Effect of strong wakes on waves in two-dimensional plasma crystals

We study effects of the particle-wake interactions on the dispersion and polarization of dust lattice wave modes in two-dimensional plasma crystals. Most notably, the wake-induced coupling between the modes causes the branches to "attract" each other, and their polarizations become elliptical. Upon the mode hybridization the major axes of the ellipses (remaining mutually orthogonal) rotate by $45^\circ$. To demonstrate importance of the obtained results for experiments, we plot spectral densities of the longitudinal and transverse waves revealing distinct fingerprints of the mixed polarization. Furthermore, we show that at strong coupling the hybrid mode is significantly shifted towards smaller wave numbers, away from the border of the first Brillouin zone (where the hybrid mode is localized for a weak coupling).Comment: 10 pages, 6 figure

Mode-coupling regimes in 2D plasma crystals

Diese Arbeit ist eine kumulative Dissertation und besteht aus drei Aufsätzen. Sie setzt die Studien der Diplomarbeit zur eigenständig kohärenten Beschreibung der wakevermittelten Modenkopplung in Plasmakristallen fort. Der erste Aufsatz untersucht die Ionengeschwindigkeitsverteilung (idf) in einem schwach-ionisierten Gas, welches einem homogenen elektrischen Feld ausgesetzt ist und in dem Ladungsaustauschkollisionen der dominante Stoßtyp sind. Die Untersuchung geht dabei nur von elementaren Grundprinzipien aus und ist somit eigenständig kohärent. Die "Referenzverteilung" wird mittels einer Monte-Carlo-Simulation (MC-Simulation) am Beispiel des energieabhängigen Wirkungsquerschnitts für Argon berechnet. Ich nutze mehrere analytische Modelle (basierend auf einem konstanten Wirkungsquerschnitt oder konstanter Stoßfrequenz) und vergleiche die entsprechenden idfs untereinander, sowie mit der Referenzlösung. Es zeigt sich, dass kein Modell für den experimentell häufig wichtigen Fall eines schwach suprathermalen Ionenstroms mit befriedigender Genauigkeit anwendbar ist. Einen konstanten Wirkungsquerschnitt und Separabilität der idf annehmend, sowie darauf folgende Maxwell-gewichtete Mittelung, reduziert die integro-differentielle Boltzmanngleichung zu einer gewöhnlichen Differentialgleichung. Ich zeige, dass ihre Lösung die Resultate der MC-Simulation, für beliebige Stärke des Ionenstroms, mit großer Genauigkeit reproduziert. Das gewonnene Modell lässt sich auf eine Vielzahl von Problemen im Bereich der komplexen Plasmen anwenden - darunter der Ladungsvorgang der Staubteilchen, die Bildung von Wakefeldern und nicht-Hamiltonische Dynamik. Im zweiten Aufsatz behandle ich das vorrangige Beispiel eines nicht-Hamiltonischen Prozesses in zweidimensionalen (2D) Plasmakristallen: Die Modenkopplungsinstabilität (MCI), induziert durch die wakevermittelte Wechselwirkung der Staubteilchen. Durch das Einbinden des Formalismus einer linearen Plasmarückantwort (zur eigenständig kohärenten Beschreibung der Teilchenwechselwirkung) wird die bisherige Theorie erweitert. Ich verwende dazu die Ergebnisse des ersten Aufsatzes für subthermale und suprathermale Ionenströme. Ein Abbildungsverfahren setzt die eigenständig kohärenten Kopplungskoeffizienten und das effektive Dipolmoment der Wakes miteinander in Beziehung. Das Dipolmoment ist ein fundamentaler Parameter, welcher die Modenkopplung im üblicherweise verwendeten "Yukawa-Punktwake-Modell" charakterisiert. Ich wende das Abbildungsverfahren auf verfügbare experimentelle Daten an. Die resultierende Größenordnung des Dipolmoment zeigt in mehreren Fällen das Vorliegen starker Modenkopplung an. Diese wurde zuvor nie systematisch untersucht. Dieses Ergebnis motiviert die Untersuchungen der dritten Veröffentlichung: Ich studiere den Einfluss starker Staubteilchen-Wake-Wechselwirkungen auf Dispersion und Polarisation von Staubgittermoden in 2D-Plasmakristallen. Die starke Kopplung bewirkt eine "Anziehung" zwischen den Moden und macht ihre Polarisationen elliptisch. Bei Hybri- disierung rotieren die Hauptachsen der Lissajous-Ellipsen um 45° (bleiben aber weiterhin senkrecht zueinander). Um die Implikationen für Experimente aufzuzeigen, berechne ich die entsprechenden Teilchenbahnen und spektrale Dichten der longitudinalen und transversalen Moden. Beide Observablen offenbaren deutliche Spuren elliptischer Polarisation. Abschließend untersuche ich die Verschiebung der Hybridisierung bei starker Kopplung. Der Effekt ist signifikant: Das Einsetzen der Hybridisierung erfolgt bei Wellenzahlen welche merklich kleiner sind als die Grenze der Brillouin-Zone (wo die Hybridmode bei schwacher Kopplung zuerst auftritt).The present work is a cumulative thesis consisting of three refereed publications. It continues the diploma studies dealing with the self-consistent investigation of wake-mediated mode-coupling in plasma crystals. In the first paper, I investigate the ion-velocity distribution function (idf) of a weakly- ionized gas, subjected to a uniform electric field and ion-neutral charge-exchange collisions. The "reference" idf, based on the energy-dependent cross-section for argon, is calculated by Monte-Carlo (MC) simulations. I consider several analytical models (based on either constant cross-section or constant collision-frequency) and compare them with each other and to MC results. It is demonstrated that none of available models applies to the experimentally often relevant situation of slightly suprathermal ion-flow. Assuming constant cross-section and separability of idf, followed by subsequent application of Maxwellian- averaging, the integro-differential Boltzmann equation is reduced to a simple differential equation. Evidently, its solution reproduces the reference idf with good accuracy for arbitrary value of field strength. These studies are of fundamental importance for a variety of problems in complex plasmas - among them the charging of dust grains, the formation of wake fields and non-Hamiltonian dynamics. The second paper deals with the primary example of non-Hamiltonian dynamics in two-dimensional (2D) plasma crystals: The mode-coupling instability (MCI), induced by the wake-mediated interactions between grains. The corresponding theory is extended by using the linear-response formalism for the self-consistent description of particle interactions. In this approach, I employ the results from the first paper for subthermal and suprathermal regimes of ion flow. A mapping procedure relates the self-consistent coupling coefficients to the effective wake dipole moment - the parameter essentially characterizing the mode coupling in the framework of conventionally used Yukawa/point-wake model. I apply the mapping to several available experiments and compare theoretically obtained dipole moments with experimental data. In several cases, the resulting magnitude of dipole moment indicates strong mode-coupling, which was never systematically studied. In the third publication, I investigate the effects of strong grain-wake interactions on dispersion and polarization of dust-lattice wave modes in 2D plasma crystals. Strong coupling causes an "attraction effect" between the modes, making their polarizations elliptical. Upon hybridization, the Lissajous ellipses major axes rotate by 45° (but remain mutually orthogonal). I show the implications for experiments by calculating representative particle trajectories and spectral densities of longitudinal and transverse waves. Both these observables reveal the distinct fingerprints of elliptical polarization. Furthermore, I investigate the shift of the hybrid mode at strong coupling. The effect is found to be significant: The hybridization onset is at wave numbers which are notably smaller than the border of the first Brillouin zone (where the onset takes place in the regime of weak coupling)

Mode-coupling regimes in 2D plasma crystals

Diese Arbeit ist eine kumulative Dissertation und besteht aus drei Aufsätzen. Sie setzt die Studien der Diplomarbeit zur eigenständig kohärenten Beschreibung der wakevermittelten Modenkopplung in Plasmakristallen fort. Der erste Aufsatz untersucht die Ionengeschwindigkeitsverteilung (idf) in einem schwach-ionisierten Gas, welches einem homogenen elektrischen Feld ausgesetzt ist und in dem Ladungsaustauschkollisionen der dominante Stoßtyp sind. Die Untersuchung geht dabei nur von elementaren Grundprinzipien aus und ist somit eigenständig kohärent. Die "Referenzverteilung" wird mittels einer Monte-Carlo-Simulation (MC-Simulation) am Beispiel des energieabhängigen Wirkungsquerschnitts für Argon berechnet. Ich nutze mehrere analytische Modelle (basierend auf einem konstanten Wirkungsquerschnitt oder konstanter Stoßfrequenz) und vergleiche die entsprechenden idfs untereinander, sowie mit der Referenzlösung. Es zeigt sich, dass kein Modell für den experimentell häufig wichtigen Fall eines schwach suprathermalen Ionenstroms mit befriedigender Genauigkeit anwendbar ist. Einen konstanten Wirkungsquerschnitt und Separabilität der idf annehmend, sowie darauf folgende Maxwell-gewichtete Mittelung, reduziert die integro-differentielle Boltzmanngleichung zu einer gewöhnlichen Differentialgleichung. Ich zeige, dass ihre Lösung die Resultate der MC-Simulation, für beliebige Stärke des Ionenstroms, mit großer Genauigkeit reproduziert. Das gewonnene Modell lässt sich auf eine Vielzahl von Problemen im Bereich der komplexen Plasmen anwenden - darunter der Ladungsvorgang der Staubteilchen, die Bildung von Wakefeldern und nicht-Hamiltonische Dynamik. Im zweiten Aufsatz behandle ich das vorrangige Beispiel eines nicht-Hamiltonischen Prozesses in zweidimensionalen (2D) Plasmakristallen: Die Modenkopplungsinstabilität (MCI), induziert durch die wakevermittelte Wechselwirkung der Staubteilchen. Durch das Einbinden des Formalismus einer linearen Plasmarückantwort (zur eigenständig kohärenten Beschreibung der Teilchenwechselwirkung) wird die bisherige Theorie erweitert. Ich verwende dazu die Ergebnisse des ersten Aufsatzes für subthermale und suprathermale Ionenströme. Ein Abbildungsverfahren setzt die eigenständig kohärenten Kopplungskoeffizienten und das effektive Dipolmoment der Wakes miteinander in Beziehung. Das Dipolmoment ist ein fundamentaler Parameter, welcher die Modenkopplung im üblicherweise verwendeten "Yukawa-Punktwake-Modell" charakterisiert. Ich wende das Abbildungsverfahren auf verfügbare experimentelle Daten an. Die resultierende Größenordnung des Dipolmoment zeigt in mehreren Fällen das Vorliegen starker Modenkopplung an. Diese wurde zuvor nie systematisch untersucht. Dieses Ergebnis motiviert die Untersuchungen der dritten Veröffentlichung: Ich studiere den Einfluss starker Staubteilchen-Wake-Wechselwirkungen auf Dispersion und Polarisation von Staubgittermoden in 2D-Plasmakristallen. Die starke Kopplung bewirkt eine "Anziehung" zwischen den Moden und macht ihre Polarisationen elliptisch. Bei Hybri- disierung rotieren die Hauptachsen der Lissajous-Ellipsen um 45° (bleiben aber weiterhin senkrecht zueinander). Um die Implikationen für Experimente aufzuzeigen, berechne ich die entsprechenden Teilchenbahnen und spektrale Dichten der longitudinalen und transversalen Moden. Beide Observablen offenbaren deutliche Spuren elliptischer Polarisation. Abschließend untersuche ich die Verschiebung der Hybridisierung bei starker Kopplung. Der Effekt ist signifikant: Das Einsetzen der Hybridisierung erfolgt bei Wellenzahlen welche merklich kleiner sind als die Grenze der Brillouin-Zone (wo die Hybridmode bei schwacher Kopplung zuerst auftritt).The present work is a cumulative thesis consisting of three refereed publications. It continues the diploma studies dealing with the self-consistent investigation of wake-mediated mode-coupling in plasma crystals. In the first paper, I investigate the ion-velocity distribution function (idf) of a weakly- ionized gas, subjected to a uniform electric field and ion-neutral charge-exchange collisions. The "reference" idf, based on the energy-dependent cross-section for argon, is calculated by Monte-Carlo (MC) simulations. I consider several analytical models (based on either constant cross-section or constant collision-frequency) and compare them with each other and to MC results. It is demonstrated that none of available models applies to the experimentally often relevant situation of slightly suprathermal ion-flow. Assuming constant cross-section and separability of idf, followed by subsequent application of Maxwellian- averaging, the integro-differential Boltzmann equation is reduced to a simple differential equation. Evidently, its solution reproduces the reference idf with good accuracy for arbitrary value of field strength. These studies are of fundamental importance for a variety of problems in complex plasmas - among them the charging of dust grains, the formation of wake fields and non-Hamiltonian dynamics. The second paper deals with the primary example of non-Hamiltonian dynamics in two-dimensional (2D) plasma crystals: The mode-coupling instability (MCI), induced by the wake-mediated interactions between grains. The corresponding theory is extended by using the linear-response formalism for the self-consistent description of particle interactions. In this approach, I employ the results from the first paper for subthermal and suprathermal regimes of ion flow. A mapping procedure relates the self-consistent coupling coefficients to the effective wake dipole moment - the parameter essentially characterizing the mode coupling in the framework of conventionally used Yukawa/point-wake model. I apply the mapping to several available experiments and compare theoretically obtained dipole moments with experimental data. In several cases, the resulting magnitude of dipole moment indicates strong mode-coupling, which was never systematically studied. In the third publication, I investigate the effects of strong grain-wake interactions on dispersion and polarization of dust-lattice wave modes in 2D plasma crystals. Strong coupling causes an "attraction effect" between the modes, making their polarizations elliptical. Upon hybridization, the Lissajous ellipses major axes rotate by 45° (but remain mutually orthogonal). I show the implications for experiments by calculating representative particle trajectories and spectral densities of longitudinal and transverse waves. Both these observables reveal the distinct fingerprints of elliptical polarization. Furthermore, I investigate the shift of the hybrid mode at strong coupling. The effect is found to be significant: The hybridization onset is at wave numbers which are notably smaller than the border of the first Brillouin zone (where the onset takes place in the regime of weak coupling)

Nonlinear regime of the mode-coupling instability in 2D plasma crystals

The transition between linear and nonlinear regimes of the mode-coupling instability (MCI) operating in a monolayer plasma crystal is studied. The mode coupling is triggered at the centre of the crystal and a melting front is formed, which travels through the crystal. At the nonlinear stage, the mode coupling results in synchronisation of the particle motion and the kinetic temperature of the particles grows exponentially. After melting of the crystalline structure, the mean kinetic energy of the particles continued to grow further, preventing recrystallisation of the melted phase. The effect could not be reproduced in simulations employing a simple point-like wake model. This shows that at the nonlinear stage of the MCI a heating mechanism is working which was not considered so far.Comment: 6 pages, 4 figure

Search for the standard model Higgs boson in the H to ZZ to 2l 2nu channel in pp collisions at sqrt(s) = 7 TeV

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Search for a W' boson decaying to a bottom quark and a top quark in pp collisions at sqrt(s) = 7 TeV

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Measurement of the t t-bar production cross section in the dilepton channel in pp collisions at sqrt(s) = 7 TeV

The t t-bar production cross section (sigma[t t-bar]) is measured in proton-proton collisions at sqrt(s) = 7 TeV in data collected by the CMS experiment, corresponding to an integrated luminosity of 2.3 inverse femtobarns. The measurement is performed in events with two leptons (electrons or muons) in the final state, at least two jets identified as jets originating from b quarks, and the presence of an imbalance in transverse momentum. The measured value of sigma[t t-bar] for a top-quark mass of 172.5 GeV is 161.9 +/- 2.5 (stat.) +5.1/-5.0 (syst.) +/- 3.6(lumi.) pb, consistent with the prediction of the standard model.Comment: Replaced with published version. Included journal reference and DO

Search for the standard model Higgs boson decaying into two photons in pp collisions at sqrt(s)=7 TeV

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Search for anomalous t t-bar production in the highly-boosted all-hadronic final state

A search is presented for a massive particle, generically referred to as a Z', decaying into a t t-bar pair. The search focuses on Z' resonances that are sufficiently massive to produce highly Lorentz-boosted top quarks, which yield collimated decay products that are partially or fully merged into single jets. The analysis uses new methods to analyze jet substructure, providing suppression of the non-top multijet backgrounds. The analysis is based on a data sample of proton-proton collisions at a center-of-mass energy of 7 TeV, corresponding to an integrated luminosity of 5 inverse femtobarns. Upper limits in the range of 1 pb are set on the product of the production cross section and branching fraction for a topcolor Z' modeled for several widths, as well as for a Randall--Sundrum Kaluza--Klein gluon. In addition, the results constrain any enhancement in t t-bar production beyond expectations of the standard model for t t-bar invariant masses larger than 1 TeV.Comment: Submitted to the Journal of High Energy Physics; this version includes a minor typo correction that will be submitted as an erratu