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Statistical parameters of nonisothermal lower ionospheric plasma in the electrically active mesosphere
Advances in Space Research 35 (2005) 1467–1471 www.elsevier.com/locate/asr
Statistical parameters of nonisothermal lower ionospheric plasma in the electrically active mesosphere S.I. Martynenko a, V.T. Rozumenko a, O.F. Tyrnov a b
a,*
, A.H. Manson b, C.E. Meek
b
Department of Space Radio Physics, Kharkiv V. Karazin National University, 4 Svoboda Square, Kharkiv 61077, Ukraine Institute Space and Atmospheric Studies, University of Saskatchewan, 116 Science Place, Saskatoon, SK, Canada S7N 5E2 Received 9 August 2004; received in revised form 9 March 2005; accepted 10 March 2005
Abstract The large V/m electric fields inherent in the lower mesosphere play an essential role in lower ionospheric electrodynamics. They must be the cause of large variations in the electron temperature and the electron collision frequency and consequently of the transition of the ionospheric plasma in the lower part of the D region into a nonisothermal state. This study is based on the datasets on large mesospheric electric fields collected with the 2.2-MHz radar of the Institute of Space and Atmospheric Studies, University of Saskatchewan, Canada (52N geographic latitude, 60.4N geomagnetic latitude), and with the 2.3-MHz radar of the Kharkiv V. Karazin National University, Ukraine (49.6N geographic latitude, 45.6N geomagnetic latitude). The statistical analysis of these data is presented by [Meek, C.E., Manson, A.H., Martynenko, S.I., Rozumenko, V.T., Tyrnov, O.F. Remote sensing of mesospheric electric fields using MF radars. J. Atmos. Solar-Terr. Phys. 66, 881–890, 2004. 10.1016/j.jastp.2004.02.002]. The large mesospheric electric fields in the 60–67-km altitude range are experimentally established to follow a Rayleigh distribution in the 0 < E < 2.5 V/m interval. These data have permitted the resulting differential distributions of relative disturbances in the electron temperature, h, and the effective electron collision frequency, g, to be determined. The most probable h and g values are found to be in the 1.4–2.2 interval, and hence the nonstationary state of the lower part of the D region needs to be accounted for in studying processes coupling the electrically active mesosphere and the lower ionospheric plasma. 2005 COSPAR. Published by Elsevier Ltd. All rights reserved. Keywords: Mesosphere; Large V/m electric fields; Nonisothermal D region plasma; Electron temperature disturbances; Electron collision frequency disturbances; Statistical models
1. Introduction Until recently, the mesosphere has traditionally been treated as a passive electrical element in studying the EarthÕs electrical environment, atmosphere/ionosphere electrodynamic coupling, and the global atmospheric electric circuit (see, e.g. Bering et al., 1998; Rycroft *
Corresponding author. Tel.: +38 057 705 12 51; fax: +38 057 705 12
61. E-mail addresses: [email protected] (S.I. Martynenko), [email protected] (V.T. Rozumenko), [email protected] (O.F. Tyrnov), [email protected] (A.H. Manson), [email protected] (C.E. Meek).
et al., 2000). At the same time, a large amount of in situ rocket measurements of large V/m mesospheric electric fields at different geographic locations have already been compiled over the past three decades (Bragin et al., 1974; Croskey et al., 1985, 1990; Goldberg, 1984, 1989, 1990; Hale, 1984; Hale and Croskey, 1979; Hale et al., 1981; Kelley et al., 1983; Maynard et al., 1981, 1984; Tyutin, 1976; Zadorozhny and Tyutin, 1998). A newly developed technique of Gokov and Martynenko (1997), Martynenko et al. (1999, 2001), and Meek et al. (2004) for remotely sensing large mesospheric electric fields has provided a means to increase data-taking rates dramatically. The presence of these DC fields must
0273-1177/$30 2005 COSPAR. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.asr.2005.03.041
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affect the lower D-region plasma parameters (see, e.g. Martynenko, 1999; Martynenko et al., 1999, 2001; Meek et al., 2004), and the ionospheric plasma in the electrically active mesosphere must undergo a transition from the isothermal state to a nonisothermal state that is characterized by a disturbance of the electron temperature. This paper reports on the statistical parameters of this nonisothermal state. The datasets on large mesospheric DC electric fields used in this study have been collected with the 2.2-MHz radar in Canada (52N geographic latitude, 60.4N geomagnetic latitude) by the Institute of Space and Atmospheric Studies, University of Saskatchewan, and with the 2.3-MHz radar in Ukraine (49.6N geographic latitude, 45.6N geomagnetic latitude) by the Kharkiv V. Karazin National University (see Meek et al., 2004).
writing Eqs. (1)–(3) the weakly ionized ionospheric plasma is assumed to be quasi-neutral, the positive and negative ion temperatures to be equal to the neutral constituent temperature, and that the effects of transport processes on local disturbances may be neglected (e.g. Martynenko, 1999). For the D region, Qe ¼ je E ¼ j2e =re :
ð5Þ
Also, the following dependences are taken into account (e.g. Gurevich, 1978; Tomko et al., 1980): r e ¼ K r ð 0Þ
e2 N ; mme
ð6Þ
me ¼ 5:8 1011 N n T 5=6 e ; d ¼ d0 ðT n =T e Þ d ¼ 0:2d0
ð7Þ
for T e =T n < 4; ð8Þ
for 4 < T e =T n < 15;
2. Model description ba ¼ f1:4 1029 ð300=T e Þ½O2 expð100=T n Þ The basic functional relations between the large mesospheric electric field features and the ionospheric D-region parameters for a quasi-steady case are given by (e.g. Martynenko, 1999; Martynenko et al., 2001; Meek et al., 2004) qi þ bd kN ba N ar ð1 þ kÞN 2 ¼ 0;
ð1Þ
qi ar ð1 þ kÞN 2 ai kð1 þ kÞN 2 ¼ 0;
ð2Þ
2Qe dme ðT e T n Þ ¼ 0; 3kN
ð3Þ
je ¼ re E;
ð4Þ
where qi is the ion production rate, bd is the effective rate at which negative ions are destroyed by electron detachment, N is the electron number density, k = N/N, N is the negative ion number density, ba is the effective rate at which the negative ions are formed by attachment of electrons to neutral constituents, ar is the effective rate of electron–ion recombination, ai is the effective rate of ion–ion recombination, Qe/N is the mean energy imparted to an electron by an external heating source, e.g., mesospheric electric field, k is BoltzmannÕs constant, me is the effective electron collision frequency, Te is the electron temperature, Tn is the neutral species temperature, d is the fractional loss of energy per electron collision with a heavy particle, je is the density of the current driven by an external mesospheric current source, re is the low-frequency electron conductivity of the ionospheric D-region plasma, and E is the mesospheric DC electric field intensity. Here, Eqs. (1) and (2) are the continuity equations for the electrons and ions, respectively, Eq. (3) is the energy equation for the electrons, and Eq. (4) is nonlinear OhmÕs law for large mesospheric DC electric fields. In
expð700=T e Þ þ 1:0 1031 ½N2 g½O2 ;
ð9Þ
1=2 1=2 300 Tn ar 6:0 10 ; Tn Te 6
ð10Þ
where Kr(0) = 1.42 (Gurevich, 1978), e is the electron charge, m is the electron mass, Nn is the number density of neutral particles, [O2] is the number density of molecular oxygen in cm3, [N2] is the number density of molecular nitrogen in cm3, Te and Tn are in K, ba in s1, ar in cm3 s1, and the subscript ‘‘0’’ is used to denote the magnitude of the plasma parameters in the absence of large mesospheric electric fields. Then, a relation for the electric field intensity E(z) in the lower part of the D region is easily obtained from Eqs. (3)–(8) (Martynenko, 1999; Martynenko et al., 2001), yielding ( ) 6=5 kmT e0 ðzÞ me ð z Þ 2 2 E ¼ dðzÞme ðzÞ 1 ; ð11Þ 0:97e2 me0 ðzÞ where Te0(z) and me0(z) are related by Eq. (7), and d(z) and Tn/Te are related by Eq. (8). The disturbed value of N(z) is given by 1=2
N ðzÞ ¼ qi ðzÞf½1 þ kðhÞ½ar ðhÞ þ kðhÞai ðzÞg
1=2
;
ð12Þ
which allows je to be specified by Eqs. (4) and (6). Here, h = Te/Te0. Hence, the set of equations (1)–(12) provides the framework for modeling studies of how the large mesospheric electric fields affect the ionospheric D-region parameters. The disturbances in the electron temperature and effective collision frequency (see Eqs. (7) and (11)) are the primary cause of disturbances in other parameters. Eq. (4) relates the large mesospheric electric
S.I. Martynenko et al. / Advances in Space Research 35 (2005) 1467–1471
fields to the low-frequency electron conductivity of the plasma. Eq. (5) takes account of large mesospheric electric field energy losses via Joule heating. Eq. (7) provides the relationship between disturbances in the electron temperature and the effective collision frequency. Eq. (8) establishes disturbances in the fractional loss of energy per electron collision with a heavy particle. Eq. (9) is used to calculate the effective rate at which the negative ions are formed by the attachment of electrons to neutral constituents. Eq. (10) shows disturbances in the effective rate of electron–ion recombination. Eq. (12) explicitly defines electron number density perturbations.
3. Statistics on disturbances in the D-region parameters The primary source for determining the histograms of the lower-ionospheric parameters is the effective electron collision frequencies me. The me values are inferred from the MF radar data collected in the 61–67-km altitude range at the Institute of Space and Atmospheric Studies (ISAS), University of Saskatchewan, Saskatoon, Canada, and in the 60–66-km altitude range at the Kharkiv V. Karazin National University, Ukraine, (Meek et al., 2004). Martynenko (2002) and Meek et al. (2004) have established that the histograms showing the distribution wE of large mesospheric electric fields in the interval 0 < E 6 2.5 V/m fit to a Rayleigh distribution as given by f ðE Þ ¼
E ðE2 =2r2 Þ e ; r2
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the primary Rayleigh distribution of large mesospheric electric fields. Fig. 1 illustrates the histogram showing the wg distribution of the disturbances in the effective electron collision frequency in the height range 61–67 km in Canada and the corresponding theoretical distributions f(g), calculated using Eq. (14), for 61, 64, and 67-km altitude; here, S1/r2 = 0.54 and me0 = 3.32 · 107 s1 for 61 km, S1/r2 = 0.54 and me0 = 2.21 · 107 s1 for 64 km, S1/ r2 = 0.18 and me0 = 1.47 · 107 s1 for 67 km. This histogram is constructed by using n = 99 samples and gives an estimate of the g-distribution first ordinary moment M1[g] = 2.42 ± 0.23 within the 0.98 confidence interval for the 61–67-km altitude range. Fig. 2 shows the histogram constructed in a similar fashion by using n = 129 samples collected over Kharkiv (Ukraine) and the corresponding theoretical distributions f(g), calculated using Eq. (14), for 60, 63, and 66-km altitude; here S1/r2 = 0.94 and me0 = 3.75 · 107 s1 for 60 km, S1/r2 = 0.84 and me0 = 2.55 · 107 s1 for 63 km, S1/r2 = 0.45 and me0 = 1.68 · 107 s1 for 66 km; M1[g] = 2.02 ± 0.14 within the 0.98 confidence interval for the 60–66-km altitude range. Fig. 3 presents a histogram showing the wh distribution of the disturbances in the effective electron collision frequency obtained in Canada and the corresponding theoretical distributions f(h), calculated using Eq. (15), for 61, 64, and 67-km altitude. Here, M1[g] = 2.91 ± 0.33. The histogram constructed in a similar way by using n = 99 samples collected over Ukraine is presented
ð13Þ
where Em = r is the most probable value of E, M1[E] = (p/2)1/2r is the mean, M2[E] = 2r2 is the second ordinary moment for the Rayleigh set, and D[E] = (2 p/2)r2 is the variance. For the Canadian site, M1[E] = 0.89 ± 0.12 V/m, where the sample mean ÆERæ= 0.89 V/m, which corresponds to r = 0.71 V/m. For the Ukrainian site, M1[E] = 0.72 ± 0.11 V/m, ÆERæ = 0.72 V/m, and r = 0.57 V/m. For the Rayleigh distribution of large mesospheric electric fields, Eq. (13), we have derived the theoretical distribution functions f(g) and f(h) for the relative disturbances in the effective electron collision frequency g = me/me0 and in the electron temperature h = Te/Te0 by making use of the deterministic functional dependences in Eqs. (7) and (11), as given by S1 2 S1 f ðgÞ ¼ 2 g g1=5 exp 2 g2 g4=5 ; ð14Þ 5 r 2r S1 S1 f ðhÞ ¼ 2 5h2=3 2h1=3 exp 2 h2=3 ðh 1Þ ; 6r 2r ð15Þ
where S 1 ðzÞ ¼ kmd0 T e0 m2e0 =ð0:97e2 Þ, f(g) = 0 for g = 1, f(h) = 0 for h = 1, and r is the standard parameter of
Fig. 1. A histogram wg showing the distribution of the effective electron collision frequencies obtained over Canada and the corresponding theoretical distribution functions f(g) in the 61–67-km altitude range. The dashed curve represents the data for an altitude of 61 km, the solid line for 64 km, and the dotted for 67 km.
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Fig. 2. A histogram wg showing the distribution of the effective electron collision frequencies obtained over Ukraine and the corresponding theoretical distribution functions f(g) in the 60–66-km altitude range. The dashed curve represents the data for an altitude of 60 km, the solid line for 63 km, and the dotted for 66 km.
in Fig. 4, where the theoretical distributions f(h) for 60, 63, and 66-km altitude are calculated by using Eq. (15). Here, M1[g] = 2.35 ± 0.19.
Fig. 4. A histogram showing the distribution, wh, of the electron temperature obtained over Ukraine and the corresponding theoretical distribution functions f(h) in the 60–66-km altitude range. The dashed curve represents the data for an altitude of 60 km, the solid line for 63 km, and the dotted for 66 km.
The analysis of the data presented in Figs. 1–4 show that the large mesospheric electric fields from the Rayleigh generator maintain the electron temperatures in the lower part of the ionospheric D region at elevated temperatures, a factor of 2 higher than Te0 and the neutral temperatures Tn. Within the 0.98 confidence interval, the disturbed Te and me values at high geomagnetic latitudes are, on average, higher than at mid-geomagnetic latitudes.
4. Conclusions
Fig. 3. A histogram showing the distribution, wh, of the electron temperature obtained over Canada and the corresponding theoretical distribution functions f(h) in the 61–67-km altitude range. The dashed curve represents the data for an altitude of 61 km, the solid line for 64 km, and the dotted for 67 km.
Eq. (15) and Figs. 3 and 4 show that the large mesospheric electric fields maintain the lower part of the ionospheric D region in a nonthermal state, which should be accounted for in the studies of mesospheric and lower ionospheric electrodynamics. The disturbances in the electron temperature and in the corresponding disturbances in the effective electron collision frequency (see Eq. (7)) provide the primary means by which the large mesospheric electric fields control the basic parameters of the lower ionosphere. The obtained theoretical differential distribution functions of relative disturbances in the electron temperature, Eq. (15), and effective collision frequency, Eq. (14), provide a necessary statistical complement to the deterministic theoretical model of disturbances in the
S.I. Martynenko et al. / Advances in Space Research 35 (2005) 1467–1471
ionospheric D region caused by large mesospheric electric fields (Martynenko, 1999; Martynenko et al., 2001; Meek et al., 2004). The histograms in Figs. 1–4 show the distributions of relative disturbances in the electron temperature and the effective electron collision frequency form the basis for the simplified empirical statistical models of disturbances in the lower ionospheric parameters in the presence of large mesospheric electric fields.
References Bering III, E.A., Few, A.A., Benkrook, J.R. The global electric circuit. Phys. Today 51, 24–30, 1998. Bragin, Yu.A., Tyutin, A.A., Kocheev, A.A., Tyutin, A.A Direct measurement of the atmospheric vertical electric field intensity up to 80 km. Cosmic Res. 12, 306–308, 1974. Croskey, C.L., Hale, L.C., Mitchell, J.D., Muha, D., Maynard, N.C. A diurnal study of the electrical structure of the equatorial middle atmosphere. J. Atmos. Terr. Phys. 47, 835–844, 1985. Croskey, C.L., Hale, L.C., Mitchell, J.D., Schmidlin, F., J, Hoppe, U.P. Electric field measurements during the MAC/EPSILON campaign. J. Atmos. Terr. Phys. 52, 1005–1065, 1990. Gokov, A.M., Martynenko, S.I. Variations in the electron collision frequency and the electric field in the lower ionosphere. Geomagn. Aeron. 37, 76–80, 1997 (in Russian). Goldberg, R.A. Middle atmospheric electrodynamics: status and future. J. Atmos. Terr. Phys. 46, 1083–1101, 1984. Goldberg, R.A. Electrodynamics of the high latitude mesosphere. J. Geophys. Res. 94, 14661–14672, 1989. Goldberg, R.A. Middle atmospheric electrodynamics during MAP. Adv. Space Res. 10, 209–217, 1990. Gurevich, A.V. Nonlinear Phenomena in the Ionosphere. Springer, New York, 1978. Hale, L.C. Middle atmosphere electrical structure, dynamics and coupling. Adv. Space Res. 4, 175–186, 1984.
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Hale, L.C., Croskey, C.L. An auroral effect on the fair weather electric field. Nature 278, 239–241, 1979. Hale, L.C., Croskey, C.L., Mitchell, J.D. Measurements of middleatmosphere electric fields and associated electrical conductivities. Geophys. Res. Lett. 8, 927–930, 1981. Kelley, M.C., Siefring, C.L., Pfaff Jr., R.F. Large middle atmospheric electric fields, fact or fiction?. Geophys. Res. Lett. 10, 733–736, 1983. Martynenko, S.I. Atmospheric electric field and disturbances of the lower ionosphere parameters. J. Atmos. Electri. 19, 1–9, 1999. Martynenko, S.I. Statistical properties of large mesospheric electric fields. J. Atmos. Electri. 22, 101–106, 2002. Martynenko, S.I., Rozumenko, V.T., Tsymbal, A.M., Tyrnov, O.F., Gokov, A.M. Mesospheric electric field measurements with a partial reflection radar. J. Atmos. Electri. 19, 81–86, 1999. Martynenko, S.I., Rozumenko, V.T., Tyrnov, O.F. New possibilities for mesospheric electricity diagnostics. Adv. Space Res. 27, 1127– 1132, 2001. Maynard, N.C., Croskey, C.L., Mitchell, J.D., Hale, L.C. Measurement of volt/meter vertical electric fields in the middle atmosphere. Geophys. Res. Lett. 8, 923–926, 1981. Maynard, N.C., Hale, L.C., Mitchell, J.D., Schmidlin, F.J., Goldberg, R.A., Barcus, J.R., Soraas, F., Croskey, C.L. Electrical structure in the high-latitude middle atmosphere. J. Atmos. Terr. Phys. 46, 807–817, 1984. Meek, C.E., Manson, A.H., Martynenko, S.I., Rozumenko, V.T., Tyrnov, O.F. Remote sensing of mesospheric electric fields using MF radars. J. Atmos. Solar-Terr. Phys. 66, 881–890, 2004. Rycroft, M.J., Israelsson, S., Price, C. The global atmospheric electric circuit, solar activity and climate change. J. Atmos. Solar-Terr. Phys. 62, 1563–1576, 2000. Tomko, A.A., Ferraro, A.J., Lee, H.S., Mitra, A.P. A theoretical model of D-region ion chemistry modifications during high power radio wave heating. J. Atmos. Terr. Phys. 42, 275–285, 1980. Tyutin, A.A. Mesospheric maximum of the electric field strength. Cosmic Res. 14, 143–144, 1976. Zadorozhny, A.M., Tyutin, A.A. Effects of geomagnetic activity on the mesospheric electric fields. Ann. Geophys. 16, 1544–1551, 1998.
Statistical parameters of nonisothermal lower ionospheric plasma in the electrically active mesosphere S.I. Martynenko a, V.T. Rozumenko a, O.F. Tyrnov a b
a,*
, A.H. Manson b, C.E. Meek
b
Department of Space Radio Physics, Kharkiv V. Karazin National University, 4 Svoboda Square, Kharkiv 61077, Ukraine Institute Space and Atmospheric Studies, University of Saskatchewan, 116 Science Place, Saskatoon, SK, Canada S7N 5E2 Received 9 August 2004; received in revised form 9 March 2005; accepted 10 March 2005
Abstract The large V/m electric fields inherent in the lower mesosphere play an essential role in lower ionospheric electrodynamics. They must be the cause of large variations in the electron temperature and the electron collision frequency and consequently of the transition of the ionospheric plasma in the lower part of the D region into a nonisothermal state. This study is based on the datasets on large mesospheric electric fields collected with the 2.2-MHz radar of the Institute of Space and Atmospheric Studies, University of Saskatchewan, Canada (52N geographic latitude, 60.4N geomagnetic latitude), and with the 2.3-MHz radar of the Kharkiv V. Karazin National University, Ukraine (49.6N geographic latitude, 45.6N geomagnetic latitude). The statistical analysis of these data is presented by [Meek, C.E., Manson, A.H., Martynenko, S.I., Rozumenko, V.T., Tyrnov, O.F. Remote sensing of mesospheric electric fields using MF radars. J. Atmos. Solar-Terr. Phys. 66, 881–890, 2004. 10.1016/j.jastp.2004.02.002]. The large mesospheric electric fields in the 60–67-km altitude range are experimentally established to follow a Rayleigh distribution in the 0 < E < 2.5 V/m interval. These data have permitted the resulting differential distributions of relative disturbances in the electron temperature, h, and the effective electron collision frequency, g, to be determined. The most probable h and g values are found to be in the 1.4–2.2 interval, and hence the nonstationary state of the lower part of the D region needs to be accounted for in studying processes coupling the electrically active mesosphere and the lower ionospheric plasma. 2005 COSPAR. Published by Elsevier Ltd. All rights reserved. Keywords: Mesosphere; Large V/m electric fields; Nonisothermal D region plasma; Electron temperature disturbances; Electron collision frequency disturbances; Statistical models
1. Introduction Until recently, the mesosphere has traditionally been treated as a passive electrical element in studying the EarthÕs electrical environment, atmosphere/ionosphere electrodynamic coupling, and the global atmospheric electric circuit (see, e.g. Bering et al., 1998; Rycroft *
Corresponding author. Tel.: +38 057 705 12 51; fax: +38 057 705 12
61. E-mail addresses: [email protected] (S.I. Martynenko), [email protected] (V.T. Rozumenko), [email protected] (O.F. Tyrnov), [email protected] (A.H. Manson), [email protected] (C.E. Meek).
et al., 2000). At the same time, a large amount of in situ rocket measurements of large V/m mesospheric electric fields at different geographic locations have already been compiled over the past three decades (Bragin et al., 1974; Croskey et al., 1985, 1990; Goldberg, 1984, 1989, 1990; Hale, 1984; Hale and Croskey, 1979; Hale et al., 1981; Kelley et al., 1983; Maynard et al., 1981, 1984; Tyutin, 1976; Zadorozhny and Tyutin, 1998). A newly developed technique of Gokov and Martynenko (1997), Martynenko et al. (1999, 2001), and Meek et al. (2004) for remotely sensing large mesospheric electric fields has provided a means to increase data-taking rates dramatically. The presence of these DC fields must
0273-1177/$30 2005 COSPAR. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.asr.2005.03.041
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affect the lower D-region plasma parameters (see, e.g. Martynenko, 1999; Martynenko et al., 1999, 2001; Meek et al., 2004), and the ionospheric plasma in the electrically active mesosphere must undergo a transition from the isothermal state to a nonisothermal state that is characterized by a disturbance of the electron temperature. This paper reports on the statistical parameters of this nonisothermal state. The datasets on large mesospheric DC electric fields used in this study have been collected with the 2.2-MHz radar in Canada (52N geographic latitude, 60.4N geomagnetic latitude) by the Institute of Space and Atmospheric Studies, University of Saskatchewan, and with the 2.3-MHz radar in Ukraine (49.6N geographic latitude, 45.6N geomagnetic latitude) by the Kharkiv V. Karazin National University (see Meek et al., 2004).
writing Eqs. (1)–(3) the weakly ionized ionospheric plasma is assumed to be quasi-neutral, the positive and negative ion temperatures to be equal to the neutral constituent temperature, and that the effects of transport processes on local disturbances may be neglected (e.g. Martynenko, 1999). For the D region, Qe ¼ je E ¼ j2e =re :
ð5Þ
Also, the following dependences are taken into account (e.g. Gurevich, 1978; Tomko et al., 1980): r e ¼ K r ð 0Þ
e2 N ; mme
ð6Þ
me ¼ 5:8 1011 N n T 5=6 e ; d ¼ d0 ðT n =T e Þ d ¼ 0:2d0
ð7Þ
for T e =T n < 4; ð8Þ
for 4 < T e =T n < 15;
2. Model description ba ¼ f1:4 1029 ð300=T e Þ½O2 expð100=T n Þ The basic functional relations between the large mesospheric electric field features and the ionospheric D-region parameters for a quasi-steady case are given by (e.g. Martynenko, 1999; Martynenko et al., 2001; Meek et al., 2004) qi þ bd kN ba N ar ð1 þ kÞN 2 ¼ 0;
ð1Þ
qi ar ð1 þ kÞN 2 ai kð1 þ kÞN 2 ¼ 0;
ð2Þ
2Qe dme ðT e T n Þ ¼ 0; 3kN
ð3Þ
je ¼ re E;
ð4Þ
where qi is the ion production rate, bd is the effective rate at which negative ions are destroyed by electron detachment, N is the electron number density, k = N/N, N is the negative ion number density, ba is the effective rate at which the negative ions are formed by attachment of electrons to neutral constituents, ar is the effective rate of electron–ion recombination, ai is the effective rate of ion–ion recombination, Qe/N is the mean energy imparted to an electron by an external heating source, e.g., mesospheric electric field, k is BoltzmannÕs constant, me is the effective electron collision frequency, Te is the electron temperature, Tn is the neutral species temperature, d is the fractional loss of energy per electron collision with a heavy particle, je is the density of the current driven by an external mesospheric current source, re is the low-frequency electron conductivity of the ionospheric D-region plasma, and E is the mesospheric DC electric field intensity. Here, Eqs. (1) and (2) are the continuity equations for the electrons and ions, respectively, Eq. (3) is the energy equation for the electrons, and Eq. (4) is nonlinear OhmÕs law for large mesospheric DC electric fields. In
expð700=T e Þ þ 1:0 1031 ½N2 g½O2 ;
ð9Þ
1=2 1=2 300 Tn ar 6:0 10 ; Tn Te 6
ð10Þ
where Kr(0) = 1.42 (Gurevich, 1978), e is the electron charge, m is the electron mass, Nn is the number density of neutral particles, [O2] is the number density of molecular oxygen in cm3, [N2] is the number density of molecular nitrogen in cm3, Te and Tn are in K, ba in s1, ar in cm3 s1, and the subscript ‘‘0’’ is used to denote the magnitude of the plasma parameters in the absence of large mesospheric electric fields. Then, a relation for the electric field intensity E(z) in the lower part of the D region is easily obtained from Eqs. (3)–(8) (Martynenko, 1999; Martynenko et al., 2001), yielding ( ) 6=5 kmT e0 ðzÞ me ð z Þ 2 2 E ¼ dðzÞme ðzÞ 1 ; ð11Þ 0:97e2 me0 ðzÞ where Te0(z) and me0(z) are related by Eq. (7), and d(z) and Tn/Te are related by Eq. (8). The disturbed value of N(z) is given by 1=2
N ðzÞ ¼ qi ðzÞf½1 þ kðhÞ½ar ðhÞ þ kðhÞai ðzÞg
1=2
;
ð12Þ
which allows je to be specified by Eqs. (4) and (6). Here, h = Te/Te0. Hence, the set of equations (1)–(12) provides the framework for modeling studies of how the large mesospheric electric fields affect the ionospheric D-region parameters. The disturbances in the electron temperature and effective collision frequency (see Eqs. (7) and (11)) are the primary cause of disturbances in other parameters. Eq. (4) relates the large mesospheric electric
S.I. Martynenko et al. / Advances in Space Research 35 (2005) 1467–1471
fields to the low-frequency electron conductivity of the plasma. Eq. (5) takes account of large mesospheric electric field energy losses via Joule heating. Eq. (7) provides the relationship between disturbances in the electron temperature and the effective collision frequency. Eq. (8) establishes disturbances in the fractional loss of energy per electron collision with a heavy particle. Eq. (9) is used to calculate the effective rate at which the negative ions are formed by the attachment of electrons to neutral constituents. Eq. (10) shows disturbances in the effective rate of electron–ion recombination. Eq. (12) explicitly defines electron number density perturbations.
3. Statistics on disturbances in the D-region parameters The primary source for determining the histograms of the lower-ionospheric parameters is the effective electron collision frequencies me. The me values are inferred from the MF radar data collected in the 61–67-km altitude range at the Institute of Space and Atmospheric Studies (ISAS), University of Saskatchewan, Saskatoon, Canada, and in the 60–66-km altitude range at the Kharkiv V. Karazin National University, Ukraine, (Meek et al., 2004). Martynenko (2002) and Meek et al. (2004) have established that the histograms showing the distribution wE of large mesospheric electric fields in the interval 0 < E 6 2.5 V/m fit to a Rayleigh distribution as given by f ðE Þ ¼
E ðE2 =2r2 Þ e ; r2
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the primary Rayleigh distribution of large mesospheric electric fields. Fig. 1 illustrates the histogram showing the wg distribution of the disturbances in the effective electron collision frequency in the height range 61–67 km in Canada and the corresponding theoretical distributions f(g), calculated using Eq. (14), for 61, 64, and 67-km altitude; here, S1/r2 = 0.54 and me0 = 3.32 · 107 s1 for 61 km, S1/r2 = 0.54 and me0 = 2.21 · 107 s1 for 64 km, S1/ r2 = 0.18 and me0 = 1.47 · 107 s1 for 67 km. This histogram is constructed by using n = 99 samples and gives an estimate of the g-distribution first ordinary moment M1[g] = 2.42 ± 0.23 within the 0.98 confidence interval for the 61–67-km altitude range. Fig. 2 shows the histogram constructed in a similar fashion by using n = 129 samples collected over Kharkiv (Ukraine) and the corresponding theoretical distributions f(g), calculated using Eq. (14), for 60, 63, and 66-km altitude; here S1/r2 = 0.94 and me0 = 3.75 · 107 s1 for 60 km, S1/r2 = 0.84 and me0 = 2.55 · 107 s1 for 63 km, S1/r2 = 0.45 and me0 = 1.68 · 107 s1 for 66 km; M1[g] = 2.02 ± 0.14 within the 0.98 confidence interval for the 60–66-km altitude range. Fig. 3 presents a histogram showing the wh distribution of the disturbances in the effective electron collision frequency obtained in Canada and the corresponding theoretical distributions f(h), calculated using Eq. (15), for 61, 64, and 67-km altitude. Here, M1[g] = 2.91 ± 0.33. The histogram constructed in a similar way by using n = 99 samples collected over Ukraine is presented
ð13Þ
where Em = r is the most probable value of E, M1[E] = (p/2)1/2r is the mean, M2[E] = 2r2 is the second ordinary moment for the Rayleigh set, and D[E] = (2 p/2)r2 is the variance. For the Canadian site, M1[E] = 0.89 ± 0.12 V/m, where the sample mean ÆERæ= 0.89 V/m, which corresponds to r = 0.71 V/m. For the Ukrainian site, M1[E] = 0.72 ± 0.11 V/m, ÆERæ = 0.72 V/m, and r = 0.57 V/m. For the Rayleigh distribution of large mesospheric electric fields, Eq. (13), we have derived the theoretical distribution functions f(g) and f(h) for the relative disturbances in the effective electron collision frequency g = me/me0 and in the electron temperature h = Te/Te0 by making use of the deterministic functional dependences in Eqs. (7) and (11), as given by S1 2 S1 f ðgÞ ¼ 2 g g1=5 exp 2 g2 g4=5 ; ð14Þ 5 r 2r S1 S1 f ðhÞ ¼ 2 5h2=3 2h1=3 exp 2 h2=3 ðh 1Þ ; 6r 2r ð15Þ
where S 1 ðzÞ ¼ kmd0 T e0 m2e0 =ð0:97e2 Þ, f(g) = 0 for g = 1, f(h) = 0 for h = 1, and r is the standard parameter of
Fig. 1. A histogram wg showing the distribution of the effective electron collision frequencies obtained over Canada and the corresponding theoretical distribution functions f(g) in the 61–67-km altitude range. The dashed curve represents the data for an altitude of 61 km, the solid line for 64 km, and the dotted for 67 km.
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Fig. 2. A histogram wg showing the distribution of the effective electron collision frequencies obtained over Ukraine and the corresponding theoretical distribution functions f(g) in the 60–66-km altitude range. The dashed curve represents the data for an altitude of 60 km, the solid line for 63 km, and the dotted for 66 km.
in Fig. 4, where the theoretical distributions f(h) for 60, 63, and 66-km altitude are calculated by using Eq. (15). Here, M1[g] = 2.35 ± 0.19.
Fig. 4. A histogram showing the distribution, wh, of the electron temperature obtained over Ukraine and the corresponding theoretical distribution functions f(h) in the 60–66-km altitude range. The dashed curve represents the data for an altitude of 60 km, the solid line for 63 km, and the dotted for 66 km.
The analysis of the data presented in Figs. 1–4 show that the large mesospheric electric fields from the Rayleigh generator maintain the electron temperatures in the lower part of the ionospheric D region at elevated temperatures, a factor of 2 higher than Te0 and the neutral temperatures Tn. Within the 0.98 confidence interval, the disturbed Te and me values at high geomagnetic latitudes are, on average, higher than at mid-geomagnetic latitudes.
4. Conclusions
Fig. 3. A histogram showing the distribution, wh, of the electron temperature obtained over Canada and the corresponding theoretical distribution functions f(h) in the 61–67-km altitude range. The dashed curve represents the data for an altitude of 61 km, the solid line for 64 km, and the dotted for 67 km.
Eq. (15) and Figs. 3 and 4 show that the large mesospheric electric fields maintain the lower part of the ionospheric D region in a nonthermal state, which should be accounted for in the studies of mesospheric and lower ionospheric electrodynamics. The disturbances in the electron temperature and in the corresponding disturbances in the effective electron collision frequency (see Eq. (7)) provide the primary means by which the large mesospheric electric fields control the basic parameters of the lower ionosphere. The obtained theoretical differential distribution functions of relative disturbances in the electron temperature, Eq. (15), and effective collision frequency, Eq. (14), provide a necessary statistical complement to the deterministic theoretical model of disturbances in the
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ionospheric D region caused by large mesospheric electric fields (Martynenko, 1999; Martynenko et al., 2001; Meek et al., 2004). The histograms in Figs. 1–4 show the distributions of relative disturbances in the electron temperature and the effective electron collision frequency form the basis for the simplified empirical statistical models of disturbances in the lower ionospheric parameters in the presence of large mesospheric electric fields.
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