Office of Telecommunications OT Report 75-76

A Versatile Three-Dimensional Ray Tracing Computer Program for Radio Waves in the Ionosphere

October 1975

R. Michael Jones and Judith J. Stephenson

Abstract: This report describes an accurate, versatile FORTRAN computer program for tracing rays through an anisotropic medium whose index of refraction varies continuously in three dimensions. Although developed to calculate the propagation of radio waves in the ionosphere, the program can be easily modified to do other types of ray tracing because of its organization into subroutines.

The program can represent the refractive index by either the Appleton-Hartree or the Sen-Wyller formula, and has several ionospheric models for electron density, perturbations to the electron density (irregularities), the earth's magnetic field, and electron collision frequency.

For each path, the program can calculate group path length, phase path length, absorption, Doppler shift due to a time-varying ionosphere, and geometrical path length. In addition to printing these parameters and the direction of the wave normal at various points along the ray path, the program can plot the projection of the ray path on any vertical plane or on the ground and punch the main characteristics of each ray path on cards.

The documentation includes equations, flow charts, program listings with comments, definitions of program variables, deck set-ups, descriptions of input and output, and a sample case.

Keywords: Ray tracing, computer program, radio waves, ionosphere, three-dimensional, Appleton-Hartree formula, Sen-Wyller formula

• Errata Sheet (23 April 1979)

• Title Page; Preface; Table of Contents; List of Tables; List of Figures; List ofInput Parameter Forms

• Abstract; Chapter 1: Introduction; Chapter 2: General Description; Chapter 3: Ray Tracing Equations; Chapter 4: Choosing and Calculating the Hamiltonian

• Chapter 5: Refractive Index Equations

• Chapter 6: Ionospheric Models; Chapter 7: Finding the Ray Paths that Connect a Transmitter and Receiver; Chapter 8: Output; Chapter 9: Deck Set Up; Chapter 10: Input; Chapter 11: Accuracy; Chapter 12: Coordinate Systems

• Chapter 13: How the Program Works; Chapter 14: Acknowledgments; Chapter 15: References

• Appendix 1: Listings of the Main Program and Subroutines in the Main Deck (6.6 MB)

• Appendix 2: Versions of the Refractive Index Subroutine (RINDEX) (6.4 MB)

• Appendix 3: Electron Density Subroutines with Input Parameter Forms

• Appendix 4: Perturbations to Electron Density Models with Input Parameter Forms

• Appendix 5: Models of the Earth's Magnetic Field with Input Parameter Forms

• Appendix 6: Collision Frequency Models with Input Parameter Forms

• Appendix 7: CDC 250 Plot Package

• Appendix 8: Sample Case (5.5 MB)

Disclaimer: Certain commercial equipment, components, and software are identified in this report to specify adequately the technical aspects of the reported results. In no case does such identification imply recommendation or endorsement by the National Telecommunications and Information Administration, nor does it imply that the equipment or software identified is necessarily the best available for the particular application or uses.