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Ion dynamics in magnetized plasmas [Elektronische Ressource] / vorgelegt von Albrecht Stark

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125 pages
Ion dynamics in magnetized plasmasInauguraldissertationzurErlangung des akademischen Grades einesdoctor rerum naturalium (Dr. rer. nat.)an der Mathematisch-Naturwissenschaftlichen Fakult¨atderErnst-Moritz-Arndt-Universita¨t Greifswaldvorgelegt vonAlbrecht Starkgeboren am 23.08.1976in HamburgGreifswald, im Marz 2006¨Dekan: Prof. Dr. K. Fesser1. Gutachter: Prof. Dr. T. Klinger2. Gutachter: Prof. Dr. T. Dudok de WitTag der Promotion: 12. Mai 2006AbstractIn magnetized plasmas the understanding of the plasma dynamics in response tomagnetic fluctuations is of particular interest. These fluctuations appear in formof linear andnonlinear wave phenomena and alsoas a change of the magnetic fieldtopology. In the context of the present thesis the influence of low-frequency elec-tromagnetic waves and topological changes of magnetic fields caused by magneticreconnection on the ion dynamics was experimentally investigated.In the linear magnetized laboratory experiment VINETA kinetic Alfv´en waveswere excited and identified via detailed measurements of the waves dispersion bymeans of magnetic fluctuation diagnostics. For the understanding of the disper-sion behavior boundary effects and the influence of collisions must be taken intoaccount. The ion velocity distribution function (IVDF) was measured with laser-induced fluorescence (LIF). The standard LIF scheme was extended to obtainphase-resolved IVDFs in case of periodic perturbations.
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Ion dynamics in magnetized plasmas
Inauguraldissertation
zur
Erlangung des akademischen Grades eines
doctor rerum naturalium (Dr. rer. nat.)
an der Mathematisch-Naturwissenschaftlichen Fakult¨at
der
Ernst-Moritz-Arndt-Universita¨t Greifswald
vorgelegt von
Albrecht Stark
geboren am 23.08.1976
in Hamburg
Greifswald, im Marz 2006¨Dekan: Prof. Dr. K. Fesser
1. Gutachter: Prof. Dr. T. Klinger
2. Gutachter: Prof. Dr. T. Dudok de Wit
Tag der Promotion: 12. Mai 2006Abstract
In magnetized plasmas the understanding of the plasma dynamics in response to
magnetic fluctuations is of particular interest. These fluctuations appear in form
of linear andnonlinear wave phenomena and alsoas a change of the magnetic field
topology. In the context of the present thesis the influence of low-frequency elec-
tromagnetic waves and topological changes of magnetic fields caused by magnetic
reconnection on the ion dynamics was experimentally investigated.
In the linear magnetized laboratory experiment VINETA kinetic Alfv´en waves
were excited and identified via detailed measurements of the waves dispersion by
means of magnetic fluctuation diagnostics. For the understanding of the disper-
sion behavior boundary effects and the influence of collisions must be taken into
account. The ion velocity distribution function (IVDF) was measured with laser-
induced fluorescence (LIF). The standard LIF scheme was extended to obtain
phase-resolved IVDFs in case of periodic perturbations. The electrical fields of
the linear Alfv´en waves, which are driven by small amplitude magnetic perturba-
tions, are however usually too small, to significantly influence the ion dynamics.
A different situation emerges for a strongly nonlinear excitation scheme: Strong
indications for wave particle interaction was found in LIF measurements made on
nonlinear Alfv´enic waves in amplitude modulated helicon plasmas.
In the toroidal experiment VTF magnetic reconnection can be driven periodi-
cally and under reproducible conditions. These precondition facilitates systematic
investigationsofmagneticreconnectionanditsinfluenceontheiondynamicswith
LIF. For the first time it was proven that ion heating is a direct consequence of
reconnection. Furthermore, it could be shown that this heating is strongly local-
ized at the magnetic X-point, which is the location where reconnection occurs.
With time-resolved measurements of the IVDF a causal connection between the
reconnection rate and the ion heating could be established. Furthermore, strong
non-thermal components of the IVDF were detected, which correlate with the
observed ion heating. Numeric simulations, based on a kinetic single particle pic-
ture, show a transfer from magnetic energy to kinetic energy of the ions, which is
consistent with the experimentally observed rise of the ion temperature.
iiiZusammenfassung
In magnetisierten Plasmen kommt dem Verst¨andnis von magnetischen Fluktua-
tionen eine tragende Rolle hinsichtlich der Plasmadynamik zu. Diese Fluktua-
tionen treten in Form linearer und nichtlinearer Wellenphanomene oder auch als¨
¨AnderungdermagnetischenTopologieauf. ImRahmendervorliegendenDisserta-
tion wurde der Einfluß von niederfrequenten elektromagnetischen Wellen und der
vontopologischenMagnetfeldanderungendurchmagnetischeRekonnektionaufdie¨
Dynamik der Ionen experimentell untersucht.
In dem linearen magnetisierten Laborexperiment VINETA wurden kinetische
Alfv´enwellen angeregt und durch detaillierte Messung der Dispersion mittels mag-
netischer Fluktuationsdiagnostiken eindeutig identifiziert. Fu¨r das Verst¨and-
nis des Dispersionsverhaltens mu¨ssen die Berandung der Wellen und der Ein-
fluß von Stoßen einbezogen werden. Mittels laserinduzierter Fluoreszenz (LIF)¨
wurde die Ionenenergieverteilungsfunktion (IEVF) gemessen. Dabei wurde das
Schemadahingehenderweitert,daßbeiperiodischenSto¨rungendesPlasmasphase-
naufgeloste Messungen der IEVF durchgefuhrt werden konnen. Die elektrischen¨ ¨ ¨
FelderderdurchvergleichsweisekleinemagnetischeSto¨rungenangeregtenlinearen
Alfv´enwellen sind jedoch in der Regel zu klein, um einen signifikanten Einfluß auf
dieIonendynamikzunehmen. Andersverhaltessichjedochbeieinemstarknicht-¨
linearemAnregungssschema: DieWelle-TeilchenWechselwirkungkonntefu¨rnicht-
lineare Anregung Alfv´enischer Wellen durch amplitudenmodulierte Helikoneigen-
moden mittels LIF nachgewiesen werden.
In dem toroidalen Experiment VTF kann magnetische Rekonnektion periodisch
und unter reproduzierbaren Bedingungen angetrieben werden. Diese Voraus-
setzungen ermoglichen systematische Untersuchungen derRuckwirkung magnetis-¨ ¨
cher Rekonnektion auf die Ionendynamik mittels LIF. Dabei ist es zum ersten
Mal gelungen, eine Ionenheizung als Folge von Rekonnektion direkt nachzuweisen.
Ferner konnte gezeigt werden, daß diese Heizung stark lokalisiert ist und nur am
magnetischenX-Punkt,demOrtderRekonnektion,auftritt. Mittelszeitaufgel¨oster
Messungen konnte ein kausaler Zusammenhang zwischen der Rekonnektionsrate
undderIonenheizunggezeigtwerden. Desweiterenwurdenstarkenicht-thermische
KomponentenderIEVFdiagnostiziert,diemitderbeobachtetenIonenheizungko-
rrelieren. Numerische Simulationen, basierend auf einem kinetischen Einteilchen-
bild, zeigen einen Transfer von magnetischer Energie zu kinetischer Energie der
Ionen, der konsistent mit dem experimentell beobachteten Anstieg der Ionentem-
peratur ist.
vContents
Abstract iii
Zusammenfassung v
1 Introduction: Ion dynamics in space plasmas 1
2 Experimental techniques and signal processing 5
2.1 General plasma diagnostics . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 Langmuir probes . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.2 Microwave interferometry . . . . . . . . . . . . . . . . . . . 9
2.1.3 Residual gas analyzer . . . . . . . . . . . . . . . . . . . . . . 10
2.2 Electric and magnetic fluctuation diagnostics . . . . . . . . . . . . . 11
2.2.1 Double probes . . . . . . . . . . . . . . . . . . . . . . . . . . 12
˙2.2.2 Low frequency B-probes . . . . . . . . . . . . . . . . . . . . 12
2.3 Laser induced fluorescence (LIF) . . . . . . . . . . . . . . . . . . . 16
2.3.1 LIF principle . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3.2 The diode laser and the optical system . . . . . . . . . . . . 19
2.3.3 Line broadening and splitting mechanisms . . . . . . . . . . 21
2.3.4 Time averaged ion temperatures and drifts . . . . . . . . . . 24
2.4 Digital signal processing . . . . . . . . . . . . . . . . . . . . . . . . 26
2.4.1 Spectral analysis . . . . . . . . . . . . . . . . . . . . . . . . 26
2.4.2 Lock-In technique . . . . . . . . . . . . . . . . . . . . . . . . 27
3 Wave dynamics 29
3.1 Alfv´en waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.1.1 Shear Alfv´en waves . . . . . . . . . . . . . . . . . . . . . . . 29
3.1.2 Kinetic Alfv´en waves . . . . . . . . . . . . . . . . . . . . . . 31
3.1.3 Effect of collisions and boundaries . . . . . . . . . . . . . . . 32
3.2 Nonlinear three-wave coupling . . . . . . . . . . . . . . . . . . . . . 34
3.3 The VINETA device . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3.1 Magnetic field configuration and plasma profiles . . . . . . . 36
viiContents
3.4 Low frequency wave propagation measurements . . . . . . . . . . . 45
3.4.1 Alfv´en wave ion dynamics . . . . . . . . . . . . . . . . . . . 53
3.5 Helicon wave modulation experiments . . . . . . . . . . . . . . . . . 55
3.5.1 Ion response to helicon wave modulation . . . . . . . . . . . 62
3.6 Discussion of Alfv´enic wave experiments . . . . . . . . . . . . . . . 63
4 Magnetic reconnection 67
4.1 Models for magnetic reconnection . . . . . . . . . . . . . . . . . . . 69
4.1.1 Reconnection experiments . . . . . . . . . . . . . . . . . . . 72
4.2 The Versatile Toroidal Facility (VTF) . . . . . . . . . . . . . . . . . 74
4.2.1 Magnetic field topology and plasma profiles . . . . . . . . . 76
4.2.2 The reconnection drive and plasma response . . . . . . . . . 78
4.2.3 Synchronized LIF setup . . . . . . . . . . . . . . . . . . . . 81
4.3 Ion response to magnetic reconnection . . . . . . . . . . . . . . . . 83
4.3.1 Localization of ion heating . . . . . . . . . . . . . . . . . . . 84
4.3.2 Correlation between ion heating and reconnection . . . . . . 87
4.3.3 Ion dynamics during reconnection drive . . . . . . . . . . . . 88
4.3.4 Non-thermal components in the IVDF . . . . . . . . . . . . 90
4.4 Discussion of reconnection experiments . . . . . . . . . . . . . . . . 92
4.4.1 Ion heating as a consequence of reconnection . . . . . . . . . 92
4.4.2 Numerical simulation of perpendicular ion heating . . . . . . 93
4.4.3 Flows and non-thermal components of the IVDF. . . . . . . 94
5 Summary 97
Bibliography 99
Curriculum vitae 109
List of publications 111
Acknowledgements 115
viii1 Ion dynamics in space plasmas
Importance and the link to laboratory plasmas
Thedynamicsofmagnetizedplasmasisabroadfieldofresearchinplasmaphysics,
since fluctuations of magnetic fields may directly influence plasma particles on
1 2the kinetic level. A variety of phenomena are known in solar , astrophysical ,
3 4fusion , and laboratory plasmas , in which an interaction of the plasma with
magnetic fields is found: In solar plasmas, flares are believed to cause particle
5heating and acceleration by large scale changes in the magnetic field topology
and the high temperatures of the solar corona is likely to be caused by plasma
6heating due to electromagnetic waves . In the earth magnetosphere, substorms
accelerate plasma particles, which subsequently travel along the magnetic field
lines towards the earth and may give rise the aurora phenomenon or may disturb
8satellite communication . In laboratory and fusion plasmas numerous examples,
9like linear and non-linear waves and instabilities, are found, too . Of particular
Figure 1.1: SolarflareobservedbytheYohkohsatelliteonJanuary13,1992.
Shown are soft X-ray emissions of the entire sun (left) and a field of
2 2 9 278.4 arcsec , corresponding to 3.3·10 km . As a reference, the solar limb
and the contour of the flare are shown as solid lines [Taken from Masuda
7et al. ].
11 Introduction: Ion dynamics in space plasmas
interestaremechanismsthatallowatransferofmagneticenergytoparticlekinetic
energy. Two prominent examples, where magnetic field fluctuations could be
experimentally correlated with the generation of energetic particles and particle
heating, are magnetic reconnection and kinetic Alfv´en waves.
Magnetic reconnection is a process that changes the magnetic field topology by
cutting and rearranging magnetic field lines. This process was suggested to be
10the key mechanism in the dynamics of solar flares . In 1992 state-of-the-art X-
11ray spectrometers aboard the Yohkoh satellite provided spatially high resolved
measurements of soft X-ray radiation during a solar flare. A part of the results is
showninFig.1.1. IncreasedX-rayradiationisobservedtooriginatefromthesolar
7flarestructureitself,indicatinglocalizedparticleheatingandacceleration . Itwas
postulated that this particle acceleration is caused by the magnetic reconnection
process.
Kinetic Alfv´en waves are often responsible for magnetic fluctuations in the con-
13text of space plasmas . Fig. 1.2 shows a schematic of the Earth’s magnetosphere.
Figure 1.2: Time-resolved spectra of the electric and magnetic field fluctu-
ations as observed on a board of one Cluster satellite (C4) during crossing
the northern cusp on March9,2002. The cluster trajectory is indicated in
the schematic plot of the Earth’s magnetosphere [Taken from ESA website
12(www.esa.int) and Sundkvist et al. ].
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