Mar 30, 2012 - For the zero B-field case, a narrow stealth band is obtained, while for ... As radio waves travel in the ionosphere, electrons of the ionosphere ...
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PIERS Draft Proceedings, Kuala Lumpur, MALAYSIA, March 27–30, 2012
Microwave Absorption in Nonuniform Plasma with Different Magnetic Field Configurations Using the Magneto-ionic Appleton-Hartree Theory M. S. Bawa’aneh1, 2 , Ahmed M. Al-Khateeb3 , Sayeed Makkiyil1 , Saud Al Awfi4 , Ibrahim Abualhaol1 , and Ghada Assayed2 , 1
Khalifa University of Science, Technology and Research, P. O. Box 573, Sharjah, United Arab Emirates 2 Department of Physics, The Hashemite University, P. O. Box 150459, Zarqa, Jordan 3 Department of Physics, College of Science, King Faisal University, P. O. Box 400, Al-Hufof, Saudi Arabia 4 Department of Physics, Faculty of Science, Taibah University, P. O. Box 30002, Madina, Saudi Arabia
Abstract— Microwave propagation in a nonuniform, collisional, and magnetized plasma slab with different magnetic field configurations is investigated using the magneto-ionic AppletonHartree theory. For the zero B-field case, a narrow stealth band is obtained, while for parallel and perpendicular propagation with respect to the B-field, results show a wider stealth band in the vicinity of ωce . An electron cyclotron frequency of about 4 GHz could result in almost total absorption of the C-band. 1. INTRODUCTION
As radio waves travel in the ionosphere, electrons of the ionosphere oscillate coherently with the electric field of the radio wave, while the motion of the positive ions may be neglected due their high inertia. Electron collisions with neutral particles of the ionosphere provides a mechanism of energy transfer from the radio wave into thermal heating of the ionosphere. Electromagnetic wave reflection, absorption and scttering in plasma has attracted much attention lately because of the special opprotunities that plasma stealth technology offers, where by changing different plasma parameters one can control the absorption rates of microwaves in plasma [1, 2]. In this work, microwave propagation in a nonuniform, collisional, and magnetized plasma slab with different magnetic field configurations is investigated, and nonuniformity in plasma is simplified by dividing the plasma slab into uniform subslabs [3, 4]. The dielectric constant withina subslab is obtained using the magneto-ionic Appleton-Hartree theory [5, 6]. This theory was developed to describe electromagnetic wave propagation in ionized media in the presence of static magnetic fields. Magneto-ionic and optical-ray theories lead to useful and satisfactory description of wave propagation and reflection. Within the magneto-ionic theory, waves are assumed to be of a plane wave nature with a complex propagation constant, namely, vary as eiωt−Kx , where ω is the EM wave frequency and K the propagation constant. Also, electron motion only is assumed to be responsible for electromagnetic response due to high mobility. 2. FORMULATION AND NUMERICAL RESULTS
To simplify the study of the EM wave interaction with the nununiform plasma, the plasma slab (with a certain density profile) is divided into uniform layers, where the propagation constant for the mth layer is given by ck (m) = ω (m)
(m)
r , where c is the speed of light in vacuum, ω is the EM
wave frequency and r the dielectric function for the mth layer. Two different methods are widely used in literature; one method depends on the summation of successive reflected and transmitted powers at the interface between each two layers (neglecting multiple reflections between them) to obtain the total reflected and transmitted powers [2], while the second method uses the scattering matrix method (SMM) where global reflection and transmission rates are calculated [4]. Considering Maxwell’s equations and ignoring thermal effects, one can obtain the magneto-ionic Appleton-Hartree equation [5, 6], namely −n2 = −
K2 =1+ μω 2
1 DT2 ± A + iB − 2(1 + A + iB)
DT4 2 + DL 4(1 + A + iB)2
,
(1)
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Final Version of PIERS Proceedings will be available on www.piers.org
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Figure 1: Normalized absorption versus wave frequency (GHz) for (a) zero B-field, (b) parallel propagation and (c) perpendicular propagation. Narrow to wide peaks in each figure correspond to initial density values N0 = 1015 , 1016 , 1017 m−3 , respectively. Other arameters are ν = 400 MHz, a = 30 cm. For (b) and (c), fce = 4 GHz. 1
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Figure 2: Normalized absorption versus wave frequency (GHz) for (a) zero B-field, (b) parallel propagation and (c) perpendicular propagation. Narrow to wide peaks in each figure correspond to collision frequency values ν = 100, 400, 800 MHz. Other parameters are N0 = 1016 m−3 , a = 30 cm. For (b) and (c), fce = 4 GHz. ωμHT ω ων L where n = √K and DL = ωμH 2 , B = ω 2 , DT = μω is the index of refraction, A = − ωpe ne e ne e , pe and HL and HT are the longitudinal and transverse components of the external dc magnetic field components, respectively. This equation governs the propagation of high frequency radio waves through a magneto-ionic medium. In the rest of this section, we will be obtaining the absorption coefficients of an electromagnetic wave incident on a nonuniform plasma with a dc magnetic field with different orientations; we will consider the three cases of magnetic fields perpendicular to the propagation direction, parallel to the propagation direction and the zero magnetic field case. All figures represent the normalized absorption rate versus the EM wave frequency (GHz). Figure 1 shows the normalized absorption versus wave frequency (GHz) for (a) zero B-field, (b) parallel propagation and (c) perpendicular propagation. Narrow to wide peaks in each figure correspond to initial density values N0 = 1015 , 1016 , 1017 m−3 , respectively. Other arameters are collision frequency ν = 400 MHz and plasma width a = 30 cm. For Figures 1(b) and 1(c), the electron cyclotron frequency fce = 4 GHz. Figure 2 shows the normalized absorption versus wave frequency (GHz) for (a) zero B-field, (b) parallel propagation and (c) perpendicular propagation. Narrow to wide peaks in each figure correspond to collision frequency values ν = 100, 400, 800 MHz. Other parameters are N0 = 1016 m−3 and a = 30 cm. For Figures 2(b) and 2(c), fce = 4 GHz. The figures show higher maximum absorption and wider peak for parallel propagation compared to perpendicular propagation and zero field case. 2
3. CONCLUSION
Microwave propagation in a nonuniform, collisional, and magnetized plasma slab with different magnetic field configurations is investigated. For the zero B-field case, a narrow stealth band is obtained, while for parallel and perpendicular propagation with respect to the B-field, results show a wider stealth band in the vicinity of ωce . An electron cyclotron frequency of about 4 GHz could
PIERS Draft Proceedings, Kuala Lumpur, MALAYSIA, March 27–30, 2012
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result in almost total absorption of the C-band. The results also show higher maximum absorption and wider peak for parallel propagation compared to perpendicular propagation. REFERENCES
1. Ginsburg, V. L., The Propagation of Electromagnetic Waves in Plasma, Pergammon, New York, 1970. 2. Laroussi, M., “Interaction of microwave with atmospheric pressure plasmas,” Int. J. Infrared Millim. Waves, Vol. 16, 2069–2083, 1995. 3. Laroussi, M. and J. Reece Roth, “Numerical calculation of the refletion, absorption and transmission of microwaves by a nonuniform plasma slab,” IEEE Transactions on Plasma Science, Vol. 21, 366–372 1993. 4. Hu, B. J., G. Wei, and S. L. Lai, “SMM analysis of reflection, absorption and transmission from nonuniform magnetized plasma slab,” IEEE Transactions on Plasma Science, Vol. 27, 1131–1136, 1999. 5. Appleton, E. V., “Wireless Studies of the Ionosphere,” Journal of the Institution of Electrical Engineers, Vol. 71, 642–650, 1932. 6. Hartree, D. R., “The propagation of electromagnetic waves in stratified medium,” Proc. Camb. phil. Soc., Vol. 25, 97–120, January 1929.
