SOME ASPECTS OF ION-ACOUSTIC WHISTLERS IN THE IONOSPHERE IN THE PRESENCE OF NEGATIVE IONS

. A study is made of the propagation of ion-acoustic whistlers in the atmosphere including the effects of negative ions. The dispersion relation, phase and group velocities of whistlers are discussed. It is shown that the presence of negative ions introduces a critical frequency which, for equal ionic masses, is equal to the ion-cyclotron frequency. Special attention is given to the group travel time of whistlers at mid-latitude and equator so that the role of negative ions on the group travel time can be determined. The cyclotron damping of whistlers in the presence of negative ions has been studied. The velocity distribution, total attenuation and the induced magnetic field are calculated from the temporal as well as spatial cyclotron damping. It is suggested that the attenuation of whistlers may cause heating of the ionosphere. It is also indicated that the measurement of the group travel time from its source to the observer at the satellite would help to diagnose the ionospheric parameters. The results of the analysis are presented by several graphical presentations. ions on low-frequency waves in different problems in the ionosphere and in the laboratory plasmas.


INTRODUCTION
Considerable studies have been made on the propagation and generation of ioncyclotron waves in multicomponent plasmas and in the ionosphere. Gurnett and his associates [I-2] have made an investigation of proton whistlers and discussed the use of whistlers for diagnostic purposes in the }onosphere. Several authors including Das and Uberoi [3][4] have also considered the role of negative ions on low-frequency waves in different problems in the ionosphere and in the laboratory plasmas. Ir spite of these investigations, various aspects of ion-acoustic whistlers in the ionosphere in the presence of negative ions have not yet receivc full attention. The main purpose of this paper is to consider a plasma model that includes the effect of negative ions, and to calculate the group travel time for the whistlers observed at the equator and at the mid-latitude. In this study, we assume that the ratio of the total number of negative ions to the positive ions is less than unity, and it varies from 0.0 to 0.5 in the ionosphere. The dispersion relation, phase and group velocities of whistlers are discussed in some detail. It is shown that the presence of negative ions introduces a critical frequency which, for equal ionic masses, is equal to the ion-cyclotron frequency. Special attention is given to the group travel time of whistlers at mid-latitude and the equator. Special attention is given to the cyclotron damping of whistlers in the presence of negative ions. The velocity distribution, total attenuation and the induced magnetic field are calculated from the temporal as well as spatial cyclotron damping.
This study reveals that the attenuation of whistlers may cause heating of the ionosphere. The measurement of the group travel time from its source to the observer at the satellite would help to diagnose the ionospheric parameters. Results of this analysis arP presented by several graphical presentations.

2.
ASSUMPTIONS AND BASIC EQUATIONS We assume that the ionosphere consists of several species of positive ions (subscript 'i') having mass mi; velocity v and number density n and the negative ions (subscript 'j') of mass mj; velocity vj; and number density nj. The corresponding quantities for electrons (subscript 'e') are, m e V e and n e. The basic system of equations governing the dynamics of ionospheric plasma are given in usual notations (Stix [7]): n @t + div (n v_a) 0  [7], and using the above equations, we obtain the general dispersion relation in the form A n 4 B n 2 + C 0 (3.1) ck where n Inl I111 is the refractive index of the wave and it is the ratio of the velocity of light to the phase velocity, A S sin20 + P cos2B (3.2) B RL sin2o + PS (1+cos 2) 4noe q H 0 p m a l"cm (3.8ab) q e for ions, q -e for electrons and negative ions. All these symbols have their usual meaning.
It is noted that the dispersion relation (3.1) is modified so that the ion cyclotron whistler propagates almost along the geomagnetic field and it approximately tends to the ion cyclotron frequency. Under these conditions, the earlier derivation of group travel time receives major contributions from the left circularly polarized (LCP) wave as compared to the contributions of the right circularly polarized (RCP) wave and finally the RCP-wave's contributions have been neglected. In our present model, the contributions of both LCP and RcP waves to the group travel time are taken into account. The characteristics of variation of the phase velocity of both RCP and LCP waves against the variation of normalized wave frequency are shown in Figures 1 and 2. In this model, the plasma is assumed to contain the ions (H+, H) and (H+, H-) in order to show the negative ion effects on the phase velocities and also to compare with the results obtained in plasmas with only positive ions (dotted lines). In moderately dense plasmas, the negative ions have significant effects on the phase velocity. Furthermore, due to addition of negative ions, it is seen that, for each Now for an ion cyclotron whistler, (--) can never be found less than 5xlO -3 at the minimum values of (h-). The resonance angle is approximately equal to . But, for O , it could occur only near the equator. The satellite observations show that a very few whistlers are found near the equator as compared with the occurrence rates at. mid-latitude [8]. So it is required to impose an appropriate condition tan2O << tan2O r, to study the whistlers at mid-latitude. Two cases are of special Due to the addition of extra ions, the circularly polarized waves would have a critical frequency at which polarization reversal may occur [7]. The addition of negative ions in the plasma will introduce a critical frequency which, for equal ionic masses, is equal to the ion-cyclotron frequency. So the expression D in (3.4c) must be zero at this frequency. Consequently, the refractive indices (3.12ab) assume the values n I (R+L)/cos20 n 2 (R+L) (3.13ab) where the expressions for R(m) and L(m) are given by m2 m2 is the cyclotron frequency of equal ionic masses and hence . .  3.25a) shows that the group velocity at the equator depends on the plasma frequency, ion-cycletron frequency, the propagation angle 0 and the concentration of negative iOFS. We plot the normalized group refractive index as a function of normalized wave frequency for various concentrations in Figure 5. In Figure 6, the variation of UQ/U 0 is plotted against the variation of the propagation angle o, for whistlers observed at the equator. We compare our results with the results obtained in the ienosphere consisting of positive ions only [results are taken from Gurnett and Shawhan [2]). It is shown that the effects of negative ions on the group velocity derived for the whistlers observed at the equator.

THE GROUP TRAVEL TIME OF WHISTLERS
The measurement of group travel time for the whistler from its source to an observer at the satellite is given by the line integral" h dh where UoL is the gFoup velocity of the LCP wave. But in our present model both the LCP and P,CP waves have contributions to the 5roup travel time and then UgL is modified tc U lhe present study shows that earlier studies have been confined to en ideal g model of ionosphere consisting of several species of positive ions. This model may be an ideal one in diagnosing he ionosphere, but the existence of negative ions in the ionosphere indicates that the previously chosen model becomes purely a degenerate case unless a preper account of negative ions is taken. Smith [9] has shown the effects of negative ions on the study of whistler propagation in the ionosphere. CYCLOTRON DAMPING OF WHISTLERS AT MID-LATITUDE As few whistlers are observed at the equator, we consider here the cyclotron damping of the mid-latitude whistlers only. When Z some protons will have a velocity component due to the thermal motion, and will experience a higher wave frequency [10]. When the wave frequency becomes equal to the cyclotron frequency of protons, then protons absorb energy by cyclotron damping. Now for a purely longitudinal wave with isotropic Maxwellian velocity distribution of ions, the dispersion relation of the LCP and RCP waves are given by (7.14) The corresponding attenuation factor B is obtained by integrating (7.14) over the prolagation path and has the form

DISCUSSIONS AND CONCLUDING REMARKS
This analysis reveals that the estimation of cyclotron damping along with the velocity distribution as well as the amplitude of the magnetic field in both cases depend on the group travel time. To show that effects of negative ions on the damping of whistlers v;e consider here the proton whistler data of Gurnett and Brice [10] for which Am(O), (0) and n(H+) are 3.7 C.P.S., 410.3 C.P.S. and 12.x I03/C.C.
respectively. The plots are considered for three different temperatures 600K, 800K and IO00K with a fixed value of x 0.1.
The variation of mi against the variation of t(m) is shown in Fig. 9. It is clear from Fig. 9 that the temporal damping starts 3 secs. delay from the starting of the whistler, and there is a steep rise of the damping at t The relative wave amplitude of the magnetic field is sensitive due to the negative ion effects on the whistler (Fig. 12). Fig. 12 shows a comparison of the effect of the negative ion (solid line) with the result obtained by Gurnett and Brice [10] (the dotted line).
The present analysis of the propagation of whistlers in the ionosphere reveals the effect of negative ions on the estimation of the group travel time as well as cyclotron damping of the ion-cyclotron whistlers. The plot of (Am)against the group travel time t(m) provides an estimation of the ion-cyclotron frequency and the relative concentration of ions. The velocity distribution, total attenuation and the induced magnetic field have been calculated from the temporal as well as spatial cyclotron damping. The results of this analysis clearly show that negative ions in the ionosphere have an effect on the technique employed to estimate the ionospheric parameters observed both at the mid-latitude as well as at the equator. Moreover, the present model indicates that the negative iorts should be taken into account in the ionosphere. Otherwise, a discrepancy on the results will occur. Finally, the present study also needs a further extension to include the following effects: (i) The thermal effects in the ionospheric plasma seem to have some important contribution to the propagation of whistlers. So a study of thermal effects on the histler in the presence of negative ions will be made in a subsequent paper.
(ii) Th stream velocity of the plasma and newly born ion effects in the ionosphere may also be taken into account. This problem may be studied in the future. For such a use, it is necessary to plot t(m) against (Am) -1/2 for several cyclotron frequencies for a set of observations. As an example, we select an arbitrary ion-cyclotron frequency, 1 (say) and make a plot of (Am)against t(m). If the frequency is small compared to the actual frequency, an upward concave line will be observed as shown in Figure 13 with the mark I. In this case, we need to increase the cyclotron frequency and repeat the plot ()-1/2 against t() to minimize the concavity. Similarly, if we have chosen high frequency then one will observe a downward concave line (marked by II) and leads to lower the arbitrary cyclotron frequency. We repeat the plots with several chosen ion-cyclotron frequencies until one should get the best straight line; the cyclotron frequency for which we should get the straight line is the actual ion-cyclotron frequency. Now the slope of the straight line obtained for mid-latitude and equatorial whistlers for the actual ion-cyclotron frequency may be used to determine the relative concentration of ions, since '(0) can be obtained from the geometry of the geomaQnetic field variations and m (0) may be used from the ionospheric data. Thus Pi the ion-cyclotron frequency and the relative concentration of ions may be obtained through the estimation of the group travel time.
(ii) Heating of the Ionosphere It is known that absorption of energy through attenuation of the waves is one of the sources of changing the physical properties of the medium. The ionosphere as well as the atmospheres of other astrophysical bodies are heated by the energy gained from the attenuated waves. Barnes [14] showed that hydromagnetic waves become damped even in collisionless plasma and the solar corona may be heated by this mechanism. Bandyopadhyaya [15] pointed out that the rotational astrophysical objects plays an important role in damping of the MHD waves and it causes heating of the rotating stars. There are several theories to explain the heating phenomena of earth's ionosphere [16][17][18][19][20], but no theory has been proved to be unique. Recently, Murtaza and Shukla [6] pointed out that the Landau damping of the lower hybrid waves can cause the electron heating, whereas the ion-cyclotron waves can heat the ions preferentially, i.e. both he plasma species could gain energy at the expense of the whistler wave. Our present analysis for the damping of whistler waves due to nonlinear interaction with the plasma particles in the ionosphere gives a new theoretical prediction for the SOME ASPECTS OF ION-ACOUSTIC WHISTERS IN THE IONOSPHERE 761 heating of the lower ionosphere. In fact, the energy absorbed in the ionosphere due to attenuation o f whistlers is not large because the energy of whistlers is not large in general. But under some suitable physical conditions, particularly in resonant cases, the nonlinear absorption of energy due to damping of whistlers may be significant and it would act as one of the important sources of heating for the earth's ionosphere. The heating rate by the process of nonlinear attenuation of whistlers would be estimated in our subsequent work. It is to be mentioned here that besides heating of the medium the damping of whistlers has also other applications. The velocity distributions and the induced electric and magnetic fields may be estimated from the damping rate of whistlers [11][12]. The detailed study and numerical estimations of these parameters would be made in the future.
Acknowledgement. This work was partially supported by the University of Central