Propagation of trans-equatorial deuteron whistlers in the low latitude topside ionosphere

JoumulofAbno&ericand Tmwtil

Pcr@manPressLtd.

Physics,

Vol.42,pp.427-435.

1980. Printed in Northem Ireland

Propagation

of tram-equatorial

deuteron whistlers in the low latitude topside ionosphere SHIGEAKI WATANABE*

Dept. of Geophysics and Astronomy,

The University of British Columbia, 2075 Westbrook Mall, Vancouver, B.C., Canada V6T lL5 and TADANORI ONDOH

Radio Research Laboratories, Tokyo, 184, Japan (Receioed 1 December 1978; in revised

form

7 August 1979)

Abstract-The high latitude limit of trans-equatorial deuteron whistlers is found to occur at latitudes where B, = B/2, in which B is the. local magnetic field at the satellite and B, is the minimum magnetic field on the field line through the satellite. The high latitude limit of trans-equatorial proton whistlers, often extends to the latitude where B, = B/4 in the autumn and winter. Trans-equatorial deuteron whistlers have a constant time interval for an echo train. The damping rate of the cyclotron resonant interaction with rare deuteron is large enough to generate deuteron whistlers. Ray tracing results for non-ducted propagation of trans-equatorial deuteron whistlers show that rays are guided by the geomagnetic field within one degree in invariant latitude for several bounces between the two hemispheres. Although the non-ducted propagation mode is L-mode, waves are reflected in the R mode at a LHR frequency after frequency between the deuteron and helium gyrofrequency after the mode changes at the cross-over frequency. 1. INTRODUCTION

In the ELF region, ion cyclotron waves are observed by satellites as ion cyclotron whistlers in the multicomponent plasma of the topside ionosphere. GURNETT et al. (1965) and BARRINGTON et al. (1966) measured upgoing proton and helium whistlers on INJUN 3 and ALOUETIX 2, respectively. LIKHTER et al. (1974), using INTERCOSMOS5VLF data, identified the trans-equatorial proton whistler by analysis of the dispersion coefficients of the electron whistlers united to the proton whistlers. TERRY (1978) has calculated the expected spectrum of upgoing proton and helium whistlers using a complex ray tracing method, and has obtained some interesting examples of the spectra expected for each type of whistler. Upgoing and trans-equatorial deuteron whistlers caused by a minor component of the ionospheric plasma, deuteron, were found by WATANABE and ONDOH (1975, 1976) from ISIS-l and 2 VLF electric field data in middle and low latitudes. The previous papers showed that upgoing deuteron * On leave from Radio Research Laboratories, 184, Japan.

Tokyo,

whistlers have an asymptotic frequency at one half of the local proton gyrofrequency, Gd2. On the other hand, the trans-equatorial deuteron whistler has an asymptotic frequency at one half of the minimum proton gyrofrequency that occurs along the geomagnetic field line through the satellites, G,,/2. In this paper we report observation of the higher limit of the trans-equatorial deuteron and trans-equatorial proton whistlers by the ISIS satellites in the longitude of Japan. Also we investigate the wave mode and the propagation mechanism for ducted and non-ducted propagation of transequatorial deuteron whistlers and trans-equatorial proton whistlers, here abbreviated to TED and TEP whistlers respectively. 2. LA-INAL

LIMIT OF TRANS-EQUATORIAL

Figure 1 shows the spectrum of a typical TED whistler observed at low latitudes. Generally, the upper limit and lower limit of the frequency range for TED whistlers (i.e. the asymptotic frequencies) lie at Gp,/2 and slightly above G&4, respectively. Therefore, it is expected that TED whistlers would not be observed in the region where B, 5 B/2

5. MiA’lM4BS-

-i.?S

because dcuteron whistlers are retlected at a IOWCI latitude on the field lint than the satellite locatIon. In Fig. 2. TED whistlers show a wedge-shaped pattern in time compressed spectra. The upper limit ~)f the ‘TED whistlers I -~Ci,,,/l! approaches the lower limit of the TED whistlcrq (slightly higher than G&4, as the satellite goes towards higher latitudes. The tip of the wedge shaped pattern on the dynamic spectrum in Fig. 2(h) shows the higher latitude limit of the TED whistlers at 20.3”N height, and B,/B is calculated to be 0.5 1 from the ~nternationai Geomagnetic Rcfcrcncc Field 1965.0 model. Figure 3(a) shows that the high latitude limits of TED whistlers observed between November 1973 and January 1974, occur at a geomagnetic latitude of 2O”N and are independent of altitude. Assuming the geomagnetic field to be that of a centered dipole, we find that the surface of B, = B/2 is independent of altitude at a geamagnetic latitude of 23.1” as shown by the dash and dot lines in Fig. 3. In the IGRF 1965.0 model the surface of B, = B/2 is located at a geomagnetic latitude of about 21”N around the Japanese longitude i--140’E) and is independent of altitude. Generally, TEP and TED whistlers have the same higher iatitude limit. The latitude limit of such TEP-TED whistlers are indicated by solid circles in Figs. 3(a and b). Exceptions occur, how-

l

CENTERED

DIPOLE

#A * 39.6” .

APP~XIMATION t

'B/2=&n lcB/C. id

Em

,111,1 #

! kbil~lH

+#j(j~__._ __-._

IGRF

=j-

_.

-

1965

0

/ i ac@/

614 E&I? I /

i I I : = I590 1 F 2

‘; f

ia i WC , x

lOO0

n)O

0.1

I,,

0.2

0.3

Bm

L

R4

.

0.5

I

0.6

I

0.7

(

18

Fig. 3(b). Magnetic field ratio B,,,/B at the high latitude limits of TED and TEP whistlers.

ever, in the fall and especially in winter. TEP whistlers during these seasons are often observed (70-S 5% of probability approximately) at higher latitudes that the limit of TED whistlers [bottom panel in Fig. 2(b)]. The latitude limits of these exceptional TEP whistlers exist outside the surface of B/B, = 2 as shown in Fig. 3(b). Signal strength of TEP whistlers at latitudes higher than the limit of TED whistler is generally weaker than in lower latitudes. At the equator, deuteron whistlers suffer from heavy deuteron cyclotron damping because VLFELF waves propagating along the geomagnetic field

interact with the equatorial plasma for a long period. At higher latitudes, the gradient of the geomagnetic field is so large that some ion cyclotron waves may propagate through the deuteron cyclotron frequency surface without heavy damping. Deuteron whistlers are reflected repeatedly in the topside ionosphere of both hemispheres. Figure 4 shows the time interval of whistler echoes vs the repetition number. The time series, A,, indicates 1 moDL 100 . 300 20’ tOD the roundtrip time interva1 of whistler echoes when GEOMAGNETIC LATITUDE the satellite and ionospheric refiection point are in Fig. 3(a). Higher latitude limits of TED and TJ2P whistlers the same hemisphere;.and the time series, B,, the as a function of geomagnetic tatitude, for whistlers ob- time interval of whistler echoes when the satellite is served near Japanese Longitudes. Higher fatitude firnits of TED whistlers and extended ‘IEP whistlers are rep- in the opposite hemisphere to the ionospheric resented by solid circles and crosses respectively. The line reflection point of whistler echoes. of B/2 = Bmin and B/4 = B,, are drawn in the centered In Fig. 4, A,, and B, are normalized by A, and dipole approximation. B, which are the first time-intervals of the echo

Propagation of trans-equatorial

DEC

deuteron whistlers in the low latitude topside ionosphere

UT 0549

18

10

ISIS-2

TlMEfSEC)

Fig. 1. (Top Panel.) An example of the echo appears between frequencies G ,/2 and G$4. and G&2. appears between frequencies e deuteron wh&>er where A,

train of a trans-equatorial deuteron whistler which The echo train of a trans-equatorial proton whistler The bottom panel shows a typical echo train of a and B, denote the time intervals.

429

UT

Fig. 2a. The compressive

0344:40 0.8’

dynamic

OS55

0351:20 19.7O

spectrum

of TED 10.7”N.

and ‘YIP whistters

1973

DEC

observed

: 33

at a latitude

13

E OHz

UT

0722:45 27.5O GEOMAGNETIC

Zh. The extended Fig. 1

higher

0&?5:00 20.3O LATITUDE latitude

0427 10.7

limit of a TEP whistler

ot

Propagation of tram-equatorial

deuteron whistlers in the low latitude topside ionosphere

431

usually much faster than the thermal velocity, the cold plasma approximation can be used in the topside ionosphere. On the other hand, when the wave frequency approaches the doppler shifted cyclotron frequency, the phase velocity of waves is then close to the particle thermal velocity. We now discuss the cyclotron wave particle interaction in a hot plasma. We calculate the effective damping length for K//B0 (wave normal vector K parallel to geomagnetic field), on the assumption of ducted propagation. If waves propagate in a uniform plasma which is described by an isotropic Maxwellian particle distribution function, the wave (L-mode) dispersion relation can be written as Fig. 4. Normalized time intervals of echoes for TED whistlers. Approximately constant rates are shown in the intervals normalized by the first interval of upgoing B,, series and down going A,, ones for six isolated echo

trains. trains. The echo train of deuteron whistlers is observed to the low latitude side of the higher latitude limit. In the neighbourhood of the geomagnetic equator, echo trains of proton whistlers are frequently observed, but deuteron echo trains lose their shape or are not clearly observed at low altitude. Since several echo trains often appear superimposed on the spectrogram, it is very difficult to distinguish between the A,, and 3, series of the specified whistler echoes. Figure 4 shows measured results of A,, and B,, for a solitary whistler echo train as shown in Fig. 1. Because the normalized time intervals of echoes, A JAI and B J& concentrate around unity, and are independent of repetition number n, we can say that all sequential echoes of the TED whistler propagate along the same geomagnetic field lines. The asymptotic frequencies of deuteron and proton whistlers are GJ2 and Gpm respectively (WATANABE and ONDOH, 1976). The profile of the TED whistler’s dynamic spectrum indicates a significant wave particle interaction. The long trail of asymptotic frequency to GpJ2 or Cd2 is caused by very low group velocity in the neighbourhood of the deuteron cyclotron frequency. Heavy deuteron cyclotron damping produces the frequency gap between G&2 and G,,/2, that is the high attenuation band between TEP and TED whistlers. Ion mass spectrometer measurement (HOFFMAN et al, 1969; TAYLOR, 1973) indicate that any decrease of the group velocity or increase in the cyclotron damping is caused by a very small amount of deuteron content, N(D)/N(H+) - 10e3. Since the phase velocity of the ion whistler is

(1) where

sls =

2~rG,

The subscripts s refer to the Sth type of particle having a charge of sign es. w, n;, fl, and 4 are the wave frequency, plasma frequency, gyrofrequency (ankle frequency) and thermal velocity, respectively. Z(CY,) is the so called plasma dispersion function or modified complex error function and defined by Z(a)=inlexp(-a’)[l+erf(ia)]. Numerical values used are found in the table of Fried and CONTE (1961) for Z(o) and in the table of FADDEYEVA and TERENTEV (1954) for -idZ(u). The real part of the frequency, W, gives the wave oscillation, and the imaginary part of frequency, y gives the growth or damping rate. Figure 5 shows an example of the effective damping length caiculated from equation (1) for appropriate ion composition and electron density in the low latitude topside ionosphere. The wave amplitude is reduced to e-’ after propagation through the effective damping length, Ldamp.As wr approaches to fl,,, Ldmp decreases. At w,l& = 0.499 (e&l, = 0.998), Ldamp becomes much less than 1 km except for T= 1000°K. We can calculate the distance for which w/Q, varies by l/1000 at an altitude of 1400 km (ISIS-2 altitude) for the centered dipole field. This characteristic distance LB of the &&, variation per mill is of the order of LB = 2 - 3 km in mid latitudes, but it becomes Ln z 5 km at 10” and Ls - 10 km at 5”. For the ion cyclotron wave propagating upward

ditlusive-equilibrium

distribution

ANCXRAMI and THOMAS (1964;

given

b’i

and is independent

of latitude. The ion density

ratio (NCION)/N~I ai to be NpiNr -0,s Nd/Ne -0.005. NHr + IN,= 0.i and N,;t/Nr ~.

the

base

level

is assumed

0.095 at an altitude

of 1000 km. The refractiv<

index of ion whistlers is computed in the c&l plasma approximation, since the wave phase velocity is much faster than the thermal velocity in the topside ionosphere. We can define the refracti\,e index n as follows (STIX, 1964); H_tb II, = -._. 2A

where

A = S sin’ 8 + P COS’0. B = RL sin* 8 + PS( 1+ cos’ f3),

C = PRL. S ='(R+ L)/2,

D=(R-

L)/2, (7)

Fig. 5. Effective damping length L-damp for ion cyclotron whistlers.

(8) along the geomagnetic field, Ldampbecomes smaller than several kilometers and LB >>Ldampat w/&I, = 0.449. Over the equator, the ion cyclotron waves cannot penetrate the barrier of w/n, = 0.5 without experiencing heavy damping or being reflected. But, in middle and high latitudes, the ion cyclotron mode can occasionally penetrate this barrier because of low temperature, low density and short distance of LB. Figure 2(b) shows that transequatorial proton whistlers were observed within the latitudinal range of 4Gp, L Gp which extends beyond the latitude range where 2G,, h GV In the above discussion, we have assumed that ion whistlers propagate along the geomagnetic field line in the ducted mode. The nonducted propagation of ion cyclotron waves will be discussed in the next section. 3. RAY TRACING Pop NONDUCI’ED PROPAGAX’ION OF ION-lNTBELOWLAmuDEToIsalE 1ONOsPEERE

Ray tracing for TED whistlers is executed by using the Adams four-point processes with the aid of the Runge-Kutta method in the initial stage. The model ionosphere assumes a multicomponent plasma of ions and electrons which is independent of latitude, and a centered dipole geomagnetic field. The plasma density model used is the

P=l-;$,

F = (RL - PS)'sin* 8 + 4P2D2 cos’ 8.

(10)

The sign of the charge, *l , is given by eL and 6 is the angle between Bo and K. An example of ray tracing of deuteron whistlers at 90 Hz is shown in Fig. 6 for the case where the initial wave normal direction is vertically upward at an altitude of 500 km and latitude of 20”. The R-mode is assumed up to an altitude of 1650 km. Then, the R-mode is converted into the L-mode at the crossover frequency (D = 0) between ad and f&-. Cyclotron damping by heavy ions, such as He* and 0’ occurs where the R-mode changes to the L-mode at low altitudes. We have assumed R-mode propagation up to high altitudes. GUR-NET-I et al. (1965) have reported that the R-mode (i.e. same mode) is generated at a crossover frequency near the critical coupling cone. Hereafter, we discuss the wave conversion at the crossover frequency from the R-mode to the Lmode, or vice versa, for all the ISIS VLF-data that we have analyzed. The ray-tracing result in Fig. 6 indicates that the invariant latitude of the ray path increased from A = 25.5” to 29.4” at geomagnetic latitudes from

Propagation of tram-equatorial

TIME

deuteroo whistlers in the low iatitude topside ionosphere

&

GEOMAGffETlC

433

LATITUDE

Fig. 6. Ray tracing result for nonducted ion cyclotron whistlers, obtained using the plasma density model of ~LNGEZRAMI and THOWU (1964). R-mode waves start vertically upward at a geomagnetic latitude of 20% and an altitude of 500 km. The left ordinate shows the delay time in seconds and the corresponding geomagnetic latitude. The upper abscissa shows the ray path altitude and the lower abscissa shows the invariant Latitude and wave normal angle. The symbols R, L, CR and LHR indicate the R-mode, L-mode, the cross-over frequency and LHR frequency, respectively.

20” to 13”. After the mode change at a geomagnetic latitude of 13”, the invariant latitude of the ray path remains at h = 29.4’, that is, the waves are trapped around the field line of A = 29.4”. In this case, the wave normal is perpendicular to the magnetic field line and is slightly inside the resonance cone. The ray crosses the equator at an altitude of 2024 km and the change from the L to R mode occurs at the crossover frequency at 1650 km in the opposite hemisphere. After passing the lower hybrid resonant frequency between Gd and Gn.+ at 1290 km aftitude, the R-mode wave is reflected at 1276 km, in a similar way to that of the LHR reflection of electron whistlers. After the LHR reflection, the mode changes again from the R-mode to the Lmode at 1660 km. Near the reflection region, of frequencies below the low hybrid resonance frequency, the wave normal angle to the field line changes slightly and the ray direction changes by 180” because the wave normal surface changes from the dumbell to the sphere in topology. In the above case, TED whistlers are guided along the geomagnetic field line corresponding to the invariant latitude 29.&P, even though we are tracing the ray of a nonducted mode. Figure 7 shows bouncing along ray paths computed for the initial wave normal angles of O“, 30” and -30” from the vertical at starting geomagnetic latitudes of 20” and 15” at an altitude of 500 km. The ion whistler rays computed for different initial wave normal angles and positions are guided along various

geomagnetic field lines such as that the invariant latitudes of the computed ray paths remain constant. The variation of invariant latitude of the ray paths after entering the stationary state is less than one degree for several bouncings between the two hemispheres. Ray tracing of deuteron whistlers shows that waves with the wave normal slightly inside the resonance cone propagate well along the

16

,

20~

YQ‘

NORTH’ ,

00 GEOMAGNETIC

-100

I

-200

LATITUDE

Fig. 7. Ray tracing of TED whistlers for different initial conditions in latitude and wave normal angle. The A curve is the ray path starting with the wave normal directed verticaliy upward. The B curve is the ray path with initia1 wave normal at 30” poleward from vertical. The C curve is started with wave normals at 30” equatorward from the vertical.

In the topside ionospheric

geomagnetic field lines. The angle between the ray vector and geomagnetic field line H,, is given h!;

.p y = tan

’

1 -.

.!3q +

’

r1iJIJ’

,),

s

‘z/l,,.

-----i--: h/I, !,

s c;,,’

(111

The values of y are less than 10.29” for the propagation of electron whistlers at f” Gp (STOREY, 1953). For ion whistlers Fig. 8 shows y vs @ for several normalized frequencies f/G,,. The angle y is computed for L-mode in the band of gyrofrequency >f> crossover frequency, and also for the Rmode in the band of crossover frequency >f > LHR frequency. It should be noted that, in the case of the deuteron whistlers, for f/G,CO.5, that y becomes very small. As f/G,, increases, y tends to becomes larger. However. y for f/G, -0.48 is slightly larger than y for f/G, =: 0.52 because of deuteron cyclotron resonance effect. Hence, the ray tends to propagate along the geomagnetic field line even for nonducted propagation, with a large wave normal, f3. When the K vector lies just inside the resonance cone, x = 3~12- jB/ becomes small. This is iIIustrated by the ray tracing in Fig. 6 which shows that for time >4secs [@/=9O”i. 10”. Since the plasma frequency is far greater than wave frequency, we can assume that /P/ >>lPx\ >>jR/, IL/, jS[, jD/ in equations (3) -(lo). We then obtain the following expression for y from equations (2) -

fZ

plasma, WC b,~v~ I!

I,

where M,/M, isthe proton to electron mass ratio. Since (f/G,)*
10 :

i l&i

iR1, ILL ISI and iDI are roughly considered to be the same order, we have As

y

s _-+.4?_! Px

s’

Y

-~+oix’i. From equation (15). y may be very small for K close to the resonance cone. If x -(-S”/D2P)““. say about lo”, then y should be zero. Near the resonance cone, equation (12) and tan X,,, = -SIP, give y - -X,,s. This leads to a reasonable situation that the ray vector is perpendicular to the resonance cone. These very small ray angles are consistent with the results computed by E, LEER et al. (1978) for a two ion cold plasma. CONCLUSION

I

Pt.

(12)

Fig. 8. Wave normal angle B vs ray angie for ion cyciotran whistlers. The wave mode for G, >f > crossover frequency and Gd >f> crossover frequency is the Lmode, and that for cross-over frequency>f>LHR is the

Our studies of Trans-Equatorial Deuteron (TED) and Trans-Equatorial Proton (TEP) whistlers observed by ISIS show that usually the higher latitude limit of TED and TEP whistlers occur where B, = B/2. A number of TEP whistler were however observed with extended higher latitude limits: the limit occuring towards locations with B,f B/4. Here an individual echo train can be clearly resolved; the alternating short and long timeintervals observed are each found to remain constant during the life of that echo train. This has been shown to be consistent with propagation of the TED whistler along the geomagnetic field lines. For ducted propagation TED whistlers would propagate, and be reflected, in the L-mode which involves propagation with the I( vector roughly parallel to the field line. The cyclotron resonance interaction of such TED whistlers with hot plasma was calculated to be suffieientiy strong to produce the spectrum pattern of the observed deuteron whistlers. The minimum frequency of TED whistlers would correspond to the cut-off frequency (L =

~opagation of tram-equatorial deuteron whistlers in the low latitude topside ionosphere

In the nonducted mode, the TED whistlers are guided by the geomagnetic field line in the proresonance mode with the K vectors lying slightly inside the resonance cone. Using a ray tracing technique the angle between the ray and field line for TED whistler was determined to be usually less than 0.1 degree. The variation of invariant latitude for TED whistler ray is less than one degree for several bounces, along the field line between the two hemispheres. The reflection of non-ducted TED whistters would occur in the R-mode at altitudes slightly below the LIIR altitude, and the minimum frequency of the TED whistler band would correspond to the LHR frequency between Gd and G,,. In both the ducted and non-ducted cases, the higher latitude limit of the TED whistler is pre-

435

dicted to be located at the position of I3, = 8/Z, whicll is consistent with our observations. However to explain the weak TEP whistlers which have an extended higher latitude limit at I?,,, = B/4 it is probably necessary to include the effects of collisions in the hot plasma calculations. Acknowledgemenrs-We would like to thank Dr. R. E.

BARRINGTON, CommunicationsResearch Center, Canada,

and NASA, U.S.A. for their support for our VLF observation from ISIS satellites received at Kashima, Japan. We would also like to thank members of the Telemetry and data processing groups, Kashima Branch, Radio Research Laboratories for their collaboration in data acquisition from the ISIS satellites. One of us (S. W,) appreciates Prof. T. WATANAS~ and Dr. D. H. BOTTLERof U.B.C. for their kindnessduring his stay at the U.B.C.

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Fume B. D. and C~NTES. D.

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J. Geophys. Res. 74, 6281.

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J. Geophys.Res. 83, 3125. Space Res. 14, 265.

1962

The ‘I’&eoryof Plasma Waves, McGraw-Hi& New York. Phif. Trans. Roy. Sot. (land.) A264, 113. J. Geophys.Res. 78, 315. I’mc. R. Sot. Land. A. 363,425. 3. Radio Res. Labs. 22, 63. Planet. Space Sci. 2& 359.

hGErRAA0

STXXEYL. R. 0. TA~OR H. A., JR TERRYP. D. WATANABE S. and ONDOHT. WATANAEIE S. and ONDOHT.

1953 1973 1978 1975 1976