High Latitude Phase Scintillation

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High Latitude Phase Scintillation

by

David MacDonald

Thesis for the degree of MASTER OF SCIENCE Plasma and Space Physics

Department of Physics

Faculty of Mathematics and Natural Sciences Supervisor : Per Høeg (University of Oslo) Co-Supervisor : Wojciech Miloch (University of Oslo)

Co-Supervisor : Yaqi Jin (University of Oslo)

June 1, 2019

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1 Abstract

This thesis was a detailed study of the correlation between global position system (GPS) scintillation at high latitudes and Kp index. Initially, the research approach was to perform a statistical analysis of the GPS phase scintillation and Kp index in Ny-˚Alesund. The results of this analysis showed diurnal and seasonal variations in phase scintillation, and solar cycle influences on phase scintillation. Ultimately, the research showed how phase scintillation correlated to high Kp index, and weakly correlated to low Kp index.

The second research approach was a three-part case study, wherein the dates, locations, and Kp index of each case were (2016/10/26 , Ny-˚Alesund and Skibotn, Kp=6-), (2017/01/30, Ny-˚Alesund, Kp=3-), and (2017/01/30, Ny-˚Alesund, Kp=2+). All of these locations were within the high latitudes. The case study used multiple instruments such as global navigation satellite service (GNSS) receivers, coherent and incoherent radars, ground based magnetometers and all sky imagers (ASI) in order to study the morphology of the ionospheric instabilities causing scintillation. The gradient drift instability and the two stream instability are common in the ionosphere and were discussed in relation to phase scintillation. The result of the case studies was that the correlation of Kp index to phase scintillation in the high latitudes is very weak. It is possible to have a high phase scintillation and low Kp index, and to have high phase scintillation for high Kp index. Further understanding of the correlation between the GPS scintillation with the Kp index will bring meaningful contributions to space weather and will have an impact on the precision of the navigation and the positioning of GPS systems at the high latitude regions.

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Acknowledgments

I would first like to thank my primary supervisor Dr.Per Høeg, my co-supervisors Wojciech Jacek Miloch and Yaqi Jin for or their valuable help and their support throughout the writing of this thesis. I am thankful for being given the opportunity to present my results at EGU 2019; to have taken a semester abroad at UNIS in Svalbard, and for the University of Oslo giving me the financial ability to do so. A very special thank you to Yaqi Jin for all of the scheduled meetings, unscheduled impromptu long winded discussions of space weather, and for being a source of motivation and positiveness during stressful times. I would like to thank Wojciech J. Miloch, for the all of the advice and for helping me to push forward with my work. I would especially like to thank Bjørn Lybekk for being unconditionally helpful whenever I needed it. This thesis wouldn’t be possible without you. Thank you to Lasse Clausen for providing me with the raw ASI and keogram images. Thank you to Andres Spicher for all of his answers to the ’quick questions’ I have bombarded you with over the past year. I am very grateful to all my fellow Space Physics Master’s students who have provided me with support and to all of my Norwegian friends for making these years something to remember. I would like to thank my family for the unconditional love and support throughout the years.

Finally, I would like to thank Kira Leitl for the patience, understanding, support and encouragement she has shown me.

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2 Introduction

At present time, the accuracy of global positioning system (GPS) signals at high latitudes are subject to scintillation caused by instabilities in the ionosphere. Such instabilities effect the amplitude and phase of the trans-ionospheric radio waves, thereby distorting the received signal. It is geomagnetic substorms at high latitudes that improve conditions for the growth rate of ionospheric instabilities, thereby generating phase and amplitude scintillation. The effects of this scintillation at high latitudes, however, is difficult to predict.

Kp index is a global measurement and is commonly used to forecast geomagnetic activity. It is therefore intuitive to relate GPS phase scintillation caused by ionospheric instabilities with Kp indices. The work in this thesis addressed whether it is accurate to relate phase scintillation with Kp indices at high latitudes.

Scintillation at high latitudes was the primary focus of this thesis. In order to meaningfully understand the results, a section on scintillation theory has been included in the background chapter 3 . This section acknowledged topics such as phase scintillation, amplitude scintillation, and relations between phase scintillation and the solar cycle.

Next, the topic of solar terrestrial background was described in this thesis. The topics covered in this section included: Plasma characteristics, the Debye length, and Frozen-in theory. Preceding the topics were a detailed description of the Sun, sunspots, and the solar cycle. Later, this section looked the Dungey cycle. The Dungey cycle explained how solar wind is transferred into the magneto sphere, dayside magnetic re-connection, transportation of magnetic field across the polar cap and nightside magnetic re-connection.

The next topic in this section explored substorm dynamics, specifically the growth, expansion, and recovery phase, and the characteristics of the aurora such as optical emissions and height profiles. To follow, the ionosphere was elaborated upon. More specifically, the production of ionization and deionization within the E-region (90-150km ) and F-region (150km-and upwards) of the ionosphere will be explored. Structures such as polar cap patches, polar cap arcs, and auroral arcs were considered. The topics of diurnal and seasonal variations in high latitudes were included in this section. Lastly, discussion of instabilities focused on the gradient drift instability (GDI) and the two-stream instability. The large-scale dynamics of the aurora contrasted with its small-scale instabilities were diligently monitored to illustrate that at high latitudes, it is possible to see that high phase scintillation is weakly dependent of Kp index.

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In northern Norway and Svalbard, the instruments used in order to obtain the results of this thesis were as follows: optical All Sky Imagers (ASI), Global Navigation Satellite System (GNSS) receivers, European Incoherent Scatter Scientific Association (EISCAT) radars, SuperDARN radars and ground-based magnetometers. The data obtained from these instruments was used to better understand the morphology of the ionosphere. The morphology of the ionosphere can be characterized by the total electron content (TEC), electron density, electron temperature, ion temperature, ion velocity, and the intensity from the ASI. Such characteristics can be related to the ionospheric instabilities by analyzing the rate of change in total electron content (ROTI), phase scintillation (σφ index), amplitude scintillation (S4 index), back-scatter obtained by SuperDARN radar and local magnetic fields from ground-based magnetometers. Such relations were discussed throughout this thesis.

To address the research question, this thesis followed two approaches: a statistical analysis and a multi- part case study. The statistical analysis compared phase scintillation to Kp index between the years of 2011 and 2019 at high latitudes. The question of how phase scintillation at high latitudes correlated with the Kp index motivated this statistical analysis. Ultimately, this dual pronged approach revealed that high Kp index shows consistent correlation with phase scintillation while low Kp index only shows weak correlation to phase scintillation at high latitudes. Seasonal and diurnal deviations in phase scintillation, as well as correlations between solar cycle and phase scintillation were addressed.

The research question was also explored via the creation of a three-part case study exploring days of high, medium, and low Kp index, and related them to the aural phenomena and scintillation at high latitudes. The motivation for this approach was to further explore the results from the statistical analysis by understanding if it is possible to observe high amounts of phase scintillation independent of Kp index at high latitudes.

Gaining a deeper understanding of correlations between GPS scintillation and Kp index will meaningfully contribute to space weather and will have an impact on the precision of the navigation and the positioning of GPS systems in the high latitude polar regions.

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3 Scintillation Theory Background

Observing the effects of scintillation is a ubiquitous experience. Some common examples would be the twinkling of a star cause by the propagation of an optical electromagnetic (EM) wave through a turbulent atmosphere or an optical distortion due to unstable heat rising from a campfire. In general, the passage of an EM plane wave through an unstable refractive index modifies the amplitude and phase of the wave [16].

Within the field of space physics, determining a specific type of scintillation, referred to as ionospheric scintillation, is of interest. The term ionospheric scintillation can be defined as rapid fluctuations in the amplitude and phase of a radio signal transmitting throughout the ionosphere [?,?]. Ionospheric scintillation is a stochastic process wherein the instabilities within the ionosphere have rapid change of index of refraction due to changes in electron density[10]. As an EM wave propagates through a medium associated with an irregular index of refraction, the wave is subject to diffraction such that the EM wave will constructively and destructively interfere. This interference may change the amplitude and phase of the initial wave. In the context of this thesis, the irregular medium were considered as the ionospheric instabilities, whereas the changes in the phase and amplitude of the signal were referred to as scintillation. Ionospheric scintillation can be categorized into phase scintillation and amplitude scintillation. Such scintillation has been related to inaccuracies in GPS location. In circumstances of high scintillation caused by ionospheric instabilities, inaccuracies in GPS signaling can have detrimental effects across a variety of user-based industries.

This following section introduces topics such as the phase scintillation (σφ index), the amplitude scintillation index (S4index), and how phase scintillation correlates to the solar cycle and sunspot number.

3.1 Phase Scintillation

Phase scintillation is due to phase variations in the received signal, and are caused by irregularities of scale size varying from hundreds of meters to a few kilometers [?,?]. The phase scintillation index is defined as the standard deviation of the carrier phase [4]. The carrier phase can be defined as the difference between the phases of the receiver-generated carrier signal and the carrier received from a satellite at the instant of the measurement[2]. The carrier phase is measured by the number of cycles generated or received, at a given start timet (a more in-depth explanation is available in the appendix 10.2). The equation for phase

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scintillation is described below:

σφ=p

< φ²>−< φ >²

Whereφis the detrended carrier phase, and the<>is the expected value. σφ is computed at time periods of 1s, 3s, 10s, 30s and 60s. The 60s time interval is the most commonly used interval in the GPS phase scintillation indices. σφ > 0.6 is known for high scintillations[3] and σφ < 0.05 is known for very weak scintillation. A value of 0.2 radians can be used to identify moderate scintillations. σφ index is commonly used for tabulating phase scintillation at high latitudes. For the scope of this thesis, phase scintillation was the primary focus of assessment.

3.2 Amplitude Scintillation

Amplitude scintillations are caused by irregularities with scale sizes of tens of meters to hundreds of meters [?,?]. S4 is defined as the standard deviation of the received signal power, normalized to the average signal power over 1 minute periods. [11].

S4=q_hI₂_i

hIi² −1

WhereI is the intensity scintillation, the brackets indicate the ensemble average. Typically, ifS4 >0.5 there is strong scintillation where amplitude scintillation can take values between 0-1 [?, ?]. It should be noted that the amplitude scinitalltion was found to be rare at high latitudes and common at lower latitudes.

Since this thesis was directed towards high latitides [4], amplitude scintillition will therefore only be briefly mentioned.

3.3 Phase Scintillation and Solar Cycle

Previous studies have suggested a strong correlation between phase scintillation occurrence, geomagnetic activity and solar flux in the high latitude [?,?]. They have determined that at high latitudes, there is less phase scintillation during times of solar minimum. Complementary to these findings, it was further discovered that there is more phase scintillation during times of a solar maximum. Because of these differences, phase

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scintillation is much more common than amplitude scintillation at high latitudes [?,?]. Solar minimum and maximum will be discussed further in section 4.2.

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4 Solar Terrestrial Background

The topics that were discussed in this section include: Plasma characteristics, the Sun, sunspots and solar cycle, Dungey cycle, substorm dynamics, aurora characteristics, ionospheric plasma, the diurnal/seasonal variations in geomagnetic activity, and common instabilities observed in the active ionosphere. Specifically, the subsection headed, Plasma characteristics discussed Debye length and sphere, and the Frozen-in concept. The Sun subsection investigated sunspots and solar cycles. Substorm dynamics introduced the growth, expansion and regression phase of substorms. Auroral characteristics subsection explained heights, wavelengths and the transitions between energy states in atoms and molecules of optical emission of 557.7nm, 630nm present in the ionosphere during aurora. The ionospheric plasma subsection introduced production and loss of ionization, E-region, F-region, structures such as polar cap patches, polar cap arc and auroral arc, and common ionospheric instabilities. Moreover, the subsections headed diurnal and seasonal geomagnetic variations were considered through the context of the high latitude locations of Svalbard and northern Norway.

4.1 Plasma Characteristics

Interactions with plasmas are an everyday experience and are used in a wide range of applications. Some of the more tangible examples of plasmas include lightning, aurora, neon signs, and fluorescent lights. Some popular examples of plasmas, in the context of space physics, include the Sun and space itself. The Sun is considered an ionized plasma due to its extremely high temperatures, whereas space is considered a very low density cold plasma.

A plasma is a quasi-neutral ionized gas consisting of positively and negatively charged particles, usually ions and electrons, which are subject to electric, magnetic and other forces. Importantly, plasmas exhibit collective behaviour and make up 99% of visible matter in our universe [1] [2] [3]. This section describes the intrinsic properties of plasmas such as Debye length and Frozen-in theory.

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4.1.1 Debye length

The Debye length is named after Peter Debye and is a measure of a charge carrier’s net electrostatic effect in a solution and its persistence. Additionally, a Debye sphere is a volume whose radius is the Debye length.

This is illustrated in figure 1 This means that in a fully ionized plasma, the electrons spherically surround the ions at a distance of the Debye length. Shown below is the equation for the Debye length.

Figure 1: Illistartion shwoing Debye length and Debye Sphere [25]

λD=q

kT ε₀ e²n

WhereλD is the Debye length, k is Boltzmann constant, n is the density andT is the temperature. A plasma is quasi-neutral, meaning that at distances larger than the Debye length, there is charge neutrality, and at distance smaller than the Debye length, the plasma cannot be considered charge neutral.

4.1.2 Frozen-in Theorem

The Frozen-in theory states that a fully ionized compressible plasma and the interplanetary magnetic field (IMF) are frozen together. Under ideal circumstances, this theory is stating that the magnetic flux through a plasma is constant over spatial and temporal variations. Figure 2 shows a cylindrical magnetic flux tube being frozen to a plasma . It is inferred that over time, the plasma is able to influence the magnetic field.

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Magneto-Hydrodynamics by Brute Force 213

• Example: You might of course have a representation of eld lines in spherical geometry as well, in which case (10.28) becomes

dr

B _r = rd

B = r sin d

B .

Actually, this form is most suitable, for instance, for representing magnetic dipoles.

It is a well known fact of basic electrodynamics that electric and magnetic eld lines are entities visualizing instantaneous elds, and that it does not make sense to follow the motion of such eld lines with time. It turns out, however, that in the limit of ideal MHD this can be considered formally possible. Properly speaking, it can be argued that in the limit of → we can identify magnetic ux tubes with particles, and in this sense we are not making any logical error in claiming that we can follow the motion of magnetic eld lines in space, as illustrated in Fig. 10.1. If one agrees to let the magnetic eld lines be carried along by the ow of particles, we have the correct behavior of B as a function of time (at least as long as the MHD model applies!). Some advantage can be obtained by this model, although also a number of paradoxes have been produced, which have their origin in a super cial application of this concept of “frozen-in eld lines.”

The analysis in this section allows for plasma compressibility, i.e., we do not assume · u = 0.

We will in reality be using only the expression (10.13).

First we introduce a notation ( S t+ t , B _t ) for a magnetic ux as

( S t + t , B _t ) ≡

!

S _t+ _t B _t · ds

where we introduced a vector ds normal to the surface S. Note that the notation allows us to consider a magnetic ux through a surface S de ned at a time t + t , while the magnetic vector eld is taken at a different time B _t ! This is a perfectly legal (although seemingly strange), and it turns out to be also a smart thing to do (Sturrock 1994). Time, t , is here placed as a subscript to indicate that we consider a xed time, and do not have time as a variable.

FIGURE 10.1

Simple illustration of “frozen-in” eld lines. Displaced and distorted magnetic ux tubes can be identi ed by the particles they enclose.

We rst write the change of magnetic ux through a surface S, which is following the motion of the uid; see, for instance, Fig. 10.2. Introducing a vector ds normal to the surface S, we have

( S t + t , B _t ₊ _t ) =

! S t+ t

B _t ₊ _t · ds ≈

t ^!

S t + t t B _t · ds +

! S t + t

B _t · ds ≈

t ^!

S t t B _t · ds +

! S t + t

B _t · ds , (10.29)

Figure 2: Simple illustration of frozen-in field line. Displaced and distorted magnetic flux tubes can be identified by the particles they enclose

Frozen-in theory can best be described by looking into the inertial and non-inertial reference frames. In the inertial reference frame, S a particle is moving with speed v, the electric and magnetic fields are E and B. In the non-inertial reference frame. S’ is moving with the particle and the electric and magnetic fields are E’ and B’. The fields given by the Lorentz transformation are shown below:

E⁰ =E+v×B B⁰=B−^v×Ec²

Where c is the speed of light and v >> c. This plasma is assumed to have collisions, due to its low temperature and density. A collision-less plasma is vulnerable to electric and magnetic forces.

In the non-inertial reference frame, there is no velocity of the electrons such that the electric field may be approximated to zero (E⁰ = 0). Therefore, the electric field of the inertial reference frame is;

E=−v×B 14

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Faraday’s law describes how temporal variations in the magnetic field is related to the electric field, as shown below:

∂B

∂t =∇ ×(v×B)

This implies that the time-dependent magnetic field is bound to the spatial changes in velocity. This is essentially the magnetic field and plasma being frozen into each other. This concept is highly relevant for Earth-related space weather phenomena, such as convection over the polar cap and magnetic re-connection.

These phenomena will be addressed further in this thesis.

4.2 The Sun

The Sun is the primary dictating force for the space weather phenomena experienced on Earth. This power comes from the Sun’s interior, which undergoes fission and fusion and produces large amounts of energy.

Convection at the surface of the Sun majorly contributes to the Sun’s magnetic field [?, ?]. Deviations in the Sun’s magnetic field can create locations of enhanced magnetic activity, referred to as sunspots. These sunspots often dampen the convection and cause a local temperature decrease, such that they appear black.

The quantity of sunspots can be associated with solar maximums, minimums, and ideally show the periodic 11 year solar cycle. Many studies have observed how the number of sunspots on the Sun’s surface oscillates, and suggest an oscillation period of approximately 11 years[?, ?,?,?,?, ?,?,?]. Therefore, every 11 years the Sun’s main magnetic field reverses, returning back to original orientation every 22 years. It should be noted that geomagnetic activity follows a similar oscillation trend [?].

The Figure 3 shows the solar cycle sunspot number progression between 2000- September 2018. Included in this figure are the smoothed values, monthly values and predicted values of the sunspots. Inferred from this graph is the past solar minimum 2009, and the peaks of the solar maximum of 2012, and 2014 i.e. the solar cycle. Currently, the number of sunspots were decreasing towards a solar minimum. It is important to understand the position in the solar cycle and the number of sunspots for the dates included in the case study of the results section. As well, it is important to understand the solar maximum and minimum for the dates included in the statistical analysis of the results section 7.1 .

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Figure 3: Description of Cycle Sunspot Number progression. Showing the smoothed monthly values, the monthly values, and the predicted values from January 2000-September 2018.[28]

4.3 Dungey Cycle

At points of increased solar activity, the Sun can exhibit emissions in the form of a solar flare. These solar flares are shown to carry particles, including electrons and protons, towards the Earth. Solar flares contribute to the auroral substorms observed on the Earth.

The Earth’s magnetic field can act as an obstacle, blocking the solar wind and causing shock front upon impact. When this occurs, the solar wind is slowed down and diverted around the Earth. Particles that enter the Earth’s magnetic field are reflected by a force known as the Lorentz force [1].The vast majority of particles that transit from the solar winds magnetic field to the Earth’s magnetosphere do so by magnetic re-connection.

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Dayside magnetic re-connection may occur when the solar wind’s magnetic field and the Earth’s magnetosphere field lines are anti-parallel [1]. In the case of dayside magnetic re-connection, frozen-in field conditions that govern behavior of the solar wind particles break down locally, due to the relatively short length-scales encountered at the magneto-pause [1]. This allows particles to diffuse and connect the Earth’s magnetosphere to solar wind magnetic field lines, forming open field lines. Along these field lines, particles transit from the solar wind to the earths magnetic field. The open field lines convect from noon to midnight over the polar cap [1].

For nightside reconnection, the reconnection is located in the tail. The newly formed closed field line eventually convects back to the dayside at lower latitudes, corresponding roughly to the auroral zone [1].

By connecting back closer to the Earth’s surface, particles gain energy from the magnetic field, eventually precipitating into the ionosphere. Following the field lines, most particles precipitate near the poles. As the particles that are frozen in the magnetic field lines are accelerated towards the Earth and the ionosphere, they collide with ions and neutral particles. The particles kinetic energy is transferred into the atmospheric molecule, causing it to transition from ground state to an excited or ionized state. The excited states can relax by the emission of a photon, giving rise to the band-like auroras we can see.

4.4 Sub-storm Dynamics

Geomagnetic activity is proportional to sunspots, solar flares, and variations in the solar wind. When there are increased amounts of geomagnetic activity, it can be classified as a substorm. A substorm has energy that is loaded from the solar wind into the magnetosphere and subsequently released into the ionosphere [?,?,?]. There are several substorm models and this section introduces the growth phase, expansion phase and recovery phase of a substorm.

4.4.1 Substorm Growth Phase

The first phase of a substorm is typically the growth phase, wherein energy from the solar wind is deposited into the magnetosphere. For southward IMF and at the magnetopause, there is magnetic recognition. This radiation will inevitably increase the amount of magnetic flux in the ionosphere, such that the polar cap will

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expand. In the night sector, the magneto tail stretches, the auroral electrojets are enhanced (pre-midnight and post-midnight), magnetic flux in the tail increases, and the cross-tail current increases. It should be noted that the polar cap size is dependent on the growth phase of the substorm and the growth phase normally lasts of the order of 1 hour.

4.4.2 Substorm Expansion Phase

The second phase of a substorm is the expansion phase. The expansion phase can be characterized as the release of stored energy in the magnetotail into the ionosphere. The signature of this phase is a sudden northward IMF. During the expansion phase, plasma is frozen to the geomagnetic field lines and precipitates down into the ionosphere. The resulting particle precipitation then causes optical emissions due to excitement and de-excitement of the particles in the ionosphere. Because of this ionization, the particle precipitation creates enhancements in ionospheric conductivity such that the auroral electrojets are enhanced simultaneously. Finally, the aurora expands poleward after the onset of this phase.

4.4.3 Substorm Recovery Phase

The last phase of a substorm is the recovery phase. In this phase, the aurora typically weakens in intensity and propagates poleward. The aurora will follow this trend until there is a quiet ionosphere again.

Furthermore, for extended periods of southward IMF, the recovery phase may coincide with the growth phase of the next substorm, such that the magnetosphere will not fully return to a quiet condition between the substorms. It should be noted that the recovery phase typically lasts 1-2 hours.

4.5 Aurora characteristics

A brief explanation of the auroral heights, optical emission wavelengths, and ionized molecules that produce aurora in the ionosphere will be provided in this section. Aurora has a specific optical emission at defined heights. The most prominent of such emissions are at wavelengths of 630nm and 557.7nm, observed as red and green respectively. The 557.7nm observation is a transition of electrons between orbitals in atomic oxygen from the metastable excited state 1S to the lower energy 1D state. The resulting green emission

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is at a height of approximately 120 km [1]. The 630nm observation obeys the previously stated electron transition in atomic oxygen, but instead results in red emission at a height of approximately 150km [1].

Auroral optical emissions are caused by transitions of electrons from high energy to low energy orbitals in atoms found in the ionosphere. The wavelength of light emission as a result of transition between two energy states, E1 and E2, can be expressed as:

λ=_E₂^hc_−E₁

In the reverse direction, light emissions at this wavelength can be absorbed by an atom to leave electrons in an excited state (E2> E1). [30]

4.6 Ionospheric Plasma

4.6.1 Ionization Production and Loss

Ionization in the ionosphere is manly due to the effects of UV solar radiation for daytime ionization and to ionization by energetic particle precipitation at night. During the daytime, the density of neutrals increases and the solar flux decreases at lower altitudes. This combination creates large structures in the ionosphere.

Deionization can occur as well, where at lower altitudes it is common for an ion to combine with an electron and separate into two neutral atoms. This is called dissociative recombination and is the most common loss process in the lower ionosphere.[31]

4.6.2 E region

The E-region ionosphere is loacted in between 90-120km, which is considered the middle of the ionosphere.

The typical electron density in the E-region are on the order of 10¹¹m³[?,?]. Due to its density, the nature of the E-region is dominated by the following dissociative recombination reactions:

N O⁺e⇒N+O O⁺₂e⇒O+O

The E-region is highly dependent on UV solar radiation. At nighttime when there is no impact of UV solar radiation, the E-region density decreases to approximately 5×10⁹m³ [?, ?].

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4.6.3 F Region

The F-region has the highest amount of density in the ionosphere and extends from 150km-upwards. The F-region will have daytime electron densities of 10¹¹−10¹²m³ The dominating species in the F-region are atomic oxygen andO+. [?,?].

O⁺+⇒O⁺+photon

At low F-region altitudes, the charge exchange is a rapid process. The reaction rate is limited by the dissociative recombination similar to that of the E-region, and therefore there has significant change in temperature and density between day and night. This change is due to the abundance of O+2 and NO+.

In the high F-region, the plasma density is only weakly reduced at night, staying at 10¹¹−10¹²m³. This observation is due to the abundance ofO⁺, where the charge exchanges limit the overall reaction rate. This thesis primarily focused on the upper E-region and lower F-region.

4.6.4 Polar Cap Patch

Polar cap patches are associated with irregularities causing disturbances in transionospheric radio waves[?,

?, ?, ?, ?, ?, ?, ?, ?]. Polar cap patches are subject to developing smaller-scale irregularities down to decameter scale through the GDI [?,?,?,?,?,?,?,?]. The patches are a result of enhanced plasma density being segmented from the dayside high-density plasma in the cusp region, and can be on the order of 100 – 1000 km [?, ?,?,?,?, ?,?].

4.6.5 Auroral Arc

Auroral arcs are the most typical auroral forms in the pre-midnight sector auroral oval. Where the arcs caused by emission of a photon in the ionosphere and are typically oriented in the east-west direction. Arc thickness in the ionosphere is typically several (or even tens of) kilometers [?, ?]. Arcs are known to have smaller structures such as instabilities on the scale of tens of meter scales [?, ?] [?, ?, ?]. Arcs often drift in north-south direction, and during increased geomagnetic activity, such as in geomagnetic substorms, arcs tend to get deformed.

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4.6.6 Polar Cap Arc

Auroral precipitation is an common mechanism in the generation of polar cap arcs [?]. Polar cap arcs are commonly observed and consist of only electron precipitation without associated ions, therefore harbouring less energy [39]. It is therefore conceivable that the ionospheric irregularities are directly created by the auroral precipitation associated with a polar cap arc [39]. Polar cap arcs are known to be associated with flow shears [?, ?, ?, ?]. Similar to polar cap patches and auroral arcs, the GDI is a common instability in the polar ionosphere, which works on the trailing edge of drifting plasma structures [?,?, ?].

4.6.7 Instabilities

Instabilities in the ionosphere are the main cause of ionospheric scintillation. This section will explore the growth rates of the two most common instabilities, the GDI and the two-stream instability, and consider how they can grow or decay depending on external factors. The linear growth rate of ionospheric instabilities that are dependent on the gradient of electron density are highlighted in this section. The causes of electron density fluctuations are primarily a GDI and two-stream instability[42].

4.6.8 Gradient drift instability

The GDI is one of the most common instabilities in the ionosphere. Past studies have related GDI and polar cap patches [45] [3] to ROTI and scintillation effects at magnetic midnight over Svalbard, pointing out that the GDI is the principal irregularity production mechanism, and shown in Figure 4 [43]. This figure shows a simulation of the GDI for a 3-D non-linear evolution of the electron density for a polar cap patch.

The patch is moving with respect to the y-axis and at time steps a)t = 0.44h, b)t = 0.9hand c)t = 1.8h [44]. From the figure, one can see that the instabilities start in the trailing edge then propagate through the patch towards the leading edge. As time progresses, the fluctuations evolve to a larger scale length, which is evident of the inverse cascade nature of the instability. [44].

The GDI can be described by the linear growth rate. Looking at the simplest case, ie 1-dimension studied by [45] is shown below:

γGDI= ^V_L⁰

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representing the irregularities while they propagate to the region of low density during the nonlinear evolution of the primary GDI. With these similarities in the observed and simulated density lineouts, we would expect the spectral characteristics of the density in the midnight-noon direction to be in very good agreement with the observations.

[18] Note that the observational data obtained from the DE 2 satellite are interpreted as one-dimensional cuts

through the ionosphere. Thus there is no precise way of determining the two-dimensional geometry of the patch.

However, in the work of Basu et al. [1990], the detailed description of the density and electric field spectra in two directions parallel and perpendicular to the antisunward convection was provided. Although their high-resolution data were not sampled simultaneously in two orthogonal directions, the provided statistical information on density and electric field spectral indices can demonstrate the spectral behavior in these two directions. It was concluded by the authors [Basu et al., 1990] that it is important to consider the magnitudes of the density and electric field perturbations as well as their spectral shape in order to

Figure 4. Density contour R = 3 at (a) t = 0.44 hours, (b)t= 0.8 hours, and (c)t= 1.5 hours.

Figure 3. Density contour R = 2 at (a) t = 0.44 hours, (b)t= 0.9 hours, and (c)t= 1.8 hours.

Figure 2. Density isosurfaces for the variable drive case at (a)t= 0 and (c)t= 3.3 hours and for the constant drive case at (b)t= 0 and (d) t= 1.2 hours. In our simulations the right side of the patch is associated with the trailing edge of the patch.

A09301 GONDARENKO AND GUZDAR: STRUCTURING IN HIGH-LATITUDE PATCHES

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Figure 4: Simulation of the GDI for a 3-D non-linear evolution of the electron density for a polar cap patch[44]

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WhereV0is the plasma drift velocity relative to the neutral gas, andL= (^dn_dx¹_n)⁻¹is the local exponential gradient length scale. In a collision case, the ions will drift relative to the electrons due to the ’pederson drift’[45]. Pedersen conductivity occurs in the direction of the polarization electric field but perpendicular to the magnetic field.

4.6.9 Two stream instability

Past studies exploring two-stream instability in the ionoshphere are Per Høeg directional changes in the irregularity drift during artificial generation of striations, and D. T. Farley, Jr. studying two-stream plasma instability as a source of irregularities in the ionosphere[46]. The two-stream instability is another velocity shear instability and is very common in ionospheric physics.

The growth rate for the two-stream instability is quite long and complicated for introduction in this thesis but can be found in the appendix if the reader wishes to know more. The main driving factor of the two-stream instability will be highlighted as below:

ψ

v_i((ω−k·vd,i)²−k²C_s²)

Where this represents the driving factor of the growth rate of the two-stream instability. Ifω²Cs², then the growth rate is going to exponentially increase.

Figure 5 shows the evolution in phase space of a two-stream instability. The development is highlighted.

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VOLUME 19, NUMBER 6

P H Y S I C A L R E V I E W L E T T E R S

7 AUGUST 1967

fluid" which moves in (x

9

v) space. This anal- ogy is well known,

^1-4

but the hydrodynamics, statistical mechanics,

⁵

and thermodynamics

⁶

'

⁷

of such a classical self-interacting fluid have not yet been examined in detail and are intrin- sically well worth studying. Numerical com- putations on fluid motion in phase space are easier than for a real fluid, and our results bring out features of the nonlinear development of an instability that extend those found in p r e - vious numerical calculations.

⁸

'

⁹

The method of calculation employed here can be used for a variety of one-dimensional Vlasov-Poisson problems, and the results may be relevant to other situations where similar equations occur, for example in gravitating systems,

^{1 0}

particle accelerators, electron tubes, micro- wave devices, and thermonuclear machines.

To study nonlinear phenomena in phase space in their simplest form, it is natural to assume t h a t / = l in certain regions a n d / = 0 elsewhere.

This model corresponds to the homogeneous incompressible fluid of classical hydrodynam- ics and has been used by several workers.

¹

""

⁴

The state of a one-dimensional system is com- pletely defined by specifying the boundary curves between t h e / = 0 a n d / = 1 regions. The equations of motion of each point on a curve are

and the potential at each instant is determined from Poisson's equation, the charge density being obtained by a geometrical construction.

This type of calculation was employed by Do- ry

²

in a study of the negative mass instabili- ty in circular particle accelerators. The main computational problem is that the curves con- tinually stretch, so that their representation by a fixed number of points becomes inaccu- rate. Our program therefore uses a list-pro- cessing technique which enables extra points to be inserted automatically, wherever they are needed. The calculation is then quite a c - curate and fast, although the- practical dura- tion of a run is still limited.

The example to be discussed is a two-stream instability, in which the electron plasma is slightly perturbed at t - 0 from an equilibrium characterized by four straight lines in phase space: / = 1 for \v

0

< \v\<v

Q

a n d / = 0 elsewhere.

Periodic boundary conditions are imposed at x= (0,L) and the parameters of the problem 298

are v

0

At/Ax = 0.25, WpAt = 1/20, andA# = L/64, where Ax is the grid used for evaluating Pois- son's equation. The unstable wave numbers are k = 2m/L with n = (1, 2), and the linear growth rates are y/(*>p =0.30, 0.315.

The most striking feature of the calculation is the behavior of t h e / = 0 "cavity" which ini- tially occupies the strip (M<it>

0

) between the two plasma layers. This must preserve con-

stant area as it deforms, and it is seen in Fig.

1 to coalesce into holes of roughly elliptical shape, so that a large-amplitude electrostat- ic wave is set up. Superimposed on this wave are coherent oscillations due to rotation of the holes in phase space, and also random fluctuations due to the motion of smaller ele- ments of the hole "fluid." The two outer curves adjust almost adiabatically to the instantane- ous potential function.

The holes are evidently being attracted to one another, and so behave like positively charged bodies with negative mass. One ex- planation is that the boundary of each hole is actually determined by the motion of negative- ly charged electrons, which are attracted to- wards a neighboring positively charged region

occupied by another hole. Alternatively, we can construct a formal analogy between any plasma problem and an equivalent gravitation- al problem, in which the law of force is attrac- tive and t h e / = 0 a n d / = 1 regions are inter- changed. We can then show rather accurate-

FIG. 1. Evolution in phase space of a two-stream in- stability from time steps 200 to 600 at intervals of 50 steps. Each step is 1/20 of a plasma period, and the horizontal and vertical coordinates are x

t

v

9

respec- tively. Periodic boundaries have been imposed and three identical periods are shown along each row. The shaded area represents the/=0 region enclosed by the plasma fluid.

Figure 5: Evolution in phase space of a two-stream instability[?]

4.7 Diurnal Variations

The diurnal variations observed in the ionosphere at Svalbard are due to the fact that Svalbard is located within the cusp on the dayside sector and mostly inside the polar cap on the nightside sector. This concept is especially relevant for the results and conclusion section 7. Figure 6 shows the electron density profiles representing average daytime and night time conditions at high latitudes. Also indicated in this figure is a profile for auroral conditions. As well, the background neutral density profile together with an average neutral atmosphere temperature profile are schematically illustrated [?]. Interpreting Figure 6 , one can see that there are significant differences between electron densities at midnight and midday for low altitude.

The electron density in a quiet ionosphere during night is lower than that at midday. This concept is demonstrated in the results and discussion of the statistical analysis approach and is discussed in more depth in further background chapters. In contrast, the electron densities during an aurora in the nighttime sector have the potential of increased density at low altitude. This is likely due to the influx of particle precipitation, ideally ionizing the ionosphere and generating free electrons and ions.

24

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4.1 The production of ionization by solar radiation 191 Sec. 4.1]

Figure 4.2. Electron density profiles representing average daytime and night-time conditions at high latitudes. Also indicated is a profile for auroral conditions. The background neutral density profile together with an average neutral atmosphere temperature profile are also schematically illustrated.

Figure 4.3. Altitude profiles of the most typical ion species in the ionosphere between 100 and 600 km, together with the corresponding electron density profile. (After Richmond, 1987.)

Figure 6: Electron density profiles representing average daytime and nighttime conditions at high latitudes.

Also indicated is a profile for auroral conditions. The background neutral density profile together with an average neutral atmosphere temperature profile are schematically illustrated.[?]

Svalbard is unique because of its high latitude location. Figure 7 shows the diurnal location of Svalbard from a geomagnetic perspective. Svalbard is located within the cusp on the dayside sector and mostly inside the polar cap on the nightside sector, which is unique for the study of space weather events.

The cusp can be defined as a funnel-shaped region in the vicinity of the polar regions at high latitudes with the presence of magnetosheath plasma, and where field lines are open due to magnetic reconnection . The polar cap can be defined as the region of open magnetic field lines encircled by the auroral oval. One important feature of the polar cap is that there is no particle precipitation. Since Svalbard is mostly in the polar cap in the night sector, during times of geomagnetic activity, the auroral oval may expand to Svalbard allowing particle precipitation and further ionization of the ionosphere. Understanding the diurnal variation of ionization in the high latitudes and the significance of Svalbard being located in the cusp in the day and mostly in the polar cap at night is crucial for interpreting the conclusions of the statistical analysis.

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SIGERNES ET AL.: REAL TIME AURORA OVAL FORECASTING – SVALTRACK II

4 Fig. 2.Animated aurora ovals as a function ofKp index [0…8] and time for 24 ^thDecember 2009

Finally, the geographic latitude and longitude of the ovals are given as

) / ( tan

) ( 2 cos

1 1

x y

z

- -

= -

=

¢

y q

p

(8)

Ó Ì Ï

<

+

>

"

=

¢ 0

0 x x

p y f

y

Note that the procedure is identical for the south magnetic pole if we assume that the Kp index is the same.

4. VISUALIZATION

The ovals are visualized with a stand alone 32bit executable Windows program called SvalTrack II. The program is written in Borland’s Delphi – Pascal and uses a Geographic Information System (GIS) unit called TGlobe ^[11]. It displays interactively mapping

data in real time onto a threedimensional spherical globe representing the Earth. The twilight zone, night

and dayside of the Earth are projected with grades of shade on the Globe as a function of time. The 3D globe can be rotated and zoomed to display a closeup of any region of the Earth.

Both the aurora Borealis and the aurora Australis ovals are projected as polygons onto the globe with an angular resolution of 1.5 ô. The equatorward boundary of the diffuse aurora is added as a polygonal line. The local position of the aurora observer is added as a point with corresponding state information of the Moon and the Sun. In addition, the circle of ~4.5 ô around the observer represents a 160 ôfield of sky view. The latter is under the assumption that the auroral emissions peaks at an altitude of ~110 km. The program also maps the position of space objects. The orbits are calculated by the use of the Simplified General Perturbations model 4 for near and deep space objects (SGP4 / SDP4) ^[12]. The model input is compatible with Figure 7: Polar cap and arural oval for varying amounts of Kp index. Indicated in red is the approximate location of Svalbard and in yellow is the approximate location of Skibotin [48]

4.8 Seasonal Variations

On Svalbard in the dark season, there is polar night between November 11 and February 15. The dark season is known as when the Sun angle towards the horizon is between 0^◦<. Therefore, the winter months in Svalbard are dark and have no influence of sunlight or photo ionization in the ionosphere. The summer

26

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months in Svalbard experience 24 hour sunlight between the dates of April 20 and August 24, at which time the angle of the Sun to the horizon is >0^◦. In the summer, there is solar UV radiation. Solar UV radiation can ionize the ionosphere, creating more free electrons as well as ions. Having seasonal variations in the density of electrons effects the growth rates of the instabilities. This topic is discussed in more detail in later sections 4.6.7. Understanding the seasonal variation of ionization due to UV solar radiation in the high latitudes is necessary for interpreting the conclusions of the statistical analysis.

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5 Observation Techniques and Methodology

5.1 Methodology

The motivation for this project has stemmed from the purposed question of whether sigma phi scintillation at high latitudes correlates to the K/Kp index. The purpose of the index K is to provide a homogeneous running record of the terrestrial effects of solar corpuscular radiation by measuring the intensity of the geomagnetic activity caused by the electric currents produced around the Earth by radiation[49]. The Kp index is defined by an algorithm dependent on the ensemble of K indices.

The Ionospheric conditions have further been determined by using optical instruments, GNSS receivers, EISCAT radars, SuperDARN radars, ground-based magnetometers, and ASI. Morphology of the irregularities such as TEC, electron density, electron temperature, Ion temperature, ion velocity, and intensity from ASI were monitored then correlated to the present instabilities by analyzing the ROTI, sigma phi scintillation (σφindex), amplitude scintillation (S4index), back-scatter obtained by SuperDARN radar, and local magnetic fields from ground-based magnetometers. The large-scale dynamics of the aurora and the small-scale instabilities of the aurora have been deduced.

5.2 GPS

The GPS constellation consist of 24 or more satellites in circular orbits of 26 600 km radius. The orbital period of these orbits is 12 sidereal hours. Typical lifetimes of the satellites are 8–10 years[?].

5.3 GNSS Receivers

A GNSS receiver works by receiving radio wave signals sent by overhead satellites which pass through the ionosphere. One of the recorded parameters in the data that the GNSS receiver collects is scintillation, where scintillation shows the fluctuations of the phase and amplitude of the received radio wave signal.

These fluctuations are due to plasma density fluctuations. The GNSS receivers utilized in this project were located in the high arctic. The data was collected by a network of GPS and many different ground-based receivers. Each satellite was at a different azimuth and elevation angle for each time of measurement, and

28

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were plotted to show TEC,ROTI,S4 σφ vs time, and location by elevation angle against azimuth. These plots were organized by color for the individual pseudo random number (PRN). Since each measurement was done along the line of sight of the satellite to receiver, each satellite’s measurement was an angular section of the ionosphere. A smaller elevation angle means a longer path length through the ionosphere.

The GNSS receivers used in the project were a NovAtel GSV4004. This receiver makes dual-frequency measurements of TEC at 1Hz, and the scintillation indiciesσφ, S4 are computed by the GNSS reciever at a rate of 50Hz[3].

5.4 All Sky Imager

The ASI is designed for the low-light application of monitoring the auroral morphology by photo. ASI that were utilized in this thesis were fixed in position and pointed directly upwards. This camera has a field-of-view of 180 degrees, and an exposure time of 10-30s. It produces images of all visible wavelengths with a 6 slotted interference filter wheel. The transmittance of an interference filter is a function of off-axis angle. The goal of minimizing the angular spread through the filter leads to the telecentric system [?,?].

There is a shutter that opens and closes to protect filters during daytime and or provide exposure control.

These cameras can have different sensors, either a CCD, EMCCD or a CMOS. A computer that has the main function of control and data acquisition is the main feature of this system. The produced images can then be used to infer the size, dynamics, and intensity of a given substorm [9].The differences in these sensors will not be discussed in this thesis. Figures 8 show a schematic of an ASI [?]

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Figure 8: Schematic drawing of a modern day ASI [?].

Ground-based auroral imaging has diverged in several directions. One such divergence occurred to achieve the highest possible spatial resolution. To demonstrate, Trondsen and Cogger [1998] have recorded auroral features smaller than 100m [Trondsen and Cogger, 1997]. Examples of narrow-field images are shown in Figure 9. ]. Another of the mentioned directions of ground-based auroral imaging is to use lines of multiple cameras in communication with a central-site computer. In this way, real-time tomography can be achieved.

Such a system called auroral large imaging system (ALIS) and was pioneered by Ake Steen in Sweden [?,?].

30

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Figure 9: Narrow field auroral image taken with a CCD detector showing auroral structures smaller than 100m. Auroral arcs (above) and auroral curls (below)

The physical location of the ASI that were utilized in this thesis were located in Ny- ˚Alesund and Tromsø.

The wavelength that has been investigated in this thesis the 557.7nm. Both of these locations fall within the arctic circle on Svalbard and in Northern Norway.

5.4.1 Keograms

The ASI information can be used to create keograms. Keograms show the meridian intensity against time.

In the case of the ASI, this means omitting all information outside the meridian line. Keograms provide a good image about the auroral activity from low to high latitudes and can provide an intensity measurement [4].

5.5 Radars

Radio detection and ranging (radar) works by transmitting a pulse or a phase-coded EM radio wave at a target volume. The radio wave is then scattered by the target volume and received by the radar. The spectral properties of the scattered radio wave can contribute to providing the physical properties of the target volume [?]. Radars can be classified by the frequency of the emitted wave. High frequency (HF) radars have frequencies between 3-30MHz, very high frequency (VHF) radars operate between 50-330MHz, and ultra high frequency (UHF) radars have frequencies between 300-1000MHz. This thesis utilized SuperDARN radars and EISCAT radars in both Svalbard and Tromsø to observe physical properties of the ionosphere

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during each case study in this section.

5.6 EISCAT Radars

EISCAT is an incoherent radar that can detect electron density Ne (m-3), electron temperature Te (K), ion temperature Ti (K)and ion line-of-site velocity, Vlos (ms-1) in the ionosphere. China, Finland, Germany, Japan, Norway, Sweden, and the United Kingdom all support EISCAT as an international research organi- zation. There are ten incoherent scatter radars in the world. For the purpose of this thesis, the EISACT radars located in Longyearbyen (ESR), and Tromsø (EISCAT VHF) were utilized.

The ESR is an UHF system (500MHz) composed of two monostatic incoherent radars; one being a steerable 32m and the other being a fixed magnetic field aligned 42m. A monostatic incoherent radar has the ability to both send and receive a signal. The Tromsø has the Tromsø VHF (224 MHz) and the Tromsø UHF (933 MHz) mono static Radars.

Incoherent scatter radars send EM wave pulses into the ionosphere. The energy contained into the wave pulses is transmitted via Thomson scattering to the electrons. Thomson scattering, as described by classical electromagnetism, can be stated as the elastic anisotropic scattering of EM radiation by a free charged particle. Thompson scattering is the low-energy limit of Compton scattering by which the particle kinetic energy and photon frequency are the same before and after the scattering event.

Due to electron motion, the frequency spectrum of the scattered radiation reflects the velocity distribution of the electrons. This is due to electron motion altering the frequency of the probing beam, explained by the Doppler effect. If the electron is moving in the field of the wave, the scattered frequency is said to be Doppler-shifted. Such a shift can arise from two effects: the moving electron experiencing the incident wave at a different frequency to the input wave, and the effect due to its motion. The electron is scattered radiation and will also be Doppler-shifted. By measuring the spectrum of the Thomson scattered radiation, the velocity distribution of the electrons can be determined.

This simple picture of the Thomson scattering process indicates that the effect of the input EM wave is to drive the electron into oscillation at the frequency of the oscillating wave, and the vibrating electron radiates energy due to its acceleration. Oscillation ceases once the input wave is removed. The electron then carries

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on with the same velocity and trajectory prior to the application of the incident wave. However, we know that EM fields carry momentum, and following scattering, the momentum of the scattered wave is changed.

Therefore, the momentum of the electron must be changed in order to conserve total momentum. Here, both the momentum and the energy imparted to the electron as a result of the scattering event, were of interest.

Due to electron motion, the frequency spectrum of the scattered radiation re ﬂ ects the velocity distribution of the electrons since electron motion alters the frequency of the probing beam due to the Doppler effect. If the electron is moving in the ﬁ eld of the wave the scattered frequency will be Doppler shifted arising from two effects: the moving electron will experience the incident wave at a different fre- quency to the input wave and, due to its motion, its scattered radiation as measured by an observer will also be Doppler shifted. By measuring the spectrum of the Thomson scattered radiation the velocity distribution of the electrons can be determined.

This simple picture of the Thomson scattering process indicates that the effect of the input electromagnetic wave is to drive the electron into oscillation at the frequency of the oscillating wave, and the vibrating electron radiates energy due to its acceleration. Oscillation ceases once the input wave is removed and the electron then carries on with the same velocity and trajectory prior to the application of the incident wave. However, we know that electromagnetic ﬁ elds carry momentum and following scattering the momentum of the scattered wave is changed, and so the momentum of the electron must be changed in order to conserve total momen- tum. Here we are interested in the momentum and the energy imparted to the electron as a result of the scattering event. Let us analyse this problem quantum mechanically where the input wave is in the form of photons and we will invoke the principles of momentum and energy conservation in the scattering process [19]. We will assume that the electron is

initially at rest and that scattering takes place in a plane.

Suppose that the electron recoils through an angle ψ and the photon is scattered through an angle φ as shown schemati- cally in ﬁ gure 1.2.

Let E

p

( E

_p

′ ) be the energy of the photon before (after) the collision and p

_e

the momentum of the electron following the collision. The relativistic expression relating the momentum and energy E

_e

of the electron is

= + ( )

E

e

( p c

e

)

2

m c (1.1)

0 2 2

where m

₀

is the rest mass of the electron and c is the velocity of light. Let us assume that the scattering process can be treated as an elastic collision between a photon and an elec- tron (assumed at rest) and that conservation of momentum and energy are considered. Momentum conservation gives the following two equations;

φ ψ

= ′ E +

c E

c cos p cos , (1.2)

p p

e

φ ψ

= ′ E −

c p

0

^p

sin

_e

sin , (1.3)

and energy conservation gives

+ = ′ + + ( )

+ −

E E m c

m c E (1 cos ) . (1.8)

p p

p 0 2 0 2

Accordingly, the energy gained by the electron (equal to the energy lost by the photon, that is, E

_p

− ′ E

_p

) is

φ φ

− ′ = −

+ −

⎛

⎝ ⎜⎜ ⎞

⎠ ⎟⎟

E E E

m c E

m c

(1 cos )

1 (1 cos )

(1.9)

p p

p

p 2

0 2

and the corresponding momentum acquired by the electron is given by equation (1.6). In typical Thomson scattering sys- tems, E

p

≈ 1 eV whereas, the rest energy of the electron is

=

m c

0 2

511 keV so that there is negligible change in the momentum of the electron as a result of the collision.

This condition is well satis ﬁ ed when E

_p

≪ m c

₀ ²

and this represents the low-energy limit of the Compton effect for

Figure 1.1.

Schematic illustration of the Thomson scattering process.

Figure 1.2.

Compton scattering (see text).

Phys. Scr.89(2014) 128001 S L Prunty

Figure 10: Schematic illustration of the Thomson scattering process[52]

Thompson scattering is the acceleration of a free electron by the incident field of a light wave and the subsequent re-radiation by the electron of EM radiation as seen in Figure 10. The electron scatters electric waves, which propagate perpendicular to the electric field[?].

The electrons exhibit emissions of EM energy, whereas the radar receives a small portion of the emission.

When the radar receives the signal, a signal analysis is performed in order to produce the double-humped Doppler-shifted power spectrum as seen in Figure 11.

From the displacement between the transmitted frequency and the centre of the double-hump, one can calculate the line-of-sight of the Doppler-shift in the bulk plasma. The electron density is given by the integral of the power spectrum. The height between the bumps and the centre gives Te/Ti. Ti can be calculated by measuring the full width half max of the spectrum [54].

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High Latitude Phase Scintillation