data in the high latitude region
Audun Olav Solberg
Master’s Thesis, Spring 2018
In this project, a comparison between density structures calculated from the multi-needle Langmuir probe mounted on the NorSat-1 satellite, and the magnetic reconnection rate calculated from the OMNI IMF-data is presented. Weak correlations between structuring of the ionosphere and the rate of magnetic reconnection suggest a more stable structural behavior in the cusp and polar cap-region. The magnetic reconnection driven instabilities like the GDI, dissolving larger structures into smaller, seems to operate on smaller spatial scales than assumed. Calculated spectral power in the cusp region shows much higher low frequency powers than in the 3 other categories:
60 degrees latitude, pre-cusp, and polar cap. Finally, a case study of the relation between power spectrum of phase scintillations in trans- ionospheric signals from a GPS satellite, measured at Ny-Ålesund, and power spectrum of density structures measured by NorSat-1 at approximately the same location and time is presented. The case study shows a close relation between the spectral slopes in the overlapping spatial areas, for the lower frequencies, and the estimate provided by Rino (1979)[Rin79].
I would like to thank my supervisor Lasse Clausen for his dedication and his good mood despite being ambushed in his office at all hours. Guiding the headless chicken in the right directions, allowed me to discover the fascinating world of space physics in a fantastic way. For always taking my inquiries seriously I would like to thank senior engineer Bjørn Lybekk. I can’t describe how much weight that was lifted from my shoulders when you found the cause for overlapping density data in the original NorSat-1 data. For using the detrending-program, guidance and simplified explanations on topics way out of my comfort zone, I would like to thank Yaqi, Andres and the others at the 4DSpace group. My daily roller coaster of excitement and disappointment would be overwhelming without Vigdis and Victoria at the Master’s office.
Letting me win a couple of easy kicker matches, and encouraging me to start the day early to brew their coffee was alpha and omega. Supplying kind and confused words in times of desperation, my family and friends kept me on a straight path towards the end goal, although the topics I introduced them to might have been somewhat annoyingly incomprehensible. My fiancé Silje was the hero I needed in my home. Supplying me with great food, keeping the apartment from falling to ashes, and a never ending belief in my success when I finally returned from the office. I can’t wait to finally marry you after all these years.
I would like to thank the Norwegian Space Center for selecting the m-NLP payload for NorSat-1, to show my gratitude to UTIAS-SFL for their
Abstract i
Acknowledgements iii
Contents v
List of Figures vii
1 Theoretical background 1
1.1 An introduction to the project . . . 1
1.2 The theoretical foundation . . . 2
2 Data sources 15 2.1 NorSat-1 and the Multi-Needle Langmuir Probe . . . 15
2.2 OMNI and GPS receiver . . . 18
3 Observations 21 3.1 Densities and Crossings . . . 21
3.2 FFT, Hamming Window and Welchs method . . . 23
3.3 Reconnection rate and correlations . . . 25
3.4 Piercing point, scintillations and linear fits . . . 28
Bibliography 39
1.1 Particle drifts . . . 4
1.2 Dungey cycle . . . 5
1.3 Ionospheric plasma density profile . . . 7
1.4 Solar zenith angle . . . 9
1.5 GDI and KHI . . . 10
1.6 Double-slope power spectra . . . 11
1.7 Piercingpoints . . . 13
2.1 NorSat-1 . . . 15
2.2 Linear fit of two biased probes . . . 17
3.1 Trajectory and density . . . 22
3.2 FFT and Welch . . . 23
3.3 Power spectra averages . . . 25
3.4 Magnetic reconnection rate . . . 26
3.5 Correlations . . . 27
3.6 Ny-Ålesund: Position, density and scintillations . . . 29
3.7 Linear fit of density and scintillation . . . 31
Theoretical background
1.1 An introduction to the project
The progression of technology has given us the ability to pinpoint our position, based on transionospheric electromagnetic (EM) waves propagating from several satellites orbiting the Earth. Precise navigation, and centimeter-scale accuracy is sought after as we look to self-driven cars, or the position of trains on a railroad. EM-waves from Global Navigation Satellite Systems (GNSS) travel through our atmosphere, where their phase and amplitude can be altered in such a way that the receiver looses lock of the signal. The ionized gas in the atmosphere stands as a great obstacle for high latitude navigation, due to its varying density. Describing the behavior of the decameter-scale ionized gas density variations in the atmosphere has previously been done by simulation or sounding rockets, carrying an electron density measuring device.
Recently, the first Norwegian scientific satellite (NorSat-1) was launched into a polar orbit, creating an opportunity to study decameter-scale electron density variation in the high latitude atmosphere periodically. This is made possible through the development and integration of the multi-needle Langmuir probe (m-NLP). Investigating the data from NorSat-1 may reveal unknown structural behavior, resulting in a better understanding of the density structures disrupting the GNSS-signals in polar regions. This project was based on 7 days of data, which is the equivalent of over one hundred
this structural behavior was done by comparing the measured power spectral density to the effect of the solar wind, and to the phase scintillations of a GNSS-receiver on Ny-Ålesund. Continued research in this field might lay a foundation for a forecast of ionospheric electron density variations, and ultimately facilitate global centimeter-scale satellite navigation.
1.2 The theoretical foundation
This section is meant to lay the theoretical foundation for the rest of the thesis. It will describe mechanisms that generate electron density structures inside the ionized part of our atmosphere, the ionosphere, and how these structures may cause transionospheric signal scintillations. We will start at the producer of energy in our solar system, the Sun, and follow the energetic particles it sends towards Earth, where the particles and the embedded magnetic field can under the right circumstances connect to the terrestrial magnetic field. As this magnetic reconnection happens between the field lines on the dayside, energetic particles are sent towards Earth, and a cycle has begun. Thereon we will study the implications of this reconnection for the high latitude density structures, before we look into how a stable or a changing electron density can affect electromagnetic signals traveling through them.
The Sun, plasma and IMF
The terrestrial atmosphere is a mixture of gases, pulled towards Earth by gravity and pushed outwards by a pressure gradient, creating an equilibrium situation with little to no leakage of gas particles to outer space. On the Sun however, we find a turbulent atmosphere made out of hot ionized gas.
The high energetic particles in this gas can escape the gravity of the Sun, and travel outwards as the solar wind. This hot ionized gas is what we call a plasma: the state where negative electrons and positively charged ions have too much energy to stay together as one neutral molecule or atom. Usually we consider the plasma to be quasi neutral, where the amount of electrons and positively charged ions is equal, for a reasonable length scale. Plasma1 makes up most of the visible matter in the universe, and can be found in everything from flames, light bulbs, lightning, the Sun, to the very matter of the solar wind, blowing between solar systems. [CS05]
1In this thesis, plasma density and electron density will both be used when seen fit.
Considering a quasi neutral plasma, both words deliver the same message.
Different approaches are used to describe the behavior of a plasma, e.g.
fluid approximations, microscopic kinetic theory, or single particle motion.
What they all have in common, is the most essential difference between a plasma and a neutral gas: free electrons and ions are heavily influenced by electric and magnetic fields, due to their own charge. Hence, the collective motion of a plasma must obey the laws of electromagnetism: Maxwells equations. In ideal magnetohydrodynamics (MHD) where we assume no creation or loss of particles and expect that the plasma we are looking at is an infinitely good conductor, we find frozen-in magnetic field lines. This is the situation where magnetic field lines are fixed within the plasma, and as the plasma or magnetic field moves, the other seems "fastened" and moves along [Pec16]. Looking at the plasma sent from the Sun, we find close to perfect conditions for ideal MHD, which leads us to the interplanetary magnetic field (IMF), embedded in the solar wind. The implications of the IMF in the context of this thesis, will be elaborated in the next section.
To explain some of the larger scale plasma motions we will see later on, a short introduction to plasma drift is necessary. A nonstationary magnetic field, a gravitational field, or an addition of an electric field can change the energy of a charged particle. Depending on the directions of the fields, different types of particle drift can occur. For this project, the case of an E-field perpendicular to the B-field is highly relevant (both considered stationary). Without going further into details, the drift velocity is governed by equation 1.1:
~ vD =
E~ ×B~
B2 , (1.1)
where~vD is the drift velocity, E~ is the electric field, and B~ is the magnetic field [Pec16].
Figure 1.1 shows some idealized stationary fields, and how they affect the particles. The second row in the figure shows the E ⊥ B, where an electric field is perpendicular to the magnetic field, which leads to electrons and ions drifting in the same direction.
Figure 1.1: 3 different kind of drifts. First row: no external force to magnetic field, resulting in a gyro motion. Second row: E ⊥ B drift, the electrons and ions drifts in the same direction, but with different gyro radii. Third row: an external force (e.g. gravity) forces the electrons and ions to drift in opposite directions. Forth row: The gradient B-drift, where particles experience changing B-field, and electrons and positive ions drifts in opposite directions. From [Pla18].
Magnetosphere, Magnetic reconnection and the Dungey cycle
For centuries it has been known that the Earth has an internal magnetic field, and it is often idealized as a magnetic dipole. Way outside the neutral particles and plasma surrounding the Earth, we call this the magnetosphere.
For lower latitudes on Earth, the fieldlines are closed from north to south, but in the polar regions, the fieldlines are "open", and have only one footprint on the surface of the Earth. As the magnetic field of the solar wind collides with the outermost closed fieldline of the magnetosphere, magnetic reconnection can occur as shown in figure 1.2. This coupling process creates electric fields and currents transferring energy, mass and momentum from the solar wind, into the magnetosphere [PB04].
Figure 1.2: Magnetic reconnection with the IMF on the dayside, starts an antisunward plasma flow in the ionosphere. The lower image shows the footprints of the magnetic fieldlines. The "cusp" is highlighted in blue. From [KR95].
For the magnetic reconnection to happen, the solar wind is bound by some constraints. The IMF’s direction, and the velocity towards Earth controls the rate of reconnection, but the main contributor is the anti parallel relation between the IMF and the terrestrial magnetic field. An estimate is given in equation 1.2.
ΦD = Λ·vx4/3·Byz·(sin(θ/2))9/2, (1.2) where ΦD is the rate of dayside magnetic reconnection, Λ is a characteristic length scale,vx is the solar wind velocity towards Earth,Byz is the magnetic flux density in the GSE yz-plane and θ is the clock angle [MGH12]. The IMF is usually described in Geocentric Solar-Ecliptic (GSE) coordinates, where the Z-axis is perpendicular to the Earth’s ecliptic, the X-axis points towards the Sun, and the Y-axis is given by the right-hand rule.
The dayside magnetic reconnection starts a movement of the magnetic fieldlines over the poles (1-6 in figure 1.2), towards the nightside, and towards magnetic reconnection on the nightside (6). After the magnetic reconnection on the nightside, the closed fieldlines move back toward the dayside at lower latitudes (7-9). This is the Dungey cycle, illustrated in figure [1.2]. Plasma along the fieldline is bound by the magnetic field such that a plasma flow from noon to midnight, across the polar cap is initiated. The plasma flows across the polar cap, and is driven by nightside magnetic reconnection to follow the rim of the polar cap and back at the starting position again, creating a twin cell pattern. The twin cell pattern created is highly affected by the IMFBy component, and figure 1.2 is an idealization.
The main focus of this thesis is however in between the open fieldlines created by the magnetic reconnection, and the closed fieldlines. This is the "cusp", highlighted in blue in figure 1.2. Spicher (2017) describes it as the funnel-shaped region in the vicinity of the polar regions at high latitudes, with the presence of magnetosheath plasma2, where fieldlines are open due to magnetic reconnection. At low latitudes, the cusp is located near magnetic noon, and its position is influenced by e.g., the IMF direction, solar wind pressure, geomagnetic activity, seasons etc. [Spi17] The cusp plays a fundamental role in energy transport between the magnetosphere and the ionosphere, and is a complex region involving precipitation and upwelling ions and electrons, as well as plasma turbulence. [Et18]
2The supersonic solar wind is shocked at the bowshock and the magnetosheath is a turbulent region behind the bowshock.
The ionosphere and its structures
Figure 1.3: The plasma density profile of the ionosphere, with an average height of the NorSat-1 satellite highlighted in light orange (600 km). The red and blue line shows the difference between day and night in the density, where both the D- and E-region are neutralized during nighttime. The F-region (containing the plasma density maximum, is the least affected region.
The ionosphere is the ionized part of the upper atmosphere, ranging from about 90 to over 1000 km above ground. It is usually divided into three regions: D, E and F-region as depicted in figure 1.3. Various processes contribute to the ionizations of neutral particles in the ionosphere. The main contributor is photoionization, where x-rays and extreme UV radiation from the Sun free an electron from a neutral particle, as seen in equation 1.3 X+photon(λ.100nm)→X++e, (1.3) where X is a neutral particle, λ is the wavelength of the photon, X+ is the positive particle, and e is a free electron.
At higher latitudes, another source of ionization also contributes: particle precipitation. In this scenario the upper atmosphere is ionized by incident energetic particles:
X+eprimary(E &12eV)→X++esecondary+eprimary, (1.4) where the index ’primary’ denotes the precipitating electron, and ’secondary’
denotes the newly produced electron. Due to its high energy (up to hundreds of keV), one energetic particle can induce many ionization events, and even the secondary ionized particles can induce ionization events themselves.
[PB04].
A process called dissociative recombination plays the most important part in neutralizing the ionosphere. The short explanation is that one positively charged ion and one electron create two neutral molecules or atoms. All this ionization and neutralizing of the ionosphere is bound by altitude, daytime and seasonal constraints. Using the Chapman function for energy deposition and absorption in the atmosphere, and combining it with other processes like transport and chemical loss, calculations for the plasma density in the atmosphere become complicated, and out of the scope for this thesis. The part of highest plasma concentration is the F-layer, as shown in figure 1.3, ranging from 150 and beyond 1000 km in altitude.
This layer is the least affected by changes between day and night, due to the low density and few collisions which are needed for the dissociative recombination. For the global scale plasma densities, the solar zenith angle is of importance, as more energy is deposited at lower latitudes, and less in the higher. This concept can be illustrated as shown in figure 1.4, where the longer path through atmosphere deposits more energy earlier (lower in latitude, and further from the surface of the Earth) due to the increased amount of particles encountered.
The plasma in the ionosphere is constantly moving, much like the wind in our atmosphere, but the forces driving its movement are very different.
As described above, one example is the Dungey cycle which drives the twin-cell pattern across the poles. As the plasma travels, it is subject to forces creating areas of higher or lower density. For the rest of this thesis, the plasma density variations in the ionosphere will be referred to as "structures".
Structuring of the plasma density in polar regions is usually credited to two main contributors: Gradient Drift (GDI) and the Kelvin-Helmholtz(KHI) instabilities (figure 1.5). The GDI is caused by a differential drift of the ions and electrons perpendicular to a plasma density gradient. The KHI occurs in in the presence of velocity shear flows in the direction perpendicular to the magnetic field [Spi+15]. Figure 1.5 a) shows the results from numerical
Figure 1.4: The position of the Sun in zenith angle illustrates that more energy is deposited in the lower latitude region, where the sun is directly above the ground. For higher latitudes where the sun is at a lower angle, more energy is deposited earlier in its path towards the ground, due to the longer distance traveled in the atmosphere.
simulations done by Gondarenko and Guzdar (2004). In their paper, the GDI can be observed in the high latitude ionosphere and is contributing to structuring the ionosphere through plasma patches traveling through the polar cap. These patches are density structures between 2 and 10 times the background density, drifting at a couple of hundred meters per second [GG04]. The top panel in figure 1.5 shows a plasma patch (colored light yellow) traveling to the left. The lower panels show the evolution of the patch at later times. As time goes by, the instability, starting at the trailing edge, dissolves the patch, generating smaller scale structures. Figure 1.5 b) shows a numerical simulation of two fluids with different densities (in different colors), moving at different velocities in the same direction.
Again, we see the generation of small scale structures as the two fluids interact. The KHI can be found in wind-induced water waves, and not surprisingly: in plasmas. This instability seems to be a small contributor to phase scintillations in transionospheric signals like the GPS signal, in comparison to other instabilities like GDI, according to Burston, Mitchell
Without digging deeper into instabilities, it is worth mentioning that both GDI and KHI are dependent on a larger scale movement of the plasma (e.g. across the polar cap), and that these kind of simulations give an indication of how the plasma in the ionosphere behaves, but can currently only be validated by in-situ measurements.
(a) GDI [GG04] (b) KHI
Figure 1.5: a) The gradient drift instability: shows the structuring of a plasma patch. The lighter area is the densest part, and from top to bottom we can see the instability starting at the trailing edge, and structuring the patch over time. b) A simulation of the Kelvin-Helmholtz instability, where two fluids with different densities pass each other, dissolving and structuring each other
Studying plasma structures is often done by using power spectra. It is shown that the ionospheric plasma irregularities should be described by power laws, and that both the low, equatorial latitude, and high-latitude F- region plasma exhibits a power law with a steeper slope at higher frequencies when represented logarithmicly. This steepening happens at a frequency at approximately 30 Hz, or a wavelength between 25 and 60 meter, much larger than the oxygen ion gyro radius (estimated to 4 meters). The steepening creates what is called a double-slope power spectra as shown in figure 1.6.
To find this "knee", the sampling rate is crucial. When sampling at to low rate, its hard to find a "knee" and single-slopes are a more common finding. Suggestions that the double-slope power spectra is a product of different configurations of the magnetic field and the field-driven instabilities dominating the kinetic process at higher frequencies, have not yet been confirmed. [SMM14].
Figure 1.6: Recent evidence from "investigation of cusp irregularities" (ICI) sounding rocket shows double-slope power spectra in the high latitude F-region. [SMM14]
Transionospheric signals and scintillations
As previously mentioned, society today is depending more and more on precise navigation through GNSS technology. The electromagnetic signal sent from the satellites has to travel longer through the ionosphere in higher latitudes, due to the satellite’s 55◦ inclination, and as the EM-signal travels through the irregularly distributed plasma densities in the high latitude ionosphere, its phase and amplitude can be shifted to such a degree that the receiver loses lock. This is the largest remaining problem for precise navigation in high latitude regions.
Plasma is a dispersive media, which is interpreted as a medium where
satellite, and its recognizable code is all stored in the phase of the signal.
The signal resides on a frequency on the L-band (1-2 GHz) for GPS. Different frequencies or bandwidths are only susceptible to certain media, but lowering the bandwidth can cause alterations from other parts of the atmosphere, for example rain, fog and cloud attenuation [HLW07]. The L-band was chosen as the best compromise between frequency availability, propagation effects and system design. Newer satellites might be better off by using the C-band (4-8 GHz), where there are fewer plasma inhomogeneities equal to the wavelength of the signal. The change of electron density along the path for a transionospheric signal like GPS can be estimated using radars3, but the problem resides in the temporal changes in the electron density along the signal path.
By understanding the evolution and movement of ionospheric plasma structures, predicting space weather4 can one day supply a more reliable transionospheric satellite signal navigation. Measuring the scintillations of transionospheric waves and in-situ density measurements might reveal the size of density structures. Rino (1979) shows that the signal’s phase can be affected by the irregular electron density, as it exhibits a dependency on the relative irregularity drift velocity and the propagation geometry [Rin79]. Investigating the relation between the density structures and the scintillations should according to Rino (1979) reveal a relation described in equation 1.5.
pn=ps+ 1, (1.5)
where pn is the power law index for the in-situ measured density, and ps is the power law index for the detrended phase scintillation.
Using data from NorSat-1 and GPS receivers gives us the opportunity to test this theory, as NorSat-1 gives us an unique chance to compare in-situ measurements of small-scale5 plasma density variations with phase scintillations measured on the ground.
3The Super Dual Auroral Radar Network (SuperDARN) consists of 35 High frequency radars, mapping the plasma convection in the F-region from "backscatter". A pulse of radio frequency energy is radiated from an antenna, and when the pulse encounters the ionospheric layer, it may be reflected back to ground. Some of the scattered energy retraces its original path, and arrives back at the transmitting point at a delayed time, which is the amount of backscattering [Tve61]
4Space weather is a term for the time varying conditions above of the terrestrial weather in our lower atmosphere, e.g. the ionosphere
5The overlapping spatial scale of 40m - 3.3km was used in this project. Decameter scales are often considered small-scale structures in space physics.
When studying the overlapping positions of NorSat-1 and the GPS receiver on Ny-Ålesund in the case study, the piercing point was used to estimate the area where the transionospheric signals passes through the F-layer. The distance from the surface of the Earth to this point is commonly set to 350 km, and it has been for his project too. This point is calculated from the azimuth (horizontal angle from geographic north), and the elevation (90 degree is zenith), which is both measured by the receiver.
For Ny-Ålesund, the piercing point is never straight above the receiver, due to its high-latitude location, and the GPS satellites orbits. This is illustrated in figure 1.7, showing 24 hours of GPS received data from Ny-Ålesund and the respective piercing points surrounding the location of the receiver. The closest piercing point is approximately 200 km south of Ny-Ålesund.
0
30
60
90
120
150 180
210 240
270 300
330
0 2 105
4 105 6 105
Position of Piercing Point from GPS tracker(at zero) Chosen position, overlap with NorSat-1
Figure 1.7: 24 hours of positional data for the piercing points around Ny- Ålesund, where the GPS receiver in use resides. The radial dimension is in meters, and the angle is from azimuth.
Data sources
2.1 NorSat-1 and the Multi-Needle Langmuir Probe
This chapter is dedicated to explain the procedures followed in this project, and how the instruments contributed to sampling the data in use. Starting at the NorSat-1 satellite with its m-NLP and how the density data was computed, before a brief introduction to the OMNI data and the GPS receiver on Ny-Ålesund.
The trajectory and the m-NLP
NorSat-1 is the first Norwegian scientific satellite orbiting Earth, and it was launched in July 2017. The satellite orbits the Earth with almost 90◦ inclination, allowing a specific polar orbit, always entering the cusp from the dayside on the northern hemisphere and exiting the polar cap on the nightside.
It is continuously measuring the ionospheric plasma density at very high sampling frequencies, thanks to the Multi-Needle Langmuir Probe (m-NLP).
Keeping the needles biased with different but fixed voltages, creates the opportunity to linearly fit the measured currents created by electrons hitting the needle [Hoa+18]. The spacecraft itself can be charged positively from the encountered ions when traveling on the nightside, and the photoionization when it is on the dayside. Hoang et al. (2018) disputes that highly energetic electron particle precipitation encountered in polar regions could charge the spacecraft to negative values [Hoa+18]. When the spacecraft is charged positively, it attracts more electrons and similarly attracting positive ions when charged negatively, which leads to neutralization.
In order to calculate the electron densities, the following assumptions are made: non-drifting, collisionless, non-magnetized plasma (if it was not valid, this would affect the linearity of the slope), and that the probe diameter is much smaller than the Debye length [Jac+10]. The assumptions are assumed valid for the positional regions used in this project, due to the altitude, velocity, size of needles and orbit of the satellite. The system can measure currents from 1 nA to 1µA, which can be translated to densities between 109 and 1012 m−3. [Bek+10] The spacecraft could as mentioned potentially be charged to high negative values in a polar orbit, so the probe biases was set to positive 7, 8, 9, and 10 V to counter the spacecraft potential, keeping a reliable value for the fitting with the linear model in equation 2.1
ne ∝ (∆I)2
∆V , (2.1)
whereneis the electron density, I is the current, andV is the biased voltage.
[Hoa+18]
The different currents from the differently biased needles create a linear relation, where the slope yields the electron density. Assuming that all probes are at the same angle relative to the magnetic field1, we can compute the electron density without knowing the electron temperature, using equation 2.1, as depicted in figure 2.2. The advantage of using four probes instead of two, is the higher accuracy in the linear fit.
1This is only valid for the polar regions, where the satellite is flying perpendicular to the magnetic field. The slightly shifted magnetic field direction in the cusp-region is negligible, and considered as perpendicular in this thesis
Figure 2.2: Linear fit from two out of four probes with biased voltages and the currents measured from equation 2.1. The figure is based on the work of Jacobsen, Pedersen and Moe (2010) [Jac+10]
Sampling frequency, Fourier transform and resolution
The maximum sampling frequency of the m-NLP on NorSat-1 is 1 kHz, and this rate combined with its orbital velocity of approximately 7.5 km/s, we can detect structures from 15 meters and larger. From the raw density measurements we calculate the spectral power density to find the power at different spatial scales2. For higher resolution we calculate the spectra from 2 seconds of data, under a Hamming window. For the more statistical approach of averaging the spectral values over multiple polar passes, a Welch- estimated power spectrum was calculated (Hamming window included), where the resolution drops to the frequency range of 4 - 333 Hz3, resulting in
measuring the plasma density but every 30 ms the satellite must send the newly measured data to local storage. This introduces a 10 ms data gap, which was linearly interpolated before any further data analysis. The linear interpolation has proven to not introduce any new structures, and is a more reliable solution then other higher order interpolation techniques, according to the 4DSpace group at UiO.
2.2 OMNI and GPS receiver
Apart from the main contributor of data for this project (NorSat-1), two other sources of data were used. The OMNI-data and data from the GPS receiver in Ny-Ålesund. Combining the three sources of data can contribute to a better understanding of the cause-effect relation between the solar wind, ionospheric plasma structuring and GPS phase scintillations.
OMNI
The data from NorSat-1 was compared to the dayside reconnection rate, which can be calculated from the OMNI-data. The OMNI-data is a collection of data from multiple sources, used to study solar wind-magnetosphere interactions [NAS18]. The measurements are lagged to the bowshock, closer to Earth than the satellites measuring. This can give an estimate of the effects the solar wind can have on the magnetosphere, and ultimately the ionosphere.
GPS receiver and scintillation analysis
As described in the introduction, we expect a connection between the in- situ measured plasma density and the phase scintillations observed in GPS signals on the ground.
To look for correlations between the power spectrum of the plasma density, and phase scintillations of transionospheric signals, the GPS receiver in Ny-Ålesund on Svalbard was used. Checking for a piercing point close to the island, at the same time as NorSat-1 passes through the area, limited the number of opportunities. For the event chosen, between the FFT (Fast Fourier Transform) of the density measurements and the scintillations, NorSat-1 passes 96 km from the piercing point. The measurements were done a little after midnight UT, when Svalbard was in the polar cap area.
Estimating an ionospheric plasma drift velocity at 1 km/s, and NorSat-1’s velocity to be 7.5 km/s in the same direction as the drift, the overlapping
spatial scales was set to two different frequency bands when the power spectra were fitted with a linear model in order to compare the spectral indexes.
Extracting the scintillation data from the GPS receiver was done from the observed phase of the signal, and removing a fourth order polynomial.
The timespan of interest was then extracted from 1 hour of detrended signal, and sent through the same power spectral process as the density data. Due to a lower sampling frequency (50 Hz) of the GPS receiver, and the slower relative movement of the density structures, the sampling length was extended to 40 seconds. Finally, the estimated equivalent spatially overlapping power spectra, fitted with linear models, was compared.
Observations
This chapter is meant to showcase the data produced from NorSat-1, OMNI and the GPS receiver at Ny-Ålesund. We will start by looking into 19 minutes of the measured densities from NorSat-1, and its trajectory over the polar region. After selecting four spatially different regions, we look at the power spectra for a single pass, before comparing the averages over 1 and 7 days. Looking for relations between the solar wind and structuring of the cusp-region is done by calculating the reconnection rate and comparing to separate variables (e.g. mean electron density or power spectra in specific frequency bands). The last section of this chapter is dedicated to the case study of a singular polar pass, when NorSat-1 is close to the GPS receiver at Ny-Ålesund. For this event we compare the power spectra of the in-situ measured density, and the phase scintillation data from the GPS receiver.
3.1 Densities and Crossings
The particular pass shown in the top panel of figure 3.1 occurred on the 15th of January 2018, between 03:50 and 04:08 UT. The figure shows the trajectory on a stereographic map, with the lower panel displaying the plasma densities calculated from the linear fit between the measured currents and the biased voltages on the probe. NorSat-1’s direction on its path is marked by the black arrow, orbiting with an approximately 90 degrees inclination. The plasma densities calculated show a smooth decrease as the spacecraft travels
19 Minutes of position data from NorSat-1 150° W
120° W 90° W
60° W 30° W
0° 30° E 60° E
90° E 120° E 150° E 180° E 75° N
90° N
03:50 03:52 03:54 03:56 03:58 04:00 04:02 04:04 04:06 04:08
UT Jan 15, 2018
0 1 2 3
Density [m-3 ]
1010 Density fluctuations
Figure 3.1: Data from NorSat-1, in a close-to 90 degree inclination orbit.
The trajectory of the satellites is marked with an arrow in the top panel.
The bottom panel is the raw density measurements from the polar crossing, with four spatial categories marked with black stars.
polar pass to another, but the smooth decrease into a rapid change is a typical image of the densities. This decrease into the cusp-region has been investigated by Goodwin et al. (2015), using Swarm in-situ observations, all-sky imager (ASI) and backscattering from SuperDARN. They where able to identify this region as the cusp [Goo+15].
To further investigate the plasma density variations in the four spatial categories, the next section shows the results from the spectral analysis of density data.
3.2 FFT, Hamming Window and Welchs method
101 102
1013 1014 1015 1016
Power
60 degrees latitude
101 102
1013 1014 1015 1016
Pre-cusp
Windowed Power Spectra Welch method
101 102
Frequency 1013
1014 1015 1016
Power
Cusp
101 102
Frequency 1013
1014 1015 1016
Polar cap
Figure 3.2: Spectral power density for 4 distinct regions during a polar pass for NorSat-1 the 15th of January, between 03:58 and 04:08 UT
Figure 3.2 shows the power spectra of the density variations at the four specified points on a logarithmic scale. The spectra is from the 15th of
lower frequencies. The bottom left panel is the cusp region, where the lower frequencies(1-30 Hz) is approximately 10 to 100 times higher than in the previous regions. The bottom right panel shows the polar cap region, with a slightly lower low-frequency power than the cusp region, but much higher than the 60 degrees latitude and the pre-cusp region. The blue line is the regular power spectra, under a Hamming-window, and the dark orange is the Welch estimate for the signal, with a 500 point size bin of data, with 300 points overlap. With a sampling rate of 1000 Hz over 2 seconds, 2000 density points were used in the FFT. Leaving a frequency spectrum in the range of 0.5 to 500 Hz, before the low-pass filter, leaving us with a trustworthy frequency range of 4 - 333 Hz. A longer sampling time would give more of an average estimate of the power, but also better resolution on all frequencies.
For comparisons and trend analysis between densities and reconnection rate in this project, a sampling time of two seconds seemed fit to give a fair trade off, and was also used by Spicher et al. (2014) when looking for double slopes power spectra when analyzing the data from the ICI sounding rocket [SMM14].
To investigate how reproducible the results shown in figure 3.2 were, we show in the left panel of figure 3.3 the daily averages for the two most structurally separated regions: 60 degrees latitude and cusp. Displaying the large difference between the power of the lower frequencies, and a more equal power for the frequencies above 100 Hz. The daily averages shows surprisingly similar powers for the same regions, even though the solar wind - magnetosphere coupling is expected to be different from day to day. The right panel shows the average power spectrum of 103 Welch-estimates. The four spatial categories have a distinct difference in amount of structuring.
From most structured to the least, we have cusp-region, polar cap, pre-cusp, and with the lowest amount of structuring: the 60 degrees latitude-region.
101 102 Frequency [Hz]
1013 1014 1015 1016
Power
Daily averages
101 102
1013 1014 1015 1016
Averages of 4 regions 60 deg Lat
Pre Cusp area Inside Polar Cap
Inside cusp/early polar cap
Figure 3.3: Left panel shows the daily averages (calculated from 14 or 15 crossings, depending on the day) of Welch estimates of 7 days, for cusp- region and 60 degrees latitude region. Right panel shows averaged Welch estimates for 103 polar passes, divided into four categories: 60 degrees latitude, pre-cusp, cusp-region and polar cap region.
3.3 Reconnection rate and correlations
As shown in figure 3.3, the power spectra are remarkably similar, so we investigate whether solar wind - magnetosphere coupling is similar too.
Figure 3.4 shows the reconnection rate between the solar wind and the magnetosphere, calculated from the OMNI data, plotted as an areagraph.
00:00 06:00 12:00 18:00 00:00 Jan 19, 2018 0
20 40
60 Reconnection rate
Time of crossing Cusp
00:00 06:00 12:00 18:00 00:00
Jan 16, 2018 0
20 40
ReconectionRate [kV]
00:00 06:00 12:00 18:00 00:00
Time [UT] Jan 17, 2018 0
20 40
Figure 3.4: Magnetic reconnection rate between solar wind and terrestrial magnetic field. 24 hours for three separate days was calculated from OMNI- data inserted into equation 1.2. The red dots symbolizes the time of cusp entrance for NorSat-1.
The three days are very different in amount of magnetic reconnection on the dayside, and the three selected crossings in figure 3.4 show (top panel) the beginning of a period of elevated reconnection rate, (middle panel) several quiet hours, and (bottom panel) a quiet period after continuous dayside reconnection for more than 6 hours. The daily variations in magnetic reconnection rate seemed to be more distinct then anticipated. To investigate the correlation between the magnetic reconnection and the spectral density, a correlation analysis was done.
Figure 3.5 shows 4 different combinations where a correlation has been looked for. "Pf" is the mean of log power spectral density in the frequency range 10-300 Hz, measured in the cusp. "DN" is the mean electron density during 2 seconds of sampling in the cusp [m−3]. "Rr1" is the mean reconnec- tion rate [kV] in the timespan of 3 hours before density measurements until 2 hours before.
1010
DN 13
13.5 14 14.5
Pf
1010
DN 0
10 20 30 40
Rr1
10-2 100 102
Rr2 13
13.5 14 14.5
Pf
10-2 100 102
Rr1 13
13.5 14 14.5
Pf
Figure 3.5: Correlation investigation between Pf, DN, Rr1 and Rr2, shows (top left) r=0.37, (top right) r=0.18, (bottom left) r=0.19 and (bottom right)
r=-0.17 which is surprisingly low.
"Rr2" is the same as "Rr1", but for a timespan from 20 minutes before until the time of density measurement.
To look for a possible correlation between the reconnection rate and the power spectra of the plasma density, a comparison between a given time interval of reconnection rate (e.g. 3 - 2 hours before time of cusp density measurement) and a frequency range (e.g. 10 - 300 Hz) in the power spectral density was done. The spatial scale corresponding to this frequency range, assuming a satellite velocity of 7.5 km/s, is approximately 25 to 750 meters. The resulting plots look quiet similar, and in figure 3.5 we can see four different combinations. In the top left panel we can see the highest
all very low correlation coefficients, indicating no causal connection between solar wind driving on the dayside and plasma structuring in the cusp region.
Several attempts to find relations or trends were attempted, amongst other: specific frequency ranges, summing the reconnection rate over different time intervals, taking the difference in power for each pass compared to the 103-pass average in a frequency range, pure solar wind components like: Bz and By, or the solar wind velocity. Every combination was plotted linear, semi-logarithmic and logarithmic. The correlation values for the spectral power density at the cusp and the reconnection rate fluctuated between -0.17 and +0.19, and the strongest linear relations were plotted in figure 3.5.
Calculating the correlation values for the polar cap region resulted in even less linear relations.
3.4 Piercing point, scintillations and linear fits
Ionospheric plasma structures have shown to disturb GPS signals as previ- ously mentioned. In this section we show a case study of the spectral power density and the GPS signal phase scintillations measured in Ny-Ålesund.
Locating a piercing point close to Ny-Ålesund and finding a time where NorSat-1 passed through the same region ended up in a approximately 96 km difference. NorSat-1 and the piercing point are in the polar cap area at the time of investigation. Figure 3.6 shows the trajectory of the NorSat-1 satellite as it passed close to Ny-Ålesund. The panel on the bottom left in figure 3.6 shows the detrended phase scintillations from the GPS receiver located on Ny-Ålesund, for the time interval 02:00 - 03:00 UT. The length of the time intervals investigated for the separate power spectra was varied to find the best compromise between resolution and positional accuracy. The 2 seconds of density data from NorSat-1 in a Welch estimated power spectrum at 02:23:44 (Svalbard area 1) and 02:23:54 UT (Svalbard area 2) is compared to the averaged Welch estimates for 103 polar passes, with the four spatial categories as mentioned previously. At these times the satellite was closest to the piercing point. We can see the difference in power fluctuating with a factor of 2 to 10 in the frequency range 10-30 Hz for the two power spectra separated by 10 seconds. The large variations between the two spectra shows the advantage of doing two separate short-time intervals, and not a longer more statistical approach.
The main focus of the overlapping power spectra is the spatial scale. As NorSat-1 moves much faster through the ionosphere than the drift velocity
-0.4 -0.2 0 0.2 0.4 -0.4
-0.2 0 0.2 0.4
150° W 120° W
90° W
60° W 30° W
0° 30° E 60° E
90° E 120° E 150° E 180° E 75° N
90° N Measured positions of NorSat-1 Land Areas
NorSat-1 Trajectory(East to West) Ny-Ålesund to Piercing Point
102 Frequency [Hz]
1014 1015 1016
Power
60 deg PreCusp Polar Cap Cusp area Svalbard Area 1 Svalbard Area 2
2 2.5 3
Time [UT]
-0.02 -0.01 0 0.01 0.02 0.03 0.04
Phase scintillations
Figure 3.6: Top left panel: map of the trajectory of NorSat-1, and a blue line from Ny-Ålesund to the piercing point. Bottom left panel: Detrended phase scintillations from GPS receiver at Ny-Ålesund from 02:00 to 03:00 UT the 15th of January 2018. Right panel: Welch estimates for two 2-second intervals, from the density data provided by NorSat-1, compared to the averaged power values.
of the ionospheric plasma itself, one can usually neglect the Doppler effect.
However, in this case we assume the plasma drift to be non-negligible, it is taken into account to calculate the spatial scales for the scintillation data. To find overlapping spatial scales when accounting for the different relative velocities of the plasma, the frequencies related to the spatial scale are different. The scintillation data is detrended, and windowed before calculating the power spectrum, and the density data is windowed before calculating the power spectrum. Doing a linear fitting of the logarithmic power-values, gives a power law index, as shown on figure 3.7. The plasma flow velocity has been assumed to be 1 km/s, leading to a spatial difference of 6.5 times the frequency. In other words: 1 Hz for the phase scintillation data is the equivalent of one variation per 1 km of plasma passing by per second, and for NorSat-1 data, 1 Hz is one variation per 6.5 km of plasma passing by per second. To get a better resolution of the lower frequencies in the density measurements, the power spectrum was computed from 10 seconds of sampled data, and for the same reason the power spectrum for the scintillations was computed from 40 seconds of data. Due to high fluctuations in the scintillation power spectrum, a Welch estimate was used to showcase the basic variation.
The result of the spectral analyses is shown in figure 3.7. The data was fitted with a linear model to find a power law index p1 (first spatial overlap) and p2 (second spatial overlap). The scintillation data is shown through a Welch estimate, which serves as a better general fit for fluctuating data.
Around 10 Hz, we can see a sharp shift in the spectral power for the density.
This "inverted knee" can also be seen around 1.5 Hz in the power spectrum for the scintillation data, which is approximately the same spatial scale (650 m). The clear double-slope power spectra was then fitted with two separate frequency ranges, for the scintillation: 0.25-1.5 Hz and 1.5-24 Hz, which closely corresponds to the density frequency range of 2-10 Hz, and 10-163 Hz. The spectral index for the scintillations is p1s = 2.49 (3.3 km - 650 m) and p2s = 0.20 (650 - 40 m). In the density spectra p1n = 3.79 and p2n = 0.42. The larger structures are close to Rino’s estimate, wherep1n ≈ p1s + 1. However, the smaller scale structures does not portray a close relation between the spectral indexes.
101 102 Frequency [Hz]
10-8 10-7 10-6 10-5 10-4
Density(10sec) Power spectra Fitted line p1= -3.79 Fitted line p2= -0.42
100 101
Frequency [Hz]
10-8 10-7 10-6
Irregularity power
Scintillations(40sec) Welch estimate Fitted line p1= -2.49 Fitted line p2= -0.20
Figure 3.7: Power spectrum for the phase scintillations (40 seconds of data) calculated from the GPS receiver, and for the density measurements from NorSat-1 (10 seconds of data), where the irregularity power is (∆N eN e )2.
Discussion
4.1 Density measurements
The opportunity to study density structures in high latitude areas periodi- cally is granted by the development and deployment of the NorSat-1 satellite with its m-NLP. However, there are still some obstacles to overcome. Ana- lyzing the data reveals some troubled areas where the probes has difficulties calculating correct currents, and ultimately the density structures. The densities calculated shows steady drops in density as the satellite enters the nightside, which can be explained by the sudden loss of photoionization.
The plasma density drop towards the cusp is, as mentioned previously, a characteristic behavior investigated by Goodwin et al. (2015) [Goo+15].
However, the density drops to almost zero during the transition through the polar cap and hints towards a problem in the biased voltages or the potential of the spacecraft, since the satellite resides in the F-region and not the E-region where the plasma density fluctuates more between day and night, as depicted in figure 1.3 [HLW07]. For the data used in this project, the areas of close to zero density measurements are avoided, sometimes pushing the polar cap region closer to the cusp, or later then originally intended. The effect of this movement of the defined polar cap region is arguably negligible.
Determining the four area categories was done by hand, based on the GPS coordinates from NorSat-1 combined with the density characteristics.
1.4, where the densities decrease from the lower latitudes into the higher, and a sudden growth as we reach the cusp and polar cap area, where open field lines and magnetic reconnection contributes to the plasma densities through electron precipitation [PB04].
Looking for structures in the deca-and hectometer scale, the repeatedly saving of data in the satellite produces some uncertainties. As the satellite processes and stores previously measured data every 30 millisecond, it stops sampling data. This gives a gap of 10 milliseconds periodically, or 75 meter of unknown densities every 225 meter. Doing a linear interpolation between the last known density point and the next, does not produce any more structures, but a clear disadvantage in measurement precision. The evaluation of the higher order interpolation methods was done by the 4DSpace group at UiO, and concluded as inferior to the linear method.
Research done by Yin et al. (2017), shows that the highest amount of phase scintillations in transionospheric GPS signals are found when the piercing point is in the cusp region [Jin+17], which can be seen in context of Rino’s (1979) theory surrounding density irregularity drift and its relation to the phase scintillations [Rin79]. This would also suggest that the cusp region is the most structured high latitude region at all times, which the results from this project supports. Unfortunately there was no suitable overlap between NorSat-1’s trajectory over Svalbard and a close by piercing point when Svalbard was in the cusp-region, in the data used for this project.
The resolution for measuring density structures provided by NorSat-1 might be to low to investigate the smaller meter-scale structures. The lack of double slope power spectra in plasma patches encountered in the cusp, hints towards a sampling frequency to low to find a "knee-point". Comparing the NorSat-1 data analyzed to recent projects using sounding rockets (e.g.
Spicher, Miloch and Moen (2014) [SMM14]), the areas selected for a power spectrum should reveal double slopes if the resolution is good enough. For the scope of this project the NorSat-1 data used seemed more fit for a statistical analysis, showcasing the general structural behavior in separate regions, and revealing the low daily fluctuations in the cusp-region.
4.2 Reconnection rate and correlations
The power spectra of the cusp-region shows surprisingly small daily fluctu- ations for all frequencies. We would assume that the structural variation would be bigger in the polar regions for days with higher dayside magnetic reconnection rate, but the days selected for this project shows little to no correlation in that regard. Simulations done of the Gradient Drift Instability, shows significant evidence of the existence of GDI in high latitude areas [GG04]. Such an instability should be visible in the structures found in the polar cap region. However, it seems that the plasma in the cusp is the most structured at almost all times, and the drift over the polar cap does not produce more structures in the decameter-scale. From the dayside mag- netic reconnection, it seemed that the largest correlation (r=0.19) between reconnection rate and spectral power density in the cusp was 20 minutes before density measurement. The correlation is surprisingly small when considering the common belief that reconnection driven instabilities like the GDI is active during this period. [GG04] Further analyses of data from NorSat-1 combined with radar backscattering and magnetometers, can show how precisely the satellite passes through the polar cap, and the likelihood of measuring the structures in a plasma patch. If the GDI is a main contributor to structuring the ionospheric plasma, the data analyzed in this project would suggest that the area of interest is the cusp region, or patches early and not later in the polar cap-region. Due to the expectation of finding supporting evidence for instabilities driven by drifts and ultimately the solar wind, evaluating the validity of the data seemed necessary. One known scenario that should be a visible trend is an increase of the average electron density in the cusp when magnetic reconnection occurs, due to the electron precipitation. In figure 3.5, the top right image shows the weak dependence on magnetic reconnection for the average plasma density in the cusp area.
This shows somewhat that the validity of the magnetic reconnection-related trend data is questionable. The weak correlation between the plasma density and the reconnection rate is also a surprise, assuming that the magnetic reconnection on the dayside contributes to particle precipitation in the cusp [PB04]. Figure 3.5 shows just some of the many different scenarios that
4.3 Phase scintillations
As a case study supported in the works of Rino (1979) [Rin79], the possibility to estimate density structures in a power spectrum by measuring the phase scintillations from transionospheric signals seemed promising. Finding a good overlap between the NorSat-1 trajectory and the piercing point close to Ny-Ålesund proved to be difficult, using only seven days of data. NorSat-1 passes close to Svalbard a few times every day, and most of them is at the same time that the piercing points is far away. However, a reasonable close fit was selected, resulting in a positional minimum for the Piercing point and NorSat-1 of 96 km, and overlapping times.
When examining the relation between the power spectra of in-situ mea- sured density structures and GPS signal phase scintillations, lower frequen- cies seemed more relevant and a longer sampling time was used to produce better resolution in low frequency powers, which lead to the comparison of typical structures in the area, and not a perfect fit for decameter-scale structures above Ny-Ålesund. In figure 3.7 the power spectra were fitted with two linear models in order to compare their spatially equivalent slopes.
Due to the "inverted knee" at approximately 650 meters of the spatial scale in the spectral power density, the spatial scales were divided into two separate areas of interest. Comparing the black lines in figure 3.7, in a spatial scale of 650 m to 3.3 km, the power law index for scintillations isp1s = 2.49, and for density: p1n = 3.79. This is close to the estimation from Rino (1979), where p1n = p1s + 1. For the smaller spatial scales of 650 - 40m, the power indexesp2s = 0.20 andp2n = 0.42 is poorly fitted to Rino’s theory. Doing a linear fitting of the low resolution scintillation data, will be a generalization and look ill fitted, even when a Welch estimate is used to smooth the data.
On the other hand, a longer sampling period would yield a more averaged value, and the comparison would not carry any specific positional relation.
As previously mentioned, the lack of larger than decameter scale structur- ing in the polar cap region is surprising, with the slow erosion from GDI or KHI in mind. Hence, the correlation between my findings and Rino’s (1979) equation might be evidence pointing towards the insignificance of
decameterscale structures in the creation of phase scintillations.
Outlook
Further use of the data gathered from the NorSat-1 satellite may reveal unknown density behaviors in high latitude regions. For a deeper dive into the four spatial structure categories looked into in this project, a longer sampling period and several consecutive FFT’s might give a better indication of the structures in the more fluctuating areas, like the polar cap and the pre-cusp. Comparing the spectral behavior in located patches to those found by sounding rockets might show some double slope power spectra, and further evidence of high latitude instabilities. Comparing the NorSat-1 data with data from SuperDARN could reveal its path through a non ideal twin cell pattern. Due to the influence of the By component of the IMF, the cells are rarely as depicted in figure 1.2, but skewed in some direction, and NorSat-1 will occasionally pass through a cell. Passing through a cell means that the plasma flow will change, and some assumption may not hold for the linear fit of the current/biased needle voltage.
From the data presented in this thesis, new measurements surrounding instabilities and structural behavior in the late cusp area could provide insight to the effect of instabilities like the GDI and KHI. Interpreting the data towards a more latent structural behavior in the cusp area, points towards a smaller dependency of the plasma movement. In the future, a real time density measurement with an onboard computer to eliminate the major disturbances, could in combination with the SuperDARN data and phase scintillation data give a better image of the smaller scale plasma behavior in high latitude areas, and ultimately the possibility to forecast
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