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The ionosphere of Mars below 80 km altitude—II
Planet. Space ki.
1971, Vol. 19.
pp.971 to 979.
Perpamon Press.
Printed in Northern
THE IONOSPHERE OF MARS ALTITUDE-II SOLAR
COSMIC
Ireland
BELOW
SO km
RAY EVENT
R. C. WHITTEN, I. G. POPPOFF and J. S. SIMS Space Sciences Division, Ames Research Center, NASA, Moffett Field, California 94035, U.S.A. and W. A. BARKER, P. T. MCCORMICK and J. DUBACH Department of Physics, Santa Clara University, Santa Clara, California 95053, U.S.A. (Received 21 December
1970)
Abstract-Models of the lower ionosphere of Mars during a solar proton event are developed using the ion chemistry discussed in a previous paper. The computed electron number densities for two representative proton spectra appear to be large enough to allow one to easily determine the entire profiles of electron concentration by means of a bistatic radar occultation experiment. 1. INTRODUCTION
In a previous paper (Whitten et al., 1970) (hereafter referred to as Paper I) we discussed the lower ionosphere of Mars under quiescent conditions. It was found that galactic cosmic rays produce a permanent low-lying electron layer which becomes quite distinct at night. At altitudes greater than -25 km, minor constituents do not appear to significantly affect the negative ion chemistry or the electron number density. However, at lower altitudes, the present lack of knowledge of some key reaction rate coefficients as well as the number density of atomic oxygen precludes the development of a unique ionospheric model. It is the purpose of this paper to show that the range of possible choices for a model could be narrowed considerably by probing the lower Mars ionosphere during a solar cosmic ray event. We shall also show that such probing is feasible with existing techniques. In the following section we calculate the ionization rate profiles for two representative solar cosmic ray events (Svestka and Simon, 1969) whose integral spectra are shown in Fig. 1. We next compute the electron and negative-ion number density profiles, using the ion chemistry discussed in Paper I. We conclude by showing that a two-frequency bistatic radar occultation experiment (Fjeldbo et al., 1965; Fjeldbo and Eshleman, 1968) could be employed to obtain the electron number density profile to altitudes very close to the surface of the planet. 2. IO;\mATION OF THE MARTIAN ATMOSPHERE BY SOLAR FLARE PROTONS The production rate per cubic centimeter of electron ion pairs can be calculated using the general formula
where W is the average energy required the stopping power of CO, for protons, the protons. The integration is carried N(E, Q) is isotropic, thus permittin g us
to produce an electron-ion pair (35 eV), dE/dh is and N(E, Sz) is the differential energy spectrum of out over energy and solid angle; we assume that to integrate over the azimuthal angle
R. C. WHITTEN
972
lb ENERGY,
FIG. 1.
er al.
I&l
lob0
MeV
I.UTEGRAL SPECTRA CORRESPONDING
TO THE MAXIMUM AND ON SEPTEMBER 2,1966.
PROTON
FLUX OS AUGUST30
where 0 is the zenith angle of the particle trajectory and EC is the energy of protons which have just enough energy to be stopped at the altitude in question (cut-off energy). Velinov (1968) has developed an analytical expression for the stopping power of an atmosphere; this expression can be employed to compute q by numerical integration
co ss
[(E2 - A,& set 19)~‘~ + E,J2
-% 0 N(E) (E2 - A,& set 6) f 2E,(E2 - A,h set @l/2
X @5[(E2 - A,h set @1/z + 2E,,]ln(E2 - A,i; set @r/2 + C, -
0.5(E2 - AlA set 0)112 [(P - A,Ji set ey + q2
[2E,, + (E2 - A,j; set fl)1/2] sin 8 de dE. I
(3)
The symbols used in Equation (3) have the following meaning: (a) Z, E,,, and E are the atomic number, rest energy, and initial kinetic energy of a solar flare proton. (b) C, = 4rre”zN,,E&nc2A where e and m are the electronic charge and mass, A and z are the target atom’s mass and atomic numbers, N,, is Avogadro’s number and c is the velocity of light. (c) The atmospheric density is p(h) = n(h)A/No where n(h) is the number density of target atoms. We have used the number density given by McElroy (1969) for a pure CO, atmosphere. (d) The atmospheric depth is i; = JT p(h) dh (e) C, = In (2mc2/Z)112where I is an average excitation energy (f) A, = ClZ2[ln (4mc”E/ZE,,)]. In the derivation of Equation (3) it is assumed that the atmosphere is flat; sphericity is taken into account by using the Chapman function (see e.g., Wilkes, 1954)
ch(e,!!!!-$!)=Rg
sin 6ieexp
[v
(1-
$$)I
csc?\k’d\k’
(4)
THE IONOSPHERE
OF MARS BELOW
80km
ALTITUDE-II
973
in place of set 0 for 0 > 65”. In Equation (4) R, is the planetary radius and H is the atmospheric scale height. The proton energy spectra shown in Fig. 1 were represented by superpositions of exponential functions which were then differentiated to obtain the N(E) used in Equation (3). Alpha particles were neglected although they could very easily have been included in the analysis if their spectra had been measured. Usually cc-particles comprise only a small fraction of the energetic particle flux and, because of their much larger 2, are absorbed mainly at considerably higher altitudes than are the protons. Hence, it is very unlikely that they would produce significant ionization in the altitude range of principal interest to our study (i.e. below 50 km). The computed ionization rate profiles which correspond to the spectra shown in Fig. 1 are presented in Fig. 2; the ionization rate profile for a quiescent day is included for comparison. 80 -
7060-
\
I
10-I IONIZATION FIG.
2.
COMPUTED
IOMZATION
\ IO
RATE
q,
Crll-3
,
I
IO2
I03
SK-’
RATE PROFILES CORRESPONDING IN FIG. 1.
TOTHE
TWO
SPECTRA SHOWN
The broken curve represents the ionization rate due to galactic cosmic rays (quiescent day). 3. ION
CHEMISTRY
The model of ion chemistry employed in the present study is the same as that presented in Paper I except that CO- has been eliminated as a possible negative ion. Ferguson (personal communication) argues that CO- is isoelectronic with N, whose ground state is virtual, implying that the ground state of CO- is also expected to be virtual; furthermore, he has failed to observe it in laboratory experiments in which it could be expected to appear in a bound state if the latter were possible. The effect of CO-, if it were present, would be to substantially reduce the electron number density near the surface, i.e., by an order of magnitude below 5 km altitude (see Paper I). Computed profiles of electron and negative ion number density are shown in Figs. 38 for the two solar proton energy spectra shown in Fig. 1 and for conditions of day and night. The assumption of quasiequilibrium is justified in these computations because the time scale for loss processes was of the order of minutes whereas marked changes in the proton spectrum were of the order of hours (ivestka and Simon, 1969). It is apparent that negative ions are expected to affect the electron number density very little above 20 km in daytime and 25 km at night.
974
R. C. WHITTEN
ef al.
60-
, IO5
CONCENTRAT10N,CW3
FIG. 3.
COMPUTED DAYTIME PROFILES OF ELECTRON AND NEGATIVE ION NUMBER CORRESPONDINGTOTHEPROTON SPECTRUMOF SEPTEMBER~.
DENSITM
used are those given in Table 1 of Paper I with p2, = pzs = 0.1 set-1 and the model atmosphere is that given in Fig. 1 of Paper I. CO- was assumed not to exist.
The rate coefficients
CONCENTRATION, Cm"
FIG. 4.
SAMEAS FIG, ~,BUTUSINGTHEPROTONSPECTRUM
OF AUGUST
30.
Probing of the electron number density below 25 km in the sunlit and dark hemispheres, using the method discussed in Section 4, may enabfe one to deduce the relative importance of photodetachment versus collisional detachment reactions like co,- + 0 -+ 0, O,-+O-+O,+e
+ co, _ 1’
Using a ‘lumped parameter’ approach (see, e.g. Whitten and Poppoff, show that the electron number density N is given by iV=
DdTu D+A+diq
+ q
(3 1970), one can
(6)
where cc is the recombination coefficient (the coefficients for dissociative and ion-ion recombination are assumed to be equal -see Paper I), 9 is the ionization rate, I) is the effective detachment rate, and A is the attachment rate. Comparison of N during daylight and just prior to sunset (before the atomic oxygen has had time to decay significantly)
THE IONOSPHERE
I
OF MARS BELOW
IO
103
IO2 CONCENTRATION,
FIG. 5.
80km
ALTITUDE-4
97s
IO5
IO4
Cm-3
CO~MPUTED MGH'ITWE PROFILES OF ELECI-RON AND NEGATIVE ION NUMBER ~ORR~~~INGTOTHE~~RPROTONSPE~U~OF SEPXZMBER~.
The rate coefficients and model atmosphere
~pysrn~~
are the same as for Fig. 3.
80 ?O-
60-
Ne
I
I05 CONCENTRATION,
FIG. 6.
Cm3
SAMEAS FIG 5. EXCEPT THAT kls = 2 x 1O-*ocm3set-I.
would enable one to determine whether or nor photodetachment is significant. In fact, if the photodetachment rate is large enough, one may be able to determine it to an order of magnitude for altitudes below 20 km. For example, if q = 40 cm-3, se&, and u = lo-6 cm3 set-l (corresponding to -10 km altitude), iv%
40 + 6 x 1031) D+2
and values of D > 0.05 set-l may be observable. By comparing Figs. 5 and 7 with 6 and 8, respectiveiy, one can see that rough bounds could also be put on the rate coefficient for the reaction C04- f COz ---t CO, + CO, + e by analyzing electron profiles produced by SCR. Thus, although it is not possible to uniquely determine the various rate coefficients which play roles in the lower Martian ionosphere, it may be feasible to determine sets of ‘lumped parameters’ which crudely describe its behavior.
R. C. WHITTEN
976
et af.
8070-
t
I
I04 CONCENTRATION,
105
cmm3
FIG. 7. COMPUTED NIGHITIME PROFILES OF ELECTRON AND NEGATIVE XON NUMBER DENSITIES CORRESPOKDINGTOTHESOLARPROTONEVENTOF&JGUST 30.
The rate coefficients and model atmosphere
are the same as for Fig. 3.
00 7060
I N,
-
E x 50-
0
:
1 I
I
I
I
I02
IO
103
CONCENTRATION,
FIG. 8. SAME AS FIG. 7 EXCEPTTHAT
4. APPLICATION
TO MARS
I
I04
10s
cme3 k,, = 2 x 10-~gcm3sec-l.
ATMOSPHERE
RADIO
PROBES
Fjeldbo et al. (1965, 1968) have successfully employed the bistatic radar occultation method to observe refractivity profiles in the upper Martian and Cytherean ionospheres and the lower atmospheres of those planets; from their data, electron and neutral particle number densities were deduced. If signals of two frequencies (e.g., one at 2300 mHz as actually used and one at 1.50mHz) were used, it would have been possible to probe the ionosphere to much lower altitudes. Although it would not be possible to identify the most important ionic reactions in the lower ionosphere with two frequency measurements, it should prove possible to significantly narrow the range of possible processes (e.g., the role of photodetachment as discussed in Section 3). Observation of the electron number density profile and the proton energy spectrum during a solar cosmic ray event is expected to offer the most favorable opportunity because the electron number densities are large at low altitudes and relatively easy to measure. If a two-frequency occultation experiment were carried on a satellite placed in orbit about Mars during an active sofar period, the probability of acquiring data during a solar
THE
IONOSPHERE
OF MARS
BELOW
8Okm ALTITUDE-II
977
cosmic ray event would be quite high. For our feasibility calculations, we assumed the satellite to be in circular orbit at an altitude of 5000 km, and transmitting CW signals at frequencies of 150 mHz and 2300 mHz as shown in Fig. 9. The higher frequency was chosen because the occultation experiments performed to date have utilized the phase shifts of the telemetry carrier wave (2300 mHz). The lower frequency of 150 mHz was determined by the requirement that refractive effects be as great as possible without introducing ambiguities that arise when phase path and gain are multivalued functions of ray path miss distance. For the ionosphere of Mars this ambiguity occurs for frequencies below about 150 mHz since the signal from certain parts of the transmitter trajectory is then received over more than one propagation path at a time. TRANSMITTER;-\. TRAJECTORY P RADAR
_
RAY
PATH
Q __----
MARS
‘\.
‘\
\
‘.
‘\I\ \ I
.--4-
1=0
;’
RAYPATH
MISS
DISTANCE
FIG. 9.
GEOMETRYOF
OCCULTATION
EXPERIMENT.
TO EARTH
RAY
BENDING
IS EXAGGERATED.
Our model of the lower atmosphere and of the ionsophere above 80 km is based on observations of Mariner 4 (see e.g. McElroy, 1969). In order to determine the possibilities of the method, we deliberately chose an electron number density profile which is more difficult to measure than one would expect during an SCR event, namely, the quiescent day profile shown in Fi g. 10. The separation of dispersive ionospheric refraction effects from the nondispersive effects of the neutral atmosphere was assured by beating the phase of the lower frequency signal against the phase of the 3146 subharmonic of the higher frequency. This beat frequency is plotted as a function of time in orbit (measured from the t = 0 point shown in Fig. 9) in Fig. Il. The right-hand end of the trace signifies tangency of the ray with the surface of the planet. The relationship between the beat frequency plotted in Fig. 11 and the electron density profile, N, can be established by considering the phase of the signals as they travel through the Martian ionosphere. The phase path of a radio signal, 4, measured in wavelengths, is given by
(8) where I, is the free space wavelength of the signal, ,u is the index of refraction, and the integral extends along the (curved) ray path from transmitter to receiver. The net effect of the ionosphere on the phase path is the result of two competing effects. The phase path tends to be shortened because the presence of free electrons advances the phase of the waves whereas the refraction of the waves causes the ray paths to be curved, tending to
R. C. IVHXmEN
978
et ui.
80 70 60 2 50 !i 2 40 ‘2 30 20 10
0 LOGa OF NUM3ER
Fro, 10. ELECTRON
NUMBER
OENSITY,
Cm-J’
DENSIN~IN THE DA?T'mffiQUKESCEXT IONOSPHERE (THE SOLID CURVE IN F1c.2 OFPAPER I),
3020-
-4o-5oc 4100
4200 TIME,set
FIG. 11. BEATFREQUENCYASA
FUNCTIOSOF~.
lengthen the phase path. Since these effects are frequency-dependent, the ray path along which the integral in Equation (8) extends is different for the higher and lower frequencies. ff we assume a negIigibIe magnetic field and also neglect the effects of electron colfisions, then, according to ~ag~etoion~~ theory, the index of refraction is related to the electron density by 80*6N* E”= 1 (9) J --7-where N, is the electron density in cm& and f is the frequency of the radar signal in Hz. The beat ‘frequency, AJ plotted in Fig. 10 is (dude) where A# = dr, - ~f~~~)~~ In this expression #Q is the phase path at the lower frequency ($50 mHz), C& is the phase path at the higher frequency (2300 mHz) and fLlf;E = 3146:
L
+!$!-d,_-?&
1-F
80.6~~ fz2
ds
1’
w--o
THE
IONOSPHERE
OF hlARS
BELOW
8Okt.n ALTITUDE-II
979
It would appear from Fig. 11 that the beat frequency data should be adequate for the inversion of the problem (Fjeldbo et al., 1965) in order to obtain the electron density profile. At the lower frequency (150 mHz) used in the feasibility calculations, there would be some signal absorption, about 7 dB for the electron number density profile shown in Fig. 10. Because electron-neutral particle collisions cannot be neglected, one shou!d use a modified form of the magnetoionic theory which takes account of electron-neutral particle collisions in the CO, atmosphere. Work is in fact under way on this aspect of the problem. Hence, the results shown in Fig. 11 are only qualitative, but are precise enough to establish the feasibility of the method. For an actual experiment one must consider the absorption of energy from the radio waves as well as the ‘caustics’ effect discussed earlier. Higher frequencies are more useful for observing larger electron number densities. 5. DISCUSSxON Several rather interesting and somewhat unexpected conclusions can be drawn from the calculations reported in both this paper and Paper I. The first is that a two-frequency occultation experiment would be sensitive enough to detect and measure the lower atmosphere electron profile even on a solar quiet day. Hence, the concept of a permanent Martian D-region can be checked. During an SCR event, electron densities are significantly enhanced, of course, and the ionosphere can be analyzed more precisely. Because the negative ion production chain starts with 0, it is obvious that the abundance of 0, could be confirmed (to order of magnitude) by such measurements; this in itself would be an important result of a two-frequency radar measurement. The surprising result is that the shape and magnitude of the lower ionosphere of Mars does not appear to be very dependent (within wide limits) on the presence or identity of minor species (except for 0,) or on reaction rates; this is somewhat contrary to current ideas about the terrestrial lower ionosphere. Ackno:vledgements-We
wish to thank Professor the bistatic radar occultation experiment.
V. R. Eshleman for the helpful discussions
concerning
REFERENCES FJELDBO,G., ESHLEMAN,V. R., GARRIOTT,0. K. and SETH, F. L., III (1965). J.geophys. Res. 70, 3701. FJELDBO,G. and ESHLE~N, V. R. (1968). Planet. Space Sci. 16, 1035. MCELROY, M. B. (1969). J. geophys. Res. 74,29. SVESTKA,Z. and SIMON, P. (1969). Solar Phys. 10, 3. VELINOV,P. (1968). J. armos. terr. Phys. 30, 1891. Wnn-rs~, R. C., POPPO~F,I. G. and &MS, J. S. (1971). Planet. Space Sci. 19,243. (Referred to as Paper I.) WHTTTEN,R. C. and POPPOFF,I. G. (1971). Funciamenlals of Aeronomy. John Wiley & Sons, New York, 1971. WILKES, M. V. (1954). Proc. Phys. Sot. B67, 304.
1971, Vol. 19.
pp.971 to 979.
Perpamon Press.
Printed in Northern
THE IONOSPHERE OF MARS ALTITUDE-II SOLAR
COSMIC
Ireland
BELOW
SO km
RAY EVENT
R. C. WHITTEN, I. G. POPPOFF and J. S. SIMS Space Sciences Division, Ames Research Center, NASA, Moffett Field, California 94035, U.S.A. and W. A. BARKER, P. T. MCCORMICK and J. DUBACH Department of Physics, Santa Clara University, Santa Clara, California 95053, U.S.A. (Received 21 December
1970)
Abstract-Models of the lower ionosphere of Mars during a solar proton event are developed using the ion chemistry discussed in a previous paper. The computed electron number densities for two representative proton spectra appear to be large enough to allow one to easily determine the entire profiles of electron concentration by means of a bistatic radar occultation experiment. 1. INTRODUCTION
In a previous paper (Whitten et al., 1970) (hereafter referred to as Paper I) we discussed the lower ionosphere of Mars under quiescent conditions. It was found that galactic cosmic rays produce a permanent low-lying electron layer which becomes quite distinct at night. At altitudes greater than -25 km, minor constituents do not appear to significantly affect the negative ion chemistry or the electron number density. However, at lower altitudes, the present lack of knowledge of some key reaction rate coefficients as well as the number density of atomic oxygen precludes the development of a unique ionospheric model. It is the purpose of this paper to show that the range of possible choices for a model could be narrowed considerably by probing the lower Mars ionosphere during a solar cosmic ray event. We shall also show that such probing is feasible with existing techniques. In the following section we calculate the ionization rate profiles for two representative solar cosmic ray events (Svestka and Simon, 1969) whose integral spectra are shown in Fig. 1. We next compute the electron and negative-ion number density profiles, using the ion chemistry discussed in Paper I. We conclude by showing that a two-frequency bistatic radar occultation experiment (Fjeldbo et al., 1965; Fjeldbo and Eshleman, 1968) could be employed to obtain the electron number density profile to altitudes very close to the surface of the planet. 2. IO;\mATION OF THE MARTIAN ATMOSPHERE BY SOLAR FLARE PROTONS The production rate per cubic centimeter of electron ion pairs can be calculated using the general formula
where W is the average energy required the stopping power of CO, for protons, the protons. The integration is carried N(E, Q) is isotropic, thus permittin g us
to produce an electron-ion pair (35 eV), dE/dh is and N(E, Sz) is the differential energy spectrum of out over energy and solid angle; we assume that to integrate over the azimuthal angle
R. C. WHITTEN
972
lb ENERGY,
FIG. 1.
er al.
I&l
lob0
MeV
I.UTEGRAL SPECTRA CORRESPONDING
TO THE MAXIMUM AND ON SEPTEMBER 2,1966.
PROTON
FLUX OS AUGUST30
where 0 is the zenith angle of the particle trajectory and EC is the energy of protons which have just enough energy to be stopped at the altitude in question (cut-off energy). Velinov (1968) has developed an analytical expression for the stopping power of an atmosphere; this expression can be employed to compute q by numerical integration
co ss
[(E2 - A,& set 19)~‘~ + E,J2
-% 0 N(E) (E2 - A,& set 6) f 2E,(E2 - A,h set @l/2
X @5[(E2 - A,h set @1/z + 2E,,]ln(E2 - A,i; set @r/2 + C, -
0.5(E2 - AlA set 0)112 [(P - A,Ji set ey + q2
[2E,, + (E2 - A,j; set fl)1/2] sin 8 de dE. I
(3)
The symbols used in Equation (3) have the following meaning: (a) Z, E,,, and E are the atomic number, rest energy, and initial kinetic energy of a solar flare proton. (b) C, = 4rre”zN,,E&nc2A where e and m are the electronic charge and mass, A and z are the target atom’s mass and atomic numbers, N,, is Avogadro’s number and c is the velocity of light. (c) The atmospheric density is p(h) = n(h)A/No where n(h) is the number density of target atoms. We have used the number density given by McElroy (1969) for a pure CO, atmosphere. (d) The atmospheric depth is i; = JT p(h) dh (e) C, = In (2mc2/Z)112where I is an average excitation energy (f) A, = ClZ2[ln (4mc”E/ZE,,)]. In the derivation of Equation (3) it is assumed that the atmosphere is flat; sphericity is taken into account by using the Chapman function (see e.g., Wilkes, 1954)
ch(e,!!!!-$!)=Rg
sin 6ieexp
[v
(1-
$$)I
csc?\k’d\k’
(4)
THE IONOSPHERE
OF MARS BELOW
80km
ALTITUDE-II
973
in place of set 0 for 0 > 65”. In Equation (4) R, is the planetary radius and H is the atmospheric scale height. The proton energy spectra shown in Fig. 1 were represented by superpositions of exponential functions which were then differentiated to obtain the N(E) used in Equation (3). Alpha particles were neglected although they could very easily have been included in the analysis if their spectra had been measured. Usually cc-particles comprise only a small fraction of the energetic particle flux and, because of their much larger 2, are absorbed mainly at considerably higher altitudes than are the protons. Hence, it is very unlikely that they would produce significant ionization in the altitude range of principal interest to our study (i.e. below 50 km). The computed ionization rate profiles which correspond to the spectra shown in Fig. 1 are presented in Fig. 2; the ionization rate profile for a quiescent day is included for comparison. 80 -
7060-
\
I
10-I IONIZATION FIG.
2.
COMPUTED
IOMZATION
\ IO
RATE
q,
Crll-3
,
I
IO2
I03
SK-’
RATE PROFILES CORRESPONDING IN FIG. 1.
TOTHE
TWO
SPECTRA SHOWN
The broken curve represents the ionization rate due to galactic cosmic rays (quiescent day). 3. ION
CHEMISTRY
The model of ion chemistry employed in the present study is the same as that presented in Paper I except that CO- has been eliminated as a possible negative ion. Ferguson (personal communication) argues that CO- is isoelectronic with N, whose ground state is virtual, implying that the ground state of CO- is also expected to be virtual; furthermore, he has failed to observe it in laboratory experiments in which it could be expected to appear in a bound state if the latter were possible. The effect of CO-, if it were present, would be to substantially reduce the electron number density near the surface, i.e., by an order of magnitude below 5 km altitude (see Paper I). Computed profiles of electron and negative ion number density are shown in Figs. 38 for the two solar proton energy spectra shown in Fig. 1 and for conditions of day and night. The assumption of quasiequilibrium is justified in these computations because the time scale for loss processes was of the order of minutes whereas marked changes in the proton spectrum were of the order of hours (ivestka and Simon, 1969). It is apparent that negative ions are expected to affect the electron number density very little above 20 km in daytime and 25 km at night.
974
R. C. WHITTEN
ef al.
60-
, IO5
CONCENTRAT10N,CW3
FIG. 3.
COMPUTED DAYTIME PROFILES OF ELECTRON AND NEGATIVE ION NUMBER CORRESPONDINGTOTHEPROTON SPECTRUMOF SEPTEMBER~.
DENSITM
used are those given in Table 1 of Paper I with p2, = pzs = 0.1 set-1 and the model atmosphere is that given in Fig. 1 of Paper I. CO- was assumed not to exist.
The rate coefficients
CONCENTRATION, Cm"
FIG. 4.
SAMEAS FIG, ~,BUTUSINGTHEPROTONSPECTRUM
OF AUGUST
30.
Probing of the electron number density below 25 km in the sunlit and dark hemispheres, using the method discussed in Section 4, may enabfe one to deduce the relative importance of photodetachment versus collisional detachment reactions like co,- + 0 -+ 0, O,-+O-+O,+e
+ co, _ 1’
Using a ‘lumped parameter’ approach (see, e.g. Whitten and Poppoff, show that the electron number density N is given by iV=
DdTu D+A+diq
+ q
(3 1970), one can
(6)
where cc is the recombination coefficient (the coefficients for dissociative and ion-ion recombination are assumed to be equal -see Paper I), 9 is the ionization rate, I) is the effective detachment rate, and A is the attachment rate. Comparison of N during daylight and just prior to sunset (before the atomic oxygen has had time to decay significantly)
THE IONOSPHERE
I
OF MARS BELOW
IO
103
IO2 CONCENTRATION,
FIG. 5.
80km
ALTITUDE-4
97s
IO5
IO4
Cm-3
CO~MPUTED MGH'ITWE PROFILES OF ELECI-RON AND NEGATIVE ION NUMBER ~ORR~~~INGTOTHE~~RPROTONSPE~U~OF SEPXZMBER~.
The rate coefficients and model atmosphere
~pysrn~~
are the same as for Fig. 3.
80 ?O-
60-
Ne
I
I05 CONCENTRATION,
FIG. 6.
Cm3
SAMEAS FIG 5. EXCEPT THAT kls = 2 x 1O-*ocm3set-I.
would enable one to determine whether or nor photodetachment is significant. In fact, if the photodetachment rate is large enough, one may be able to determine it to an order of magnitude for altitudes below 20 km. For example, if q = 40 cm-3, se&, and u = lo-6 cm3 set-l (corresponding to -10 km altitude), iv%
40 + 6 x 1031) D+2
and values of D > 0.05 set-l may be observable. By comparing Figs. 5 and 7 with 6 and 8, respectiveiy, one can see that rough bounds could also be put on the rate coefficient for the reaction C04- f COz ---t CO, + CO, + e by analyzing electron profiles produced by SCR. Thus, although it is not possible to uniquely determine the various rate coefficients which play roles in the lower Martian ionosphere, it may be feasible to determine sets of ‘lumped parameters’ which crudely describe its behavior.
R. C. WHITTEN
976
et af.
8070-
t
I
I04 CONCENTRATION,
105
cmm3
FIG. 7. COMPUTED NIGHITIME PROFILES OF ELECTRON AND NEGATIVE XON NUMBER DENSITIES CORRESPOKDINGTOTHESOLARPROTONEVENTOF&JGUST 30.
The rate coefficients and model atmosphere
are the same as for Fig. 3.
00 7060
I N,
-
E x 50-
0
:
1 I
I
I
I
I02
IO
103
CONCENTRATION,
FIG. 8. SAME AS FIG. 7 EXCEPTTHAT
4. APPLICATION
TO MARS
I
I04
10s
cme3 k,, = 2 x 10-~gcm3sec-l.
ATMOSPHERE
RADIO
PROBES
Fjeldbo et al. (1965, 1968) have successfully employed the bistatic radar occultation method to observe refractivity profiles in the upper Martian and Cytherean ionospheres and the lower atmospheres of those planets; from their data, electron and neutral particle number densities were deduced. If signals of two frequencies (e.g., one at 2300 mHz as actually used and one at 1.50mHz) were used, it would have been possible to probe the ionosphere to much lower altitudes. Although it would not be possible to identify the most important ionic reactions in the lower ionosphere with two frequency measurements, it should prove possible to significantly narrow the range of possible processes (e.g., the role of photodetachment as discussed in Section 3). Observation of the electron number density profile and the proton energy spectrum during a solar cosmic ray event is expected to offer the most favorable opportunity because the electron number densities are large at low altitudes and relatively easy to measure. If a two-frequency occultation experiment were carried on a satellite placed in orbit about Mars during an active sofar period, the probability of acquiring data during a solar
THE
IONOSPHERE
OF MARS
BELOW
8Okm ALTITUDE-II
977
cosmic ray event would be quite high. For our feasibility calculations, we assumed the satellite to be in circular orbit at an altitude of 5000 km, and transmitting CW signals at frequencies of 150 mHz and 2300 mHz as shown in Fig. 9. The higher frequency was chosen because the occultation experiments performed to date have utilized the phase shifts of the telemetry carrier wave (2300 mHz). The lower frequency of 150 mHz was determined by the requirement that refractive effects be as great as possible without introducing ambiguities that arise when phase path and gain are multivalued functions of ray path miss distance. For the ionosphere of Mars this ambiguity occurs for frequencies below about 150 mHz since the signal from certain parts of the transmitter trajectory is then received over more than one propagation path at a time. TRANSMITTER;-\. TRAJECTORY P RADAR
_
RAY
PATH
Q __----
MARS
‘\.
‘\
\
‘.
‘\I\ \ I
.--4-
1=0
;’
RAYPATH
MISS
DISTANCE
FIG. 9.
GEOMETRYOF
OCCULTATION
EXPERIMENT.
TO EARTH
RAY
BENDING
IS EXAGGERATED.
Our model of the lower atmosphere and of the ionsophere above 80 km is based on observations of Mariner 4 (see e.g. McElroy, 1969). In order to determine the possibilities of the method, we deliberately chose an electron number density profile which is more difficult to measure than one would expect during an SCR event, namely, the quiescent day profile shown in Fi g. 10. The separation of dispersive ionospheric refraction effects from the nondispersive effects of the neutral atmosphere was assured by beating the phase of the lower frequency signal against the phase of the 3146 subharmonic of the higher frequency. This beat frequency is plotted as a function of time in orbit (measured from the t = 0 point shown in Fig. 9) in Fig. Il. The right-hand end of the trace signifies tangency of the ray with the surface of the planet. The relationship between the beat frequency plotted in Fig. 11 and the electron density profile, N, can be established by considering the phase of the signals as they travel through the Martian ionosphere. The phase path of a radio signal, 4, measured in wavelengths, is given by
(8) where I, is the free space wavelength of the signal, ,u is the index of refraction, and the integral extends along the (curved) ray path from transmitter to receiver. The net effect of the ionosphere on the phase path is the result of two competing effects. The phase path tends to be shortened because the presence of free electrons advances the phase of the waves whereas the refraction of the waves causes the ray paths to be curved, tending to
R. C. IVHXmEN
978
et ui.
80 70 60 2 50 !i 2 40 ‘2 30 20 10
0 LOGa OF NUM3ER
Fro, 10. ELECTRON
NUMBER
OENSITY,
Cm-J’
DENSIN~IN THE DA?T'mffiQUKESCEXT IONOSPHERE (THE SOLID CURVE IN F1c.2 OFPAPER I),
3020-
-4o-5oc 4100
4200 TIME,set
FIG. 11. BEATFREQUENCYASA
FUNCTIOSOF~.
lengthen the phase path. Since these effects are frequency-dependent, the ray path along which the integral in Equation (8) extends is different for the higher and lower frequencies. ff we assume a negIigibIe magnetic field and also neglect the effects of electron colfisions, then, according to ~ag~etoion~~ theory, the index of refraction is related to the electron density by 80*6N* E”= 1 (9) J --7-where N, is the electron density in cm& and f is the frequency of the radar signal in Hz. The beat ‘frequency, AJ plotted in Fig. 10 is (dude) where A# = dr, - ~f~~~)~~ In this expression #Q is the phase path at the lower frequency ($50 mHz), C& is the phase path at the higher frequency (2300 mHz) and fLlf;E = 3146:
L
+!$!-d,_-?&
1-F
80.6~~ fz2
ds
1’
w--o
THE
IONOSPHERE
OF hlARS
BELOW
8Okt.n ALTITUDE-II
979
It would appear from Fig. 11 that the beat frequency data should be adequate for the inversion of the problem (Fjeldbo et al., 1965) in order to obtain the electron density profile. At the lower frequency (150 mHz) used in the feasibility calculations, there would be some signal absorption, about 7 dB for the electron number density profile shown in Fig. 10. Because electron-neutral particle collisions cannot be neglected, one shou!d use a modified form of the magnetoionic theory which takes account of electron-neutral particle collisions in the CO, atmosphere. Work is in fact under way on this aspect of the problem. Hence, the results shown in Fig. 11 are only qualitative, but are precise enough to establish the feasibility of the method. For an actual experiment one must consider the absorption of energy from the radio waves as well as the ‘caustics’ effect discussed earlier. Higher frequencies are more useful for observing larger electron number densities. 5. DISCUSSxON Several rather interesting and somewhat unexpected conclusions can be drawn from the calculations reported in both this paper and Paper I. The first is that a two-frequency occultation experiment would be sensitive enough to detect and measure the lower atmosphere electron profile even on a solar quiet day. Hence, the concept of a permanent Martian D-region can be checked. During an SCR event, electron densities are significantly enhanced, of course, and the ionosphere can be analyzed more precisely. Because the negative ion production chain starts with 0, it is obvious that the abundance of 0, could be confirmed (to order of magnitude) by such measurements; this in itself would be an important result of a two-frequency radar measurement. The surprising result is that the shape and magnitude of the lower ionosphere of Mars does not appear to be very dependent (within wide limits) on the presence or identity of minor species (except for 0,) or on reaction rates; this is somewhat contrary to current ideas about the terrestrial lower ionosphere. Ackno:vledgements-We
wish to thank Professor the bistatic radar occultation experiment.
V. R. Eshleman for the helpful discussions
concerning
REFERENCES FJELDBO,G., ESHLEMAN,V. R., GARRIOTT,0. K. and SETH, F. L., III (1965). J.geophys. Res. 70, 3701. FJELDBO,G. and ESHLE~N, V. R. (1968). Planet. Space Sci. 16, 1035. MCELROY, M. B. (1969). J. geophys. Res. 74,29. SVESTKA,Z. and SIMON, P. (1969). Solar Phys. 10, 3. VELINOV,P. (1968). J. armos. terr. Phys. 30, 1891. Wnn-rs~, R. C., POPPO~F,I. G. and &MS, J. S. (1971). Planet. Space Sci. 19,243. (Referred to as Paper I.) WHTTTEN,R. C. and POPPOFF,I. G. (1971). Funciamenlals of Aeronomy. John Wiley & Sons, New York, 1971. WILKES, M. V. (1954). Proc. Phys. Sot. B67, 304.