Nonlinear sheath potential. The potential energy (in arbitrary units) of a dust particle, depending on its distance from the equilibrium height within the sheath. The usually assumed parabolic potential well (solid) is com pared to a nonlinear sheath, evaluated with the first (dashed) and first and second (dotted) anharmonic terms of the expansion of the potential energy, as determined by my measurements. . . . . . . . . . . . . . . . . . . . . .
Vertical Pairing. Particle configurations at 2 Pa: dependence of vertical sep aration between the particles on peak to peak voltage between the electrodes of the discharge chamber (left), and the corresponding spatial configuration (right). Open symbols are used for configurations that are not paired ver tically, and closed symbols for paired configurations, lines are used to guide the eye. The striped area in the left figure highlights forbidden configura tions, as particles would fall to the lower electrode for such low rf power. . Convergence of vertical and horizontal resonance frequencies: influence of the rf peak to peak voltage on the vertical and horizontal resonance fre quency of a single particle in the sheath of an rf discharge at 1Pa. The striped area highlights the minimum rf power necessary to levitate the par ticle in the sheath against gravity. . . . . . . . . . . . . . . . . . . . . . . .
A.1 Example for the scaling index method. (a) The point setX. (b) Spectra of scaling indices log(P(α(xi, aobtained at di)) + 1) fferent scalesagraph. The fora= 1.0 is emphesized, the vertical lines highlightα= 0.8 andα= 1.5 respectively. (c) Pointsxi∈Xwere colored by their scaling indices at scale a= 0.for1: red αi<0.8, green for 0.8≤αi<1.5, and blue for 1.5≤αi. . A.2 Illustration of linear and nonlinear effects. (a) The original time series x(t). (b) xa(t) derived from x(t(c) x) by randomizing the Fourier amplitudes. p(t) derived from x(t. . . . . . . . . . . .) by randomizing the Fourier phases. A.3 2D embedding using delay coordinates. (a) Original x(tx() plotted vs. t+dt). (b) Randomized Fourier amplitudes xa(t) vs. xa(t+dt). (c) Randomized Fourier phases xp(t) vs. xp(t+dtthree graphs use the same delay). All dt= 0.7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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A.4
Figures
Spectrum of scaling indices obtained from the delay coordinate represen tation. P(α) was calculated usingα2(x, aThe black curve shows= 1). the spectrum of the original data, the red curve represent the randomized Fourier amplitudes, and green the randomized Fourier phases. . . . . . . .
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Acknowledgments
Dear Greg, I would like especially to thank you for inviting me on this demanding, ad venturous and unique journey. When I came to MPE in 1998, complex plasmas had been freshly entitled colloidal plasmas by you, and the Plasmakristall group consisted of six people: Hubertus Thomas, Alexei Ivlev, Uwe Konopka, Dirk Goldbeck, Milenko Zuzic and me. From then on you managed to get thewho is whoof complex plasmas, plasma physics, plasmadiagnostics, engineering and application, and dusty plasmas in geosciences to collaborate with our group, join our group as postdocs or senior scientists, and to grow it into something that most people would consider a research institute. Thanks for this opportunity. Many thanks go to the MaxPlanckGesellschaft and the Institute for Extraterrestrial Physics who supported my PhD studies in many ways, and which provided a unique basic research environment for the emerging field of complex plasmas. To all my friends at work, all of you fellow scientists I am proud to share my time with, Id like to say, that this is the best time of my life. My work would not have been the same without your individual scientific prowess and your support and encouragement as colleagues. I believe that our complex plasma group is the best and most successful group in the world, because all of us tried hard to improve collectively our research, instead of improving our individual CVs. Hubertus, thanks for trusting in me, and involving me in the Plasma Crystal projects and not to forget the financial support. Last but not least I would like to thank my friends and family who might have suffered some collateral damage along the way, but never blaming me or holding a grudge against me, for bad tempers when I was stressed, overworked, or just not satisfied with my scientific success. I enjoy my life around you.