The relationship of auroral absorption to the electron energy distribution of the plasma

PImel. Pnnted

Space Sci., Vol. 32, No. 4, pp. 391-398, in Great Britain.

1984.

0032~ 0633/8453.00+0.00 Q 1984 Pergamon Press Ltd.

THE RELATIONSHIP OF AURORAL ABSORPTION TO THE ELECTRON ENERGY DISTRIBUTION OF THE PLASMA JOELLE

Herzberg

Institute

MARGOT-CHAKER

of Astrophysics,

National Canada

and A. G. McNAMARA

Research Council K 1A OR6

(Received in final

form

of Canada,

Ottawa,

Ontario,

15 July 1983)

Abstract-An amoral absorption event in the D-region of the atmosphere has been studied by simultaneous measurements ofelectron temperature, electron density and hyperthermal electrons with a Langmuir probe, and of radio absorption coefficient by 30 MHz riometers. The absorption of the radio waves cannot be explained only by the enhancement of the electron density but requires that the electron collision frequency v be increased above its normal value by the presence of a high energy tail in the electron distribution function. A model is used to determine the characteristics of the hyperthermal electrons in order to evaluate their contribution to the collision freauencv and to the absorption coefficient. Good agreement is found between theoretical and experimental values. 1

_

1. INTRODUCTION

Geomagnetic and aurora1 activity is frequently accompanied by a radio wave absorption called aurora1 absorption. Such an event is characterized by increased absorption due to modification ofthe aurora1 plasma parameters resulting from the entry ofenergetic particles into the upper atmosphere. For a long time, it has been known that the maximum absorption at high latitudes generally lies in the range 60-90 km and Hultqvist (1964b) mentions that in most of the studied cases, the peak is located at an altitude higher than 72 km so that the aurora1 absorption occurs in the Dregion of the ionosphere. This is the result of the relatively high collision frequencies in this region and of the enhanced ionization due to the penetration of aurora1 electrons down to these altitudes. To reach the lower level of the ionosphere, the incoming spectrum of particles must have a hard component with electrons having an energy exceeding 30 keV (Hargreaves, 1979). Most authors consider that the absorption is produced mainly by the electron density enhancement rather by an increasing of the collision frequency. Generally, no investigation is made concerning the latter and its influence on results. Miyazaki (1975) deduced a collision frequency profile from electron density and absorption measurements assuming that the collision frequency could be represented by a loglinear law with altitude. The study was performed on 14 aurora1 absorption events and the same profile of collision frequency for the 14 cases was sufficient to explain the different measured absorptions. On the

NRCC

23048. 391

other hand, no substantial enhancement ofthe collision frequency was observed compared to undisturbed profiles in the high-latitude region. However, as indicated by Hargreaves (1980) and Hultqvist (1964a),in some cases calculations of specific absorption are uncertain because of the uncertainty of the collision frequency. Due to the high variability of the aurora1 plasma and also to the insufficient number of data in the D-region, it is often difficult to obtain comparable aurora1 absorption events. The phenomena involve an incoming electron spectrum of which the flux and the shape are variable so that the same absorption could be obtained for different initial conditions for the ionizing electron spectrum. It seems that, at least in some cases, the enhancement of the collision frequency could play a role in the absorption process. As mentioned by Reid (1964), the new electrons created by the primaries are produced with substantial energies and take a finite time to reach thermal equilibrium so that, during this time, they are capable of absorbing wave energy by virtue of their collisions with neutral species. Thus under certain conditions, the contribution of the non-thermal electrons might be an observable part of the total absorption. However, to our knowledge, no experimental evidence has been published. Our purpose is to show that, under certain conditions, the aurora1 absorption is essentially related to the increase of collision frequency. We present a case in which the electron density enhancement is not sufficient to explain the absorption of radio wave energy. It is shown that a strong increase ofthe collision frequency is produced by the high-energy tail of the electron distribution function. This non-thermal

J. ~ARGOT-CHAIR

392

and A. G. MCNAMARA

component is su~ciently populated to be clearly seen by a Langmuir probe and leads to an enhancement of the cothsion frequency by about a factor of 10 at about 75 km. 2. ELECTRON ~MPERATUR~

DENSITY AND MEASURE~E~

The rocket (Right AAF-IV-17) was launched from Churchill at 05:25:00.3 U.T. on 14 January 1969 (23 : 25 : 00.3 L.T.) during an aurora1 absorption event. The data anrtlyzed were obtained from a spherical probe of radius rP = 0.32 cm, mounted at the extreme forward end of payload.The altitude rangeinvestigat~d was the D-region between 74 and 98 km, this latter altitude corresponding to the apogee of the rocket. The 98 km apogee was particularly favourable for these measurements since it ensures maximum accuracy of the measurement-the probe velocity was subsonic through much of the region, changes due to ionization g~dients during the voitage sweeps were minimized, and a large number of sweeps were obtained for analysis. The order of magnitude of the electron density and temperature shows that the probe operated in the orbital-motion-limited regime so that the classical probe theory could be employed over the investigated altitude range (~cNamara, 1969). In part of the flight, the probe characteristics show the presence of a strong hypertherma1 electron component characterized by distortion ofthelinear ion collection siope as the probe potential is made sufficiently negative. At some point the slope rapidly changes and the ion wing adjusts to its normal level marking the disappearance of a hyperthermai component..she point where the hy~rthermai electron current is located is around - 3.5 V. An observed V-I characteristic, with a normal thermal one dotted, is shown in Fig. 1. A detailed discussion of the method employed in the analysis of the probe data and of the accuracy of our measurements in the D-region will be undertaken in a further paper (to be published). Presently, we give only the electron density and temperature profiles obtained during the flight AAF-IV-17. The electron temperature profile is presented in Fig. 2. It is seen that the temperature T, covers the range 240-600 K from 84 to 98 km. Below 84 km, the accuracy of the electron temperature measL~rement deteriorated because the signal was too small for adequate determination of the temperature. We have assumed that below 84 km, the electrons were in thermal equilibriulll with the neutrat species so that ‘&has been taken equal to 200 K. The error introduced in the

I,

PROBE

A0

FIG.

1.

VOLTAGE

I

2

(VOLTS 3

PROBE VOI~TAGE~URR~~TCHARA~~RIST~C IN THE

PRIBENCE

OF A HYPER~ERMAL

ELECTKON

COMPONENT

NEAR

3.5 eV. The dashed line indicates the characteristic of the thermal background with the hyperthermal component removed.

electron density measurement is only weakly influenced by this assumption. The apparent random variation of the electron temperatures displayed in Fig. 2 may be attributed to several causes. The primary cause of the scatter in T, values is believed to be due to the rather small number of data points (5--10 data points even at the digitization rate of 1000 samples s- ‘) which occur on the exponential rise of thermal electron current during the sweep when T, is very low. Other possible sources of variation are a real temporal variation in T,, or small rapid fluctuations in the vehicle potentiaf due to spin and coning motions. The latter perturbations are small and are minimized by the very short duration of the exponential rise portion of the V-Xcharacteristic. Spin and wake disturbances to the probe current are rendered negligible by the axial symmetry of the probe on the extreme forward tip of the payload. A mean profile, indicated by the solid line on this figure has been calculated byaleast squaremethod. it will benoted that the measured electron temperatures at upper altitudes are in good agreement with previous measurements in the aurora1 ionosphere (~c~amara, 1969 ; Jespersen et al., 1964).

The relationship

of aurora1

absorption

to the electron

I

I

I

I

400

500

600

TEMPERATURE

1

951

I I03

701 IO' THERMAL

ELECTRON

I 104 DENSITY

/ 105

(m-3)

Frc.3. THERMAL ELECTRONDENSITY PROFILE,WMPARED TOA TYPICAL MID-LATITUDE NIGHT-TIME PROFILE (BELROSE et al., 1972).

T, cx 200 K below 84 km

3. ABSORPTION

COEFFICIENT

COLLISION

AND

FREQUENCY

During the flight AAF-IV-17, an absorption measurement was performed by means of two 30 MHz riometers. The beam of one was pointed down range and the other was pointed in the polar direction. The recorded absorption vs time are represented in Fig. 4 for the two riometers. They indicate similar values which are indicative of a uniform absorption over a large region. Hence, the altitude profiles are not subject to spatial variations. The rocket was launched during the decreasing phase of the absorption, but during the flight the absorption was nearly constant and equal to about 0.9 dB as can be seen in Fig. 4. Our purpose is to explain the measured value of the absorption coefficient, A, which is given by the expression (Hargreaves, 1979) A = 4.5 lo-’

751/

393

(K I

FIG. 2. ELECTRONTEMPEKATIJRE PROFILE. the mean profile and the dashed line the approximation

‘The electron density profile is given in Fig. 3 where it is compared to a typical quiet mid-latitude night-time profile (Belrose et al., 1972). It is observed that the ionosphere was strongly disturbed during this event. The enhancement of the electron density n, is particularly important below 90 km. The penetration of ionizing primary electrons down to 74 km involves initial energies higher than 100 keV.

100

of the plasma

300 ELECTRON

The full line represents

energy distribution

n,(WrW~ dH s ?(H) + 0?(N)

(1)

where all the parameters are expressed in M.K.S. units, o, n, and v being respectively the angular frequency of the radio wave, the electron density and the effective electron-neutral collision frequency. In relation (I), the integration should be performed over all ionospheric heights H. However, because aurora1 absorption essentially occurs in the D- and lower E-regions as discussed in the introduction, we restrict the integration to the altitudes covered during the flight.

394

J. MARGOT-CHAKER and A. G. M~NAMARA

m 0.6 Q ; 0.8 0 E l.Og 1.2 % ci 1.4-

Polar

riometer

T-o 1

I

I 0

I

I

200

300

I

100 FLIGHT

TIME

(SEC)

FIG. 4. ABSORPTION COEFFICIENT vs TIMEFOR DOWNRANGE ANDPOLAR30 MHz RIOMETERS. The heavy bar marks the interval over which the rocket data were analyzed.

In order to determine A, a profile of collision frequency is needed. It can be determined at each altitude interval by using the relation (Heald and Wharton, 1965) v(H)

=

-

1 u;,N(H)fJ(l+ 3%(H) s 0

-I_

dfo(H, 4

x ___ do

v4nv2 dv

(2)

where N, 0 are respectively the neutral density and the electron-neutral collision cross-section for momentum transfer and Jo is the electron distribution function which, in a first approximation, will be assumed to be Maxwellian so that 3/z

x exp ( -mu2/2kTe(ff))

(3)

where m denotes the mass of the electron. The collision cross-section c has been taken from Gilardini (1972). For energies lower than 2.5 eV, CTis well represented by the expression given by Mantas (1973) assuming the atmosphere is composed of 80% of N, and 20% of 0,. Above 2.5 eV, we have fitted the experimental results of Gilardini with an empirical law given by : a(E ? 2.5 eV) = 1.21 lo-i9

E”.ih (m’)

where E is expressed in eV. The collision cross-section is plotted in Fig. 5.

(4) (T

The neutral density profile has been taken from the 1959 ARDC model. Knowing n,(H), T,(H) and N(H), the collision frequency at each point, v(H), can be calculated from the relation (2). The profile obtained is given in Fig. 6 where it is compared with one of the two profiles used by Hultqvist (1964a). The absorption coefficient can be derived from the relation (I) by using f= w/27r = 30 MHz. The differential absorption profile dA/dH is presented in Fig. 7 where it can be seen that maximum absorption occurs around 86-90 km. The integral (1) is estimated by assuming that the differential absorption varies linearly between each calculated point. An absorption close to 0.2 dB is obtained. This value is lower by a factor of 4.5 than the measured absorption (- 0.9 dB). Even if the contributions of altitudes lower than 74 km and higher than 98 km are taken into account, it is clearly impossible to explain the high value of the measured absorption only by the electron density enhancement. The only phenomena able to increase substantially the absorption is that the collision frequency is enhanced above its normal value, due to the contribution of the non-thermal electrons observed on the probe characteristics.

4. INFLUENCE OF THE HYPERTHERMAL ELECTRONS ON PLASMA PARAMETERS For reasons which will be largely discussed in a further paper (to be published), we assume that the nonMaxwellian part of the electron distribution function

The relationship of aurora1 absorption to the electron energy distribution of the plasma

I Manta,

1973

2 Gllordini,

lo-20L

1972

1

I111111

10-1

IO.2

395

IO ENERGY

(eV)

F1c.5. ELECTRON-NEUTRALCOLLISIONCROSS-SECTIONFOR MOMENTIJMTRANSFERASAFUNCTIONOFTHEENERGY.

Gaussian

can be represented by a Gaussian function centered on E, = 3.5 eV. Experimental (Lee et al., 1980) and theoretical (Jasperse, 1977) works support these assumptions concerning the electron distribution tail in the ionosphere. Thus the total distribution function can be written as

wheref,

and f, are respectively

312

the Maxwellian

exp (- mv2/2kTe)

fo(4 = neo $$ (

P>

f;(u) = ~,,a exp(-m(v--,,,)‘/2kT,).

(5)

.1’(u)= fo(4 +f,(u)

parts given by

and the

I

I. Collision

frequency

proflle

from

2 Collusion

frequency

proflle

for o Maxwellion

2

3

4 Ix’, COLLISION

5

(7)

A schematic plot off for T, = 600 K is given in Fig. 8. n the Maxwellian and eu and n,, are respectively Gaussian densities, v,, is the velocity corresponding to

tot -

7c

(6)

Hultqvist,

6 FREQUENCY

7

1964

o.

distribution

8

9

IO

II

(IO+%-‘)

FIG.6. ELECTRON-NEUTRALCOLLISIONFRE~UENCYPROFILEFORAMAXWELLJANJ~ISTRIHUTIONCOMPAREI~WI~H A PROFILEUSED BY HuLTQvJsT(~~~~~).

396

J. MARGOT-CHAKER and

iO0

-

Total

;i T

absorption

= 0.2 d6

go->

A. G. MCNAMARA

density n,, is needed. By applying the Langmuir theory to a Gaussian function, a relation between the hyperthermal current i,, and the related density can be found. The derivation of this relation will be given in more detail in the further paper previously mentioned. We show that i,,, can be approximated by :

: 0 w I

i,, = -4nr&.,eJ~ 80 -

701, 2

4 6 dA &lFFERENT’AL

8

10 ABSORPTION

12

14

( 10-3dE/hm)

(1 + &).

(12)

On the other hand, it is found experimentally that the floating potential V, varies from about - 2 to - 0.35 V. For such values, it can be easily shown that the thermal electron current i,, is quite negligible with respect to the ion current ii. Thus for V 6 V,, the total current I = ii + i,, where

16

FIG. 7. DIFFERENTIAL ABSORPTION PROFILE dA/dH. is given by the area delimited by dA/dH and is about 0.2 dB.

ii = 4n?.;eni(~~‘z(

1 - ;)

(13)

The total absorption

eEi being the ion energy assumed

equal to the neutral

the energy E, (3.5 eV) and T,, which represents the standard deviation, is related to the width at half-height Wby: ,,(eV)=E,=(Jq-&)l/lnZ

(8)

where E,,, and W are expressed in eV. In the relation (7), the normalization chosen such that eRj”i(u)4xu2uz dv = ne,.

factor

c( is

(9)

I The width W is assumed to be sufficiently small to ensure that E, << E,. This condition is well satisfied if W < E,/2. Such a value for W is in good agreement with the experimental and theoretical works previously mentioned. Thus if E, <
fo TE=6000K

i

(10) The following calculations have been performed by assuming W = 1 eV. Now, the collision frequency can be derived from relation (2) by replacing f0 by f =fO +fi. Relation (2) becomes 1 v(H) = -__ m N(H)cT(v)v; 3%(H) s 0

x

(fo(u)+ftW)v4nv2

where n,(H) = n,,(H) + n,,(H). In order to evaluate v(H), the hyperthermal

du (11)

E, ELECTRON

ENERGY

(eV)

FIG.8. SCHEMATICPLOT OF THE ELIXTRONDISTRIBUTION FUNCTION~"=~~+~, FORT,= 600K,E, = 3.5eVand W= electron

~I, II ev

The relationship of aurora1 absorption to the electron energy distribution of the plasma particle energy. By combining Ei << E,, it finally gives n

e’

=-

dl

397

(12) and (13) and taking I//-Ei

(14)

112

dV

where dl/dV is then the slope of the current collected by the probe in the ion accelerating regime between - 3.5 V and the floating potential V’, the latter being measured with respect to the plasma potential. The hyperthermal electron density n,, obtained by means of relation (14) is given in Fig. 9. It is observed to be nearly constant down to 81 km and then decreases sharply with altitude below 81 km. By comparing the densities neo and n,, (Figs. 3 and 9)it can be seen that the ratio n,,/n,, decreases with altitude. Thus the relative weight of the tail of the distribution in the integral (11) plays a more important role as the height decreases. By applying the relation (ll), a new collision frequency profile is obtained as shown by profile 2 in Fig. 10 where it is compared to profile 1 of a purely Maxwellian distribution. An enhancement by a factor of about 10 is observed at lower altitudes whereas the profiles become similar at upper heights. The differential absorption profile dA/dH obtained by taking into account the hyperthermal electrons is also compared to the profile calculated on the basis of a Maxwellian distribution function in Fig. 11. It clearly shows that the hyperthermal component strongly increases the absorption and tends to displace the maximum absorption toward lower altitudes. The integration of dA/dH from 74 to 98 km leads to an absorption coefficient A = 0.8 dB which is close to the experimental value (0.9 dB).

,011~10’5

I. For D Maxwellion

dlstrlbutlon

2 For a Maxwell~an

+ hyperthermal

IO”

10’6 U,

component

COLLISION

10’8

FREOUENCY

fs-‘I

FIG. 10.ELECTRON-NEUTRAL COLLISIONFREQUENCY PROFILE TAKING INTO ACCOUNT THE HYPERTHERMAL ELECTRON DENSITY.

5. DISCUSSION

AND CONCLUSION

We have shown in the preceding section that the absorption during this event can be explained by the occurrence of a high energy tail on the electron distribution function. This tail has been assumed to have a Gaussian shape centered on E, = 3.5 eV. This assumption is in agreement with the experimental evidence of a sudden rise of an electron component of the current at a potential close to -3.5 V and this observation has mainly determined our choice of E,. However, it is possible that E, is not located exactly at 3.5 eV so that it is useful to test the influence on our results of variations in IZw. 100 I Absorption function 2 Absorpllon

1

:

e

w I

B”/-

701---II__I___L_L._l__L_J 0 NE,

100 200 HYPERTHERMAL

component

3

90 t

300

400

ELECTRON

500

600

DENSITY

700

(cme3)

F1c;.9. HYPISRTHEKMAL ELECTRON DENSITY PROFILE.

‘&

DIFFERENTIAL

for 0 Maxweil~an

d,sir,butlon

= 0 2dB toklng

the hyperthermal

into OCCOU~+ = 0.8dB

ABSORPTION

i10-2dB/km)

900

FIG. 11. DIFFEK~NTIAL

ABSOKPI ION

HYPERTHERMAL

TAKING INTO ACCOUNT

ELECTRON

DENSITY.

Thetotalabsorptionisabout0.8 dB.

THE

398

J. MARGOT-CHAKER and A. G. MCNAMARA

Physically, the presence of bumps in the tail of the electron distribution function can be explained qualitatively as follows. In the range ofenergy between 0.5 and 10 eV are located the levels of vibrational and electronic excitation of 0, and N,. Each of these levels is associated with a cross-section having a narrow shape so that the total cross-section C will present a spiked structure. It can be easily understood that where C is large, the electrons are lost with a large rate whereas when it is small, they are lost with a small rate. Thus, the electron distribution is expected to exhibit dips associated with large values of C and bumps associated to small values. The maximum cross-section for the vibrational excitation of N, is located at about 2.2 eV and the threshold for the first electronic excitation 0, is at about 4.5 eV. Consequently the bump of the electron distribution is expected to lie somewhere between 2.2 and 4.5 eV. If we let E, and W vary respectively between 3 and 4 eV and 0.5 to 1.5 eV, the range 2.24.5 eV is approximately covered. We have found that these uncertainties in E, and W lead to an error less than 4”//, on the total absorption value and can be considered as negligible. The uncertainty related to the neutral atmospheric model could influence the value of the absorption which depends on the neutral density through the collision frequency. From this point of view, it is important to test how strongly the assumed neutral density profile affects the resulting absorption. The results presented in this paper were obtained from the ARDC 1959 model and the absorption coefficient is found to be equal to 0.8 dB. The same calculation has been performed by taking the U.S. standard atmosphere 1976 and 1966 models. In the second case, values for the 60” latitude in January have been used. The absorption coefficients derived from the two atmospheric models are respectively 0.79 and 0.71 dB. Thus the maximum error due to the assumed values of the neutral density is about 11% and lies in the range ofexperimental errors. It is furthermore noted modified

that

the location whichever

assumed. The result

of the absorption the

neutral

density

peak

is not

profile

is

of our investigation is that the relatively high absorption measured during the flight AAF-IV-17 cannot be explained only by enhanced ionization due to the penetration of energetic particles in the D-region of the aurora1 ionosphere. It has been shown that the absorption results essentially from non-thermal electrons which constitute a non-negligible part of the electron distribution function. Their density is not sufficient to substantially increase the total electron

concentration but it contributes to a strong increase in the collision frequency which is responsible for the absorption. Finally the good agreement between theoretical and experimental absorption supports the validity of our method for the calculation of the collision frequency profile.

REFERENCES Belrose, J. S., Ross, D. B. and McNamara, A. G. (1972) Ionization changes in the lower ionosphere during the solar eclipse of 7 March

1970. J. atmos. terr. Phys. 34,627.

Gilardini, A. (1972) Low Energy Electron Collisions in Gases. J. Wiley and Sons, New York. Hargreaves, J. K. (1979) The Upper Atmosphere and Solar Terrestrial Relations: Introduction to Space Environment. Van Nostrand-Reinhold. Hargreaves, 3. K. (1980) D-region electron densities derived by incoherent scatter radar during amoral absorption spike events. J. atmos. terr. Phys. 42, 783. Heald, M. A. and Warton, C. B. (1965) Plasma Diagnostic with Microwaves. J. Wiley and Sons, New York. Hultqvist, B. (1964a) On the height of aurora1 absorption I. P&net. Space Sci. 12, 579. _ Hultavist. B. (1964b) On the height of amoral absorption II. Pldnet.‘Spa>e Sci.‘lZ, 1035. Jasperse, J. R. (1977) Electron distribution function and ion concentration in the Earth’s lower ionosphere from Boltzmann-FokkerPlanck theory. Planet. Space Sci. 25, 743. Jespersen, M., Petersen, O., Rybner, J., Bjelland, B., Holt, O., Landmark, B. and Kane, J. A. (1964) Electron and ion density observations in the D-region during aurora1 absorption. Planet. Space Sci. 12, 543. Lee, J. S., Doering, J. P., Potemra and Brace, L. H. (1980) Measurements of the ambient photoelectron spectrum from Atmospheric Explorer: IAE-1 measurements below 300 km during solar minimum conditions. Planet. Space Sci. 28,947. McNamara, A. G. (1969) Rocket measurements of plasma densities and temperaturesin visual aurora. Can. J. Phys. 47, 1913. Mantas, G. P. (1973) Electron collision processes in the ionosphere. Aeronomy Report No. 54. University of Illinois, Urbana, September 1973. Minzner,R.A.,Champion,K.S. W.andPond,H.L.(1959)The ARDC Model atmosphere 1959. Air Force Surveys in Geophysics No. 115, Bedford, Massachusetts. Miyazdki, S. (1975) Relation between lower ionospheric electron density profiles and cosmic noise absorption during aurora1 zone disturbances. J. Geomagn. Geoelect. 27, 113. Reid, G. C. (1964) The contribution of non-thermal electrons to aurora1 absorption of radio waves. J. geophys. Res. 69, 3296. U.S. Standard Atmosphere supplements (1966). Environmental Science Services Administration. National Aeronautics and Space Administration, United States Air Force. U.S. Standard Atmosphere (1976) National Oceanic and Atmospheric Administration. National Aeronautics and Space Administration, United States Air Force.