Polarization geometry of magnetohydrodynamic turbulence
Polarization geometry of magnetohydrodynamic turbulence
Raphael Skalidis
skalidis@caltech.edu
TAPIR, Mailcode 350-17, California Institute of Technology, Pasadena, CA 91125, USA
Introduction
Introduction
This document provides supplementary material for Skalidis, R. (2026), “Polarization geometry of magnetohydrodynamic turbulence”.
It contains illustrative trajectories based on a simple phenomenological toy model for the non-linear term in the Bloch-analogue equation (Eq. 15).
In the interactive plot, the reader can vary the initial polarization state, the Alfvénic parameters, and the damping rates to explore how the coherence vector evolves on the Poincaré sphere.
A permanent copy will be also archived on Zenodo and the Wolfram Library Archive upon publication of the companion paper.
It contains illustrative trajectories based on a simple phenomenological toy model for the non-linear term in the Bloch-analogue equation (Eq. 15).
In the interactive plot, the reader can vary the initial polarization state, the Alfvénic parameters, and the damping rates to explore how the coherence vector evolves on the Poincaré sphere.
A permanent copy will be also archived on Zenodo and the Wolfram Library Archive upon publication of the companion paper.
Trajectories on the Poincaré sphere
Trajectories on the Poincaré sphere
WevizualizatetrajectoriesoftheBloch-analogueequationusingasimpledissipativetoymodelforthenonlinearterm,-,intheBloch-analogueequation:-.andrepresentsasymmetricdissipationtensorthatisequalto:
D
k
Γ
i,j
s
∂
t
s
k
Ω
k
s
k
Γ
ij
s
Ω
k
k
∥
V
A
s
1
Γ
ij
Out[]=
Γ
ij
γ11 | γ12 | γ13 |
γ21 | γ22 | γ23 |
γ31 | γ32 | γ33 |
Thecoefficientscontrolthedampingratesofcross-helicity,residualenergy,andphasecoherence,respectively.Allowingdifferentdampingratesaccountsforthepossibilitythatnonlinearinteractionspreferentiallydestroysomepolarizationpropertiesmoreefficientlythanothers.
γ
ij
Perpendicular sector: s⟂s1
Perpendicular sector: ⟂
s
s
1
An illustrative trajectory of a diffusing polarization vector initialized in the - plane with 0.15, π/3,π/2, and . The red point shows the initial position.
s
2
s
3
γ
22
θ
0
ϕ
0
p1
Out[]=
Parallel sector: s∥s1
Parallel sector: ∥
s
s
1
An illustrative trajectory of a diffusing polarization vector initialized along the axis with with 0.15, π/2.1,0, and .
s
1
γ
11
θ
0
ϕ
0
p1
Out[]=
Interactive plot
Interactive plot
Out[]=
