Download A statistical study of incoherent scatter plasma line enhancements

A statistical study of incoherent scatter
plasma line enhancements during the
International Polar Year ’07-’08 in
Svalbard
Michael Runo Ludwig Hammarsten
Space Engineering, masters level
2016
Luleå University of Technology
Department of Computer Science, Electrical and Space Engineering
A statistical study of incoherent scatter
plasma line enhancements during the
International Polar Year ’07-’08 in
Svalbard
Michael Ludwig Runo Hammarsten
Supervisor: Associate Professor Nickolay Ivchenko
Examiner: Dr. Victoria Barabash
Department of Computer Science, Electrical, and Space engineering
Luleå University of Technology
This thesis is submitted for the degree of
Master of Science in Space and Atmospheric Physics
November 2016
Acknowledgements
I would like to thank Nickolay Ivchenko and Nicola Manuel Schlatter for making this thesis
possible by taking the time to supervise the research that I did. Many thanks to Victoria
Barabash for examining this thesis and being the first who inspired me to focus my work into
ionospheric research. I am grateful for my family which supported me through my education,
the Ringvägen Rangers, last but not least, Sempai Ronnie Pettersson who introduced me to
Kyokushin Kai.
Osu no Seishin.
Abstract
There was a large radar campaign during 2007 and 2008, the International Polar Year (IPY),
and at that time the EISCAT Svalbard Radar was operated and measured the ionosphere continuously at most times. This report presents statistical results from an electron enhancement
point of view. Until now there has been some research into the field and results based on the
ions in the ionosphere, and the enhancements we refer to as Naturally enhanced ion acoustic
lines (NEIALs). Plasma line data from May 2007 to February 2008 has been analysed in
order to find and classify enhancements as NEIALs have been classified but with respect to
the electron distribution instead of the ion distribution. A method of detection was developed
in order to differentiate the enhancements from the background with a relation between the
minimum and maximum power of each measured dump. Results show that there is a large
difference between the downshifted plasma lines and the upshifted plasma lines, both has a
range distribution peak at 180 km and the upshifted plasma line has another peak at 230 km
which the downshifted plasma line does not. The occurrence rate of the enhancements was
1.64 % for the downshifted plasma line and 4.69 % for the upshifted plasma line. Three
different types of enhancements are classified using the variance distribution for the peak
frequency of that detected dump, Single, Profile, and Diffuse. The Single enhancements have
a bit different spectral, range, and time of day distributions than of the Profile and Diffuse
distributions. The Diffuse classifications are mostly wrong classifications and aliasing and it
is very similar to Profile enhancements as seen by its distribution.
Table of contents
List of figures
xi
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Introduction
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1 Naturally Enhanced Ion Acoustic Lines (NEIALs) . . . . . . . .
1.1.2 Plasma Line Enhancements (PLEs) . . . . . . . . . . . . . . . .
1.1.3 The European Incoherent Scatter Scientific Association (EISCAT)
1.1.4 Magnetic Local Time (MLT) . . . . . . . . . . . . . . . . . . . .
1.2 The state of research of ionospheric enhancements . . . . . . . . . . . .
Theory
2.1 Density fluctuations in space plasmas . . . .
2.2 Instabilities . . . . . . . . . . . . . . . . . .
2.2.1 Parametric decay of Langmuir waves
2.2.2 The Beam instability . . . . . . . . .
2.2.3 Strong Langmuir turbulence . . . . .
2.2.4 Weak Langmuir turbulence . . . . .
2.3 Incoherent scatter theory . . . . . . . . . . .
2.4 Power density spectrum . . . . . . . . . . . .
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Data Analysis
3.1 International Polar Year . . . . . . . . . . . . . . . . . .
3.2 Detection and classification of plasma line enhancements
3.2.1 Method of detection . . . . . . . . . . . . . . .
3.2.2 Method of classification . . . . . . . . . . . . .
3.2.3 Thresholds . . . . . . . . . . . . . . . . . . . .
3.2.4 Enhancement characteristics . . . . . . . . . . .
3.2.5 Frequency band filter artefact . . . . . . . . . .
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Table of contents
3.3
3.4
4
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Spectral and range distributions of the plasma line enhancements .
3.3.2 Temporal distributions of the plasma line enhancements . . . . .
3.3.3 Occurrence as functions of range versus frequency . . . . . . . .
3.3.4 Backscatter power spectral and range distributions . . . . . . . .
3.3.5 Backscatter power Cut 1 distributions . . . . . . . . . . . . . . .
3.3.6 Backscatter power Cut 2 distributions . . . . . . . . . . . . . . .
Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.1 Relations to Local K-index . . . . . . . . . . . . . . . . . . . . .
3.4.2 Correlation with electron temperatures . . . . . . . . . . . . . . .
Discussion
References
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List of figures
1.1
2.1
2.2
3.1
3.2
3.3
3.4
An illustration of Earth’s magnetic dipole field. Day side (noon MLT) is on
the left side, which is towards the Sun, and night side (night MLT) is on the
right side. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
Parallelogram showing the simultaneous matching of frequency and wavenumber for (A) electron decay instability, (B) parametric decay instability, (C)
stimulated Brillouin backscattering instability, and (D) two-plasmon decay
instability. From [Francis, F. Chen 1984] . . . . . . . . . . . . . . . . . . .
Doppler shift of the power spectrum. . . . . . . . . . . . . . . . . . . . . .
8
12
Single enhancement. The top graph shows the upshifted plasma line power
profile as a function of range versus frequency, the middle figure shows the
normalized pm
ˆ ν versus frequency, and the bottom figure shows the variance
of p̂rν p versus range. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Profile enhancement. The top graph shows the upshifted plasma line power
profile as a function of range versus frequency, the middle figure shows the
normalized pm
ˆ ν versus frequency, and the bottom figure shows the variance
of p̂rν p versus range. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Diffuse enhancement. The top graph shows the upshifted plasma line power
profile as a function of range versus frequency, the middle figure shows the
normalized pm
ˆ ν versus frequency, and the bottom figure shows the variance
of p̂rν p versus range. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Aliasing. The top graph shows the upshifted plasma line power profile as a
function of range versus frequency, the middle figure shows the normalized
pm
ˆ ν versus frequency, and the bottom figure shows the variance of p̂rν p
versus range. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
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xii
List of figures
3.5
3.6
3.7
3.8
3.9
3.10
3.11
3.12
3.13
3.14
3.15
3.16
3.17
3.18
3.19
3.20
3.21
3.22
3.23
Data dump without median filter. Downshifted plasma line on the left and
upshifted to the right. Top graphs are the measured power versus frequency.
The bottom graphs are the mean power over height for each frequency
channel. The mean values are shown above each graph. . . . . . . . . . . .
Data dump with median filter. Downshifted plasma line on the left and
upshifted to the right. Top graphs are the measured power versus frequency.
The bottom graphs are the mean power over height for each frequency
channel. The mean values are shown above each graph. . . . . . . . . . . .
Histograms of the total number of enhancements during IPY. . . . . . . . .
Histograms of the different types of DWS enhancements during IPY. . . . .
Histograms of the different types of UPS enhancements during IPY. . . . .
Histograms of the total number of enhancements per hour during IPY. . . .
Histograms of the total number of the three different DWS enhancements
per hour. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Histograms of the total number of the three different UPS enhancements per
hour. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Ratio of Enhancements/Dumps per hour . . . . . . . . . . . . . . . . . . .
Scatter plot of the total number of enhancements during IPY as a function of
Range vs Frequency. DWS PL in the top graph and DWS PL in the bottom
graph. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Scatter plot of the number of Single enhancements during IPY as a function
of Range vs Frequency. DWS PL in the top graph and DWS PL in the bottom
graph. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Scatter plot of the number of Profile enhancements during IPY as a function
of Range vs Frequency. DWS PL in the top graph and DWS PL in the bottom
graph. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Scatter plot of the number of Diffuse enhancements during IPY as a function
of Range vs Frequency. DWS PL in the top graph and DWS PL in the bottom
graph. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mean power per frequency for the DWS PLEs and the UPS PLEs. . . . . .
Maximum power per frequency for the DWS PLEs and the UPS PLEs. . . .
Mean power per frequency for each type for the DWS PLEs and the UPS PLEs.
Maximum power per frequency for each type for the DWS PLEs and the
UPS PLEs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mean power per range gate for the DWS PLEs and the UPS PLEs. . . . . .
Maximum power per range gate for the DWS PLEs and the UPS PLEs. . .
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List of figures
3.24 Mean power versus the method of detection, Cut 1. The top graph are the
uncut graph, then for each row the axis have been cut. . . . . . . . . . . . .
3.25 Maximum power versus the method of detection, Cut 1. For each row the
axis have been cut. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.26 Maximum and mean power versus the method of detection, Cut 2. For the
bottom graph, the axis have been cut. . . . . . . . . . . . . . . . . . . . . .
3.27 Peak Frequency bin and local K-index above Longyearbyen in Svalbard
during IPY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.28 Peak Range gate and local K-index above Longyearbyen in Svalbard during
IPY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.29 Peak Frequency bin and local K-index above Longyearbyen in Svalbard
during IPY during October. . . . . . . . . . . . . . . . . . . . . . . . . . .
3.30 Peak Frequency bin and local K-index above Longyearbyen in Svalbard
during IPY during August. . . . . . . . . . . . . . . . . . . . . . . . . . .
3.31 Mean Electron temperatures at two different height ranges, the peak frequencies for the upshifted and downshifted plasma lines, and the local K-index
on October 22nd. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xiii
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Chapter 1
Introduction
1.1
Background
In order to know how the solar wind interacts with planetary magnetospheres and atmospheres, several different kind of measurements can be done via e.g. satellites, sounding
rockets, coherent- & incoherent scatter radars. This thesis focus on the measurements of the
bulk properties of the ionosphere using an incoherent scatter radar (ISR). The wavelengths
used in radar experiments are set to around 30-60 cm, this is done to be able to excite the
whole electron Debye cloud that is surrounding each ion at heights around 110-400 km.
The properties that the ISR systems are able to measure, assuming Thompson scattering,
are ion line of sight velocities, ion and electron temperatures, and electron densities. Since
it is the line of sight velocity that is measured the received signal will be Doppler shifted
and, thus, the extracted Power Density Spectrum (PDS) will present two ion lines and two
plasma lines, one up- and one downshifted. The ion line is based on the Debye shield created
by the electrons that are surrounding the ions which, in the ionosphere will scatter a fairly
large signal in comparison to the the scatter of single electrons that the plasma line is based on.
At times, the PDS is enhanced beyond thermal levels. These enhancements are referred to
as Naturally Enhanced Ion Acoustic Lines (NEIALs) or Ion Line Enhancements (ILEs) in
general, and Plasma Line Enhancements (PLEs).
1.1.1
Naturally Enhanced Ion Acoustic Lines (NEIALs)
Naturally enhanced ion acoustic lines are radar incoherent backscatter measurements that
are enhanced beyond thermal level, typically by a magnitude order of up to 4. NEIALs
are mostly seen at heights around 300-700 km but they do occur at heights from 130 km
2
Introduction
up to above 1500 km as well. These enhancements are estimated to have a transverse size
of a few hundreds of meters up to a few kilometers, i.e. fine scale e nhancements. At first
NEIALs were discarded as satellite clutter, but when taking a closer look in the raw dumps
of the radar measurements it did not add up to match each satellite clutter with a satellite
trajectory due to different altitude and time distributions of the events. In the past several
years there has been much research into trying to explain these enhancements and if, and
how they are connected to particle precipitations [Foster, J. C. et al. 1988, Schlatter, N. M.
2014, Sedgemore-Schulthess, F. and St. Maurice, J.-P. 2001].
1.1.2
Plasma Line Enhancements (PLEs)
As the ionosphere is enhanced PLEs are observed, altough it is not that common as the
NEIALs due to the difference in a much lower backscatter power. Research with focus on
the Plasma line enhancements has not been that extensive as the research into ion line enhancements, until about ten years ago. Mainly, the attention has been towards the connection
between the plasma line and the ion line in regards to the temporal and power distributions
between them [Schlatter, N. M. 2014, Strömme, A. et al. 2005].
1.1.3
The European Incoherent Scatter Scientific Association (EISCAT)
EISCAT is a collaboration between Sweden, Germany, China, Japan, United Kingdom,
Finland, France, and Norway. EISCAT has several incoherent scatter radars, one of them is
located in Svalbard which is the were the dataset in this thesis is based upon. Another stations
are located in Norway, Sweden, and Finland. The EISCAT Svalbard Radar consists of two
antennas, one fixed field-aligned antenna of 42 m diameter and one fully-steerable parabolic
dish antenna of 32 m diameter. It operates in the 500 MHz band with a peak transmitter
power of 1 MW.
1.1.4
Magnetic Local Time (MLT)
Magnetic local time is used to indicate how the Earth is oriented in respect to the Sun’s
magnetic field. In Svalbard, where the radar measurements was done, MLT is defined as
UT + 3 hours. i.e. 9 UT is 12 MLT etc. At noon MLT, Earth is aligned towards the Sun on
one side of the magnetic pole and night MLT is at the opposite side of the magnetic pole, as
presented in the illustration in figure, Source: MOP, [1].
1.2 The state of research of ionospheric enhancements
3
Fig. 1.1 An illustration of Earth’s magnetic dipole field. Day side (noon MLT) is on the left
side, which is towards the Sun, and night side (night MLT) is on the right side (MOP [1]).
1.2
The state of research of ionospheric enhancements
A statistical study of ionospheric enhancements during IPY made by [Schlatter, N. M. 2014]
focused on anomalous radar echoes that is probably connected to to Langmuir turbulence
(LT). The signatures of the Langmuir turbulence can in some cases be observed as enhanced
backscatter power in the ion line and in the plasma line. Two classes of plasma line enhancements were found, one distribution that is limited in both frequency and altitude and one
class which have a broad frequency and altitude distribution. In the study they found that
plasma line enhancements occur in more than 60 % of the events at altitudes at about 220 km
and 170 km with a frequency near 3 MHz for the latter one.
Chapter 2
Theory
2.1
Density fluctuations in space plasmas
We start by introducing a stationary test particle, an ion in this case, into a neutral plasma.
Then, according to statistical mechanics, the electron and ion densities in equilibrium will
become
ni,e = n0 e−qφ /Ti,e
(2.1)
where n0 is the mean number density, q is the particle charge, φ is the potential around a test
ion due to the attraction of electrons, and the temperature T in eV. Using Poisson’s equation
to solve for the potential and we get
∆φ = −
ρ
e
n0 e2 1
1
e
1
e
= (Ne − Ni − δ (r)) =
( + )φ − δ (r) = 2 φ − δ (r)
ε0 ε0
ε0 Te Ti
ε0
ε0
λD
(2.2)
where, ε0 is the permittivity of free space, δ (r) is representing the introduced test particle.
λD is defined by
1
1
1
= 2+ 2
2
λe
λD λi
where
2
λi,e
=
ε0 Ti,e
n0 e2
where λD is the Debye length. The solution to 2.2 is
(2.3)
(2.4)
6
Theory
φ=
e
e−r/λD
4πε0 r
(2.5)
and it is obvious that, outside the Debye length the potential drops rapidly and the cloud
becomes neutralized. Density fluctuations can be expressed by introducing perturbations
to the orbits of the ions and electrons induced by the Debye shielding. When electrons are
passing by the test ion they will slightly be attracted towards the ion while ions will be
repelled away from the ion. Statistically this will create a net charge of −e around ions (half
of an electron and half of an ion) [Farley and Hagfors, T. 2008]. The scattering cross section
is proportional to the electron radius squared which in this case will create a scattering cross
section of one quarter of an electron due to the Debye cloud. The electron and ion frequencies
are given by
s
ωi,e =
ni,e q2
rad/s
ε0 mi,e
(2.6)
where m is the particle mass. If we apply a magnetic field to the plasma then the charged
particles will start to gyrate and the gyro frequency is given by
ωci,e =
|q|B
rad/s
mi,e c
(2.7)
where B is the magnetic field in the center of the gyro motion. If we combine the equations
for the electron frequency, the electron gyro frequency, and the Debye length, we can express
the superposition as a waveform. The electron waves, hereby referred to as Langmuir waves,
are longitudinal, electrostatic waves with the frequency
ωL2 = ωe2 (1 + 3k2 λe2 ) + ωc2e sin2 θ
(2.8)
where k is the wave number and θ is the pitch angle with respect to the magnetic field [Chen,
F. Francis 1984[3]].
If we are considering field aligned currents, then equation 2.8 is reduced to
ωL2 = ω p2 (1 + 3k2 λe2 )
(2.9)
2.2 Instabilities
2.2
7
Instabilities
At times the power density spectrum is enhanced for a short time. There are two main
types of enhancements; Naturally enhanced ion acoustic lines (NEIALs) and Plasma line
enhancements (PLEs). The characteristics of these enhancements are, in the case of the ion
line, one or two raised shoulders and a zero Doppler shift peak. In the case of the plasma
line, one or two raised shoulders. The major model for the source of these enhancements
are: Beam instabilities causing parametric decay of Langmuir waves [Forme, 1993, 1999;
Strömme et al, 2005].
2.2.1
Parametric decay of Langmuir waves
Figure 2.1 show the dispersion relations of the ion acoustic waves (straight lines), the electron
plasma waves (wide parabola), the electromagnetic waves (narrow parabola), and the incident
pump wave (ω0 ) and the two decay waves (ω1 and ω2 ) [Francis, F. Chen 1984]
• (A) Electron decay instability: A large amplitude electron plasma wave can decay into
a backward moving electron plasma wave and an ion acoustic wave.
• (B) Parametric decay instability: An incident electromagnetic wave of large phase
velocity (ω0 /k0 ∼ c) excites an electron plasma wave and an ion acoustic wave moving
in opposite directions. Since k0 is small, k1 ∼ k2 for this instability.
• (C) Parametric backscattering instability: A light wave excites an ion acoustic wave
and another light wave moving in the opposite direction (stimulated Brillouin backscattering). A light wave can also excite an electron plasma wave and a backwarding
moving light wave (stimulated Raman backscattering).
• (D) Two-plasmon decay instability: An incident light wave decays into two oppositely
propagating electron plasma waves (plasmons). Frequency matching can be satisfied
only if ω0 ∼ 2ω p (i.e., ne = nc /4 where nc is the critical density where ω0 = ω p ).
8
Theory
Fig. 2.1 Parallelogram showing the simultaneous matching of frequency and wavenumber
for (A) electron decay instability, (B) parametric decay instability, (C) stimulated Brillouin
backscattering instability, and (D) two-plasmon decay instability. From [Francis, F. Chen
1984]
2.2 Instabilities
2.2.2
9
The Beam instability
The beam instability is often referred to as the Bump-on-tail instability which is the main
mechanism used to explain the growth of Langmuir waves. The beam of supra-thermal
electrons provides the free energy for the waves to grow to a certain amplitude. When the
following relations are satisfied, kλd << 1 and γ << ωr , where k is the wave number, λd is
the Debye length, γ is the wave instability, and ωr is the real part of the frequency, the gentle
bump approximation holds. The wave growth increases with beam density and velocity, and
it decreases with the beam temperature. Several mechanisms have been proposed to explain
the quenching of the wave growth [Briand, C 2015]:
• Spatial collapse for strong amplitude waves (strong turbulence)
• Nonlinear evolution of wave-particles interaction (quasi-linear flattening or electron
trapping)
• Nonlinear wave-wave interaction (weak turbulence) Langmuir turbulence (LT)
There are three types mechanisms of quenching of growth of the Langmuir waves, i.e.
weak LT, strong LT, and quasi-linear flattening or electron trapping. Only the weak LT and
the strong LT is presented in this thesis.
2.2.3
Strong Langmuir turbulence
Interactions of phase-coherent waves has to be taken into account with the linear dispersion
in strong LT theory. Localised wave packets will occur due to the ponderomotive force which
expels the plasma and nonlinear self-focusing of the wave packets will intensify the electric
field in regions with lower density. Scatter from stationary cavities created in the strong LT
may be observed as a zero Doppler shift feature in radar echoes if the Bragg condition is
fulfilled. The zero Doppler shift features are hard to distinguish from the ion line shoulders
in the E region due to the low ion temperatures.
2.2.4
Weak Langmuir turbulence
In weak LT theory the ion and electron acoustic waves are described by their linear dispersion
relation and it is valid until the Langmuir wave growth exceeds a threshold and it follows
one of the decays according to case (A) in figure 2.1. The decay continues as a cascade if
there is enough energy until the energy accumulates in the so-called condensate and weak
Langmuir turbulence description is not valid anymore and the strong Langmuir turbulence
has to be considered [Schlatter et al. 2014].
10
2.3
Theory
Incoherent scatter theory
If we consider the radiation from a single electron which is absorbing an incoming electric
field E0 , it will then accelerate according to the momentum equation
u̇ue =
−e
E i (0,t)
me
(2.10)
where Ei is a linearly polarized electric field incident on an electron at origin with velocity
ue . The scattered electric field is given by
E s (rr s ,t) =
′
−eµ0
r
u
r
×
[r
×
u̇
(t
)]
s
s
e
4πr3
(2.11)
′
where µ0 is the permeability in vacuum, c is the speed of light, and t = t − rcs is the retarded
time. If we put eq.2.10 in eq.2.11, then we get an expression of the strength of the scattered
field as a function of the incident scattered field strength:
E s (rr s ,t)| =
|E
′
re
E i (0,t )|
sinχ|E
rs
(2.12)
where sinχ is the linear polarization angle between Ei and rs , and re is the electron radius.
′
We assume that the magnitude of the incident electric field Ei (0,t ) is constant throughout
the scattered volume. The phase is not constant and can be described by
eiφ (t) = e−i(ω0t−(kki −kks )·rr p ) ei(kki ·RRi +kks ·RRs )
(2.13)
where r p is a point where some particular electron scattered the incident field, r i = R i + r p ,
′
and r s = R s − r p . We therefore refer to Ei (0,t ) as E0 and thus eq.2.12 becomes
Es,p (t) =
re
sinχE0 e−i(ω0t−(kki −kks )·rr p ) ei(kki ·RRi +kks ·RRs )
rs
(2.14)
The last term of eq.2.14 in the exponential is a constant phase term and can therefore be
removed and we can put k = k s − k i so that eq.2.14 becomes
Es,p (t) =
re
sinχE0 e−i(ω0t+kk·rr p )
rs
(2.15)
In the case of backscatter sin2 χ = 1 and equation 2.15 we get
Es,p (t) =
re
E0 e−i(ω0t+kk·rr p )
rs
(2.16)
11
2.4 Power density spectrum
By assuming a distribution of electrons then scattering from a continuous medium can be
derived and by following the derivation by [Farley and Hagfors, T. 2008[4]] we get:
Rs ,t) =
Es (R
1
ks × (ks × E 0 )εV (kk ,t)
4πε0 Rs
(2.17)
where, for a plasma with no magnetic field and no collisions, the dielectric constant is given
by
ω p2
n0 e2
ε
= 1− 2 = 1−
(2.18)
ε0
ω
me ε0 ω 2
Now, since Es is the sum of many small contributions that are random it follows from the
Central Limit Theorem of probability that it is a Gaussian random variable with zero mean.
All information in a Gaussian variable is found in the Fourier transform of the unnormalized
autocorrelation function (ACF), the power spectrum, which is the presentation that is used
for the analysis.
2.4
Power density spectrum
The autocorrelation of a stationary complex stochastic process is given by
ACFz (τ) =< z(t) ∗ z(t − τ) >
(2.19)
where z is a stochastic process at a given time t, z* is the complex conjugate of a stochastic
process at another time (t-τ). The power spectral density is given by the Fourier transform of
ACFz (τ). In figure 2.2 there is a presentation of the power density spectrum. There are four
peaks, two for red shifted electrons and two for blue shifted electrons. Figure 2.2 presents
only two peaks. The ion lines are not analysed in this Master thesis, except for a single case
study.
12
Theory
Fig. 2.2 Doppler shift of the power spectrum.
The height of the peaks are dependent on the electron density, i.e. how many electrons
that back-scatter the electric field, the width of the spectrum is influenced mainly by collisions
and the Doppler shift is due to the motion of the ionosphere.
Chapter 3
Data Analysis
3.1
International Polar Year
The EISCAT Svalbard Radar (ESR) was operated continuously from March 2007 to March
2008. The IPY project was organized by the WORLD Meteoroligical Organization and the
International Council of Science and it was a collaboration between different radar stations
such as: ESR, Poker Flat Radar (PFISR), Millstone Hill, Sondrestrom, Irkutsk Radar, and
the SuperDARN Network, in order to gather as much data as possible.
A new pulse coding that covers low altitudes up to about 500 km with improved low altitude
statistics. Primary observations used the 42 m antenna and plasma line measurements on
the 32 m antenna, both field-aligned. The focus was on the E and F regions with a 30x30 µs
alternating code, 6 s integration time, and a 24.4 % beam duty cycle.
The data for the downshifted and upshifted plasma lines are presented in arrays of range
versus frequency:
Pr1 · · · Prν
.
.
P = .. . . . ..
(3.1)
P11 · · · P1ν
where P = Downshifted (D) or Upshifted (U) Plasma line, r is the number of range gates,
and ν is the number of frequency bins used in the measurement.
From mid of December 2007 the centre frequency of the spectral band was changed with a
shift of 0.8 MHz. This was done in order to observe an enhancement that seemed to appear
below the limit of the first spectral band.
• Spectrum
14
Data Analysis
– Frequency bandwidth until mid December: 1.67 MHz (±3.17 MHz to ±4.83 MHz)
– Frequency bandwidth from mid December: 1.67 MHz (±2.37 MHz to ±4.03 MHz)
– 768 Frequency bins (ν)
– 2.17 kHz resolution per bin
• Range
– Range: 127 km to 278 km
– 33 Range gates (r)
– 4.5 km height resolution per gate
3.2
Detection and classification of plasma line enhancements
In order to detect and classify the plasma line enhancements in the ionosphere, a new method
has been developed which will be presented and discussed throughout this thesis. The main
work during the project has gone into adapting and testing the thresholds used in order to get
somewhat reliable results. The change of center frequency during the IPY run do not have an
impact on the detection and classification. The change of center frequency will be adapted
when doing calculations and statistics. The examples that will be presented in this section
only presents the first frequency band.
3.2.1
Method of detection
Frequency power profile distribution based thresholding
According to equation 3.1, the IPY measurements is retrieved in two matrices, one for the
downshifted plasma line and one for the upshifted plasma line. If we take the mean power
for each frequency bin of the matrix P which results in the vector Pmν .
33
∑ Prν
Pmν =
r=1
Then we normalise Pmν
pm
ˆ ν=
33
= (Pm1 · · · Pm768 )
Pmν − min(Pmν )
max(Pmν ) − min(Pmν )
(3.2)
(3.3)
in order to get the relation between the minimum power and the maximum power in the
measurement. After these steps the threshold is set based on the mean value of pm
ˆ ν . During
3.2 Detection and classification of plasma line enhancements
15
noise, no enhancements, the mean value should be around 0.5 as shown in figure 3.6 the
mean value is more towards 0.4 due to artefact remains of the band width filter. When an
enhancement is detected the frequency bin of Pmν with the highest power is used to make
the enhancement classification.
3.2.2
Method of classification
Range power profile distribution based thresholding
The frequency bin of Pmν with the highest power is used to make the classification

Prν p

P33ν p
 . 
=  .. 
P1ν p
and by normalising Prν p we get the relation between the minimum and maximum value of
that frequency bin
p̂rν p =
Prν p − min(Prν p )
max(Prν p ) − min(Prν p )
(3.4)
and in order to differentiate between the different types of enhancements the variance of p̂rν p
is used.
16
Data Analysis
3.2.3
Thresholds
The thresholds used to sort the enhancements from the background were, with a first cut of
the normalized mean power over altitude for each frequency gate with a mean value of less
than 0.2. Since the power is normalized, when there is an enhancement the relative value
of the mean power will be very small compared to the value of the enhancement power. A
second cut is made using the variance of the mean power over range for each frequency
channel; if below 3.5e-02 then the enhancement is classified as a single, between 3.5e-02 and
5.5e-02 then the enhancement is classified as diffuse, and if above 5.5e-02 then it is classified
as a profile. The different thresholds were set up by manually testing for the best possible
detection and classification. Following, is a summary of the different thresholds.
Detection
• Noise: mean of pm
ˆ ν ∼ 0.5
• Enhancement: mean of pm
ˆ ν ≤ 0.2
Classification
• Single: variance of p̂rν p ≤ 0.035
• Profile: variance of p̂rν p ≥ 0.055
• Diffuse: variance of 0.035 < p̂rν p < 0.055
– Diffuse enhancements consists mostly of
wrong classifications and artefacts
Since the method of detection is not using a threshold of a certain value of power and only
the relation between the minimum and maximum value, the power of the enhancement is not
in focus.
3.2.4
Enhancement characteristics
The different classes of enhancements are presented with three different graphs from different
dumps during IPY. Top graphs are relative power distribution as a function of range versus
frequency with the maximum power (in K/Hz), middle graphs are a visual representation
of the enhancement detection with the mean value of pm
ˆ ν , and the bottom graphs are a
representation of the enhancement classification with the variance of p̂rν p .
3.2 Detection and classification of plasma line enhancements
17
Single
The Single enhancement has a very small and focused spectral and range distribution as can
be seen in the top graph in figure 3.1 which shows the power distribution as a function of
range versus frequency. The top graph is auto scaled between the minimum and maximum
power.
• Variance of p̂rν p : Small
Fig. 3.1 Single enhancement. The top graph shows the upshifted plasma line power profile as
a function of range versus frequency, the middle figure shows the normalized pm
ˆ ν versus
frequency, and the bottom figure shows the variance of p̂rν p versus range.
18
Data Analysis
Profiles
The Profile enhancement has a broad, but focused, spectral and range distribution as is shown
in the top graph in figure 3.2 which shows the power distribution as a function of range
versus frequency. The top graph is auto scaled between the minimum and maximum power.
• Variance of p̂rν p : High
Fig. 3.2 Profile enhancement. The top graph shows the upshifted plasma line power profile
as a function of range versus frequency, the middle figure shows the normalized pm
ˆ ν versus
frequency, and the bottom figure shows the variance of p̂rν p versus range.
3.2 Detection and classification of plasma line enhancements
19
Diffuse
The Diffuse enhancement consists mostly of wrong classifications due to the choice of
thresholds but it also contains artefact’s due to filter aliasing, system interference, etc as can
be seen in the top graph in figure 3.3 which shows the power distribution as a function of
range versus frequency. The top graph is auto scaled between the minimum and maximum
power.
• Variance of p̂rν p : Medium
Fig. 3.3 Diffuse enhancement. The top graph shows the upshifted plasma line power profile
as a function of range versus frequency, the middle figure shows the normalized pm
ˆ ν versus
frequency, and the bottom figure shows the variance of p̂rν p versus range.
20
Data Analysis
Aliasing
Figure 3.4 is an example of a probable filter or sampling aliasing artefact that has been
classified as a Diffuse enhancement.
Fig. 3.4 Aliasing. The top graph shows the upshifted plasma line power profile as a function
of range versus frequency, the middle figure shows the normalized pm
ˆ ν versus frequency,
and the bottom figure shows the variance of p̂rν p versus range.
3.2.5
Frequency band filter artefact
In Figure 3.5, the artefact of the frequency band filter is noticeable by looking at the bottom
graphs. In order to remove this artifact from each dump, a 2d median filter was applied. The
result of this filtering is shown in figure 3.6. The artifact of the filter is still in the background
but with a bit less impact which enables the thresholding to be more precise.
3.2 Detection and classification of plasma line enhancements
21
Fig. 3.5 Data dump without median filter. Downshifted plasma line on the left and upshifted
to the right. Top graphs are the measured power versus frequency. The bottom graphs are the
mean power over height for each frequency channel. The mean values are shown above each
graph.
Fig. 3.6 Data dump with median filter. Downshifted plasma line on the left and upshifted to
the right. Top graphs are the measured power versus frequency. The bottom graphs are the
mean power over height for each frequency channel. The mean values are shown above each
graph.
22
3.3
Data Analysis
Results
In this section the findings of the IPY analysis are presented for the downshifted and the
upshifted plasma line. Hereafter the downshifted plasma line will be referred as DWS PL
and the upshifted plasma line as UPS PL. Data was collected from 173 days between May
22nd 2007 to February 6th 2008 and the number of dumps that were analysed are 1,876,165,
the amount of detected DWS PLEs are 30,797, and the amount of UPS PLEs are 88,058.
This corresponds to an occurence rate of 1.64 % DWS PLEs and 4.69 % UPS PLEs. Due
to the change of centre frequency there will be much less enhancements below |3.17| MHz
which will be quite visible.
3.3.1
Spectral and range distributions of the plasma line enhancements
In figure 3.7 the DWS PL is represented in red in the first column and the UPS PL is
represented in blue in the second column. The top row shows the number of enhancements
per frequency bin and the second row shows the number of enhancements per range gate.
Fig. 3.7 Histograms of the total number of enhancements during IPY.
It is noticeable that the UPS PL has a second peak that the DWS PL do not have at
∼230 km. Also, the UPS PL has a distribution above 4 MHz as the DWS PL does not have.
Both have their main distribution in a spectral range of ± 3.4 MHz to ± 4 MHz and at 190km
height range. In figure 3.8 and figure 3.9 the three different types of enhancement are shown
3.3 Results
23
for the DWS PL and the UPS PL. The Single enhancement has quite a different distribution
than the main distribution of PLEs. The largest distribution of Single enhancements are
located at ±3.2 MHz and ±4.8 MHz and at a range located around 170 km. Both for the
DWS PL and the UPS PL, the Single enhancements are not that common but still it, its
distribution is noticable. When comparing the Single enhancements with the Profile and the
Diffuse enhancements between the DWS PL and the UPS PL, there are two main attributes
that differs between them, firstly its the second peak in the UPS PL Profile and Diffuse
distributions at 230 km, and secondly it is the distributions above 4 MHz for the Profile and
Diffuse enhancements that does not seem to be that common for the DWS PL Profile and
Diffuse enhancements.
Fig. 3.8 Histograms of the different types of DWS enhancements during IPY.
24
Data Analysis
Fig. 3.9 Histograms of the different types of UPS enhancements during IPY.
3.3.2
Temporal distributions of the plasma line enhancements
Figure 3.10 presents the total number of DWS PLEs and UPS PLEs per hour that were
detected. The main distribution of enhancements, for both plasma lines, is located around
8-9 UT (Universal Time) which corresponds to 11-12 MLT (Magnetic Local Time). In the
UPS PL a small peak around 19-20 UT is noticeable which corresponds to 22-23 MLT.
3.3 Results
25
Fig. 3.10 Histograms of the total number of enhancements per hour during IPY.
in the spectral and range distribution of the different types of enhancements, the Single
enhancement has a bit different temporal distribution in comparison to the Profile and Diffuse
temporal distributions as well. The main distribution occurs at noon MLT as was presented
in figure 3.10 is also presented in figure 3.11 and figure 3.12 and the peak distribution of the
Single enhancements occur a few hours earlier, around 9 MLT.
Fig. 3.11 Histograms of the total number of the three different DWS enhancements per hour.
26
Data Analysis
Fig. 3.12 Histograms of the total number of the three different UPS enhancements per hour.
In figure 3.13, the total occurrence rate of DWS PLEs and UPS PLEs per hour are as
shown with respect to the number of dumps analyzed per hour. As presented in figure 3.11
and figure 3.12, the main distribution of enhancements occur at noon MLT vid an occurrence
rate of 3 % for the DWS PLEs and 11 % for the UPS PLEs. The second peak of the UPS PL
has an occurrence rate of about 4-5 %.
Fig. 3.13 Ratio of Enhancements/Dumps per hour
3.3 Results
3.3.3
27
Occurrence as functions of range versus frequency
The number of enhancements as a function of range versus frequency are presented in this
subsection to show the relation between the distribution in range and the distribution in
frequency. At ±3.17 MHz there is a visible line of where the edge of the frequency band
are before the shift during mid December. In figure 3.14 the total number of enhancements
are shown, DWS PL in the top graph and the UPS PL in the bottom graph. The second peak
in range and the extended distribution in frequency for the UPS PL is presented very well
in figure 3.14. In some figures there is a visible interference artefact at ∼4.1 MHz and ∼ ±
4.4 MHz.
Fig. 3.14 Scatter plot of the total number of enhancements during IPY as a function of Range
vs Frequency. DWS PL in the top graph and DWS PL in the bottom graph.
Figure 3.15, figure 3.16, and figure 3.17 shows the number of enhancements as a function
of range versus frequency for each type of the three enhancements. When comparing figure
3.15 and figure 3.16, it is clear that the classification method have been distinguishing these
type of enhancements from each other with some miss classifications. The main distributions
of these different types of enhancements clearly differs from each other.
28
Data Analysis
Fig. 3.15 Scatter plot of the number of Single enhancements during IPY as a function of
Range vs Frequency. DWS PL in the top graph and DWS PL in the bottom graph.
Fig. 3.16 Scatter plot of the number of Profile enhancements during IPY as a function of
Range vs Frequency. DWS PL in the top graph and DWS PL in the bottom graph.
3.3 Results
29
By looking at figure 3.17, you could get an indication that the Diffuse enhancements are
a collection of wrong classifications as its distributions seem to be a mix of the Single and
Profile distributions.
Fig. 3.17 Scatter plot of the number of Diffuse enhancements during IPY as a function of
Range vs Frequency. DWS PL in the top graph and DWS PL in the bottom graph.
3.3.4
Backscatter power spectral and range distributions
The backscatter power is represented in Kelvin per Hertz. In figure 3.18 and figure 3.19, the
mean and maximum power per frequency are shown for the DWS PLEs and the UPS PLEs.
Both the mean and maximum power are quite high at the edges of the first placement of the
band filter (∼ ±3.17 MHz and ∼ ±4.83 MHz) in comparison to the rest of the spectrum in
the measured frequency band. In figure 3.19 the artefacts due to interference are visible at ∼
4.1 MHz and ∼ 4.4 MHz. There is two main attributes that separates the DWS PL and the
UPS PL from another, in the DWS PL there seems to be a distribution at ∼-3.6 MHz that
does not appear in the UPS PL, and in the UPS PL there is a distribution at the edge of the
second placement of the band filter at ∼2.37 MHz that does not appear in the DWS PL. The
second attribute might not appear due to less detected enhancements in the DWS PL.
30
Data Analysis
Fig. 3.18 Mean power per frequency for the DWS PLEs and the UPS PLEs.
Fig. 3.19 Maximum power per frequency for the DWS PLEs and the UPS PLEs.
In figure 3.20 and figure 3.21 the mean and maximum power per frequency are shown for
the DWS PLEs and the UPS PLEs for each of the different types of enhancements, Single,
Profile, and Diffuse. Even though the Single enhancement has its main distribution at the
first used band’s edges, all of the different types of enhancements have their peak power at
3.3 Results
31
those frequencies. When presenting each individual type of enhancement it is a bit clearer in
how their backscatter power distributions are. The attributes that differs the DWS PL from
the UPS PL that were discussed about figure 3.18 and figure 3.19, you can see that those
attributes are due to Profile enhancements at large but also due to Diffuse enhancements.
Fig. 3.20 Mean power per frequency for each type for the DWS PLEs and the UPS PLEs.
32
Data Analysis
Fig. 3.21 Maximum power per frequency for each type for the DWS PLEs and the UPS
PLEs.
In fgure 3.22 and figure 3.23 the enhancement backscatter power per range gate is shown.
Here it seems that the power distribution in range is reasonable equal between the DWS
PLEs and the UPS PLEs since the second peak within the UPS PLE distribution is not that
visible. According to figure 3.23, the maximum power of the UPS PL is somewhat stronger
at 150-180 km than at the same range of the DWS PL.
3.3 Results
33
Fig. 3.22 Mean power per range gate for the DWS PLEs and the UPS PLEs.
Fig. 3.23 Maximum power per range gate for the DWS PLEs and the UPS PLEs.
3.3.5
Backscatter power Cut 1 distributions
The relation between the measured backscatter power and the method of detection and the
method of classification are presented in this subsection.
34
Data Analysis
Cut 1 is the method of detection which firstly calculates the mean backscatter power over
range for each frequency bin into a resulting power vector. A vector that is 768 elements
in length which is then filtered with a mean filter. Figure 3.25 and figure 3.24 are scatter
plots of the maximum backscatter power and mean backscatter power versus the method of
detection, i.e. the mean value of the backscatter power vector of Cut 1.
Since Cut 1 are a measure of the mean backscatter power then it should exist a linear
relation between the vector of Cut 1 and the mean backscatter power of the dump. This is
quite clear as shown by figure 3.24. There are some interesting deviations form the linear
relation though. The main difference between the DWS PL and the UPS PL is the distribution
at very weak mean backscatter power and a small Cut 1 value. Then it seems to exist two
kind of distributions when increasing the mean backscatter power and the Cut 1 value when
looking at the second row.
Fig. 3.24 Mean power versus the method of detection, Cut 1. The top graph are the uncut
graph, then for each row the axis have been cut.
In figure 3.25 row four there is a clear difference betwen the DWS PL and the UPS PL
when there is a very low backscatter power. The main distribution for both the DWS PL and
the UPS PL are pretty much equal, that when increasing the Cut 1 value, which is a measure
of the mean power of the dump, the maximum backscatter power is stable and quite low in
comparison to the peak maximum backscatter power in row one.
3.3 Results
35
Fig. 3.25 Maximum power versus the method of detection, Cut 1. For each row the axis have
been cut.
3.3.6
Backscatter power Cut 2 distributions
In figure 3.26, the mean and maximum backscatter power is plotted against Cut 2, which is
the variance of the range power profile distribution for the peak frequencies of the detected
enhancements. There is a clear signature of two different distributions in both the DWS
PL and the UPS PL. One that has a very small variance over range but with a broad power
distribution and one with a small power but very large variance distribution. The slightly
stronger signature in the UPS PL might be because more enhancements were detected for the
UPS PL than for the DWS PL.
36
Data Analysis
Fig. 3.26 Maximum and mean power versus the method of detection, Cut 2. For the bottom
graph, the axis have been cut.
3.4
3.4.1
Case Studies
Relations to Local K-index
The local K-Index at Longyearbyen in Svalbard is plotted against the peak frequencies, peak
ranges, and power of the enhancements and dumps in order to see if there is any correlation
between high auroral activities and the different enhancement distributions. The K-Index
is a measure of how active the aurora is using magnetometer measurements. The K-Index
has the resolution of hours. In order to get a good overview all of the plots are normalized
and by that it is easy to see if there is any correlation. Figure 3.27 and figure 3.28 show the
overall peak frequencies and peak ranges that were detected during the IPY plotted with the
local K-Index. By a first look it is clear that the K-Index has a periodic behavior and it seems
that when the K-Index is on its upside there are more enhancements at the edges of the band
filter in comparison to when the K-Index is low where there are not that frequent with side
enhancements. A correlation between the K-Index and the peak ranges is not that easy to see,
as presented in figure 3.28.
3.4 Case Studies
37
Fig. 3.27 Peak Frequency bin and local K-index above Longyearbyen in Svalbard during
IPY.
Fig. 3.28 Peak Range gate and local K-index above Longyearbyen in Svalbard during IPY.
When the side enhancements are detected, are presented by figure 3.29 and figure 3.30,
where we only look at October and August. Here the side enhancements occurrs at the times
when the derivative of the K-index changes from positive to negative and vice versa. i.e.
when the "overall enhancement of the ionosphere" changes drastically. The spaces that are
blank at the end of October, beginning and end of August have no detected enhancements.
38
Data Analysis
Fig. 3.29 Peak Frequency bin and local K-index above Longyearbyen in Svalbard during IPY
during October.
Fig. 3.30 Peak Frequency bin and local K-index above Longyearbyen in Svalbard during IPY
during August.
3.4.2
Correlation with electron temperatures
Following figure will show the electron temperatures calculated via the ion line measurements
during different days at two different heights, the peak frequencies for the downshifted plasma
line and the upshifted plasma line, and the local K-Index during different days. In figure 3.31
there are some side enhancements during early noon MLT and midnight MLT, and during
noon MLT there are some enhancements that seem to follow the structure of a profile since it
3.4 Case Studies
39
is detected at noon MLT. Worth noticing is that the side enhancements are detected when
there is an increase in electron temperatures.
Fig. 3.31 Mean Electron temperatures at two different height ranges, the peak frequencies
for the upshifted and downshifted plasma lines, and the local K-index on October 22nd.
Chapter 4
Discussion
It is clear that the enhancement distributions of the downshifted plasma line and the upshifted
plasma line are quite similar with a few exceptions where one of them, the second peak
in range in the upshifted plasma line, is quite a large exception. The second peak exists
in the downshifted plasma line as well but it is not at all that frequent as for the upshifted
plasma line, a factor of eight, the number of enhancements detected, between the two peaks
in the downshifted plasma line where it is a factor of two between the peaks in the upshifted
plasma line. The second peak is probably due to precipitating electrons that are coming down,
field aligned during auroral activities. The difference between DWS PL and UPS PL, when
looking at the two different cuts versus power, is large at low backscatter power and small
value of cut 1 and cut 2. This indicates that the second peak in the UPS PL consists mostly
of electrons with a lower source of free energy than the electrons of the first peak, i.e. during
enhancements backscatter power is related to the free energy source. When looking at the
different types of enhancements the Single enhancements have quite a different distribution
then the rest, in spectral, in range, and in temporal distributions. The large difference in range
and spectral distribution could indicate that the enhancements that this method classifies
could be due to aliasing and measurement issues. Still, the Single enhancements occurs a few
hours earlier than the main DWS and UPS distribution, what this means is not quite clear
and should be investigated further. When comparing the electron temperatures calculated
through the ion line measurements it seems in the single case study of October 22nd that
the side enhancements, are correlated with the increase of temperatures. This correlation is
strengthen by the case studies of the local K-index during August and October where the
side enhancements are clearly correlated with a high K-index.
42
Discussion
Recommendations for future work
Improving the classification of the different types of plasma line enhancements should be
prioritized, especially looking into the difference between the distributions of the Single and
the Profile enhancements. Since the present method of classification is very sensitive to the
distribution over range for the peak frequency the wrong classifications between Profile and
Diffuse enhancements has to be corrected. Maybe through another cut in frequency and
compare these methods to get a better classification. Also, doing more case studies in order
to find correlations between the temperatures, the local K-index, and the different types of
enhancements. Regarding how the measurements can be improved, the temporal resolution
is of most important if the receiver is sensitive enough to register an enhancement in action.
By doing this improvement, correlations with small, concentrated, and short arcs might be
derived.
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