevin
equation. The fundamental reason for this is the deviation of the electron displacements
parallel to
B
from Gaussian statistics, despite the fact that displacement variances are
well modeled by the Brownian model. Certainly, a non-Gaussian process cannot be fully
characterized by a model that specifies its first and second moments only; this is particularly
true for the estimation of the characteristic function of the process
e
j
k
·
Δ
r
e
that depends on all
the moments of the process distribution.
8. ISR spectrum for the magnetized ionosphere including Coulomb collision
effects
The general framework of incoherent scatter theory formulates the spectrum in terms of the
Gordoyev integrals or the corresponding single-particle ACFs for each plasma species. As
discussed above, in the case of Coulomb collisions, the single-ion ACF can be approximated
using the analytical expression (45). However, in the case of the electrons, the approximation
of the electron motion as a Brownian process is not accurate, and thus, Monte Carlo
calculations were needed to model single-electron ACFs and Gordeyev integrals for different
sets of plasma parameters.
