Understanding the Effects of Peaks in the Electron Velocity Spectrum on the Incoherent Scatter Plasma Line

Abstract:

We explain the surprising features in the power of plasma line spectra observed by Djuth et al., 2018 (DCZ) using the Arecibo Incoherent scatter radar. They identified the features as the result of ionization by lines in the solar spectrum, and concluded that two properties of the observations are difficult to explain, the frequency location of the features and the observation of narrow valleys as well as peaks. They show evidence that the latter vary in frequency as $\cos^{.97} \gamma$ where $\gamma$ is angle of the observation to the magnetic field.

The population of electrons in the daytime ionospheric plasma has of three parts. The thermal or Maxwellian part is the largest, providing nearly all of the restoring force for the plasma oscillation. Next is the photo electron tail, containing electrons with speeds necessary to induce charge fluctuations (charge dressing) necessary to excite the plasma waves at the relevant frequencies. Last is the several narrow peaks that result directly from the ionization process by solar EUV, providing the the electrons that make up the tail when damped, and, as we show, increasing the damping of the generated plasma waves, creating the valleys that DCZ describe. They also create small peaks when $\gamma \neq 0$.

Using the solution of Hagfors (1989), allowing an arbitrary electron velocity density function, we discuss two simple limiting cases useful for an intuitive understanding, and show examples of the general case computed by numerical integration. First, when $\gamma = 0$, an approximate analytic solution showing valleys (but no peaks) is simple, especially since the damping depends only on the imaginary part of certain integrals in the equations. Second, an inspection of the equations shows that the angular frequency of the solution depends on $\cos \gamma$ when the gyro frequency is large. In the general case, peaks are also possible, and the valleys weaken as $\gamma$ increases.

We show that the ratio of the depth of a valley relative to the surrounding spectrum is equal to the square root of ratio between the height of the peak and the the surrounding tail.

Djuth, Carlson, and Zhang, (2018) Incoherent radar studies of daytime plasma lines, Earth, Moon, and Planets, 121 (1-2), 13-43.

Hagfors (1989), Incoherent scatter radar observations of the ionosphere, Handbook for MAP, 30, ch 10, 333-364