Understanding the Data

The Plasma Wave Zoo
• Neatly organized in a textbook :)
• Not so much in the data :(
• However, Identification and characterizing is accomplished utilizing very similar methods and analytical tools

Raw Time Series Data
• Can identify waves and wave packets from time series data
• Can deduce basic wave characteristics
 Period
 Frequency
 Wavelength
• Can be extremely messy
• Identifying higher frequency waves can be extremely tedious

Spectral Analysis
• Resolved in frequency and time
• Techniques:
 Windowed Fourier Transform, Wavelet Transform
• Useful for:
 Identification of wave activity (frequency and time)
 Description of polarization
 etc

Spectral Analysis: Identification
Bow shock crossing
 Wave activity upstream of the shock at ~ 2-3 Hz
Dimmock et al, 2013

Spectral Analysis: Polarization
MP crossing (dusk flank)
• Mode Conversion
 Amplification in δB
PERP
 Sharp transition from
Compressional to perpendicular magnetic wave power
Johnson and Cheng, 2001

Spectral Analysis: Polarization
Traversal of the high-altitude cusp
Sundkvist et al, 2005
δE/δB-ratio on the order of the local Alvfén speed in the low frequency range
 waves are electromagnetic

Filtering
16
15
14
13
12
11
• Easier identification of wave packets
10
9
8
• Not always a good representation of wave
7
13.46
13.462
13.464
13.466
13.468
13.47
13.472
13.474
13.476
13.478
13.48
structure
• Raw data is still extremely important

Minimum Variance Analysis (MVAB)
• ∇ ∙B=0 (1-D)
• Estimates direction normal to current layer, wave front, etc.
• Construct a valuable coordinate system from the MIN, INT and
MAX variance directions
[X
MIN
X
INT
X
MAX
]

MVAB (cont’d)
• MP Current layer:
X
MIN
 Boundary normal

MVAB (cont’d)
Boundary Normal Coordinates
B
N
= B∙X
MIN
Bi-polar variation in
B
N
 one of many signatures of a
Kelvin Helmholtz wave at the flank magnetopause

MVAB (cont’d)
Wave Front:
X
MIN
 k-vector (direction of propagation)
Enter: hodogram representation

Hodograms
Hodor-grams?
Trace of the magnetic field in planes defined by pairs of the MIN, INT and MAX variance directions

Hodograms (cont’d)
• k-vector determined
• from MVAB (X
MIN
)
B
INT
VS B
MAX
 polarity
Cluster 1
θ kB
≈ 95°
Elliptical
R-handed
Cluster 4
θ kB
≈ 92°
Elliptical
R-handed

Dispersion Relation
• Dispersive wave
 Different frequencies travel at different speeds
• Dispersion Relation
 ω(k)
 Unique to wave!!
• Determine experimentally
 Identify plasma wave!!
• Multi-spacecraft techniques
 Wave Telescope
 K-filtering

Dispersion Relation (cont’d)
Multi-spacecraft observations of signal
Adequate satellite separation
Multi-spacecraft technique
Full k-vector
Experimental Dispersion

Dispersion Relation (cont’d) k-filtering
Dimmock et al, 2013

Questions?