The use of micropulsation “whistlers” in the study of the outer magnetosphere

Planet.

Space Sci. 1965.

Vol. 13. pp. 773 to 779.

Pergamon

Press Ltd.

Printed

in Northern

Ireland

THE USE OF MICROPULSATION “WHISTLERS” IN THE STUDY OF THE OUTER MAGNETOSPHERE R. L. DOWDEN and M. W. EMERY Physics Department, University of Tasmania, Australia (Received 8 March 1965) Abstract-Certain types of micropulsation dynamic spectra show a series of rising tones Based on this idea and a previous thought to be caused by dispersion in the magnetosphere. analysis it is shown that these spectra can be used to evaluate the plasma density in the outer magnetosphere (five to eight Earth radii) in a way analogous to that used for VLF whistlers. The method is applied to micropulsations observed at Hobart in April, 1964. The results indicate a substantial decrease in plasma density beyond about five Earth radii in broad agreement with previous VLF work. 1. INTRODUCTION

It has been suggested (I) that the sequence of rising tones observed in dynamic spectra of certain types of geomagnetic micropulsations might be an expression of dispersion of a hydromagnetic wave packet guided by a magnetic field line through the magnetosphere in a way similar to VLF whistlers. Dynamic spectra calculated on this hypothesis show good agreement with observed spectra. (l) This suggests that it should be possible to obtain plasma density (N, - R,) profiles from information contained in observed dynamic spectra. A method of doing this is developed here. This method is based on a study of propagation in the “micropulsation mode” given previously(2) (referred to here as Paper 1). It was shown there that the observed dispersion should be that of a single “universal” dispersion if frequency and time is suitably normalised. The problem is to find these two normalisation factors which then determine the path (or 8,) and the plasma density (NJ at the top of the path respectively. It should be stressed that the dispersed times have been determined by the time intervals (as a function of frequency) between successive echoes and not the spectral shapes of the rising tones themselves which may depend on an emission process. 2. DETERMINATION

OF PATH (g,,)

It was shown in Paper 1 that if travel times are normalised to their value at zero frequency and frequencies normalised to the minimum proton gyrofrequency along the path (go), the frequency-time (A, - T) dispersion curve is “universal” for latitudes greater than about 50”. This means that, in principle at least, observed dispersion curves obtained from dynamic spectra of micropulsations can be used to determine the paths (field lines) along which the micropulsations were propagated. Measurement of travel time at zero frequency and at frequency f would give T and consequently 1, at f,and hence g,. However, observed micropulsations do not extend down to zero frequency so that modified methods have to be devised. 2.1

Method 1

The first method is based on one devised by Smith and Carpenterc3) for the similar problem of determining the path travelled by VLF whistlers which do not extend up to the 773

R. L. DOWDEN

114

and M. W. EMERY

nose frequency. Measurements of travel time ((t u, tL) are made at two frequencies fu and fL. The best accuracy is obtained if these frequencies are the highest and lowest at which accurate measurements can be made. Then since t(0) is common to both tU and tL, and since 7 is “universal”: t&L

=

%/TL

=

s(fLlfv,fvlg3

The function S which has been deduced from Paper 1 (Fig. 9) is shown in Fig. 1. From this set of curves the measured ratios fL/fu and t,/t, determine fu/go and thus g,.

FIG. 1. THEUNIVERSAL PARAMETERS USEDIN METHOD 1 SHOWN ASAFUNCTIONOF VARIOUS VALUES OF fL/fv.

2.2

fulgo FOR

Method 2

Many events have a restricted range of frequency. For these Method 1 is difficult to use. Usually the total number of hops is large so that the dispersion or incremental increase in travel time At over a small range of frequency A f is easily measured. If these are expressed in terms of the average travel time and frequency we get: = mJ

THE USE OF MICROPULSATION

“WHISTLERS’

775

The universal function l(&) has been calculated by graphical differentiation of the universal T(&) curve derived in Paper 1. This is shown in Fig. 2. 2.3

Method

3

For some events dispersion may not be measurable. VLF nose whistlers have an upper cut-off frequency at about 14 times the nose frequency. * At high latitudes (65”, say) this would correspond to il, N 0.55. If this is caused by thermal broadening of the electron cyclotron resonance (*) then an analogous cut-off for micropulsations caused by protons would be expected c5)at about 31,N 0.6. If the highest observed frequency (fmax) is limited only by this process then g, = 1*7f,,,. This “method”, though of doubtful validity, is useful as a last resort. 3. DETERMINATION

OF PLASMA

DENSITY

For latitudes greater than about 50” the scale frequency is given by equation (7) of Paper 1, rearranged to the form: a = 5.7t”(0)g05’3 x 1O-6 MC/S

(1)

where t(0) is the zero frequency travel time in seconds for one complete (there and back) trip and g, is in cycles per second. The quantity t(0) is not measured directly but deduced from the measured value t(&) and T(&) as given in Fig. 9 of Paper 1. The concept of scale frequency is used because it is quasi-constant in the magnetosphere. The plasma density N, at the top of the path in particles per cm3 is numerically equal to 23 ag, for a in MC/S and g, in c/s. The radial distance of the top of the path is equal to 7.8 g; 113 in Earth’s radii. For a non-dipole field this (R,) can be regarded as a convenient parameter. The main errors in the determination of scale frequency will be caused by uncertainty of il, (and consequently T) at which the travel time is measured. If (1) is differentiated with respect to I,, it can be shown: Aa -= a

-

fp

(25 + 5/3) 0

Thus travel time should be measured at a low frequency where 5 is small (see Fig. 2). Note that for R, N 0.5 the percentage error in scale frequency is about three times that of 1,. 4. RESULTS

Dynamic spectra have been made of 15 micropulsation events recorded near Hobart, Tasmania during April, 1964. The spectrum of No. 13 is shown in Fig. 1 of Paper 1. Some of the data scaled from each event is shown in Table 1. Values deduced from this, and additional data not shown, are shown in Table 2. In most cases all three methods have been used. Some of the extreme values of scale frequency (a) seem to correspond with extreme values of deduced normalised maximum frequency I,(max). This is probably caused by errors in deducing Lo as discussed above. Since the deduced value of go (and R,) depends on the measuredf(max) and the deduced L,(max), such errors would tend to produce a spurious variation of a with R,. Values determined by method 3 would not show this * This is based on ratios calculated by one of us (R.L.D.) from published 14)data scaled from all available (57) nose whistlers of high quality. The ratio appeared to be independent 3.5 kc/s to 13 kc/s and had a median of 1.23 f 0.05 (quartile range). 4

of nose frequency over the range

776

R. L. DOWDEN

and M. W. EMERY

$5-

0

*5

1.0

f

FIG. 2. THE UNIVERSALPARAMETER E USED IN METHOD 2 AS A FUN~ION OF NORMALISED FREQUENCY A,. THE UPPER CURVE IS AN EXTENSION: ITS SCALE IS SHOWN AT THE TOP.

error. To test this the a(&,) values were plotted in Fig. 3. It is seen that the distribution of values deduced by methods 1 and 2 is similar to that of the method 3 values. Thus the dependence of a on R,, which does not appear in VLF whistler measurements of the lower magnetosphere (R, - 2 to 5 Earth radii), seems to be a real effect. Values of N,,(R,) deduced from the a(go) values in Table 2 are shown plotted in Fig. 4. Also shown is SmithW distribution derived from VLF nose whistler which fits a model of TABLE 1. EXPERIMENTAL Event No.

Date (April ‘64)

(U.T.)

1 2

4th 4th

: 5 6 7 8 9 10 11 12 13 14 15

4th 4th 4th 4th 5th 6th 6th 6th 10th 15th 15th

Time

DATA

fmsx*

f&*

f(f;nax)

(C/S)

(c/s)

0945 1025

0.7 0.8

0.5 0.6

130 100

1405 1320 1454 1705 2038 1440 1240 1415 1748 1750 1940 1030

1.3 1.1 1.4 1.8 1.4 1.6 1.0 1.1 1.5 0.7 1.4 1.4 1.5

0.8 0.5 1.0 I.6 1.2 0,7 0.9 1.0 0.6 0.9 1.0

110 75 95 60 80 90 170 120 120 135 125 125t 140

* Highest and lowest frequencies reached t Measured at l-2 c/s

(=a

THE USE OF MICROPULSATION

171

“WHISTLERS”

.

. 0

A

00

A 0

.

. A

0 0

A

.

Am

Crp

A

.

d 0

*

1-o 2-A 3-.

I

FIG.~.

1

A

f

I

1

6

5

SCALE FREQUENCYVALUESFROM

R,

I

I

(earth‘lrodii)

TABLETPLOTTEDASAFUNC~ONOF

Ro.

constant scale frequency (a N 1 MC/S). Our results do not fit such a model and in addition the N, values are about an order of magnitude lower than an extrapolation of Smiths. 5. DISCUSSION

We now propose to show that our results are in broad agreement with VLF whistler measurements. This is necessary to give an experimental basis to this theory of “micropulsation whistlers” so that it can be used with some confidence in later work. Recent observations of VLF “knee” whistlers show (‘) “that the magnetospheric ionisation profile often exhibits a ‘knee’, that is, a region at several Earth radii in which the ionisation density drops rapidly from a relatively normal level to a substantially depressed There is one”. The reduction in plasma density is about one order of magnitude.“) evidence”) that “the knee exists at all times in the magnetosphere, and that its position varies, moving inward with increasing magnetic activity”. Thus our data can be reconciled to VLF whistler data by assuming a “knee”, at R,, N 5 as shown (dashed curve) in Fig. 4. Dynamic spectra of high latitude VLF whistlers of unusually low nose frequency (corresponding to R, - 7) have been published recently by Carpenter.(s) Assuming that these are “short” whistlers we have deduced (by a technique described in referencet3)) scale frequencies of the order of 100 kc/s. This is in reasonable agreement with our measurements in this region as shown in Fig. 3.

778

R. L. DOWDEN

and M. W. EMERY

TABLE 2. DEDUCED DATA Event No.

Method

&(max)

1

: 2

3 1 : 1 2 1 2 1 2 2 3 3 1

9

10 11

12

13

14

15

: 1 2 3 1 2 1 2 3 1 2 3 1 2 3 1 2 3 1 2

0.67 O-76 060* 0.70 0.74 060* 044 o-71 0.76 0.80 0.61 0.61 0.84 0.60” 060’ 0.65 0.69 ;:;* 0.82 0.60* 0.51 0.48 0.74 0.78 0.60” O-68 066 0.60* 0.86 0.80 0.60* O-66 @64 0.60* O-49 0.56

&

;:; ::; 2.5 1.5 l-7 l-6 2.3 2.3 2.2 3-l 2.3 2-4 2-3 2-7 1.2 1.2 l-6 2.2 23 2-o 1.9 2.5 1.1 1.1 1.2 1.6 1.7 2.3 2.2 2.3 2.4 3-l 2-7

t(O) (set) 76 58 74 44 42 54

&c%) 25 20 20 16 :: 90

g z z 48 52 18 34 46 45 45 50 67 65 98 40 40 24 24 34 24 31 38 30 20 36 42 38 38 45 41

: 60 2 50 ; 70 35 30 120 130 140 45 35 120 25 25 40 30 1:; 100 130 140 300 190

+ Assumed for method 3. 6. CONCLUSIONS

We have shown that there is broad agreement between plasma density measurements deduced from micropulsation dynamic spectra and those from VLF whistler measurements. A more crucial test would be the comparision of measurements made from simultaneous observations of micropulsations and high latitude VLF whistlers from the same region of the magnetosphere. It should be pointed out that the accuracy of measurements from micropulsations is considerably less than that obtained from VLF whistlers. This is largely due to the limit* in dynamic spectral detail imposed by the uncertainty principle Af. At - 1. On the other hand micropulsations have certain advantages : the very low tape speeds required * We

have gone beyond this limit by measuring times over many echoes in each event.

THE USE OF MICROPULSATION

“WHISTLERS”

779

1000

100

N&Ii31

/

10

Method I

1- o 2-A 3-•

2

FIG. 4. PLASMADENSITIES IN THEEQUATORIAL PLANE(NJ DEDUCED FROMTABLE2 PLOITEDAS A FIJNCnONOF i?,,. THB TWO PARALLEL CURVES CORRESPOND TO SMITH'.@" VLF WHISTLER MEASUREMBNTS. TIIECUR~BLABELLEDU = 45 KC/SlSAN ATTBMPTTOFITOURDATATOAMODEL OF CONSTANTSCALEFREQUBNCY. THY BROKEN CURVBIS ANAT-I'BMPTTORECONCILE BOTH SETS OF DATA

BY A “KNEED”

DISTFUBUTION(‘).

(we record at 64 in per hr) allow continuous recording and, as our results appear to show, high latitude phenomena (I?,, - 8) can be observed at low latitudes. REFERENCES 1. 2. 3. 4.

J. A.JACOBS and T. WATANABE, J. Amos. Terr.Phys.26,835

(1964).

R. L. DOWDEN, Planet. Space Sci. 13, 761 (1965). R. L. SMITHand D. L. CARPENTER, J. Geophys. Res. 66,2582 (1961). H. B. LIEMOHNand F. L. SCARF,J. Geophys. Res. 69,833 (1964). 5. R. L. DOUTDEN, Cyclotron emissioninthe“micropulsation mode” (to be published). 6. R. L. SMITH, J. Geophlw. Res. 66, 3709 (1961). 7. D. L. CARPENTER, J. Geoph,vs. Res. 68, 1675 (1963). 8. D. L. CARPBNTER, J. Geophys. Res. 68,3727 (1963). &3IOMe-B3BeCTHbIe BIlAbIMHKpOIIy.ZbCaqHH B g?fHaMHYeCKllX CIIeKTpaX 06HapymxBaIOT pRA HapOCTaIO~ElX TOHOB, npo~3~0~21MbIx, KaK HonaraIOT, gmznepcnet B MarHHTOC@epe. Ha OCHOBe TaKOti IIpe~IIOC~JIK~IEIIIpe~bI~yIm4XaHaHJIH30ByKa3bIBaeTCH, YTO 3TH CIIeKTpbI MOryT 6bITb HCIIOJIb30BaHbI AJIR OqeHKM IIJIOTHOCTIIIIJIa3MbIBO BHeIIIHetiMarHHTOCf#epe (OT IIRTH a0 BOCbMH paA&IyCOB 3eMJIII)IIOCpeACTBOM TOP0 me npHeMa, ~0~0pb1ti npHMeHaeTcR fina aTMoc@epBnx CBHCTKOB BecbMa ~k13~0ti paAIf09acToThI. 3~0~MeTo~HpllnaraeTc~11~M~1Kponyabca4~~1~,Ha6nlo~aeMb1x~ro6apTe, B aIIpeJIeI%%&. Pe3yJIbTaTbI yKa3bIBaIOT Ha 3HaVllTeJIbHOeCOKpameHHe B IIJIOTHOCTEI IInaaMHsanpe~eJIoMnpn6n. na~~pa~~ycoB3eMnu,s~ocornacyeTc~,~ 061qax sepTax, c IIpeAbIny4HMEi M3bICKaHHRMM Ha IIpeAMeT BeCbMa HH3KOZt pafiAO'IaCTOTbI.