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Observations of Magnetic Waves in the Voyager Data Set
Marios Socrates Dimitriadis, Charles Smith
Introduction
Solar wind consists of highly energetic particles radiating from
the sun at very high speeds (approx. 400 km/s). Magnetic
waves that travel through the solar wind are measured by
Voyager 1 and 2 and their analysis yields a possible
explanation for their formation.
Scientific theory
Doppler shift: It’s a phenomenon occurring due to the relative
motion of the source and receiver of a wave. It results in a
difference between the observable frequency of the receiver
and the source. It is given by the formula:
ωsc = ωp + k*Vsw
(1)
where ωsc is the receiver’s frequency, ωp is the source
frequency, Vsw is the velocity of the solar wind and k is the
vector of propagation of the wave.
Methodology
Using equation (1) and (2) we can
assume ωp to be negligible.
ωsc = k*Vsw =
|k||Vsw|cos(ΘBR) = |k||Vsw|
for the solar wind to be parallel to the
magnetic field. Thus:
|κ|=ωsc/|Vsw|
Magnetic field: It is a vector field that occurs as an effect of
electric currents and magnetic materials.
Parker (Archimedes spiral): The phenomenon occurring due
to the rotation of the Sun which results in the perpendicular
stretching of the magnetic field.
|Vp| = (Ωcp/ωsc)(Vsw) =
(Ωcp/ωsc)(400km/s)
Ωcp = ωp + k*Vp
(2)
where Ωcp is the cyclotron frequency of the particle and Vp is
the velocity of the particle.
The observable waves can be resonant, a property which can
arise if certain conditions are satisfied and backed by data.
Mathematical manipulation and usage of data can yield
possible values of the particle velocity under the resonance
condition.
If there’s fast moving and slow moving particles interacting with
the solar wind a parallel stretching of the magnetic field can
occur which aligns the magnetic field with the direction of
movement of the solar wind (Vsw) (thus counteracting the
parker spiral and equating ΘBR to 0 deg).
If the solar wind expands perpendicularly it cools off in that
direction faster than in the parallel direction. Thus the kinetic
energy and velocity is higher in the parallel direction than in the
perpendicular causing a beam of particles parallel to the k
vector that can resonate in the same way thus constructing the
wave.
Diagram 2: Density and ωsc
Also
Ωcp = k*Vp =
|k||Vp|cosφ = |k||Vp| =
ωsc|Vp|/|Vsw|
Resonance condition: For a particle to resonate with a wave
the horizontal distance of gyration must equal the wavelength
of the wave:
Diagram 1: Ωcp and ωsc plot
diagram
Which is the condition the two frequencies
must satisfy for the waves to be resonant.
Calculating this we can find a possible
value for the velocity of the particles
under the resonance condition.
Diagram 3: Density, Temperature, magnetic power, angle ΘBR and
velocity of solar wind plot
Data analysis
The events of interest yielded wave and
cyclotron frequencies, ωsc and Ωcp
differing by a factor of 10 (diagram 1).
Angle ΘBR approximates 0 deg
(Diagram 2). The density – fsc (diagram
3) shows a lack of correlation between
these two parameters, pointing away from
the possibility of non-resonant waves
(Gary et Al 1976)
Conclusion
The resulting relationship between Ωcp and
ωsc shows that the particle velocity must
equal the Alfven speed (40km/s). Angle ΘBR
approximates 0 deg. This is a strong
implication that the waves were resonant.
The lack of correlation in diagram 3 points
through proof by contradiction that the
waves are resonant. 18/19 events satisfy the
1/10 ratio and the 19th event requires further
examination.
References
Gary et Al 1976