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
Whistler Wave Formation
Part of the
radiation
emitted by
lightning is
launched into
the magnetosphere as a
whistler
wave.
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.
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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 of
whistler wave propagation
Refractive index or dispersion relation:
 pe
 kc 
     1
 (  ce cos )
 
2
2
Group velocity:
2
vg 
ce cos 

 2c
k
 pe
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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, , f - trajectory of whistler,
• rr , r , rf – 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'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
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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 Lshell over which the whistler has travelled
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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
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References
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