1. Whistlers, Magnetospheric Reflections, and Ducts Prepared by Dan Golden, Denys Piddyachiy, and Naoshin Haque Stanford University, Stanford, CA IHY Workshop on Advancing VLF through the Global AWESOME Network

2. 2 Whistler Wave Formation Very good conductors in ELF/VLF range (300 Hz - 30kHz) Electromagnetic radiation emitted by lightning discharge propagates in the Earth-ionosphere waveguide with the speed of light, c. This is called a radio atmospheric or sferic for short. Part of the radiation emitted by lightning is launched into the magneto- sphere as a whistler wave.

3. 3 What is a whistler?  Signature of electromagnetic wave emitted by lightning flash after it has traversed the magnetosphere  Produces a sound resembling a whistle of descending pitch in radio receivers  Magnetosphere is dispersive  Different frequencies propagate at different group velocities  Lower frequencies arrive later in time than higher frequencies  v group ~ √f

4. 4 First order approximation of whistler wave propagation Refractive index or dispersion relation: Group velocity:

5. 5 Regions of Propagation Observable on the ground, whistlers propagate mostly in the plasmasphere or inner magnetosphere.

6. 6 EM Wave Propagation in Magnetosphere  Generally, waves in magnetosphere follow complex trajectory  Field aligned density irregularities known as “ducts” serve as guiding structures  Waves traveling in ducts maintain direction along magnetic field  Ducted waves arrive normal to ionospheric boundary and can be observed on the ground

7. 7 MR Whistlers

8. 8 Ray Tracing Ray tracing can be used to explain the trajectories of whistler wave: Unknowns: r  - trajectory of whistler,  r,  ,   – wave vector of whistler. Refractive index  at any specific point can be found through Appleton-Hartree equation:

9. 9 Ray Tracing for MR Whistlers An example of numerical solution for whistlers.

10. 10 Modeling of MR whistlers

11. 11 Guiding by the Earth's Magnetic Field  The Earth's magnetic field is capable of loosely guiding electromagnetic waves  Waves in a cold plasma (e.g. the Earth's plasmasphere) preferentially travel parallel to magnetic fields, and resist motion perpendicular to magnetic fields

12. 12 Ducts  Field-aligned ducts may provide necessary guidance to allow waves to be completely bound to field lines  Ducts may either be density enhancements (“crests”) or density depletions (“troughs”)  Ducts cannot be directly observed, e.g., by satellites, because they comprise too small a percentage of the plasmasphere  The existence of ducts is still only a theory, though one that agrees very well with experimental evidence  All whistlers detected on the ground have propagated in ducts

13. 13 The Need for Ducts  Without ducts, whistler-mode rays (e.g., from terrestrial lightning) will be partially guided along magnetic field lines, but will generally not return to Earth  Without additional guiding structures, there would be no way for whistlers to be observed from the ground Whistler

14. 14 Multi-hop whistlers (Palmer Station, Antarctica)

15. 15 Plasmaspheric Property Measurements using Ducts  Because a ducted whistler essentially follows a single field line, we can determine properties of the plasma over its path from its shape  Amount of dispersion gives clues as to total electron content through which the wave has travelled  Time between whistler and originating lightning flash (sferic) gives clues as to the L- shell over which the whistler has travelled

16. 16 Tarcsai Algorithm Solve this system of equations Trace whistler on spectrogram Make initial guess for variables Use minimization procedure to choose final values variables based on minimizing least squares error of calculated trace vs. plotted trace

17. 17 References  Kivelson, M.G., and C.T. Russel, Introduction to space physics, Cambridge University Press, 1995.  Spasojevic, M., Global Dynamics of the Earth's Plasmasphere, Stanford Univ., PhD thesis, 2003.  Carpenter, D.L., Remote sensing the Earth’s plasmasphere, Rad. Sci. Bull, 2004.  Inan, U. S., D. Piddyachiy, W. B. Peter, J. A. Savaud, M. Parrot, DEMETER Satellite observations of lightning-induced electron precipitation bursts, Geophysical Research Letters (under review), 2007.  Helliwell, R. A., “Whistlers and Related Ionospheric Phenomena,” Dover Publications, Inc., Mineola, NY, 1965/2006  Walker, A. D. M., 'The Propagation of Very Low-Frequency Radio Waves in Ducts in the Magnetosphere', Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 69-93, Vol. 321, No. 1544, 1971  Tarcsai, Gy., 'Routine whistler analysis by means of accurate curve fitting', Journal of Atmospheric and Terrestrial Physica, 1447-1457, 37, 1975  Khosa, P. N., Lalmani, M. M. Ahmed and V. K. Rawal, 'An estimate of the duct life time from low latitude ground observations of whistlers at Varanasi', Earth, Moon and Planets, 329-333, V28 N3, 1983  Kimura, I, 'Whistler mode propagation in the Earth and planetary magnetospheres and ray tracing techniques', Space Science Reviews, 449-466, 42, 1985  Burgess, W. C., 'Lightning-Induced Coupling of the Radiation Belts to Geomagnetically Conjugate Ionospheric Regions', Ph.D. Thesis, Stanford University, 1993  Kondrat'ev, I. G., A. V. Kudrin and T. M. Zaboronkova, 'Electrodynamics of Density Ducts in Magnetized Plasmas', CRC Press, 1999  Strangeways, H. J., 'Lightning induced enhancements of D-region ionisation and whistler ducts', Journal of Atmospheric and Solar-Terrestrial Physics, 1067-1080, 61, 1999  Bortnik, J., 'Precipitation of Radiation Belt Electrons by Lightning-Generated Magnetospherically Reflecting Whistler Waves', Ph.D. Thesis, Stanford University, 2004