Analytic properties of the whistler dispersion function |
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| Affiliation: | 1. Lanzhou Institute of Seismology, Lanzhou, 730000, Gansu, China;2. China University of Geosciences (Wuhan), Wuhan, 430000, Hubei, China;1. O.Ya. Usikov Institute for Radio-Physics and Electronics, National Academy of Sciences of the Ukraine, 12 Proskura Street, Kharkov, 61085, Ukraine;2. Institute of Physics of the Earth, Russian Academy of Sciences, 10 Bolshaya Gruzinskaya, Moscow, 123995, Russia;3. Hayakawa Institute of Seismo Electromagnetics Co. Ltd. (Hi-SEM), UEC Alliance Center #521, 1-1-1Kojima-cho, Chofu-shi, Tokyo, 182-0026, Japan;4. The University of Electro-Communications (UEC), Advanced Wireless & Communications Research Center (AWCC), 1-5-1Chofugaoka, Chofu-shi, Tokyo, 182-8585, Japan;5. Str. Luisetti 12, 10040, Cumiana, TO, Italy;6. Chubu University, International Digital Earth Applied Science Research Center, 1200 Matsumoto-cho, Kasugai, Aichi, 487-8585, Japan;1. Physics Division, Institute of Nuclear Energy Research, 1000 Wenhua Rd. Jiaan Village, Longtan District, Taoyuan City 32546, Taiwan;2. Institute of Plasma Physics of the CAS, Za Slovankou 1782/3, 182 00 Prague 8, Czech Republic;3. Department of Engineering Science and Ocean Engineering, National Taiwan University, No. 1, Sec. 4. Roosevelt Rd. 10617 Taipei, Taiwan;1. Institute of Physical Chemistry “Ilie Murgulescu”, Romanian Academy, 202 Splaiul Independentei, 060021 Bucharest, Romania;2. Centre for Energy Research, Hungarian Academy of Sciences, Konkoly-Thege Str. 29-33, H-1121 Budapest, Hungary;3. NANOM MEMS SRL, Rasnov, Romania;4. National Institute for Research and Development in Microtechnologies, 077190 Bucharest, Romania;1. Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education, Harbin Institute of Technology, Harbin, 150090, China;2. Key Lab of Smart Prevention and Mitigation of Civil Engineering Disasters of the Ministry of Industry and Information Technology, Harbin Institute of Technology, Harbin, 150090, China;3. Earthquake Engineering Research & Test Center, Guangzhou University, Guangzhou, China |
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| Abstract: | The analytic properties of the dispersion function of a whistler are investigated in the complex frequency plane. It possesses a pole and a branch point at a frequency equal to the minimum value of the electron gyrofrequency along the path of propagation. An integral equation relates the dispersion function to the distribution of magnetospheric electrons along the path and the solution of this equation is obtained. It is found that the electron density in the equatorial plane is very simply related to the dispersion function. A discussion of approximate formulae to represent the dispersion shows how particular terms can be related to attributes of the electron density distribution, and a new approximate formula is proposed. |
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