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Temperature enhancement induced by ionosphere heating in low altitude region
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Progress in Natural Science 18 (2008) 1339–1343 www.elsevier.com/locate/pnsc
Temperature enhancement induced by ionosphere heating in low altitude region Bin Xu a,*, Jian Wu b, Zhensen Wu a, Jun Wu b, Haiqin Che b, Yubo Yan b, Kun Xue a b
a School of Science, Xidian University, Xi’an 710071, China National Key Laboratory of Electromagnetic Environment, China Research Institute of Radiowave Propagation, Beijing 102206, China
Received 12 February 2008; received in revised form 19 March 2008; accepted 9 April 2008
Abstract The assumption that the electron temperature is approximately equal to the ion temperature is not rational during the high frequency (HF) heating in low ionosphere region. Thus, using the theoretical formula of incoherent scatter spectra with collisional plasma, the incoherent scatter data are analyzed during ionosphere heating at 91.7 km height on August 15th 2006. The enhancements of electron temperature are obtained, and the incremental percent is up to 37% and 46% at the universal time of 10:22 and 10:30, respectively. By using the same initialization value, the ionosphere heating process is simulated by Ohmic theory and the experimental results are basically consistent with the simulation. Ó 2008 National Natural Science Foundation of China and Chinese Academy of Sciences. Published by Elsevier Limited and Science in China Press. All rights reserved. Keywords: Incoherent scatter spectra; Ohmic theory; Ionospheric heating; Electron temperature
1. Introduction With the advantage of high precision, wide range and multi-parameters detection, incoherent scatter radar has become the most effective detection instrument of ground base. The enhancements of the incoherent scatter spectrum were observed during the ionosphere modification in low latitude from the early 1970s [1,2]. At high latitudes the first observation was performed in Tromsø [3,4]. In 1992, Rietveld et al. [5] and Kohl et al. [6] reviewed the enhancement of ion line and plasma line during ionospheric heating. According to the observation of electron density and temperature oscillations, the mechanics and the scale of fluctuation are given by Honary et al. [7]. Peak electron temperature enhancements of up to 50% were measured by Robinson [8] and by Stocker et al. [9] in the daytime *
Corresponding author. Tel./fax: +86 10 69731740. E-mail address: [email protected] (B. Xu).
and more obvious results were found at night [10]. Ashrafi et al. presented the heater-induced altitude descent of ion line enhancement [11]. However, all the studies concentrate on the high ionosphere, and only the recent observation in D region was given by Kero [12]. In low altitude ionospheric region, there is a large measurement error and a low spectral resolution. Thus, the ratio between electron and ion temperature is supposed to be a constant in incoherent scatter data analysis, which is effective for the common observation. However, the electron temperature is enhanced by HF heating, and the assumption is not reasonable. Using Sheffield’s theory, the incoherent scatter spectra in collisional plasma are presented in this paper. On the basis of this theoretical model, the incoherent scatter data are inversed during ionosphere heating at 91.7 km height with the independent electron temperature and collision frequency. And the inversion results are compared with the simulation based Ohmic theory.
1002-0071/$ - see front matter Ó 2008 National Natural Science Foundation of China and Chinese Academy of Sciences. Published by Elsevier Limited and Science in China Press. All rights reserved. doi:10.1016/j.pnsc.2008.04.010
1340
B. Xu et al. / Progress in Natural Science 18 (2008) 1339–1343
2. Theoretical spectra with a collisional plasma
where a and b are the electron and ion thermal velocity, a ¼ 1=kkD (kD is Debye length), and ye and yi are defined as
According to the theoretical results of incoherent scatter spectra deduced by Sheffield [13], the spectral density function is given by 2 ð1 þ C i Þ2 Be þ 2Z C e Bi ð1Þ Sðk; xÞ ¼ 2 e e
y e ¼ ðx ice Þ=ka
ð12Þ
y i ¼ ðx ici Þ=kb
ð13Þ
where subscripts i and e denote the ions and electrons, respectively, k is the wave vector and x is the Doppler frequency, Z is the charge number, and e is the dielectric function
Fig. 1 shows the ion line spectra peak obtained by the EISCAT tau2pl experiment from 9:38 to 11:14 on 15 August 2006 near 91.7 km. In order to see the difference between the heated and unheated, the heater was switched on/off every 4 min. The antenna of transmitting and receiving site in Tromsø, Norway, was directed along the geomagnetic field. As shown in Fig. 1, ion spectra are obviously affected by ionosphere heating. With the heater on, the power peak falls, which will affect the inversion of ionospheric parameters. In the analysis of incoherent scatter spectra, ne, Te, Ti and vi are the direct inversion variables above 107 km height. However, on account of a large collision frequency and a little temperature difference between ions and electrons, the independent inversion variables were changed into ne, Ti, vi and ci in a lower height and Te was supposed to be equal to Ti approximately. This is designed for a long statistical study of collision frequency and it is rational for the common observation. However, the assumption above is not tenable for special events study, such as particles precipitation or ionosphere heating. The particles temperature will be enhanced by these events, and it is not rational that the ratio of Te to Ti is a constant. In our inversion of heating data, electron temperature is used as an independent variable. In order to have fewer inversion variables and a better precision, at the unheated time 10:18 and 10:26, the temperature ratio is chosen as 1.17, which comes from GUISDAP (Grand Unified Incoherent Scatter Design and Analysis Package). And at the heating time 10:22 and 10:30, Te is separated from Ti. In the low ionospheric region, there is a large measurement error and a low spectral resolution. In this case, Levenberg–Marquart (LM) algorithm will receive a local extremum. Whereas the pattern search method, a global
e ¼ 1 þ Ci þ Ce
ð2Þ
Cq and Bq are defined as Z þ1 1 4pZe2 nq k @fq =@m Cq ¼ dm 1 þ Dq 1 mq k 2 x k m icq (Z ) þ1 cq fq jDq j2 dm 2 Bq ¼ 2 2 cq j1 þ Dq j ðx k mÞ þ c2q 1
ð3Þ
ð4Þ
where the subscript q can be i or e, mq is the particle mass, e is the electronic charge, nq is the number density, fq is the velocity distribution function, m is the velocity vector, cq is the effective collision frequency appropriate to the species over which we are taking an ensemble average, and Dq is Z þ1 fq dm ð5Þ Dq ¼ icq x k m icq 1 In this study, we consider only collision between the charged and neutral particles in the condition of lower ionosphere. In thermodynamic equilibrium, the velocity distributions are Maxwellian, then Dq, Cq and Bq can be given as Z ye ice 2 2 0:5 2 2 expðy e Þ De ¼ expðp Þdp þ ip expðy e Þ ð6Þ ka 0 Z yi ic expðp2 Þdp þ ip0:5 expðy 2i Þ ð7Þ Di ¼ i 2 expðy 2i Þ kb 0 Z ye 1 2 Im 2 expðy Þ expðp2 Þdp Be ¼ e 2 kaj1 þ De j 0 jDe j2 0:5 2 ð8Þ þ ip expðy e Þ 2 ce j1 þ De j Z yi 1 2 Bi ¼ Im 2 expðy i Þ expðp2 Þdp kbj1 þ Di j2 0 2 jDi j 0:5 2 ð9Þ þip expðy i Þ 2 ci j1 þ Di j Ce ¼
Z ye a2 expðp2 Þdp ip0:5 y e expðy 2e Þ 1 2y e expðy 2e Þ ð1 þ De Þ 0
Ci ¼
3. Analyses of incoherent scatter data
a2 1 2y i expðy 2i Þ ð1 þ Di Þ
Z
yi
ð10Þ expðp2 Þdp ip0:5 y i expðy 2i Þ
0
ð11Þ
Fig. 1. The power peak of ion line spectra.
B. Xu et al. / Progress in Natural Science 18 (2008) 1339–1343
search method, is used to improve this problem. In our analysis, the collision frequency of ions ci is used as an inversion variable and the collision frequency of electrons is given by Schlegel et al. [14] pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð14Þ ce ¼ 0:357ci mi T e =me T i The two heated and unheated power spectra and the fitted values are presented. In Figs. 2 and 3, we can see that the incoherent scatter spectra descend during heating. The increases of electron temperature and collision frequency or the decreases of electron density and ion temperature can result in the change. However, due to its small mass, electron is accelerated by artificial electric field easily. The accelerated electrons collide with other electrons or ions and neutral particles, and the direction of electron velocity is changed. The kinetic energy of the electron obtained from high frequency (HF) electric field is converted into electron thermal energy, which is represented as the increase of electron temperature. In light of the large mass difference between the ion and electron, the impact on ion temperature is faint. On account of the positive correlation between Ti and ci, the effect of heating on ci is very small too. With the ERP (effective radiation power) of 20 MW, pump frequency of 4.544 MHz and heating time of 4 min,
1341
Table 1 The inversion results of ionosphere parameters
10:18 10:22 10:26 10:30
ne ðm3 Þ
T e ðKÞ
T i ðKÞ
mi ðHzÞ
1.95e10 1.80e10 1.49e10 1.29e10
182 249 142 208
156 170 121 125
18518 20750 15500 23000
there is not an obvious change of the electron density in our experiments. Thus, it is anticipative that the amplitude change of the power spectra is produced by electron temperature. The inversion results are given in Table 1. As expected above, there is no obvious change in the electron density, ion temperature and collision frequency, and the electron temperature has a large augment. At the time of 10:22 and 10:30, the incremental percent is up to 37% and 46%, respectively. 4. Comparison with the simulation results The experimental results were already presented, and on the basis of Ohmic theory, the simulation of high power radio wave in lower ionosphere was studied. Radio wave in ionosphere is described by the well-known AppletonLassen dispersion relation: n2 ¼ 1
X rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 Y ðsin hÞ ðY sin hÞ4 4ð1X þ ðY cos hÞ 1 iZ 2ð1X iZÞ iZÞ2
ð15Þ
2
where the normalized frequencies X, Y, Z are defined as
Fig. 2. The power spectra at 10:18 and 10:22.
X ¼ fN2 =f 2 ¼ ne e2 =4p2 e0 me f 2
ð16Þ
Y ¼ fH =f ¼ eB=2pme f
ð17Þ
Z ¼ ce =2pf
ð18Þ
where fN is the ionospheric plasma frequency, fH is the gyromagnetic frequency and f is the incident wave frequency; e0 stands for the permittivity of vacuum and B is the geomagnetic field, which is obtained within a dipole field approximation. The angle between the wave vector and the direction of magnetic field is denoted by the symbol h. The electron-neutral collision frequency ce is given by Pashin et al. [15] ce ¼ 1:7 1011 ½N2 T e þ 3:8 1010 ½O2 T 1=2 e þ 1:4 1010 ½OT 1=2 e The intensity of wave at the height h is Z h ERP f ImðnÞdh I ¼ 2 exp h 0 c
Fig. 3. The power spectra at 10:26 and 10:30.
ð19Þ
ð20Þ
By using an ideal gas approximation for electron gas, the electron energy and continuity equations are described by the nonlinear differential equations [16]:
1342
B. Xu et al. / Progress in Natural Science 18 (2008) 1339–1343
3 dT e 4pfI ¼ ImðnÞ k B ne L dt 2 c
ð21Þ
dne ¼ Q an2e dt
ð22Þ
where kB is the Boltzmann constant, L is the sum of all electron energy loss-function [17], a is the recombination coefficient [18], and Q is the electron generation rate, which is given by the initial condition dne/dt = 0. The variations of electron temperature and density with time can be obtained by the numerical difference method. The neutral atmosphere parameters are taken from MSIS90-model [19], and the charge particles parameters are given by IRI95 [20] and corrected by the EISCAT measurement results. The time development of the two heating cases is obtained. The electron density almost has no change and the electron temperature development is shown in Fig. 4. In heating case 1, the steady-state electron temperature is 256 K, which is very close to our measured value. In heating case 2, the value is 191 K, which has some difference from the inversion result. In the low ionosphere region, there is a large error in measurement and we do not have enough spectral resolution. Furthermore, the diffusion effect is neglected by the Ohmic theory, and the initial parameters used by simulation are not the real ionosphere condition. 5. Conclusion The incoherent scatter radar data are analyzed during ionosphere heating at 91.7 km height and comparison of our experimental results and the theoretical simulation is presented. In the analysis of incoherent scatter data, there is a boundary at the height of 107 km. In the lower region, the temperature ratio of ion to electron is supposed to be a constant. It is served for a long parameter statistic and ionosphere model. In usual conditions, a large temperature difference is rarely found. However, in the study of special event, we must be careful of dealing with it. The data at the time of 10:22 and 10:30 are pro-
Fig. 4. Evolution of the electron temperature.
cessed, and in order to obtain a better fitted result, a global search method is chosen. As shown by the inversion results, the enhancement of electron temperature is obvious, and it is the major factor resulting in the change of spectra shape. Using the same initialization value, the ionosphere heating process in low altitude region is simulated by Ohmic theory. The simulation results suggest that in our experiment setting, the electron density almost has no change and the enhancement of electron temperature is consistent with our measurement basically. Due to the large measurement error, it is difficult to compare the data analysis results with numerical simulation results in low altitude region, and more rigorous theoretical model and more experiment case illustration are needed in our further work. Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant No. 40310223) and by the National key Laboratory of Electromagnetic Environment (LEME).The authors thank the EISCAT Scientific Association. References [1] Gordon WE, Carlson HC. Ionospheric heating at Arecibo: first tests. J Geophys Res 1971;76:7808–13. [2] Gordon WE, Carlson HC. Arecibo heating experiments. Radio Sci 1974;9:1041–7. [3] Jones TB, Robinson T, Kopka H, et al. Phase changes induced in a diagnostic radio wave passing through a heated region of the aurora ionosphere. J Geophys Res 1982;87(A3):1557–64. [4] Jones TB, Robinson T, Stubbe P, et al. EISCAT observation of heated ionosphere. J Atmos Terr Phys 1986;48(A1): 1027–35. [5] Rietveld MT, Kohl H, Kopka H, et al. Introduction to ionospheric heating at Tromsø-I Experimental overview. J Atmos Terr Phys 1993;55(4):577–99. [6] Kohl H, Kopka H, Stubbe P, et al. Introduction to ionospheric heating at Tromsø-II Scientific problems. J Atmos Terr Phys 1993;55(4):601–13. [7] Honary F, Stocker AJ, Robinson TR, et al. EISCAT observations of electron temperature oscillations due to the action of high power HF radio waves. J Atmos Terr Phys 1993;55(10):1433–48. [8] Robinson TR. The hearting of the high latitude ionosphere by high power radio wave. Phys Rep 1989;179(2/3):79–209. [9] Stocker AJ, Honary F, Robinson TR, et al. EISCAT observation of large scale electron temperature and density perturbations caused by high power HF radio waves. J Atmos Terr Phys 1992;54(11/12): 6285–97. [10] Rietveld MT, Kosch MJ, Blagoveshchenskaya NF, et al. Ionospheric electron heating, optical emissions and striations induced by powerful HF radio waves at high latitude: aspect angle dependence. J Geophys Res 2003;108(A4). doi:10 1029/2002JA009543. [11] Ashrafi M, Kosch MJ, Honary F. Heater-induced altitude descent of EISCAT UHF ion line enhancements: observations and modeling. Adv Space Res 2006;38:2645–52. [12] Kero A, Bosinger T, Pollar P, et al. First EISCAT measurement of electron-gas temperature in the artificially heated D-region ionosphere. Ann Geophys 2000;18:1210–5. [13] Sheffield J. Plasma scattering of electromagnetic radiation. New York: Academic Press; 1975.
B. Xu et al. / Progress in Natural Science 18 (2008) 1339–1343 [14] Schlegel K, Kohl H, Rinnert K. Temperature and collision frequency in the polar E region measured with the incoherent scatter technique. J Geophys Res 1980;85(A2):710–4. [15] Pashin AB, Belova EG, Lyatsky WB. Magnetic pulsation generation by a powerful ground-bases modulated HF radio transmitter. J Atmos Solar-Terr Phys 1995;57:245–52. [16] Rietveld MT, Kopka H, Stubbe P. D-region characteristics deduced from pulsed ionospheric heating under auroral electrojet conditions. J Atmos Terr Phys 1986;48:311–26.
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[17] Stubbe P, Varnum WS. Electron energy transfer rates in the ionosphere. Planet Space Sci 1972;20:1121–6. [18] Gurevich AV. Nonlinear phenomena in the ionosphere. Berlin: Springer; 1978. [19] Hedin AE. Extension of the MSIS thermospheric model into the middle and lower atmosphere. J Geophys Res 1991;96(A2): 1159–72. [20] Bilitza D. International Reference Ionosphere – status 1995/96. Adv Space Res 1997;20:1751–4.
Progress in Natural Science 18 (2008) 1339–1343 www.elsevier.com/locate/pnsc
Temperature enhancement induced by ionosphere heating in low altitude region Bin Xu a,*, Jian Wu b, Zhensen Wu a, Jun Wu b, Haiqin Che b, Yubo Yan b, Kun Xue a b
a School of Science, Xidian University, Xi’an 710071, China National Key Laboratory of Electromagnetic Environment, China Research Institute of Radiowave Propagation, Beijing 102206, China
Received 12 February 2008; received in revised form 19 March 2008; accepted 9 April 2008
Abstract The assumption that the electron temperature is approximately equal to the ion temperature is not rational during the high frequency (HF) heating in low ionosphere region. Thus, using the theoretical formula of incoherent scatter spectra with collisional plasma, the incoherent scatter data are analyzed during ionosphere heating at 91.7 km height on August 15th 2006. The enhancements of electron temperature are obtained, and the incremental percent is up to 37% and 46% at the universal time of 10:22 and 10:30, respectively. By using the same initialization value, the ionosphere heating process is simulated by Ohmic theory and the experimental results are basically consistent with the simulation. Ó 2008 National Natural Science Foundation of China and Chinese Academy of Sciences. Published by Elsevier Limited and Science in China Press. All rights reserved. Keywords: Incoherent scatter spectra; Ohmic theory; Ionospheric heating; Electron temperature
1. Introduction With the advantage of high precision, wide range and multi-parameters detection, incoherent scatter radar has become the most effective detection instrument of ground base. The enhancements of the incoherent scatter spectrum were observed during the ionosphere modification in low latitude from the early 1970s [1,2]. At high latitudes the first observation was performed in Tromsø [3,4]. In 1992, Rietveld et al. [5] and Kohl et al. [6] reviewed the enhancement of ion line and plasma line during ionospheric heating. According to the observation of electron density and temperature oscillations, the mechanics and the scale of fluctuation are given by Honary et al. [7]. Peak electron temperature enhancements of up to 50% were measured by Robinson [8] and by Stocker et al. [9] in the daytime *
Corresponding author. Tel./fax: +86 10 69731740. E-mail address: [email protected] (B. Xu).
and more obvious results were found at night [10]. Ashrafi et al. presented the heater-induced altitude descent of ion line enhancement [11]. However, all the studies concentrate on the high ionosphere, and only the recent observation in D region was given by Kero [12]. In low altitude ionospheric region, there is a large measurement error and a low spectral resolution. Thus, the ratio between electron and ion temperature is supposed to be a constant in incoherent scatter data analysis, which is effective for the common observation. However, the electron temperature is enhanced by HF heating, and the assumption is not reasonable. Using Sheffield’s theory, the incoherent scatter spectra in collisional plasma are presented in this paper. On the basis of this theoretical model, the incoherent scatter data are inversed during ionosphere heating at 91.7 km height with the independent electron temperature and collision frequency. And the inversion results are compared with the simulation based Ohmic theory.
1002-0071/$ - see front matter Ó 2008 National Natural Science Foundation of China and Chinese Academy of Sciences. Published by Elsevier Limited and Science in China Press. All rights reserved. doi:10.1016/j.pnsc.2008.04.010
1340
B. Xu et al. / Progress in Natural Science 18 (2008) 1339–1343
2. Theoretical spectra with a collisional plasma
where a and b are the electron and ion thermal velocity, a ¼ 1=kkD (kD is Debye length), and ye and yi are defined as
According to the theoretical results of incoherent scatter spectra deduced by Sheffield [13], the spectral density function is given by 2 ð1 þ C i Þ2 Be þ 2Z C e Bi ð1Þ Sðk; xÞ ¼ 2 e e
y e ¼ ðx ice Þ=ka
ð12Þ
y i ¼ ðx ici Þ=kb
ð13Þ
where subscripts i and e denote the ions and electrons, respectively, k is the wave vector and x is the Doppler frequency, Z is the charge number, and e is the dielectric function
Fig. 1 shows the ion line spectra peak obtained by the EISCAT tau2pl experiment from 9:38 to 11:14 on 15 August 2006 near 91.7 km. In order to see the difference between the heated and unheated, the heater was switched on/off every 4 min. The antenna of transmitting and receiving site in Tromsø, Norway, was directed along the geomagnetic field. As shown in Fig. 1, ion spectra are obviously affected by ionosphere heating. With the heater on, the power peak falls, which will affect the inversion of ionospheric parameters. In the analysis of incoherent scatter spectra, ne, Te, Ti and vi are the direct inversion variables above 107 km height. However, on account of a large collision frequency and a little temperature difference between ions and electrons, the independent inversion variables were changed into ne, Ti, vi and ci in a lower height and Te was supposed to be equal to Ti approximately. This is designed for a long statistical study of collision frequency and it is rational for the common observation. However, the assumption above is not tenable for special events study, such as particles precipitation or ionosphere heating. The particles temperature will be enhanced by these events, and it is not rational that the ratio of Te to Ti is a constant. In our inversion of heating data, electron temperature is used as an independent variable. In order to have fewer inversion variables and a better precision, at the unheated time 10:18 and 10:26, the temperature ratio is chosen as 1.17, which comes from GUISDAP (Grand Unified Incoherent Scatter Design and Analysis Package). And at the heating time 10:22 and 10:30, Te is separated from Ti. In the low ionospheric region, there is a large measurement error and a low spectral resolution. In this case, Levenberg–Marquart (LM) algorithm will receive a local extremum. Whereas the pattern search method, a global
e ¼ 1 þ Ci þ Ce
ð2Þ
Cq and Bq are defined as Z þ1 1 4pZe2 nq k @fq =@m Cq ¼ dm 1 þ Dq 1 mq k 2 x k m icq (Z ) þ1 cq fq jDq j2 dm 2 Bq ¼ 2 2 cq j1 þ Dq j ðx k mÞ þ c2q 1
ð3Þ
ð4Þ
where the subscript q can be i or e, mq is the particle mass, e is the electronic charge, nq is the number density, fq is the velocity distribution function, m is the velocity vector, cq is the effective collision frequency appropriate to the species over which we are taking an ensemble average, and Dq is Z þ1 fq dm ð5Þ Dq ¼ icq x k m icq 1 In this study, we consider only collision between the charged and neutral particles in the condition of lower ionosphere. In thermodynamic equilibrium, the velocity distributions are Maxwellian, then Dq, Cq and Bq can be given as Z ye ice 2 2 0:5 2 2 expðy e Þ De ¼ expðp Þdp þ ip expðy e Þ ð6Þ ka 0 Z yi ic expðp2 Þdp þ ip0:5 expðy 2i Þ ð7Þ Di ¼ i 2 expðy 2i Þ kb 0 Z ye 1 2 Im 2 expðy Þ expðp2 Þdp Be ¼ e 2 kaj1 þ De j 0 jDe j2 0:5 2 ð8Þ þ ip expðy e Þ 2 ce j1 þ De j Z yi 1 2 Bi ¼ Im 2 expðy i Þ expðp2 Þdp kbj1 þ Di j2 0 2 jDi j 0:5 2 ð9Þ þip expðy i Þ 2 ci j1 þ Di j Ce ¼
Z ye a2 expðp2 Þdp ip0:5 y e expðy 2e Þ 1 2y e expðy 2e Þ ð1 þ De Þ 0
Ci ¼
3. Analyses of incoherent scatter data
a2 1 2y i expðy 2i Þ ð1 þ Di Þ
Z
yi
ð10Þ expðp2 Þdp ip0:5 y i expðy 2i Þ
0
ð11Þ
Fig. 1. The power peak of ion line spectra.
B. Xu et al. / Progress in Natural Science 18 (2008) 1339–1343
search method, is used to improve this problem. In our analysis, the collision frequency of ions ci is used as an inversion variable and the collision frequency of electrons is given by Schlegel et al. [14] pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð14Þ ce ¼ 0:357ci mi T e =me T i The two heated and unheated power spectra and the fitted values are presented. In Figs. 2 and 3, we can see that the incoherent scatter spectra descend during heating. The increases of electron temperature and collision frequency or the decreases of electron density and ion temperature can result in the change. However, due to its small mass, electron is accelerated by artificial electric field easily. The accelerated electrons collide with other electrons or ions and neutral particles, and the direction of electron velocity is changed. The kinetic energy of the electron obtained from high frequency (HF) electric field is converted into electron thermal energy, which is represented as the increase of electron temperature. In light of the large mass difference between the ion and electron, the impact on ion temperature is faint. On account of the positive correlation between Ti and ci, the effect of heating on ci is very small too. With the ERP (effective radiation power) of 20 MW, pump frequency of 4.544 MHz and heating time of 4 min,
1341
Table 1 The inversion results of ionosphere parameters
10:18 10:22 10:26 10:30
ne ðm3 Þ
T e ðKÞ
T i ðKÞ
mi ðHzÞ
1.95e10 1.80e10 1.49e10 1.29e10
182 249 142 208
156 170 121 125
18518 20750 15500 23000
there is not an obvious change of the electron density in our experiments. Thus, it is anticipative that the amplitude change of the power spectra is produced by electron temperature. The inversion results are given in Table 1. As expected above, there is no obvious change in the electron density, ion temperature and collision frequency, and the electron temperature has a large augment. At the time of 10:22 and 10:30, the incremental percent is up to 37% and 46%, respectively. 4. Comparison with the simulation results The experimental results were already presented, and on the basis of Ohmic theory, the simulation of high power radio wave in lower ionosphere was studied. Radio wave in ionosphere is described by the well-known AppletonLassen dispersion relation: n2 ¼ 1
X rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 Y ðsin hÞ ðY sin hÞ4 4ð1X þ ðY cos hÞ 1 iZ 2ð1X iZÞ iZÞ2
ð15Þ
2
where the normalized frequencies X, Y, Z are defined as
Fig. 2. The power spectra at 10:18 and 10:22.
X ¼ fN2 =f 2 ¼ ne e2 =4p2 e0 me f 2
ð16Þ
Y ¼ fH =f ¼ eB=2pme f
ð17Þ
Z ¼ ce =2pf
ð18Þ
where fN is the ionospheric plasma frequency, fH is the gyromagnetic frequency and f is the incident wave frequency; e0 stands for the permittivity of vacuum and B is the geomagnetic field, which is obtained within a dipole field approximation. The angle between the wave vector and the direction of magnetic field is denoted by the symbol h. The electron-neutral collision frequency ce is given by Pashin et al. [15] ce ¼ 1:7 1011 ½N2 T e þ 3:8 1010 ½O2 T 1=2 e þ 1:4 1010 ½OT 1=2 e The intensity of wave at the height h is Z h ERP f ImðnÞdh I ¼ 2 exp h 0 c
Fig. 3. The power spectra at 10:26 and 10:30.
ð19Þ
ð20Þ
By using an ideal gas approximation for electron gas, the electron energy and continuity equations are described by the nonlinear differential equations [16]:
1342
B. Xu et al. / Progress in Natural Science 18 (2008) 1339–1343
3 dT e 4pfI ¼ ImðnÞ k B ne L dt 2 c
ð21Þ
dne ¼ Q an2e dt
ð22Þ
where kB is the Boltzmann constant, L is the sum of all electron energy loss-function [17], a is the recombination coefficient [18], and Q is the electron generation rate, which is given by the initial condition dne/dt = 0. The variations of electron temperature and density with time can be obtained by the numerical difference method. The neutral atmosphere parameters are taken from MSIS90-model [19], and the charge particles parameters are given by IRI95 [20] and corrected by the EISCAT measurement results. The time development of the two heating cases is obtained. The electron density almost has no change and the electron temperature development is shown in Fig. 4. In heating case 1, the steady-state electron temperature is 256 K, which is very close to our measured value. In heating case 2, the value is 191 K, which has some difference from the inversion result. In the low ionosphere region, there is a large error in measurement and we do not have enough spectral resolution. Furthermore, the diffusion effect is neglected by the Ohmic theory, and the initial parameters used by simulation are not the real ionosphere condition. 5. Conclusion The incoherent scatter radar data are analyzed during ionosphere heating at 91.7 km height and comparison of our experimental results and the theoretical simulation is presented. In the analysis of incoherent scatter data, there is a boundary at the height of 107 km. In the lower region, the temperature ratio of ion to electron is supposed to be a constant. It is served for a long parameter statistic and ionosphere model. In usual conditions, a large temperature difference is rarely found. However, in the study of special event, we must be careful of dealing with it. The data at the time of 10:22 and 10:30 are pro-
Fig. 4. Evolution of the electron temperature.
cessed, and in order to obtain a better fitted result, a global search method is chosen. As shown by the inversion results, the enhancement of electron temperature is obvious, and it is the major factor resulting in the change of spectra shape. Using the same initialization value, the ionosphere heating process in low altitude region is simulated by Ohmic theory. The simulation results suggest that in our experiment setting, the electron density almost has no change and the enhancement of electron temperature is consistent with our measurement basically. Due to the large measurement error, it is difficult to compare the data analysis results with numerical simulation results in low altitude region, and more rigorous theoretical model and more experiment case illustration are needed in our further work. Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant No. 40310223) and by the National key Laboratory of Electromagnetic Environment (LEME).The authors thank the EISCAT Scientific Association. References [1] Gordon WE, Carlson HC. Ionospheric heating at Arecibo: first tests. J Geophys Res 1971;76:7808–13. [2] Gordon WE, Carlson HC. Arecibo heating experiments. Radio Sci 1974;9:1041–7. [3] Jones TB, Robinson T, Kopka H, et al. Phase changes induced in a diagnostic radio wave passing through a heated region of the aurora ionosphere. J Geophys Res 1982;87(A3):1557–64. [4] Jones TB, Robinson T, Stubbe P, et al. EISCAT observation of heated ionosphere. J Atmos Terr Phys 1986;48(A1): 1027–35. [5] Rietveld MT, Kohl H, Kopka H, et al. Introduction to ionospheric heating at Tromsø-I Experimental overview. J Atmos Terr Phys 1993;55(4):577–99. [6] Kohl H, Kopka H, Stubbe P, et al. Introduction to ionospheric heating at Tromsø-II Scientific problems. J Atmos Terr Phys 1993;55(4):601–13. [7] Honary F, Stocker AJ, Robinson TR, et al. EISCAT observations of electron temperature oscillations due to the action of high power HF radio waves. J Atmos Terr Phys 1993;55(10):1433–48. [8] Robinson TR. The hearting of the high latitude ionosphere by high power radio wave. Phys Rep 1989;179(2/3):79–209. [9] Stocker AJ, Honary F, Robinson TR, et al. EISCAT observation of large scale electron temperature and density perturbations caused by high power HF radio waves. J Atmos Terr Phys 1992;54(11/12): 6285–97. [10] Rietveld MT, Kosch MJ, Blagoveshchenskaya NF, et al. Ionospheric electron heating, optical emissions and striations induced by powerful HF radio waves at high latitude: aspect angle dependence. J Geophys Res 2003;108(A4). doi:10 1029/2002JA009543. [11] Ashrafi M, Kosch MJ, Honary F. Heater-induced altitude descent of EISCAT UHF ion line enhancements: observations and modeling. Adv Space Res 2006;38:2645–52. [12] Kero A, Bosinger T, Pollar P, et al. First EISCAT measurement of electron-gas temperature in the artificially heated D-region ionosphere. Ann Geophys 2000;18:1210–5. [13] Sheffield J. Plasma scattering of electromagnetic radiation. New York: Academic Press; 1975.
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