as the magnetic flux density and ion cyclotron frequency are reduced. Thus the greatest contribution to the transit time occurs in the equatorial region near the top of the path. Since the double-hop transit time of the wave packet is assumed to correspond to the hm emission fine structure repetition period, temporal variations in repetition period may be interpreted in terms of changes in the magnetospheric plasma density and the propagation path latitude.
Obayashi ( 1 964) has obtained equation (9.8) in a more practical form by assuming a dipole geomagnetic field and an inverse cube
law magne tospheric plasma density distribution of the type suggested by Smith ( 1 961 ) and Liemohn and Scarf ( 1 964). Equation ( 9. 8)
then become s
where a i s the radius o f the earth , L the Mc ilwain parameter ,
10
the geomagnetic latitude , and fHc the ion cyclotron frequency atthe point where the field aligned path passes through the equatorial plane. B and 0 N 0 are constants (B 0 = 3. 1x10-5 Wb/m2; N 0 = 101 0;m3).
Computed frequency-time patterns for echoing sequences of an
ion cyclotron wave packet using equation (9. 9) are shown in Figure
9. 1 . Qualitative comparison of the se theoretical re sults with
observed frequency-time spe ctra of hm emissions indicates that
emissions must originate be tween L= 4 and 5. 6 ( 40 = 60° to 65°)
(Jacobs and Watanabe , 1964; Obayashi, 1964). However , as pointed
out by Obayashi, this assume s that the present plasma density
distribution is an appropriate representation of the magnetosphere.
It is apparent from observed hm emission spectra that me chanisms producing high and low frequency cutoffs must be operative .
Mechanisms for the se cuto ffs are discussed later (sections 9.3.1 and
9. �. 1) .
The first experimental evidence for the existence of ion cyclotron wave packe ts in the magne tosphere has been pre sented by
Smith et al . ( 1 964). VLF results from Injun 3 and Aloustte satellite s
indicate dispersed forms of atmospheries which appear remarkably
similar to the dispersed first hop signal in the left-hand diagram
of Figure 9.1. Furthermore , the upper frequency limits of the signals were approximately the ion cyclotron frequency for protons in the plasma surrounding the satellites.
9.3 E CIT TION OF HM EMISSIONS.
A number of mechanisms have recently been suggested for the generation of hm emissions (Obayashi, 1964; Wentworth and Tepley 1964; Cornwall, 1965). All assume that emissions are generated in the magnetosphere by either Doppler shifted cyclotron radiation or Cerenkov radiation from the energetic particles in the medium.
Detailed treatments of the various types of charged particle radiations, plasma wave-particle beam interactions and instabilities likely to occur in the magnetosphere are beyond the scope of the present study and will not be considered. Instead, a brief summary of the processes necessary for the development of hm emission generation theories will be given.
9.3.1 Radiation from Charged Particles.
The velocity of a charged particle moving along an external field is the vector sum of a component parallel to the field and a component transverse to the field which rotates at a rate
corresponding to the cyclotron frequency. Cerenkov radiation
occurs when the longitudinal velocity of the charged particle exceeds the electromagnetic wave phase velocity in the medium. Radiation is emitted in the forward direction and the sign of the charge of the emitting particle is unimportant. In the case of cyclotron radiation the emitted wave frequency is the Doppler shifted particle cyclotron frequency or its harmonics. Here two cases are
distinquished, the normal Doppler shifted cyclotron radiation in which the longitudinal particle velocity is less than the wave phase velocity, and the anomalous Doppler shifted cyclotron radiation in which the particle velocity is greater than the phase velocity of the emitted wave.
For an observer in the plasma the frequency of the particle radiation is given by
f I -=
1 - (u/cp tH )µ_ cosG
( 9.1 0 ) ( p = o , + 1 ' +-
2 ' . . . )where f is the wave frequency , fH the cyclotron frequency,u the longitudinal particle velocity, and
e
the angle between the direction of wave propagation and u.the radiation of cyclotron harmonic s.
The integer p accounts for The case p=o results in Cerenkov radiation while p > o produces normal cyclotron radiation and p
<
0 anomalous cyclotron radiation.The general di spersion relation (Ginzburg, 1961) is obtained by
• I
substituting equation (9.4b) into equation (9.10) and assuming f�f
and S =0. For the L wave
(9.11) The upper sign corresponds to the normal cyclotron radiation and the lower sign to the anomalous radiation. This equation may be used to calculate the frequencies of emission from specified values of u/VA. It is of interest to note that the emitted wave frequency is inversely related to the particle velocity for constant VA. Therefore, in a particle beam with a specified velocity
distribution,the lowest frequency emitted is determined by the highest energy particle s in the beam.
9.3.2 Plasma ave - Particle Beam Int eractions
In the above theory the radiation results from single charged particles. However, both Ginzburg (1961) and Obayashi (1964) have shown that the energy of single charged particle radiation at Pc1 frequencies is insuffieient to produce emissions of the amplitude recorded at the earth's surface. It may be suggested that a large number of radiating particles will produce hm emissions.
However, radiation of this type is generally inailerent and although it may explain certain types of VLF emissions it will not explain the discrete structure of hm emissions. It is therefore necessary
to invoke collective action effects between the particle beam and the plasma which lead to wave amplification or coherency in
particle radiation. The resultant emission intensity is much greater than in the non-coherent case. Mechanisms producing