1. 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.
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.
Resonance condition: For a particle to resonate with a wave the horizontal distance of gyration must equal the wavelength of the wave:
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.
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|
Also
Ωcp = k*Vp =
|k||Vp|cosφ = |k||Vp| = ωsc|Vp|/|Vsw|
|Vp| = (Ωcp/ωsc)(Vsw) =
(Ωcp/ωsc)(400km/s)
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.
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)
Diagram 1: Ωcp and ωsc plot Diagram 2: Density and ωsc diagram
Diagram 3: Density, Temperature, magnetic power, angle ΘBR and velocity of solar wind plot
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