Radio-frequency synchrotron radiation from trapped electrons above the auroral zones

phtlet. space sci. 1969, Vol. 17, pp. 389 to 402. Pcrmnon Pmm. Printed in Northem Ireland

RADIO-FREQUENCY SYNCHROTRON RADIATION FROM TRAPPED ELECTRONS ABOVE THE AURORAL ZONES JOHN F. VESECKY Department of Astronomy, University of Leicester, Leicester, England* Abstract-Electrons from the outer Van Allen Belt emit synchrotron radiation most strongly in the radio-frequency range from 5 to 20 MHz when substantial electron fluxes enter the relatively strong geomagnetic fields above the aurora1 zones, i.e. B w 0.15 G and L w 45. Estimates made on the basis of average electron fluxes indicate that the brightness observed by a high altitude Earth satellite would be comparable only with the dimmest portion of the galactic radio background. However the electron flux in this region is highly variable and at times the observed brightness will appear a great deal bri hter than average. Discrimination between synchmtron radiation and the cosmic backgroun t on the basis of polarization is shown to be an applicable technique. INTRODUCTION

The possibility that radio-frequency synchrotron radiation generated by geomagnetically trapped electrons might be observed from the Earth at VHF (30-300 MHz) frequencies was investigated by Dyce and Nakada (1959) with the conclusion that at 30 MHz the emission would be well below the cosmic radio background. However in July of 1962 the Star&h high altitude nuclear explosion injected large numbers of electrons into the inner trapped particle belt and radio observations at 30 and 50 MHz were made by Dyce and Horowitz (1963) and others. Peterson and Hower (1963) successfully analysed these observations in terms of a synchrotron model. As the inner radiation belt returned to normal the observed radio noise approached the background level previous to Starfish, reaching a level within 10 per cent of the background by the end of 1963. Hower and Peterson (1964) considered the case of synchrotron radiation from aurora1 electrons as observed from a ground-based site at Stanford, California. They concluded that “the synchrotron process could quite probably provide a detectable emission from the auroral zone during very severe disturbances” and hence might explain the occasional observation of HF (3-30 MHz) and VHF radio noise from the aurora at midlatitude stations, e.g. Seed (1958), Egan and Peterson (1960), and Hower and Dunlap (1966). Several factors regarding the generation and propagation of synchrotron radiation make satellite observations preferable to ground based ones-principally a satellite’s freedom of position makes it possible to optimize the geometrical factors governing synchrotron radiation from a particular region. In addition high-altitude satellite observations are not handicapped by the high electron density portions of the ionosphere which limit groundbased observations to frequencies above the local ionospheric penetration frequency. The problem considered here concerns possible high-altitude satellite observations of 5-20 MHz synchrotron noise generated by trapped electrons in the magnetospheric regions above the aurora1 zones. The motivation for studying this problem is twofold: first, by means of satellite observations at HF radio-frequencies it appears possible to obtain information about trapped particles above the aurora1 zones in bulk as a function of time, * On leave from the Center for Radar Astronomy, Stanford University and the Stanford Research Institute, Stanford, California, U.S.A. 389 7

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JOHN F. VESECKY

which would be helpful in understanding magnetospheric phenomena; and second, this source of radio noise could be a cause of confusion during satellite radio observations such as those of the N.A.S.A. Radio Astronomy Explorer program if not properly taken into account. In the sections below the formulas relevant to the radiative transfer of radiofrequency energy from the aurora1 electrons to a satellite observer are set out and a model of the magnetospheric plasma is described. This leads to an estimate of the radio brightness to be observed by a high-altitude satellite and a comparison with other possible radio noise sources. A discussion of the use of polarization discrimination as a means of identifying synchrotron noise is then followed by some concluding remarks. SYNCHROTRON

RADIATION FROM ENSEMBLES OF ELECTRONS

To discuss the strength of radio frequency radiation observed at a satellite we consider the brightness b, i.e. the energy flux per unit bandwidth at the observer arriving per unit solid angle measured in units* of W, m2, Hz-l and sterad-r. If as will be shown below the ray paths along which the energy flows from the emitting region to the observer can be considered to be straight lines (refractive index w 1) and absorption along these ray paths can be neglected, a solution to the radiative transfer equation is given by bJf)=UfJ+

wJ(f, s) ds = b,O

+ bssnCf)

where the line integral is taken along the ray path from the observer at s,, to infinity. We shall regard the brightness at the observer b,, as composed of contributions from distant cosmic sources b, and from synchrotron radiation emitted by aurora1 electrons b,,,. The emission coefficient Jcf, s) is given by

J(f, 4 = /omPC.L E, W(E) dE

(2)

where P is the power per unit frequency bandwidth per unit solid angle radiated in the synchrotron mode by an electron with energy in the interval dE centred on E and N(E) is the number density of electrons with energies in the interval dE centred on E. P is influenced by a multitude of parameters which are summarized as follows: radiofrequency of observationf, kinetic energy of the electron E, instantaneous radius of curvature of the electron trajectory R (R itself is a function of the magnetic field flux density B, the electron energy E, and the angle a which the electron velocity vector makes with the local magnetic field direction, i.e. a is the electron pitch angle), angle y.~between the direction of emission and the instantaneous orbital plane of the electron, and refractive index ,U of the medium in which the emitting electron is located. In the case at hand several simplifying assumptions can be made as discussed below. For a general review of synchrotron radiation several comprehensive accounts are available, e.g. Peterson and Hower, 1966; Bekefi, 1966; and Ginzburg and Syrovatskii, 1965. The first simplifying assumption is that the electrons in question are in uniform circular motion, a = 42. While this is not strictly true, a does tend to be close to 42 since as a approaches zero the particle tends to approach the Earth’s surface closely and become lost by collisions with particles of the neutral atmosphere. In addition the effect on P of ,u in the emitting medium can be neglected-as shown by Ginzburg and Syrovatskii (1965)provided the frequency of observation is much greater than 2fp2{3fo where fp and f. are the * Rationalizedmks units are used unless stated otherwise.

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plasma and electron cyclotron frequencies in the emitting medium. It is necessary here to distinguish between the electron cyclotron frequency, eB/2?zm, (e and m, being the electron charge and rest mass), and the gyrofrequency for relativistic electrons, fg= fo/y (ybeing the ratio of total electron energy E + E. to the electron rest energy ,!&= 511 kev). It will be shown later that for the region considered here fgM 106 Hz and f.w 4 x 10s Hz; hence for frequencies of observation greater than about 200 kHz the effect of p in the emitting medium can safely be neglected. It should be noted here that the effect discussed above is concerned with the synchrotron emission process itself and not with the effects of p on ray path geometry. To neglect the effects of p on ray path geometry we must further restrict f such that f > f,or f.all along the ray path. Since we will be concerned only with f > 5 MHz and since the ray paths considered will not pass through regions wherefDand f. are greater than the values given above, the effect of p may be neglected in either case. The influence of y on P is quite important for the case at hand. Since we have assumed the case of uniform circular motion (a = 7r/2), y becomes simply the complement of the angle between the ray path and the geomagnetic field direction at the point of emission. Peterson and Hower (1966) make an approximation to the variation of P with y which is relevant here. They note that if, as in the case considered here, f13fo,yS > 0.1, then the variation of P with p can be viewed as a radiation pattern which is approximately gaussian in shape for the energies with which we shall be concerned. The value of y at which the value of P falls by + is given as pl12 M 1.6 x 10s(BF)l12rad. (3) As a further approximation we shall view the variation of P(y) as being P(0) for 1~1< yiry,, and zero elsewhere. Now if we consider only a single electron, P is not a continuous function off. In fact it is non-zero only at harmonics of the gyrofrequency fnand can be written as

where 8 is the Dirac delta function and P, is the power per unit solid angle radiated by the nth harmonic. The factor yE,lf relates a frequency bandwidth to the spread in electron energies which radiate into this bandwidth on the nth harmonic, i.e. the factor is laE/af I evaluated for a specified n knowing nfo = fy.Making the appropriate simplifications in the formula given by Panofsky and Phillips (1962) we have for P,,(E, B, y) P,(E, B, Y) = ~Jn’p(nB),

Iyl <

~1/2

(5) P,(E, B, ~1 = 0 ’ ltvl>

~1/2

where fi = v/c electron velocity divided by light velocity, cois the permittivity of free space, and J,,’ is the first derivative of the nth order Bessel function. We have then for the emission coefficient when jyl < yl12,

J(fs 4 =n+,IE.(B,f),

4 ~1y

j+W,, 4

C-9

where E,, and y are defined by n = fyFo = (E,, + Eo)flE,,fo . Jcf s) is then a function of the observation frequency and the particular point along the ray path which is being

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JOHN

F. VFBECKY

considered. More specifically the quantities which determine J are the angle V, the geomagnetic flux density B, and the differential energy spectrum of the electrons at the points. The evaluation of J requires appropriate models of the geomagnetic field and the trapped electron environment. Here we shall use a dipole model for the geomagnetic field and the trapped electron environment model will be taken up in the section below. There are two relevant absorption mechanisms which are of concern here: fist the sort of collision type absorption encountered in the terrestrial ionosphere in which energy is lost from a wave by means of collisions between free electrons and ambient ions or neutral molecules and second synchrotron self-absorption, i.e. just the reverse of the synchrotron process itself. In the first instance the absorption coefficient K, is given by Ratcliffe (1962, Chap. 9) for the case when f,Jf < 1 and f > vas

(7) where v is the collision frequency between free electrons and ions or neutral molecules. While an ensemble of energetic electrons spiraling in a magnetic field can radiate energy they can likewise absorb energy from a passing wave. Emile le Roux (1960) found that the absorption coefficient averaged over an ensemble of electrons of various energies could be written simply as

where p is the number density of electrons having total energies ET in a range dE, about ET, and Ap dET is the power radiated by electrons with energies in the range dE, about ET per unit solid angle per Hz in a specific direction with a specific polarization. The evaluation of absorption by these two mechanisms will be undertaken later. Since the ray paths to be considered are such that f 3 f,or fo, hence ,U w 1, ray paths can be taken as straight lines. There is however another propagation effect which must be considered, namely the depolarization of initially polarized radiation due to Faraday rotation. As is well known an initially linearly polarized wave travelling through a magnetoionic medium, where f > f9and fo, will have have its plane of polarization rotated through and angle A0 as it travels along the ray path, where A8 is given by Kraus (1966) as A&’M 2.37 x loPf-s

NTB

for conditions such that the QL or quasi-longitudinal Chap. 8)) holds, i.e. where

COS 4

ds

approximation

(9) (see Ratcliffe (1962,

In the above, NT is the local electron number density and 4 the angle between the ray path and the geomagnetic field direction. For the region under consideration the QL condition will hold for all 4 G 87”. For 4 very close to 90” the QT or quasi-transverse approximation will hold, in which case the amount of Faraday rotation will be according to Kraus (1966) about Be/2m,w times the amount predicted by the QL approximation, where o is

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the wave angular frequency. For the case considered here the ratio Be/2mp is about 0.02 atf= 10 MHz. Hence the QL approximation will provide an approximate upper limit to the amount of Faraday rotation A8 and will be the only case considered here. To illustrate depolarization by means of Faraday rotation consider a length of ray path D over which the emission is uniform and linearly polarized in a single direction and over which Faraday rotation ABDoccurs. Now if A0, Q v, the observed emission will remain linearly polarized at the observer; but if A0, > 7~,linearly polarized waves in all directions will be present and the resultant sum will appear randomly polarized. MAGNETOSPHERIC PLASMA MODEL

In constructing a suitable plasma model to evaluate the emission and absorption coefficients and propagation effects two ranges of electron energy are of principal concern: high energy (250 keV G E G 3 MeV) which determines the synchrotron emission coefficient and the component of absorption due to synchrotron self-absorption, and thermal electrons (E G 10 ev), which govern the geometry of the ray path and the component of absorption due to the collision mechanism. In the case of high energy electrons the model of Vette et al. (1966) has been adopted. It represents a codification of numerous satellite measurements made in the period close to August 1964. The model consists in essence of the quantityj,(E, B, L), the omnidirectional flux of electrons in the energy range AE about E at a location in the radiation belts specified by the parameters B and L as devised by McIlwain (1961). Dividing j,, by the velocity of an electron of energy E and converting units the quantities N and p in Equations (6) and (8) can be determined as functions of E, B and L. Large temporal variations have been observed in the trapped electron component of the outer Van Allen belt. At present four prominent types of temporal variations have been observed: (1) Williams (1966a and 1966b) has described dayside variations which show a striking 27-day periodicity and correlation with the planetary magnetic activity index Kp, (2) diurnal variations with noon to midnight ratios of 40: 1 have been reported by Williams (1966b), (3) Maehlum and O’Brien, 1963; Williams and Palmer, 1965; and Williams, 1967 have reported large variations at the times of magnetic storms, (4) Frank and Van Allen (1966) have shown the existence of a slow inward drift of the lower boundary of the outer belt which is correlated with the decrease in solar activity from 1958 to 1964. The point in mentioning these several types of variations is, of course, that the synchrotron emission can be expected to experience similar large time variations. Williams (1966a) for example has observed variations of more than a factor of 108in data from satellite 1963 38c at an altitude of 1100 km and L from 3 to 5. The electron fluxes of the model of Vette et al. (1966) which will be used in estimating the synchrotron emissions are approximate averages between extreme values measured by Frank et al. (1965) with Explorer XIV. Hence it would not be unreasonable to expect occasional increases of 1 to 2 orders of magnitude over the values of b,,, calculated on the basis of the Vette model. To obtain an estimate of the thermal electron density, which is in effect the total electron density NT since thermal electrons are so much more dense than those of higher energy, typical data from the Alouette I topside sounder satellite are extrapolated by means of a power law h*, h being the height above the Earth’s surface. Alouette I electron number density vs. height data from Thomas et al. (1966) which correspond to autumn daytime, solar minimum conditions above magnetic dip latitude 55”N fit a relation of the form N,(h) = ah-8, where NT is the electron number density (m+), h is the height (m) and

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JOHN F. VESECKY

a = 6-2 x lOa’, very well for 400 km G h G 1000 km. Hence extrapolating according to this relation we have at h = 4000 km, i.e. the region of interest here, NT w 108 m-s which implies fD M 105 Hz. Although this is a rather crude estimate NT would have to be more than a factor of three greater than this estimate to affect the results below. ESTIMATED RADIO BRIGHTNESS AS SEEN BY A SATJZLLIlX OBSERVEX In order to apply Equation (1) we must know both the ray path geometry and the emission coefficient along the ray path JCr; 8). Figure 1 illustrates the observational geometry /DIPOLE

-DIPOLE

MAGNETIC FIELD LINES

AXIS

MAGNETIC DIPOLE COORDINATE,

R - EARTH RADII

FIO. 1. A VIEW TAREN PERPRNDXULAR TU THE DIPOLE AXIS OF A DIPOLE MODEL FOR THE GRGMAGNETIC FIRLD SHOWING THE (R, A) COORDINATES OF THE DOMINANT RhQlTlNG REGION. Ray paths being considered will pass through the emitting region toward the observer while

perpendicular to the plane of the figure.

in which the ray paths being considered will pass through the emitting regions toward the observer while perpendicular to the plane of the figure, i.e. perpendicular to the dipole axis. While this observational geometry is not the only possible choice, it does come reasonably close to maximizing b,,, while minimizing propagation effects along the ray path. This geometry is also easily visualized. Since only frequencies greater than 5 MHz will be considered and since both the maximum plasma ($P M 100 kHz) and the maximum electron cyclotron frequencies cfO M 450 kHz) are very much smaller than this, the refractive index may be taken as unity and the ray paths as straight lines. It should be noted that for satellite observations to occur along the ray paths considered here the satellite must be at an altitude greater than that of the emitting region (h w 4000 km). Once the ray path geometry is known the emission coefficient JV; s) can be calculated first using the dipole model for the geomagnetic field to calculate B, L and y at any point s

SYNCHROTRON RADIATIONFROM TRAPPEDELECTRONS

395

along the ray path. Then the Vette et al. (1966) magnetospheric plasma model plus Equations (5) and (6) yields Jcf s). As mentioned previously the electrons are treated as if they were in uniform circular motion, pitch angle equals 90”. Absorption of two different sorts must be considered. Collision type absorption is easily calculated from Equation (7) provided a reasonable estimate for Y, the collision frequency, can be made. The collision frequency for collision between electrons and both ions and neutral molecules is given by Ratcliffe (1962, Chap. 4) as Y= 1.8 x 10-14(T/300)1~BN, + 6.1 x 10-0(T/300)-S~“N,

(11)

where T is the temperature and N, and Nt the neutral molecule and ion number densities. At the altitudes of interest the neutral atmosphere is so thin that it can make only an insign%ant contribution to Y. Models by da Rose (1966) and experimental measurements by Farley (1966) indicate that ion temperatures in the neighbourhood of 500-3OflO”Kare appropriate to altitudes of 400 km and higher. Since YCCpIa the 500°K temperature implies the greatest absorption. Taking Tat 500°K and NI = NT = 108m-a we tid that Yw @7 Hz. At a frequency of 5 MHz in the region of interest, i.e.fp M 100 kHz, Equation (7) yields K, = 5 x lo-19 nepers m- l. Along the ray paths in question this figure represents a maximum of K,. This type of absorption can thus be neglected. A value of K,, the synchrotron self-absorption coefficient, was obtained by evaluating Equation (8) numerically for conditions at the heart of the inner Van Allen belt, where absorption by this process would be of considerably greater effect than in the conditions considered here. This calculation yielded K8 = 3.2 x IO-l4nepers m-l for f= 1 MHz, B w 0.127 G, L M 1.35 and y = 0. We may thus neglect synchrotron self-absorption as well as collision type absorption. To evaluate the integral of Equation (1) the integral is approximated by a sum over the L shells through which the ray path passes, i.e. -Jcf, s) ds :yi(J, B, L) As(L) (12) L dli. #60 where As(L) is the ray path length within a particular L shell. This is necessary because values of N(E) from the Vette et al. (1966) model are available only for discrete values of L and B-in the region of interest values of L are given at intervals of 0.2. The limits over which the sum is taken, i.e. Line to &,,., are determined by the angle + between the ray path and the geomagnetic field which is of course just the complement of ty. Thus an ‘effective’portion of the ray path is determined along which 1~1c ylfa and hence Jcf B, L) is non-zero according to Equations (5) and (6). The estimates of b_(f) resulting from the use of Equation (12) are shown in Figs, 2 and 3, Fig. 2 showing the spatial change in b,, for frequencies in the 5-20 MHz range and Fig. 3 showing barn(f) for L w 4.4 and B M 0.12 and 0.16 G. The values of L and B referred to in Figs. 2 and 3 are,those at the point along the ray path where tc,= 0, i.e. the point where the ray path intersects the plane of Fig. 1. As is evident from Fig. 2 the region considered represents a broad relative maximum of b,,. Additional spot checks show that this region represents a maximum over 2 c L < 5, i.e. ray paths passing through the region of L m 4.4 and B M 0.14 G show the maximum value of bBy,,for 5 < f c 20 MHz. This is true simply because it is in this region that significant outer belt electron fluxes interact with the geomagnetic field to optimize synchrotron emission for 5 < f < 20MHz. Uf)

=

396

JOHN F. VESECKY

Fw. 2. DISTFSBUTION OF OBSBRWD BRIGHTNESSwrm THE REGION IN (B, L) SPACE FROM WHICH THB DOMINANT CKWTIUBUTION COMBS AT FREQUENT IN THB 50-20 MHz RANOR; THJI SXID LINE IMPLIES B m 0.16 G AND THE DASIED LINE Bw 0.12 G.

FREOUENCY

Wlz)

F&. 3. DEVON OF OBSRVED BRIGHTNESS WITH FRBQLIJINC~ FOR RAY PATHS ALONG WHEH THE DOhfINANT CCWTRIBUTION COMES PROM THE REGION L w 4.4 AND B M 0.12 OR 0.16 G.

The range in electron energy which produces the dominant portion of besn is naturally of interest since it is just this energy range which could be studied by observing b,,. As a typical example consider a ray path passing through the region L w 4.6, 3 M @I4 G in Fig. 1. At f = 10 MHz 50 per cent of bssn comes from electrons with energies between 400 keV and 2 MeV and 80 per cent from the energy range 250 keV-25 MeV. Note also from Fig. 3 that bay,(J) cc f-l. COhfPARISON OF 6,

WITH RADIO BACKGROUND NOISE

Fig. 4 estimates of b,, are compared with estimates of the cosmic noise background. Estimates of the cosmic radio background in the frequency range considered here are rather difficult since the masking effect of the ionosphere makes ground-based observations In

SYNCHROTRON

RADlATION

FROM TRAPPED ELECTRONS

ELLlS( 1964) OROUND BASED

_.,..~.-./

\

WART2 M841 ALOUETTE -

397

./

-ic__

1100 X AVFiftAt3E FLUX1 PARTHASARAYHV W661 GROUND BASED

AURORALCASE 00 X AVERAGE f3.l

AURORAL‘CILSE (AVERAGE FLUX)

ELLISt tS66) be,

GROUND BASh

-4

/

\

b*,

c.-r-

bgc--I

\ I

I

I

lo6

1

f

lo’

I

I

IO’ tf

FREQUENCYfHzf

FIG. 4. cbd.P-

OFSYWEROTRGN JXMWIONFROMAROVETHE AuRORALREGIONS(b,,) S3VERAL l?STlMATESOF THE IXSMIC NOISE BACKGROUND (&Q).

WSTIi

diflkult and satellite observations suffer from the difficulty of deploying high resolution antennas from spacecraft. In Fig. 4 the results labelfed Ellis (1964 and 1966) and Parthasarathy (1966) are shown as representatives of ground-based measurements while the measurements of Hartz (1964) are showu as representative of satellite measurements. The curves of Ellis (1964) observed at a galactic latitude and lon~tude of about O-80“ and 325” respectively represent the maximum value of the cosmic background li,. Estimates of a minimum value for b, are not readily available; however the 47 MHz survey by Ellis and Hamilton (1966)-labelled Ellis (1966) in Fig. 4-indicated that for regions along the galactic plane, the brightness was less than 5 x 10-B W m-a Hz-1 sterad.-l and we shall take this as an estimate of the minimum value of b,. The spectral curve of Fig. 3 is shown multiphed by unity* teu and one hundred to illustrate the approximate levels to be expected during periods of both average and enhanced electron flux. The curve of Fig. 3 corresponds to an average value of the omnidirectional electron flux (.?Z> 05 MeV) of 1.5 x lw” electrons m-a set-l, at B = 0.14 0, L = 4.6. The upper curves thus correspond to flux levels of about 15 x 101’and 15 x lo” electrons m-2 XC-~. As was noted by Frank et al. (1965), the increases in electron ffwr in the outer

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JOHN F. VESECKY

belt usually favours the higher energy electrons. For example, the E > 230 keV electron flux might increase by a factor of 10, while the E > 1.6 MeV flux increased by a factor of 100. Such a situation would tend to increase the synchrotron emission at higher frequencies more than at lower ones, making the aurora1 case curves more horizontal. As can be seen the detection of aurora1 synchrotron emission against the cosmic background will not be easy, for on the average the aurora1 radio brightness is only comparable with the dimmest portion of the cosmic background and thus would be dominant only when viewed against this portion of the cosmic background. At times of enhanced electron flux the prospects are brighter, but bsyn is still less than b, in the brightest portion of the cosmic background. However, a scheme involving polarization discrimination, which is described below, brightens the prospects of observing b, a good deal further. The considerations above involve only a comparison with the radio background due to cosmic sources. Radio noise from the Sun and terrestrial sources should also be considered though they could be discriminated against on the basis of direction or signal characteristics. In considering these sources it is necessary to make the comparison on a flux basis rather than brightness since it is unlikely that satellite antennas will be able to resolve the Sun at wavelengths around 30 m. To estimate the flux S, at the satellite antenna due to aurora1 synchrotron emission the solid angle s2 subtended by the source must be known. As an example case suppose the satellite is orbiting at a geocentric radius of 2 Earth radii and has an antenna pointed such that ray paths to the antenna from the region in question are perpendicular to the geomagnetic dipole axis, i.e. the situation of Fig. 1. The region in question bounded by the lines marked L = 4.0, L = 50, B = O-12 and B = O-16 is then at a distance of about 1 Earth radius and the aforementioned boundaries subtend an angular region about 0.15 by O-2 rad. or sl, = 0.03 sterad. We have then for the average auroral electron flux andf = 10 MHz, S, = bsrnQd M IO-% W m-a Hz-r. This value for S, can not be directly compared with values for the quiet time solar flux at f = 10 MHz because to the author’s knowledge no such measurements have yet been made. Based on the theoretical brightness distribution of Smerd (1950) the solid angle subtended by the radio Sun at f = 10 MHz is Q, < 1O-3 sterad. Hence, extrapolating the results given by Kundu (1965) to f m 10 MHz and assuming an antenna beam solid angle equal to QA, i.e. greater than Q,, yields S, m lO-% W m-2 Hz-l and we see that S, M S,. The quiet Sun is then in general less likely to be a source of interference than the cosmic background considered earlier, The disturbed Sun will of course produce a signal as much as 105-104 times stronger than the quiet Sun at these wavelengths and hence at these times would very likely obscure any aurora1 noise even if the sun were in a direction not close to the maximum antenna response. The possibility of interference from terrestrial sources should not be overlooked. A simple example is instructive. Consider a 10 kW transmitter situated at the subsatellite point operating in a 10 kHz bandwidth at a frequency of 10 MHz with an antenna gain of unity toward the satellite. The flux density at the satellite (assumed here as above to be at an altitude of one Earth radius) S, M 2 x 10-15 W m-B Hz-l, which is nine orders of magnitude greater than S, calculated above. Lightning would provide greater power over a wider bandwidth though it occurs only occasionally at a particular spot. This could indeed be a serious problem. Fortunately there are several mitigating factors. To begin with only terrestrial radio sources near the subsatellite point are likely to interfere since terrestrial signals not coming from this region would in general be blocked by the ionosphere. The details of this situation are, of course, dependent on ionospheric conditions, the

SYNCHROTRON

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FROM TRAPPED ELECTRONS

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radio-frequency of observation, and the terrestrial source location. In addition this subsatellite region could well coincide with an uninhabited portion of the Earth’s surface where transmitters seldom operate and where lightning is infrequent, e.g. the polar regions. In fact the satellite is likely to be over polar regions when it is closest to the emitting region. Overall then, cosmic background noise is most likely to make auroral synchrotron emission unobservable. DISCRIMINATING AGAINST THEi COSMIC BACKGROUND ON THE BASIS OF POLARIZATION

At frequencies of around 10 MHz the cosmic background is presumably randomly polarized though to the author’s knowledge no measurements have been made-Muller et al. (1963) at 610 MHz and Mathewson and Milne (1964) at 408 MHz have measured polarized components in the galactic background which are on the average a few per cent or less. Since synchrotron radiation is strongly polarized at the source, it is in principle possible to detect it against the stronger but randomly polarized cosmic background. By the use of rather simple techniques, a strongly polarized signal can be detected against a randomly polarized signal more than 10 times stronger. It thus seems worthwhile to investigate this technique in connection with aurora1 synchrotron emission. Knowing something about the polarization of the signal would of course be useful on its own account. In the case of straight line ray paths the electric vector of the radiation from an electron in circular motion is polarized in a direction perpendicular to the magnetic field at the source provided the ray path is perpendicular to the magnetic field at the source, i.e. ty = 0. If fp # 0, an out-of-phase component, perpendicular to the aforementioned component, will also be present causing the emitted radiation to be elliptically polarized. However, for small values of y(& 1/2y), this cross polarized component will be less than 10 per cent of the principal component and will never exceed it. Although we have assumed in making our estimates of b, that all along the ‘effective’portion of the ray path the electrons perform uniform circular motion with y = 0, this is of course not strictly the case in reality. However the electrons do have pitch angles close to 90” and electrons with y near zero will make the major contribution to b,,,. Hence the synchrotron emission from auroral electrons will be strongly polarized at a satellite observer provided the Faraday rotation depolarization effect mentioned previously is negligible. In Fig. 5 the amount of Faraday rotation for a ray path of length one earth radius is plotted for several values of 4. The curves are drawn only where the QL approximation is valid. Since the ‘effective’portions of the ray paths are, in all cases considered, less than 1 Earth radius (generally on the order of several tenths) and since over most of the ‘effective’ portion 4 is close to 90” (a typical value would be 4 < 80”), it is safe to say that the polarization discrimination technique could be used at frequencies of 8 MHz and above and in all likelihood down to about 5 MHz. As can be seen from Fig. 4 a factor of 10 or more improvement in the detectability of b,,, vis-a-vis b, by the use of this technique would put enhanced aurora1 synchrotron noise on a par with the brightest cosmic background. CONCLUDING REMARKS

In view of the discussion above, the detection by satellite observations of synchrotron noise at frequencies of 5-20 MHz from trapped electrons above the aurora1 zones appears distinctly possible under appropriate circumstances. Favourable conditions would occur during times when the high energy electron flux above the auroral zones is enhanced, e.g. during geomagnetic storms, and when the emitting region L m 4.5, B w 0.14 G is viewed

JOHN F. VESECKY

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$I::/

I 2

5

IO

20

50'

FREOUENCY(Ht)

by the satellite observer against the dimmer portions of the cosmic background. The use 01 polarization discrimination in the observing receiver system would most certainly be a great asset, enhancing the polarized synchrotron component by a factor of 10 or more relative to the randomly polarized cosmic background. A satellite antenna capable of moderate resolution (=lO-20” beamwidth) would also be a considerable asset in that it would localize the region from which the synchrotron noise is emitted and insure that the emitting region would fill the antenna beam for a significant portion of the satellite orbit. There are in effect two aspects to aurora1 synchrotron noise in that it can be either the desired signal or an interfering one. In the first case the signals would be of significance in the observation of trapped electrons. While satellite particle detectors give rather specific information about trapped particles at a specific point in space at a specific time, synchrotron emission observations would give information regarding a large volume of space as a function of time. Such observations could provide a sort of overall view of the response of aurora1 electrons in the energy range 250 keV-2.5 Mev to relatively short time scale changes in solar activity. As was noted above the observed synchrotron emission is a function of many parameters and hence observations of the strength, polarization and frequency spectrum of synchrotron emission cannot uniquely determine the flux, energy spectrum and pitch angle distribution of the emitting electrons. However by making reasonable assumptions regarding some parameters others can be determined. For example

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FROM TRAPPED ELECTRONS

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it is well known that if the energy spectrum of the emitting electrons is given by N(E) dE = KJ14 dE, the frequency spectrum of the synchrotron emission from high energy electrons is proportional tof+r-1)‘2J. As was mentioned briefly in connection with measurements of the cosmic radio background, various satellites containing receivers operating in the MF (300 kHz-3 MHz) and HF (3-30 MHz) ranges have been orbited. In making estimates of the cosmic background from data obtained by these satellites the effects of synchrotron emission from geomagnetically trapped particles have been neglected. This neglect is most probably justified since these spacecraft carried only low resolution antennas. However in the future low frequency radio astronomy satellites, e.g. the NASA Goddard Radio Astronomy Explorers, with antennas of substantial resolution at MF and HF frequencies will be launched. As antennas of higher resolving power are employed, synchrotron radio noise from trapped electrons becomes more significant as a possible source of interference. The possibility of interference will be particularly great when high resolution surveys of low brightness regions of the sky are attempted. AcknowZe&ement.r-The author would express his thanks to his colleagues at the University of Leicester and at the Center for Radar Astronomy and Dr. A. M. Peterson in particular for advice and encouragement. The author is also grateful for financial support from the University of Leicester, the National Aeronautics and Space Administration, and Tri-Services Contract Nonr 225 (83) admiistered by the OtBce of Naval Research.

BEKE~,G. (1966). Radio&n Processes in Plasmas, p. 117. Wiley, New York. DA Rosa, A. V. (1966). The theoretical timedependent behavior of the ionospheric electron gas. J. geophys. Res. 71,4107. DYCE,R. B. and HOROWITZ, S. (1963). Measurements of synchrotron radiation at central Pacific sites. J. geophys. Res. 68,713.

Dvcs, R. B. and NAKADA,M. P. (1959). On the possibility of detecting synchrotron radiation from electrons in the Van Allen belts. J. geophys. Res. 64,1163. &MN, R. D. and b3TERSON, A. M. (1960). Am-oral noise at HF. J. geophys. Res. 65,383O. Em, G. R. A. (1964). Spectra of the galactic radio emissions. Nature, Lmd. ?oq 171. EUIS, G. R. A. and HAMUTON,P. A. (1966). Cosmicradio noise survey at 4-7 MC/S. Astrophys. J. 143,227. FARLBY,D. T. (1966). Observations of the uatorial ionos here using incoherent backscatter. EIcctron Density Projles in the Ionosphere and Exosp“4, re (Ed. J. F ri!agen). North-Holland, Amsterdam. FRANK,L. A. and VAN ALLEN, J. A. (1966). Correlation of outer radiation zone electrons (E, > 1 MeV) with the solar activity cycle. J. geophys. Res. 71,2697. FRANK, L. A., VANALLEN,J. A. and HILLS,H. K. (1965). A study of charged particles in the Earth’s outer radiation zone with Explorer XIV. J. geophys. Res. 69,217l. GINZBURQ,V. L. and SYROVATSKII, S.I. (1965). Cosmic magnetobremsstrahlung (synchrotron radiation). Annual Review of Astronomy and Astrophysics (Ed. L. Goldberg et al.), p. 297. Annual Reviews Inc., Palo Alto, California. HARTZ, T. R. (1964). Observations of the galactic radio emission between l-5 and lOMc/s from the alouette satellite. Annis Astrophys. 27, 823. Howe, G. L. and DUNLAP,F. C. (1966). High frequency am-oral noise. J.geophys. Res. 71,1512. HOWER,G. L. and PETERSON, A. M. (1964). Synchrotron radiation from auroral electrons. J.geophys. Res. 69, 3995. KRAUS, J. D. (1966). Radio Astronomy, p. 144. McGraw-Hill, New York. KUNDU,M. R. (1965). Solar Radio Astronomy, p. 117. Interscience, New York.

LE Roux, E. (1960). Theorie classique de I’absorption d’energie de rayonnement par des particules. Ads Astrophys. 23, 1010. MAEHLUM, B. and O’BRIEN,B. J. (1963). Study of energetic electrons and their relationship to auroral absorption of radio waves. J. geophys. Res. 68,997. MATHEWSON, D. S. and MILK, D. K. (1964). A pattern in the large-scale distribution of galactic polarized radio emission. Nature, Land. 203, 1273. McILw~~N, C. E. (1961). Coordinates for mapping the distribution of trapped particles. J. geophys. Res. 66,368l.

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E. M., BROVW,W. N. and TINBINXN, J. (1963). Galactic background MULL.P.R, C. A., BE-, polarization at 610 MHz. Nature, Lend. 200,155. PANOFSKY,W. K. H. and PHILLIPS,M. (1962). CZassicalElectricity and Magnetism, 2 Edn, p. 369. AddisonWesley, Massachusetts. PARTHA.%RATHY, R. (1966). Private communications. Prrngsos A.3M. and HOWER,0. L. (1963). Synchrotron radiation from high energy electrons. J. geophys. *, PETERSON,A. M. and HOWER,G. L. (1966). Theoretical model of synchrotron radiation and comparison

with observations. Radiation Trapped in the Earth’s Magnetic Field (Ed. B. M. McCormac), p. 718. Riedel, Holland. RATCUFF%, J. A. (1962). 7% Magneto-ionic Theary and its Applications to the Zonosphere, Cambridge University Press, Cambridge. SBBD,T. J. (1958). Observations on the aurora australis. J. geophys. Z&s. 63,517. SMFXD,S. F. (1950). Radio-frequency radiation from the quiet sun. Aust. J. scknt Res. A3, 34. THOMAS, J. O., RYCROFF,M. J., CXXIN,L. and CHAN,K. L. (1966). The topside ionosphere, II, experimental results from the Alouette I satellite. Electron Density Profiles in the Ionasphere and Exosphere (Ed. J. Frihagen), p. 322, North-Holland, Amsterdam. Vanx, J. I., LUCERO,A. B. and Wruor-rr, J. A. (1966). Models o the TrappedRadiation Environment,Vol. 2: Inner and Outer Zone Electrons. National Aeronauctics an dfSpace Administration, Washington, D.C. W-, D. J. (1966a). A 274~ periodicity in outer zone trapped electron intensities. J.geophys. Res. 71, 1815. W-, D. J. (1966b). Outer xone electrons. Radiation Trapped in the Earth’s Magnetic FieM (Ed. B. M. McCormac). Riedel, Holland. Ww, D. J. (1967). On the low-altitude trapped electron boundary collapse during magnetic storms. J. geophys. Z&s.72,1644. W~LUMS, D. J. and P-R, W. F. (1965). Distortions in the radiation cavity as measured by an 1100 km. polar orbiting satellite. J. geophys. Res. 70, 557.