Whistlers, MagnetosphericReflections, 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

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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.

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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

vgroup ~ √f

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First order approximation ofwhistler wave propagation

2 22 1

( cos )pe

ce

kc

Refractive index or dispersion relation: Group velocity:

cos2 ce

gpe

v ck

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Regions of Propagation

Observable on the ground, whistlers propagate mostly in the plasmasphere or inner magnetosphere.

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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

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MR Whistlers

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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:

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Ray Tracing for MR Whistlers

An example of numerical solution for whistlers.

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Modeling of MR whistlers

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Guiding by the Earth'sMagnetic 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

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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

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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

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Multi-hop whistlers(Palmer Station, Antarctica)

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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

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Tarcsai Algorithm

Solve this system of equationsTrace whistler on spectrogramMake initial guess for variablesUse minimization procedure to choose final values variables based on minimizing least squares error of calculated trace vs. plotted trace

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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