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Results of rocket measurements in the lower auroral ionosphere
Journal of Atmospheric andTerrestrial Physics, 1969,Vol.31,pp.835-844.Pergamon Press.Printed inNorthern Ireland
Results of rocket measurements in the lower auroral ionosphere K. FOLKESTAD, B. LANDMARK and G. SLOVLI Norwegian Defence Research Establishment, Kjeller, Norway and J. A. KANE NASA Goddard Space Flight Center, Greenbelt, Maryland, U.S.A. (Received 7 November
1968; in revised form
9 January
1969)
Abskact-The present work reports on rocket measurements of electrons, positive ions and From the particle data particles with energies greater than 40 keV in the ionospheric D-region. This in turn is combined with the the height variation of the production of ion-pairs is derived. electron and ion measurements in an attempt to estimate the numerical values of the ion-ion recombination coefficient CQ. The results indicate a variation of CQfrom 10e6 to lo-’ cm set-l in the height range from 70 to 80 km.
1. INTRODUCTION THIS paper is concerned with the presentation of the outcome of an Areas rocket flight conducted to measure the flux of incoming energetic particles and the distribution of electrons and positive ions in the lower part of the aurora1 ionosphere. By combining the results of the simultaneous measurements it is possible to estimate recombination rates and the negative ion content in the region considered. It is recognized nowadays that problems in mass spectrometer measurements in the lower ionosphere are most likely explained in terms of water conglomerates leading to hydrated ions. Little is known, however, of the actual reaction rates involved. Therefore, a complete quantitative description of D-region recombination rates, including the effects of water ions, can not be given at present. The recombination processes treated in this work are represented by simple molecular dissociative and mutual ionic loss mechanisms. The adequacy of this classical approach is commented upon at the end of the paper. Pertinent information on the rocket flight and experiments is given in section 2. The following sections are devoted to a description of some basic theoretical considerations and a presentation of the methods applied for deriving the ion production from the flux data and the conversion of measured probe currents to a positive ion profile. Results of the analyses are presented and discussed in the final sections. 2. FLIGHT CHARACTERISTICS The rocket was launched at Andeya (69”N, 16”E) in Northern Norway at 04.50 U.T. on October 13th 1967. Peak altitude was 87 km. From photoelectric effects observed in one of the probe experiments it is inferred that U.V. sunrise occurred at about 82 km. Electron densities were measured by means of a conventional Faraday rotation technique based on three frequencies in the range from 4.5 to 13 MHz. Two Gerdien DC probes, operating at fixed biases, collected positive and negative 835
836
K. FOLKESTAD,B. LANDMARK, G. SKOVLI and J. KANE
particles. The probes were mounted at the front end of the rocket, symmetrical about the rocket axis and in such a manner as to permit free flow of atmospheric gases between the plates of the condensers. The entrance areas had a rectangular form. Screens were applied at both ends to prevent the effects of stray-fields. As detectors for energetic particles were used a Geiger-Miiller tube and a surface barrier semiconductor device The Geiger-Miiller experiment was designed to respond to electrons and protons with energies greater than 40 keV and 500 keV respectively. Corresponding energy levels for the other counter were 130 keV and 410 keV. An illustration of the payload structure is given in Fig. 1. 3. THEORETICAL CONSIDERATIONS Neglecting effects of movements and diffusion the rate of production of positive ions is given by the following well-known expression: dN+ __ = 4 - a,ft. NC2 dt where q is the production function and ueii. the effective recombination coefficient: a,tf. = (I + J)(a, +
%)*
(2)
denotes the ratio between negative ions and electrons, cc, and ui designate the dissociative electron-ion and the ion-ion recombination coefficients respectively. Under equilibrium conditions the net production dN+/dt is zero and the effective recombination coefficient is determined by the ratio between the production and the square of the electron density:
,I
Qff. = q/Ne2.
(3)
In the following treatment we assume that the equilibrium description remains valid. An estimate of the error made by setting dN+/dt equal to zero is given in the appendix. To examine the effective recombination rate, and the quantities il, ad and ai on which it depends, it is necessary to attain some information on the rate of ionization and its variation with height. 4. PRODUCTION OF ION PAIRS In making an estimate of q we have essentially adopted a method outlined by MAEDA (1963). The following simplifying assumptions have been made: (i) the earth’s magnetic field is vertical (ii) the electron content in the region considered is caused solely by the incoming primary electrons (iii) scattering is negligible in the precipitation process. 35 eV has been used as the energy required to produce an ion-pair. An appreciable amount of the incoming energetic electrons may be scattered into the upper hemisphere. REES (1963) estimates a scatter loss of 17 per cent. However, the uncertainty associated with the process of determining the geometrical factor of the particle detectors generally corresponds to more than any likely scatter loss. Furthermore it is noted that whereas the inclusion of scattering would lower the value of q, production sources excluded by restriction (ii) would
Fig. 1. Arcas payload structure.
Rocket measurements in the lower aurora1 ionosphere
837
lead to an increase in the rate of ionization. Within the frame of the present work, where the emphasis is not on strict quantitative considerations, it is felt that the assumptions stated above are iustified. The differential intensity of primary electrons at atmospheric depth X is written: (4) = jo(E) exp {-X/LX(E) cos PI) ”
where @ denotes the angle with the magnetic field and x(E) a function of the energy, expressed empirically as : x(E) = 3.15 . 10-7E2.2.
(5)
Numerical values for the atmospheric depth employed in the computations are based on the COSPAR standard atmosphere (1961). The differential spectrum of incident electrons is assumed to be given by jo(E)
dE = AE-” dE.
(6)
Total flux of electrons in a energy range E,-E, penetrating a unit area transverse to the magnetic field at atmospheric depth X is found by integration: I(X)
= 2~ /:ff cjo(E)
sin B cos p exp [ - x(EEos @) dE d/? .
0
(7)
The amount of particles absorbed in a unit volume is approximately given by AN = 1(x)
-
I(X
Ax
+ AX)
.
(8)
By comparing computed particle fluxes with the measured data the constants For comparison with the GeigerMiiller observations the integration has been performed over the energy range 40-1000 keV. The practical procedure has been to divide equation (4) by the constant A given in equation (6) and integrate this normalized expression over the actual energies, keeping /3, X and n constant. By repeating the integration for different values of /3 and n a series of angular spectra is found. The spectra so constructed are approximated by analytic functions of the form (cos p)r. In the further procedure these functions are used as models to compute the fluxes which would be observed by the particle detectors, taking into account the actual trajectory, detector orientation and opening aperture. The process outlined is applied at different heights and the results checked for consistency with the actual measured partial intensities. The differential spectrum of incident electrons giving the best fit to the measurements is found to given by:
A and n in equation (6) may be determined.
jo(E)
dE = 4.2. 1013E-5dE.
(0)
5. DERIVATIONOF HEIGHT DISTRIBUTIONOF POSITIVEIONS Interpretation of measurements with ion probes in the ionospheric D-region is known to be complicated by: (i) disturbing effects associated with the velocity
838
K. FOLEESTA~,B. LANDMARK,G. SKOVLIand J. KANE
of the vehicle in the relatively dense atmosphere and (ii) a lack of detailed knowledge of the sheath structure in the immediate surroundings of the probe. Generally the behaviour of probes in this part of the ionosphere has to be described in terms of a continuum theory. In practical applications simplifying assumptions are unavoidable. For the free-molecular regime the current collected by a plane probe of area A may be expressed as (2):
I=
N+ev+ --pl
cos6 .fI
where v+ is the mean thermal velocity of the ions, 6 the angle between the rocket’s velocity vector and the normal to the probe. The quantity fl, termed the velocity factor, is a function of the ratio b between the velocity of the rocket and the ion’s thermal velocity (SCHARFMABN et al., 1967):
fI =
exp
[-($)2] 4
2b
[l +efi($)] ’
(11)
It has been pointed out by SCHARFMANet al. (1967) that provided the probe does not disturb the flow, formula (10) may be applicable also in the continuum regime. A corresponding velocity factor developed for a spherical probe has been used by SA~ALYN et al. (1964) for deriving ion densities at heights down to 60 km. For b < 1 the collection of ions is dominated by their thermal motion. For rocket velocity exceeding the ion thermal velocity formula (10) essentially reduces to the expression for ion collection derived by conventional Gerdien theory (PEDERSEN, 1964). In converting the measured positive particle currents to ion densities the basic assumptions have been: (i) in the region where b -=c 1, approximately above 80 km, the amount of particles entering the gridded probe opening is adequately described by formula (lo), (ii) b e1ow 80 km the probe samples the volume defined by the rocket velocity vector and the opening area projected normal to this vector. Condition (ii) is equivalent to assuming a laminar flow through the probe. It is expected that the flow structure around the probe deviates considerably from the free-flow configuration in the lower part of the flight. From what is known of the streamline structures around vehicles travelling at supersonic speeds it is inferred that a part of the ions in the sample volume is forced out of the column before entering the probe. Condition (ii) therefore will lead to an underestimation of the ion densities in the lower D-region. An estimate of the required corrections is given in the next section. 6. EXPERIMENTAL RESULTS AND DISCUSSION The electron distribution obtained by the Faraday rotation technique is shown in Fig. 2. Shown also are the measured values together with the estimated upper limit for the height distribution of positive ions. In estimating the errors associated with the measure positive ion distribution numerical computations presented by SONIN (1967), illustrated in Fig. 3, for a supersonic blunt probe were found useful.
Rocket measurements in the lower aurora1 ionosphere
839
I sos5-
Arcar flight October 13 1967
60-
70Estimated
upper limit
for
65-
Big.
2. Height distributions of electron- and ion- densities obtained by Faraday rotation technique and by the Gerdien-experiment respeotively.
the
‘OjI.O-
Bier-IOV
9
8 5 Adopted
correction
curve
10-I -
I
70 Altitude,
0
km
Fig. 3. Ratio of calculated to “swept-out” current densities after SONIN (1967) Adopted correction curve included.
The screen at the Gerdien entrance is electrically connected to the rocket body. Since the negative floating potential of the vehicle in this part of the ionosphere normally is less than 1 V, Sonin’s calculations pertinent to the problem considered here refer to a collector travelling at Mach 3 and negatively biased by 0.5 V with respect to the ambient plasma. At 70 km he found a ratio of “sweptout” current density to calculated density of about 10, the ratio decreasing
K. FOLEESTAD,B. LAND-K,
840
G. SKOVLIand J. KANE
upwards with falling atmospheric density. The results considered in the present report are presumably less seriously affected by aero-dynamic shock-waves than those treated by Sonin, partly because the vehicle speed corresponds to a smaller Mach-number than that employed in his analysis and partly due to the form of the probe. It is expected that stagnation effects on the flow velocity ahead of the probe will be less pronounced with a screened Gerdien than in the case of a collector at the head of a blunt-nose structure. A strict evaluation of the ratio of the current densities in the actual rocket flight is necessarily rather involved. The adopted correction curve shown in Fig. 3 4,
cm-3 SIX“
Qrff.a
cm3 sex-’
E s i
Fig. 4. Variation with height of computed rate of ionization, q, and effective recombination coefficient derived from the ratio q/Ne2.
is regarded as giving a plausible height variation of the upper limit of the required correction. The rate of ionization versus altitude, derived by using the method described in section 4, is presented in Fig. 4 together with the height variation of the effective recombination coefficient as defined by equation (3). A notable feature is the high values reached by aeii. in the low altitude range. A similar pronounced increase in the ratio q/Areain the height interval 80-90 km has been reported by MCDIARMID and BUDZINSKI (1964) for a rocket flight at aurora1 latitudes. Based on LF propagation measurements and partial reflection studies BELROSE et al. (1964) deduced “effective” recombination loss rates in good agreement with the results of McDiarmid and Budzinski. The reliability of the derived effective recombination coefficients is influenced by the uncertainty in calibrating the particle detectors, the inherent inaccuracy in the method applied and the assumptions made for converting the particle fluxes to ionization and the errors associated with the measured electron content
Rocket measurements in the lower aurora1 ionosphere
841
N,. From an overall estimate the derived values for a,ri. are thought to be accurate within a factor of 2. Figure 5 presents the height variation of 1 derived from the relation 1 = N+/N, - 1. In the calculations the estimated upper boundary for the positive ion content depicted in Fig. 2 was applied. The reason for this will become clear at the end of the section. It is noted that the values for the ratio N-/N, are consistent with results found by JESPERSEN et al. (1968). With the experimentally determined %-profile and the variation of a,rI_ given in Figure 4 the altitude dependence of ai may be obtained from equation (2)
Fig. 5. Variation of A determined by the relation A = N+/Ne - 1.
for selected values of ad. Smoothed results of such computations are given by the curves in Fig. 6. Values selected for ad, from lo--’ to 1O-s cm3 set-i, are in agreement with experimental findings of GUNTONand SHAW (1965) for electron-ion recombination in NO. Laboratory studies of similar processes in nitrogen and oxygen by KASNER (1967) and KASNER and BIONDI (1967) give recombination rates in the same measurements in oxygen no systematic range. Except from the recombination dependence upon pressure was observed in these laboratory results. Wherever a temperature dependence is found in laboratory measurements of ad, it is characterized by an inverse temperature relation. This would imply that in the height range from 70 to 80 km ad should exhibit an increasing tendency, contrary to the observed variation of aetf, in the same height interval. Thus, taking account of the available data on ad and examining the measured and computed results displayed in Fig. 2 to 6 we are led to the following conclusions : (1)
It does not seem reasonable to expect that the substantial increase of CX,~~. from 85 km and downwards is explainable in terms of changes in the dissociative recombination coefficient.
842
K. FOLKESTAD,B. LANDIURK, G. SKOVLIand J. KANE
ai,
cm3set-'
Fig. 6. Altitude dependence of the ion-ion recombination coefficient, ui, for selected values of GL~.
(2) With uI in range lo-’ to 1O-6 cm3 see-l the observed positive ion densities are consistent with ion-ion recombination coefficients of the same order of magnitude. (3) The analysis reveals a height variation in ui, the coefficient decreasing from about 1O-6 cm3 see-l at 70 km to lo-’ cm3 set-l at 80 km. Above 80-82 km meaningful values for tli are obtained only for ud > 5 . lo-’ cm3 set-l. A value of ai, of about 1O-6 cm3 set-l is more than an order of magnitude higher than ion-ion recombination coefficients obtained in laboratory experiments. Applying a positive ion distribution between the measured distribution and the estimated upper limit given in Fig. 2 would lead to still larger recombination rates. If the discrepancy which obviously exists between our experimental findings and the results of laboratory investigations can be ascribed to the presence of hydrated ions the present results indicate that a solution of the D-region recombination problems can not be sought in terms of a theory based solely on the conventional parameters 1, CQand ai. AcknowZedgements-The work reported upon in this article was part of a co-ordinated research programme between Scandinavian groups and NASA, organized through its Office of International Affairs. The work at NDRE was partly sponsored by the Royal Norwegian Council for Scientific and Industrial Research. REFERENCES HELROSE J. S., BODE L.R. and HEWITTL. W. GUNTONR. C. and SHAWT. M.
1964
Radio Sci. 68D, 1319.
1965
Phys. Rev. 140, 755.
Rocket measurements
JESPERSENM., KANE J. A. and LANDMARKB. KASNER W. H. KASNER W. H. and BIONDI M. A. MAEDA K. MCDIARMID I. B. and BUDZINSIUE. E. REES M. H. SAGALYN R. C. and SMIDDY M.
SONIN
in the lower aurora1 ionosphere 1968
J. Atntosph. Terr. Phys. 30, 1955.
1967 1967 1963 1964 1963 1964
Phys. Rev. 164, 194. Bull. Am. phys. Sot. 12, 216. J. geophye. Res. 86, 185. Can. J. Phys. 42,204s. Planet. Space Sci. 11,1209. Space Research IV (Edited by P. MILLER), p. 37 1, North-Holland, Amsterdam. J. geophys. Res. 72, 4547.
1967
A. A.
843
Reference is also made to the following unpublished material: PEDERSENA.
1964
SCHARFMBN W. E., BREDFELTH., GUTHARTH. and MORITA T.
1967
FOA Report A607, Research Institute of National Defence, Sweden. Proceedings of the Third Symposium on the Plasma Sheath-Plasma Electroof Hypersonic Flight, magnetics AFCRL-67-0280.
APPENDIX An estimate of dN+/dt, neglected in equation (3), may be obtained by examining the riometer records taken during the rocket ilight. The 27 MHz riometer observations measured at the rocket launching site in the period concerned are shown in Fig. 7.
d
ti
0
0
Fig. 7. Riometer absorption at time of flight. Sinoe N+=N-+N,=(l+d)N, equation
(12)
(1) may be written: 1 -
(1 +1,%
-
N, $
= u,!~. Nea
.
(13)
Assuming that 1 does not vary with time the last term on the lefthand side is zero and the problem is restricted to a study of the time derivative of the electron content N,. In the following we denote as A, and A, the riometer absorption corresponding to the measured proGle, shown in Fig. 7, and the absorption after a lapse of time At respectively.
a44
I(. FOIJUCSTAD,B. LANDMARK, G. SKO~LI and J. U
With the basio assumption that the form of the electron density distribution is retained in conditions of varying absorption A, and A,, are linearly related and we may write for the rate of change of N, at a height hl: (14) To a first approximation we may take the quiet day cosmic noise level as corresponding to zero absorption. With this provision the absorption quantities in equation (14) are easily determined from the riometer records; 90 set were selected for At. Table 1 displays the results of the derivatives: Table 1. Reduction of rate of production due to time-change of N, (1 + A)
Height (km) 70 80
ds,
(el crne3set-‘) 25 166
Percentage of q 18 10
It may be concluded that provided the assumptions in the treatment above approximately hold good, the inclusion of dN+/dt in equation (1) would not alter a,o. appreciably.
Results of rocket measurements in the lower auroral ionosphere K. FOLKESTAD, B. LANDMARK and G. SLOVLI Norwegian Defence Research Establishment, Kjeller, Norway and J. A. KANE NASA Goddard Space Flight Center, Greenbelt, Maryland, U.S.A. (Received 7 November
1968; in revised form
9 January
1969)
Abskact-The present work reports on rocket measurements of electrons, positive ions and From the particle data particles with energies greater than 40 keV in the ionospheric D-region. This in turn is combined with the the height variation of the production of ion-pairs is derived. electron and ion measurements in an attempt to estimate the numerical values of the ion-ion recombination coefficient CQ. The results indicate a variation of CQfrom 10e6 to lo-’ cm set-l in the height range from 70 to 80 km.
1. INTRODUCTION THIS paper is concerned with the presentation of the outcome of an Areas rocket flight conducted to measure the flux of incoming energetic particles and the distribution of electrons and positive ions in the lower part of the aurora1 ionosphere. By combining the results of the simultaneous measurements it is possible to estimate recombination rates and the negative ion content in the region considered. It is recognized nowadays that problems in mass spectrometer measurements in the lower ionosphere are most likely explained in terms of water conglomerates leading to hydrated ions. Little is known, however, of the actual reaction rates involved. Therefore, a complete quantitative description of D-region recombination rates, including the effects of water ions, can not be given at present. The recombination processes treated in this work are represented by simple molecular dissociative and mutual ionic loss mechanisms. The adequacy of this classical approach is commented upon at the end of the paper. Pertinent information on the rocket flight and experiments is given in section 2. The following sections are devoted to a description of some basic theoretical considerations and a presentation of the methods applied for deriving the ion production from the flux data and the conversion of measured probe currents to a positive ion profile. Results of the analyses are presented and discussed in the final sections. 2. FLIGHT CHARACTERISTICS The rocket was launched at Andeya (69”N, 16”E) in Northern Norway at 04.50 U.T. on October 13th 1967. Peak altitude was 87 km. From photoelectric effects observed in one of the probe experiments it is inferred that U.V. sunrise occurred at about 82 km. Electron densities were measured by means of a conventional Faraday rotation technique based on three frequencies in the range from 4.5 to 13 MHz. Two Gerdien DC probes, operating at fixed biases, collected positive and negative 835
836
K. FOLKESTAD,B. LANDMARK, G. SKOVLI and J. KANE
particles. The probes were mounted at the front end of the rocket, symmetrical about the rocket axis and in such a manner as to permit free flow of atmospheric gases between the plates of the condensers. The entrance areas had a rectangular form. Screens were applied at both ends to prevent the effects of stray-fields. As detectors for energetic particles were used a Geiger-Miiller tube and a surface barrier semiconductor device The Geiger-Miiller experiment was designed to respond to electrons and protons with energies greater than 40 keV and 500 keV respectively. Corresponding energy levels for the other counter were 130 keV and 410 keV. An illustration of the payload structure is given in Fig. 1. 3. THEORETICAL CONSIDERATIONS Neglecting effects of movements and diffusion the rate of production of positive ions is given by the following well-known expression: dN+ __ = 4 - a,ft. NC2 dt where q is the production function and ueii. the effective recombination coefficient: a,tf. = (I + J)(a, +
%)*
(2)
denotes the ratio between negative ions and electrons, cc, and ui designate the dissociative electron-ion and the ion-ion recombination coefficients respectively. Under equilibrium conditions the net production dN+/dt is zero and the effective recombination coefficient is determined by the ratio between the production and the square of the electron density:
,I
Qff. = q/Ne2.
(3)
In the following treatment we assume that the equilibrium description remains valid. An estimate of the error made by setting dN+/dt equal to zero is given in the appendix. To examine the effective recombination rate, and the quantities il, ad and ai on which it depends, it is necessary to attain some information on the rate of ionization and its variation with height. 4. PRODUCTION OF ION PAIRS In making an estimate of q we have essentially adopted a method outlined by MAEDA (1963). The following simplifying assumptions have been made: (i) the earth’s magnetic field is vertical (ii) the electron content in the region considered is caused solely by the incoming primary electrons (iii) scattering is negligible in the precipitation process. 35 eV has been used as the energy required to produce an ion-pair. An appreciable amount of the incoming energetic electrons may be scattered into the upper hemisphere. REES (1963) estimates a scatter loss of 17 per cent. However, the uncertainty associated with the process of determining the geometrical factor of the particle detectors generally corresponds to more than any likely scatter loss. Furthermore it is noted that whereas the inclusion of scattering would lower the value of q, production sources excluded by restriction (ii) would
Fig. 1. Arcas payload structure.
Rocket measurements in the lower aurora1 ionosphere
837
lead to an increase in the rate of ionization. Within the frame of the present work, where the emphasis is not on strict quantitative considerations, it is felt that the assumptions stated above are iustified. The differential intensity of primary electrons at atmospheric depth X is written: (4) = jo(E) exp {-X/LX(E) cos PI) ”
where @ denotes the angle with the magnetic field and x(E) a function of the energy, expressed empirically as : x(E) = 3.15 . 10-7E2.2.
(5)
Numerical values for the atmospheric depth employed in the computations are based on the COSPAR standard atmosphere (1961). The differential spectrum of incident electrons is assumed to be given by jo(E)
dE = AE-” dE.
(6)
Total flux of electrons in a energy range E,-E, penetrating a unit area transverse to the magnetic field at atmospheric depth X is found by integration: I(X)
= 2~ /:ff cjo(E)
sin B cos p exp [ - x(EEos @) dE d/? .
0
(7)
The amount of particles absorbed in a unit volume is approximately given by AN = 1(x)
-
I(X
Ax
+ AX)
.
(8)
By comparing computed particle fluxes with the measured data the constants For comparison with the GeigerMiiller observations the integration has been performed over the energy range 40-1000 keV. The practical procedure has been to divide equation (4) by the constant A given in equation (6) and integrate this normalized expression over the actual energies, keeping /3, X and n constant. By repeating the integration for different values of /3 and n a series of angular spectra is found. The spectra so constructed are approximated by analytic functions of the form (cos p)r. In the further procedure these functions are used as models to compute the fluxes which would be observed by the particle detectors, taking into account the actual trajectory, detector orientation and opening aperture. The process outlined is applied at different heights and the results checked for consistency with the actual measured partial intensities. The differential spectrum of incident electrons giving the best fit to the measurements is found to given by:
A and n in equation (6) may be determined.
jo(E)
dE = 4.2. 1013E-5dE.
(0)
5. DERIVATIONOF HEIGHT DISTRIBUTIONOF POSITIVEIONS Interpretation of measurements with ion probes in the ionospheric D-region is known to be complicated by: (i) disturbing effects associated with the velocity
838
K. FOLEESTA~,B. LANDMARK,G. SKOVLIand J. KANE
of the vehicle in the relatively dense atmosphere and (ii) a lack of detailed knowledge of the sheath structure in the immediate surroundings of the probe. Generally the behaviour of probes in this part of the ionosphere has to be described in terms of a continuum theory. In practical applications simplifying assumptions are unavoidable. For the free-molecular regime the current collected by a plane probe of area A may be expressed as (2):
I=
N+ev+ --pl
cos6 .fI
where v+ is the mean thermal velocity of the ions, 6 the angle between the rocket’s velocity vector and the normal to the probe. The quantity fl, termed the velocity factor, is a function of the ratio b between the velocity of the rocket and the ion’s thermal velocity (SCHARFMABN et al., 1967):
fI =
exp
[-($)2] 4
2b
[l +efi($)] ’
(11)
It has been pointed out by SCHARFMANet al. (1967) that provided the probe does not disturb the flow, formula (10) may be applicable also in the continuum regime. A corresponding velocity factor developed for a spherical probe has been used by SA~ALYN et al. (1964) for deriving ion densities at heights down to 60 km. For b < 1 the collection of ions is dominated by their thermal motion. For rocket velocity exceeding the ion thermal velocity formula (10) essentially reduces to the expression for ion collection derived by conventional Gerdien theory (PEDERSEN, 1964). In converting the measured positive particle currents to ion densities the basic assumptions have been: (i) in the region where b -=c 1, approximately above 80 km, the amount of particles entering the gridded probe opening is adequately described by formula (lo), (ii) b e1ow 80 km the probe samples the volume defined by the rocket velocity vector and the opening area projected normal to this vector. Condition (ii) is equivalent to assuming a laminar flow through the probe. It is expected that the flow structure around the probe deviates considerably from the free-flow configuration in the lower part of the flight. From what is known of the streamline structures around vehicles travelling at supersonic speeds it is inferred that a part of the ions in the sample volume is forced out of the column before entering the probe. Condition (ii) therefore will lead to an underestimation of the ion densities in the lower D-region. An estimate of the required corrections is given in the next section. 6. EXPERIMENTAL RESULTS AND DISCUSSION The electron distribution obtained by the Faraday rotation technique is shown in Fig. 2. Shown also are the measured values together with the estimated upper limit for the height distribution of positive ions. In estimating the errors associated with the measure positive ion distribution numerical computations presented by SONIN (1967), illustrated in Fig. 3, for a supersonic blunt probe were found useful.
Rocket measurements in the lower aurora1 ionosphere
839
I sos5-
Arcar flight October 13 1967
60-
70Estimated
upper limit
for
65-
Big.
2. Height distributions of electron- and ion- densities obtained by Faraday rotation technique and by the Gerdien-experiment respeotively.
the
‘OjI.O-
Bier-IOV
9
8 5 Adopted
correction
curve
10-I -
I
70 Altitude,
0
km
Fig. 3. Ratio of calculated to “swept-out” current densities after SONIN (1967) Adopted correction curve included.
The screen at the Gerdien entrance is electrically connected to the rocket body. Since the negative floating potential of the vehicle in this part of the ionosphere normally is less than 1 V, Sonin’s calculations pertinent to the problem considered here refer to a collector travelling at Mach 3 and negatively biased by 0.5 V with respect to the ambient plasma. At 70 km he found a ratio of “sweptout” current density to calculated density of about 10, the ratio decreasing
K. FOLEESTAD,B. LAND-K,
840
G. SKOVLIand J. KANE
upwards with falling atmospheric density. The results considered in the present report are presumably less seriously affected by aero-dynamic shock-waves than those treated by Sonin, partly because the vehicle speed corresponds to a smaller Mach-number than that employed in his analysis and partly due to the form of the probe. It is expected that stagnation effects on the flow velocity ahead of the probe will be less pronounced with a screened Gerdien than in the case of a collector at the head of a blunt-nose structure. A strict evaluation of the ratio of the current densities in the actual rocket flight is necessarily rather involved. The adopted correction curve shown in Fig. 3 4,
cm-3 SIX“
Qrff.a
cm3 sex-’
E s i
Fig. 4. Variation with height of computed rate of ionization, q, and effective recombination coefficient derived from the ratio q/Ne2.
is regarded as giving a plausible height variation of the upper limit of the required correction. The rate of ionization versus altitude, derived by using the method described in section 4, is presented in Fig. 4 together with the height variation of the effective recombination coefficient as defined by equation (3). A notable feature is the high values reached by aeii. in the low altitude range. A similar pronounced increase in the ratio q/Areain the height interval 80-90 km has been reported by MCDIARMID and BUDZINSKI (1964) for a rocket flight at aurora1 latitudes. Based on LF propagation measurements and partial reflection studies BELROSE et al. (1964) deduced “effective” recombination loss rates in good agreement with the results of McDiarmid and Budzinski. The reliability of the derived effective recombination coefficients is influenced by the uncertainty in calibrating the particle detectors, the inherent inaccuracy in the method applied and the assumptions made for converting the particle fluxes to ionization and the errors associated with the measured electron content
Rocket measurements in the lower aurora1 ionosphere
841
N,. From an overall estimate the derived values for a,ri. are thought to be accurate within a factor of 2. Figure 5 presents the height variation of 1 derived from the relation 1 = N+/N, - 1. In the calculations the estimated upper boundary for the positive ion content depicted in Fig. 2 was applied. The reason for this will become clear at the end of the section. It is noted that the values for the ratio N-/N, are consistent with results found by JESPERSEN et al. (1968). With the experimentally determined %-profile and the variation of a,rI_ given in Figure 4 the altitude dependence of ai may be obtained from equation (2)
Fig. 5. Variation of A determined by the relation A = N+/Ne - 1.
for selected values of ad. Smoothed results of such computations are given by the curves in Fig. 6. Values selected for ad, from lo--’ to 1O-s cm3 set-i, are in agreement with experimental findings of GUNTONand SHAW (1965) for electron-ion recombination in NO. Laboratory studies of similar processes in nitrogen and oxygen by KASNER (1967) and KASNER and BIONDI (1967) give recombination rates in the same measurements in oxygen no systematic range. Except from the recombination dependence upon pressure was observed in these laboratory results. Wherever a temperature dependence is found in laboratory measurements of ad, it is characterized by an inverse temperature relation. This would imply that in the height range from 70 to 80 km ad should exhibit an increasing tendency, contrary to the observed variation of aetf, in the same height interval. Thus, taking account of the available data on ad and examining the measured and computed results displayed in Fig. 2 to 6 we are led to the following conclusions : (1)
It does not seem reasonable to expect that the substantial increase of CX,~~. from 85 km and downwards is explainable in terms of changes in the dissociative recombination coefficient.
842
K. FOLKESTAD,B. LANDIURK, G. SKOVLIand J. KANE
ai,
cm3set-'
Fig. 6. Altitude dependence of the ion-ion recombination coefficient, ui, for selected values of GL~.
(2) With uI in range lo-’ to 1O-6 cm3 see-l the observed positive ion densities are consistent with ion-ion recombination coefficients of the same order of magnitude. (3) The analysis reveals a height variation in ui, the coefficient decreasing from about 1O-6 cm3 see-l at 70 km to lo-’ cm3 set-l at 80 km. Above 80-82 km meaningful values for tli are obtained only for ud > 5 . lo-’ cm3 set-l. A value of ai, of about 1O-6 cm3 set-l is more than an order of magnitude higher than ion-ion recombination coefficients obtained in laboratory experiments. Applying a positive ion distribution between the measured distribution and the estimated upper limit given in Fig. 2 would lead to still larger recombination rates. If the discrepancy which obviously exists between our experimental findings and the results of laboratory investigations can be ascribed to the presence of hydrated ions the present results indicate that a solution of the D-region recombination problems can not be sought in terms of a theory based solely on the conventional parameters 1, CQand ai. AcknowZedgements-The work reported upon in this article was part of a co-ordinated research programme between Scandinavian groups and NASA, organized through its Office of International Affairs. The work at NDRE was partly sponsored by the Royal Norwegian Council for Scientific and Industrial Research. REFERENCES HELROSE J. S., BODE L.R. and HEWITTL. W. GUNTONR. C. and SHAWT. M.
1964
Radio Sci. 68D, 1319.
1965
Phys. Rev. 140, 755.
Rocket measurements
JESPERSENM., KANE J. A. and LANDMARKB. KASNER W. H. KASNER W. H. and BIONDI M. A. MAEDA K. MCDIARMID I. B. and BUDZINSIUE. E. REES M. H. SAGALYN R. C. and SMIDDY M.
SONIN
in the lower aurora1 ionosphere 1968
J. Atntosph. Terr. Phys. 30, 1955.
1967 1967 1963 1964 1963 1964
Phys. Rev. 164, 194. Bull. Am. phys. Sot. 12, 216. J. geophye. Res. 86, 185. Can. J. Phys. 42,204s. Planet. Space Sci. 11,1209. Space Research IV (Edited by P. MILLER), p. 37 1, North-Holland, Amsterdam. J. geophys. Res. 72, 4547.
1967
A. A.
843
Reference is also made to the following unpublished material: PEDERSENA.
1964
SCHARFMBN W. E., BREDFELTH., GUTHARTH. and MORITA T.
1967
FOA Report A607, Research Institute of National Defence, Sweden. Proceedings of the Third Symposium on the Plasma Sheath-Plasma Electroof Hypersonic Flight, magnetics AFCRL-67-0280.
APPENDIX An estimate of dN+/dt, neglected in equation (3), may be obtained by examining the riometer records taken during the rocket ilight. The 27 MHz riometer observations measured at the rocket launching site in the period concerned are shown in Fig. 7.
d
ti
0
0
Fig. 7. Riometer absorption at time of flight. Sinoe N+=N-+N,=(l+d)N, equation
(12)
(1) may be written: 1 -
(1 +1,%
-
N, $
= u,!~. Nea
.
(13)
Assuming that 1 does not vary with time the last term on the lefthand side is zero and the problem is restricted to a study of the time derivative of the electron content N,. In the following we denote as A, and A, the riometer absorption corresponding to the measured proGle, shown in Fig. 7, and the absorption after a lapse of time At respectively.
a44
I(. FOIJUCSTAD,B. LANDMARK, G. SKO~LI and J. U
With the basio assumption that the form of the electron density distribution is retained in conditions of varying absorption A, and A,, are linearly related and we may write for the rate of change of N, at a height hl: (14) To a first approximation we may take the quiet day cosmic noise level as corresponding to zero absorption. With this provision the absorption quantities in equation (14) are easily determined from the riometer records; 90 set were selected for At. Table 1 displays the results of the derivatives: Table 1. Reduction of rate of production due to time-change of N, (1 + A)
Height (km) 70 80
ds,
(el crne3set-‘) 25 166
Percentage of q 18 10
It may be concluded that provided the assumptions in the treatment above approximately hold good, the inclusion of dN+/dt in equation (1) would not alter a,o. appreciably.