Estimation of the Specific Real Phase and Group Refractive Indexes By The Altitude In The Earth’s Ionized Region Using The First Order Appleton-Hartree Equations


  • An Khắc Đào a) Institute of Theoretical and Applied Research (ITAR), Duy Tan University, Trang An Complex, Hanoi 100000
  • Dong Chung Nguyen
  • Diep Dao at Department of Geography and Environmental Studies, University of Colorado – Colorado Springs 2, USA


The First order Appleton-Hartree equations, Microwave propagation


Abstract: The specific phase and group refractive indexes concerning the specific phase and group velocities of single and packet electromagnetic waves contain all interactions between the electromagnetic waves and the propagating medium. The determination of the specific refractive indexes vs. altitude is also a challenge and complicated problem. Based on the first-order Appleton-Hartree equations and the values of free electron density by altitude this paper outlined the numerical estimated results of the specific real phase, group refractive indexes vs. the altitude from 100 km up to 1000 km in the ionized region. The specific real phase refractive index has value smaller than 1, corresponding to this value, the specific phase velocity is larger than the light speed (c) meanwhile the value of the specific real group refractive index is larger than 1, the specific group velocity will always be smaller than light speed (c). These estimated results are agreed with the theory and forecasted model predicted. These results could be applied for both the experiment and theoretical researches, especially for application in finding the numerical solution of mathematics problems of Wireless Information and Wireless Power Transmissions.

Author Biographies

Dong Chung Nguyen

Dong Chung Nguyen received Eng. Degree in Engineering Physics (2010), From 2010-2013 he studied in Vietnam Atomic Energy Institute. He joined to in the Lab. of Energy materials and Devices, IMS-VAST since 2013 as an assistant researcher. He received MSc degree in 2016. Since 2016 he is PhD. Student in Division of Materials Science, Nara Institute of Science and Technology, Takayama, Ikoma, Nara, Japan. His study fields are simulation of array antenna and Microwave Power Transmission (MPT) using microwaves power beam. Recently he focused on problems concerning the PID analysis techniques of the solar cell efficiency.

Diep Dao, at Department of Geography and Environmental Studies, University of Colorado – Colorado Springs 2, USA

Diep Dao (Thi Hong Diep Dao) is Assistant Professor at Department of Geography and Environmental Studies, University of Colorado – Colorado Springs 2, USA. She received Ph.D. (2013) from University of North Carolina at Charlotte, USA; M.Sc. of Geography & Urban Regional Analysis (2005) from University of Calgary, Canada, and Geomatic Engineering B.E. (2002) from University of New South Wales, Australia, From 2003-2007 She is Research Scientist, Center for Space Technology Applications, Vietnamese Academy of Science and Technology (VAST), Hanoi, Vietnam. Her interests are: Geographical Information Science, Spatial Analysis, Spatial Data Mining, GeoComputation, and Satellite-based Positioning and Navigation System (GNSS). See more on