The S-DALINAC facility — Operational experience from the accelerator and the experimental installations

Auerhammer, J.; Genz, H.; Gräf, H.‐D.; Hahn, R. von; Hoffmann-Stascheck, P.; Lüttge, C.; Nething, U.; Rühl, K.; Richter, A.; Rietdorf, T.; Schardt, P.; Spamer, E.; Thomas, F.; Titze, O.; Töpper, J.; Weise, H.

doi:10.1016/0375-9474(93)90708-6

Cited by 22 publications

(5 citation statements)

References 4 publications

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“…Figure 1 shows some of the investigated cavities as well as their dimensions. First experiments using superconducting instead of normally conducting resonators were performed in a desymmetrized Bunimovich-stadium-billiard and a truncated hyperbola-billiard [4,20,21] using the 2K-cryostats of the superconducting electron linear accelerator S-DALINAC [22] in Darmstadt. Recently, a desymmetrized 3D-Sinai-billiard [23,24] was experimentally investigated in a new and very stable 4K-bathcryostat.…”

Section: Methodsmentioning

confidence: 99%

Correlation-hole method for the spectra of superconducting microwave billiards

et al. 1997

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The spectral fluctuation properties of various two-and three-dimensional superconducting billiard systems are investigated by employing the correlation-hole method. It rests on the sensitivity of the spectral Fourier transform to long-range correlations and is thus an alternative technique to study chaotic dynamics. First, we apply the method to the eigenfrequencies that are extracted from the measured resonances. Second, we analyze the unfolded raw spectra, including the shape of the resonances. The merit of the method lies in a clear separation of the statistics due to the positions and due to the shape of the resonances. However, we show that statistical fluctuations of the intensities of the resonances have a strong impact on the observable. Therefore, the visibility of the correlation hole is studied as a function of the number of independent statistical variables entering into the intensities. The visibility improves if independent spectra are superimposed.

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Section: Methodsmentioning

confidence: 99%

Correlation-hole method for the spectra of superconducting microwave billiards

et al. 1997

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“…The microwaves were transmitted into and out of the cavity by two small antennas in the lid. The whole resonator was cooled down in Helium-atmosphere at a temperature of 2K and a pressure of 38mbar in one of the cryostats of the superconducting Darmstadt electron linear accelerator S-DALINAC [28] together with the accelerating structures. With this setup we have measured microwave spectra in transmission (antenna 1 for input and antenna 2 for output) as well as in reflection (same antenna for excitation and detection) using a Hewlett Packard network analyzer (model HP8510B) in a frequency range between 0 and 20GHz, respectively.…”

Section: Methodsmentioning

confidence: 99%

Chaotic dynamics in a three-dimensional superconducting microwave billiard

et al. 1996

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We present first measurements on a superconducting three-dimensional, partly chaotic microwave billiard shaped like a small deformed cup. We analyze the statistical properties of the measured spectrum in terms of several methods originally derived for quantum systems like eigenvalue statistics and periodic orbits and obtain according to a model of Berry and Robnik a mixing parameter of about 25%. In numerical simulations of the classical motion in the cup the degree of chaoticity has been estimated. This leads to an invariant chaotic Liouville measure of about 45%. The difference between this figure and the mixing parameter is due to the limited accuracy of the statistical analysis, caused by both, the fairly small number of 286 resonances and the rather poor desymmetrization of the microwave cavity. Concerning the periodic orbits of the classical system we present a comparison with the length spectrum of the resonator and introduce a new bouncing ball formula for electromagnetic billiards.PACS number(s): 05.45.+b, 41.20.Bt, 84.40.Cb * Present address:

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“…Typical qualities of normally conducting cavities are in the range of 10 3 -10 4 (Stöckmann, 2006) and one can distinctly identify abut 1000 resonances through the smudging. The workaround to this unavoidable impediment eventually came from the cryostats of a linear accelerator at Darmstadt, the S-DALINAC (Auerhammer et al, 1993). Gräf et al (1992) discovered that a superconducting niobium billiard, immersed in a liquid He bath at 4 K, could yield Q ∼ 10 5 to even 10 7 -a remarkable thousandfold improvement upon the experiments of old!…”

Section: A Microwave Billiards: the Physicist's Pool Tablementioning

confidence: 99%

Nodal portraits of quantum billiards: Domains, lines, and statistics

Jain,

Samajdar

2017

Preprint

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We present a comprehensive review of the nodal domains and lines of quantum billiards, emphasizing a quantitative comparison of theoretical findings to experiments. The nodal statistics are shown to distinguish not only between regular and chaotic classical dynamics but also between different geometric shapes of the billiard system itself. We discuss, in particular, how a random superposition of plane waves can model chaotic eigenfunctions and highlight the connections of the complex morphology of the nodal lines thereof to percolation theory and Schramm-Loewner evolution. Various approaches to counting the nodal domains-using trace formulae, graph theory, and difference equations-are also illustrated with examples. The nodal patterns addressed pertain to waves on vibrating plates and membranes, acoustic and electromagnetic modes, wavefunctions of a "particle in a box" as well as to percolating clusters, and domains in ferromagnets, thus underlining the diversity-and far-reaching implications-of the problem. CONTENTS3. Periodic orbits of nonseparable, integrable billiards 48 C. Graph-theoretic analysis 49 D. Difference-equation formalism 50 1. Circles (and annuli/sectors thereof) 50 2. Ellipses and elliptic annuli 50 3. Confocal parabolae 51 4. Right-angled isosceles triangle 51 5. Equilateral triangle 51 E. Counting with Potts spins 52 VII. Experimental realizations 52 A. Microwave billiards: The physicist's pool table 52 B. The S-matrix and transmission measurements 54 C. The perturbing bead method 56 D. Current and vortex statistics 57 VIII. Concluding remarks 60 Acknowledgments 61 A. Isoperimetric inequalities 61 1. Rayleigh-Faber-Krahn and related inequalities 61 2. Payne-Pólya-Weinberger inequality 62 3. Szegö-Weinberger inequality 62 References 62

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The S-DALINAC facility — Operational experience from the accelerator and the experimental installations

Cited by 22 publications

References 4 publications

Correlation-hole method for the spectra of superconducting microwave billiards

Correlation-hole method for the spectra of superconducting microwave billiards

Chaotic dynamics in a three-dimensional superconducting microwave billiard

Nodal portraits of quantum billiards: Domains, lines, and statistics

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