# Plasma Irregularities In The Lower Ionosphere

Yurij Kyzyurov

Main Astronomical Observatory NASU, 27 Akademika Zabolotnogo Str., 03680 Kiev, Ukraine

Abstract. The way of obtaining an analytic expression for the spectrum of plasma irregularities resulted from turbulent

mixing of the lower ionosphere is described in this report. Using the expression, possible changes in the irregularity

spectrum and in the level of plasma density fluctuations under changes from daytime to nighttime ionosphere conditions

are analyzed. It is shown that the fluctuation level and the slope of the spectrum have to be larger at night.

Keywords: Ionosphere; Plasma; Ionospheric irregularities; Turbulence.

PACS: 94.05-a; 94.05Lk; 94.20.-y; 94.20.Vv; 94.20.wg

INTRODUCTION

The ionosphere can be considered as a mixture of ion-electron plasma and neutral gas. In its lower part the

plasma is a passive contaminant involved in motions of the neutral gas. Evidently motions of the gas play a very

important role in dynamics of the ionosphere especially below the turbopause level (an altitude in the region 100-

120 km) [1]. In particular, random plasma irregularities at these altitudes are generated by neutral air turbulence [1-

5]. Because of the strong collisional damping in the lower ionosphere, not always generation of fluctuations in

plasma density there may be explained by theory of plasma instabilities [4, 6]. Plasma irregularities induced by

neutral turbulence in the lower ionosphere were observed during radar and in situ rocket experiments (see, e.g., [1-

5]). Theory of the plasma irregularities is presented in [1], where, however, their spectrum is not discussed.

The aim of this report is to obtain an expression for the spectrum of plasma irregularities resulted from turbulent

mixing in the lower ionosphere, and, using the expression, to analyze changes in the spectrum and in the level of

fluctuations under changes from day-time to night-time ionosphere conditions. For the fixed height h in the

ionosphere, local values of the mean plasma density N0 and the length-scale LN of the gradient in N0 at night are

smaller than those during the day-time [7].

An expression for the irregularity spectrum was derived in [4]. Unlike [4], where the ionospheric irregularities

induce by neutral turbulence are presented as superposition of random plasma waves in the absence of gradient in

N0, a situation with conventional fluid turbulence creating irregularities through mixing of plasma in the lower

ionosphere in the presence of the gradient will be considered here. In this work an approach developed for

description of plasma irregularities in the mid-latitude sporadic-E [8] will be used.

DERIVATION OF EQUATION DESCRIBING GENERATION OF PLASMA

FLUCTUATIONS IN THE IONOSPHERE BELOW THE TURBOPAUSE

To describe turbulent mixing in the lower ionosphere, a three fluid model is usually adopted [1, 4, 8]. Since the

charged particles (ions and electrons) are passive contaminant, they have no influence on motions of the neutral gas,

and the velocity field U(x, t) of the gas may be treated as a known function of position and time. We assume that the

gas is incompressible one, and hence U satisfies ∇⋅U=0. The present model is based on the continuity and

momentum equations for both the ions and electrons, along with the quasi-neutrality.

where subscript s denotes the species (s≡ e, i for electron or ion, respectively), qs is the particle charge (qi= –qe= e),

ms is the particle mass, vs is the velocity, E is the electric field, b=B/B is the unit vector along the geomagnetic field,

Ωs=qsB/msc is the charged particle gyro-frequency, vTs is the particle thermal velocity, νs is the collision frequency of

the electrons or ions with neutrals (Coulomb collisions do not play a significant role because the gas is only very

weakly ionized in the altitudes of interest).

The system of equations (1)-(2) is valid for sufficiently slow processes, when the time-scales are larger than the

mean time between collisions of ions with neutrals t>>νi

–1, and the length-scales are larger than the ion mean free

path l>>Λi. The turbulent mixing in the lower ionosphere satisfies these conditions.

Taking into account that below the turbopause Ωi<<νi, and if the only electric field considered is that required to

prevent charge separation (due to E electrons tend to follow ions), then after eliminating E from (2), we can obtain

the velocity of local ion drift (or the plasma drift as a whole) induced by the gas motions [1]

here DA is the ambipolar diffusion coefficient.

Substitution (3) in (1) gives an equation that describes the evolution of plasma density if the plasma is a passive

contaminant embedded in the gas flow

In the case of turbulent flow, the velocity field U includes a random ingredient whose statistical properties are

assumed known. Such a velocity field generates random perturbations of plasma density. The velocity and plasma

density fields may be separated into mean and fluctuating parts: . Lengthand

time-scales of u and N1 are small compared with the scales of variation of mean quantities u0 and N0. Restricting

the consideration to an inertial interval of the turbulence, one can say about homogeneous and isotropic turbulence

[9]. Using properties of homogeneity and isotropy of the turbulence, along with the mentioned features of the U- and

N-fields, from (4) we derive an equation describing generation of plasma fluctuations by turbulent velocity field u:

Here LN=N0|∇N0|–1 is the length-scale of gradient in N0, n is the unit vector along this gradient, δN=N1/N0 is the

relative fluctuations in plasma (electron) density. Just the relative electron-density fluctuations are measured during

rocket experiments [2, 3].

The equation (5) describes the formation of plasma fluctuations with length-scales l<LN. It may be seen from (5)

that the first term on the right-hand side is more important for the fluctuations of larger length-scales l>Ωiνi

–1LN,

whereas the second for smaller ones l<Ωiνi

–1LN. It means that the process in which the neutral turbulence in

conjunction with the mean plasma-density gradient produce plasma fluctuations by mixing regions of high and low

density dominates at larger length-scales, while the interaction of plasma embedded in the turbulent motions of gas

with geomagnetic field is more important for smaller ones.

SPECTRA OF PLASMA IRREGULARITIES IN THE LOWER IONOSPHERE

The Fourier transform of (5) in space and time is

where δNkω=δN(k, ω), ukω=u(k, ω), k″= k – k′, and ω″= ω – ω′.

The convolution term on the left-hand side of (6) represents the contribution of mode interaction in the process of

plasma fluctuation generation. If we take it into account through the coefficient of turbulent diffusion DT, then

CONCLUSION

It is shown with the use of (13) – (15) that under change in the ionosphere conditions from day to night, the RMS

level of plasma-density fluctuations in the irregularities smaller than 400 m generated by the neutral turbulence may

change from 0.03 to 0.05, and the power index p (if the spectrum is approximated by a power law k–p) from 1.9 to

2.25, i.e., the spectrum slope has to increase. The obtained results do not contradict to data of observations [2, 3].

Thus the plasma irregularities in the lower ionosphere have to respond to changes in the ionospheric parameters.

REFERENCES

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2. O. Royrvik and L. G. Smith, J. Geophys. Res. 89, 9014-9022 (1984).

3. K. Schlegel, J. Atmos. Terr. Phys. 54, 715-723 (1992).

4. A. V. Gurevich, N. D. Borisov and K. P. Zybin, J. Geophys. Res. 102, 379-388 (1997).

5. K. Schlegel and A. V. Gurevich, Ann. Geophys. 15, 870-877 (1997).

6. Y. S. Dimant and R. N. Sudan, J. Geophys. Res. 102, 379-388 (1995).

7. S. I. Martynenko and L. F.Chernogor, Geomagn. Aeron. 16, 658-665 (1976).

8. Yu. V. Kyzyurov, Ann. Geophys. 18, 1283-1292 (2000).

9. W. D. McComb, Rep. Prog. Phys. 58, 1117-1206 (1995).

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