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A new technique for precision ion implantation has been developed. A scanning probe has been equipped with a small aperture and incorporated into an ion beamline, so that ions can be implanted through the aperture into a sample. By using a scanning probe the target can be imaged in a non-destructive way prior to implantation and the probe together with the aperture can be placed at the desired location with nanometer precision. In this work first results of a scanning probe integrated into an ion beamline are presented. A placement resolution of about 120 nm is reported. The final placement accuracy is determined by the size of the aperture hole and by the straggle of the implanted ion inside the target material. The limits of this technology are expected to be set by the latter, which is of the order of 10 nm for low energy ions. This research has been carried out in the context of a larger program concerned with the development of quantum computer test structures. For that the placement accuracy needs to be increased and a detector for single ion detection has to be integrated into the setup. Both issues are discussed in this thesis. To achieve single ion detection highly charged ions are used for the implantation, as in addition to their kinetic energy they also deposit their potential energy in the target material, therefore making detection easier. A special ion source for producing these highly charged ions was used and their creation and interactions with solids of are discussed in detail.
In the present work we applied the Optically read out PArticle track Chamber, OPAC, for the measurement of radial dose distributions, d(r), around tracks of heavy ions passing through the gas-filled sensitive volume of the chamber. The measured data were compared with d(r) functions derived from data calculated with the Monte Carlo particle transport code, TRAX – which is used for the heavy ion therapy planning at GSI. To measure this quantity we have used here an optically read out time projection chamber (OPAC) with a parallel-drift field and one or several electron and light amplification stages. The two dimensional projection of the three dimensional ionization pattern caused by the ionizing particle passing through the chamber is captured by an image intensified CCD camera. The work is motivated by the role the radial dose distribution plays in the estimation of the relative biological effectiveness (RBE) of heavy ions, e.g. in radiation therapy and in radiation protection. The most successful model for high-dose irradiation with ions (applicable e.g. for heavy ion therapy) is found to be the local effect model (LEM). The present work intends to deliver measured data for one of the basic physical parameters which serve as input for the application of the local effect model: the radial dose distribution, d(r). The first goal of our measurement program was the measurement of d(r) distributions around carbon ions of different energies from 400 MeV/u down to the Bragg peak regions. We found an excellent agreement between the measured and simulated distributions at all carbon energies for the r–range in which the measurements deliver useful results. The lower limit of this range is about 100 nm and the upper limit is 6000 nm at a resolution of down to 33 nm - if scaled to water density. Despite the simplifications in the TRAX code (e.g. binary encounter theory for the emission ionization electrons), the discrepancies between the simulated and measured d(r) distributions are found to be lower than the measurement uncertainties at most measured carbon ion energies in almost the whole observed r-range. Hence, within the limitations of our measurements we can conclude that the precision of TRAX is sufficient to simulate the d(r) distributions around carbon ions to serve as input parameter for therapy planning. However, this conclusion is only valid for larger radial distances (r >100 nm). For smaller radial distances the measured data are dominated by the diffusion. Apart from carbon ion tracks, tracks of very heavy ions (40Ar, 84Kr and 238U) were also measured with OPAC. The simulated d(r) values were typically slightly or significantly higher than the measured data in the 100 nm < r < 5000 nm region. The experience has shown: the heavier or the faster the ion, the higher the discrepancies. On the one hand, we found a surprisingly good agreement between measurements and simulations if the ions had energies of around 50 MeV/u (i.e. relatively low energy). On the other hand, at higher energies, simulated data underestimate the measured ones by up to a factor of two in the region of 100 nm < r < 1000 nm for 84Kr (E = 650 MeV/u) or in the region of 100 nm < r < 6000 nm for 238U (E = 1 GeV/u). A possible reason for these discrepancies is that the BEA model, used in TRAX for the production ionization electrons, is not adequate for very heavy projectiles. The energy values of the very heavy ions were selected with the aim of comparing the track structures - and namely the d(r) distributions - of ions with largely different atomic mass but similar LET values. From the Z-dependency of the stopping power we know that for heavier ions a higher specific ion energy (expressed in MeV/u) is required to provide the same LET. For example the common LET of 315 keV/micro-m was achieved at largely different specific energy levels of 4,4 MeV/u for 12C, 65 MeV/u for 40Ar and 650 MeV/u for 84Kr ions. The difference in the track structures was expected mainly due to the different ion velocities and thus e.g. different ranges of d-electrons. This expectation could be confirmed by the measurements. The reason why - in line with the simulations - no strong differences could be observed in the d(r) distributions of the argon and krypton ions is the relatively small difference in the velocities of the both ion types in conjunction with the limited range in r, where the data can be compared. In contrary, the d(r) function of the carbon ion shows a qualitatively different behavior than the heavier ions inside the observable radius-range - in agreement with the simulations.
In this thesis, I study the phase diagram of dense, locally neutral three-flavor quark matter as a function of the strange quark mass, the quark chemical potential, and the temperature, employing a general nine-parameter ansatz for the gap matrix. At zero temperature and small values of the strange quark mass, the ground state of quark matter corresponds to the color–flavor-locked (CFL) phase. At some critical value of the strange quark mass, this is replaced by the recently proposed gapless CFL (gCFL) phase. I also find several other phases, for instance, a metallic CFL (mCFL) phase, a so-called uSC phase where all colors of up quarks are paired, as well as the standard two-flavor color-superconducting (2SC) phase and the gapless 2SC (g2SC) phase. I also study the phase diagram of dense, locally neutral three-flavor quark matter within the framework of a Nambu–Jona-Lasinio (NJL) model. In the analysis, dynamically generated quark masses are taken into account self-consistently. The phase diagram in the plane of temperature and quark chemical potential is presented. The results for two qualitatively different regimes, intermediate and strong diquark coupling strength, are presented. It is shown that the role of gapless phases diminishes with increasing diquark coupling strength. In addition, I study the effect of neutrino trapping on the phase diagram of dense, locally neutral three-flavor quark matter within the same NJL model. The phase diagrams in the plane of temperature and quark chemical potential, as well as in the plane of temperature and leptonnumber chemical potential are presented. I show that neutrino trapping favors two-flavor color superconductivity and disfavors the color–flavor-locked phase at intermediate densities of matter. At the same time, the location of the critical line separating the two-flavor color-superconducting phase and the normal phase of quark matter is little affected by the presence of neutrinos. The implications of these results for the evolution of protoneutron stars are briefly discussed.
For this thesis photon and pi0 spectra in Gold-Gold-collisions at an energy of sqrt(s_NN) = 62 GeV were measured using the STAR-experiment at RHIC. Heavy ion collisions allow to study strongly interacting matter under extreme condiditons in the laborartory. Nuclear matter is strongly compressed and heated. Theories predict in a system of strongy interacting matter at high temperature and pressure a phase transition from hadronic matter, in which quarks are bound into hadrons, to a plasma of free quarks and gluons (QGP). To study the properties of this created medium, a number of different observables is available. One possibility to determine the temperature of such a system, is to measure the photon emission from the medium. The experimental difficulty is that there are more mechanisms producing photons than just the thermal production. Photons are produced in hard scattering processes or can be the result of the interaction of hard partons with the medium. According to theoretical calculations the photon yield from hard processes exceeds the thermal production for transverse momenta above 3 GeV/c. Photons from hard processes and thermal photons are referred to as direct photons, because they are produced inside of the medium. The largest part of the photons below pt=3GeV/c, however, comes from electromagnetic decays of hadrons in the final state of the collision. The largest fraction comes from the pi0- and the eta-mesons. Their contribution to the photon spectra can be determined by measuring the spectra of these decaying particles and calculating the resulting, corresponding photon spectra. The experimental difficulty is to measure these spectra to an accuracy of a few percent because the decay photons make up about 90% of all photons in the relevant phase space region. The STAR-experiment provides different detectors to measure photons and pi0-mesons. The primary detector for this kind of measurement are the electromagnetic calorimeters. However, the analysis described in this thesis uses the time projection chamber (TPC). Because photons don't carry electric charge and the TPC is only sensitive to charged particles, a conversion of the photon into an electron-positron-pair is required. This happens inside the electromagnetic fields of the nuclei and the electrons in the atomic shell of the detector material in the experimental setup of STAR. The resulting electron and positron tracks are measrued in the TPC. In chapter 3 the reconstruction of conversions from the measured tracks is described. Chapter 4 discusses the efficiency of the measurement, which is determined with a Monte-Carlo-Method, and the uncertainties of the correction. Chapter 5 presents the results of the analysis. The data set, on which the analysis is based, consists of Gold-Gold-Collisions an a center of mass energy of sqrt(s_NN)=62GeV. The selection criteria for individual events during data taking and during the analysis are explained. The data set is divided into four centrality selection classes. The first result are the transverse momentum and rapidity spectra of inclusive photons for all four centralities and the whole data set. Pi0-spectra versus transverse momentum for the four centralities and the whole data set are also shown. The pi0-spectra are compared to the spectra of pi0-mesons measured by the PHENIX-Collaboration at the same energy and with pi0-spectra measured by STAR at full RHIC energy. In addition a comparison to charged pi+- and pi--spectra is shown, which were also measured by the STAR collaboration. It is attempted to extract the fraction of direct photons by dividing the spectra of inclusive photons by the spectra of simulated decay photons. In these simulations pi0- and eta-spectra are modeled based on the pi+- and pi--spectra. Studying the uncertainties of this procedure shows that the size of the uncertainties is of the same magnitude as the signal of direct photons. Also the systematic uncertainties of the pi+- and pi--spectra are similar. Therefore the measurement of direct photon spectra is not possible. In chapter 6 possibilities are described to reduce the large systematic uncertainties. In addition it is discussed, what could be done with an already existing data set at full RHIC energy and how the addition of a dedicated converter during a future data taking period could reduce the systematic errors. The result of this thesis are inklusive photon and pi0 spectra. The systematic uncertainties were extensively studied. It is described, which enhancements are necessary to provide the perspective for measuring direct photons in the area of 1 to 3 GeV/c transverse momentum.
Nuclear matter, that takes the form of protons and neutrons under normal conditions, is subject to a phase transition at high temperatures and densities, liberating the quarks and gluons that are usually confined in nucleons and creating a medium of free partons: the Quark-Gluon-Plasma. It is generally believed that this state of matter can be created in relativistic collisions of heavy nuclei. The study of the medium created in these collisions is the subject of heavy-ion physics. One topic within this field are particles with high transverse momentum, that are created in initial hard collisions between partons of the incoming nuclei. The energetic partons lose energy due to interactions with the medium before they fragment into a jet of hadrons. Due to momentum conservation, these jets are usually created as back-to-back pairs, or less commonly as three-jet or photon-jet events, where a single jet is balanced by a hard photon. The energy loss can be measured using correlations between particles with high transverse momenta. A trigger particle is selected with very high transversemomentum and the distribution of the azimuthal angle of associated particles in the same event is studied, relative to the azimuth of the trigger particle.These azimuthal correlations show a peak for opening angles around 0 from particles selected from the same jet, and a second peak at opening angles around 180 degrees from back-to-back di-jets. Random combinations with the underlying event generate a flat background, extending over the full range of opening angles. The STAR experiment observed a modification of these correlations in central Au+Au collisions, where trigger particles with 4GeV < pT(trigger) < 6GeV and associated particles with 2GeV < pT(trigger) < 4GeV were selected. A strong suppression has been observed for away-side correlations in central Au+Au collisions, relative to p+p, d+Au and peripheral Au+Au data. This can be explained by assuming two partons going in opposite directions, where at least one has to travel a large distance through the medium, causing energy loss and effectively removing the event from the analysis. For near-side correlations, no significant modification has been observed, which can be explained by surface emission, assuming that the observed jets have travelled only a short distance in themedium, not leaving enough time for interactions with the medium. Both trigger- and associated particles in a correlation analysis with charged hadrons are subject to modifications due to the medium. This can be avoided by using photon-jet events instead of di-jets, because the photon does not interact with the medium and therefore provides the best available measure of the properties of the opposite jet in the presence of the underlying event. This thesis studies azimuthal correlations between regions of high energy deposition in the electro-magnetic calorimeter as trigger- and charged tracks as associated particles. The data sample had been enriched by online event selection, allowing for the selection of trigger particles with a transverse energy of more than 10GeV and associated particles with more than 2,3 or 4 GeV. The away-side yield per trigger particle is strongly suppressed like in correlations between charged particles. The near-side yield is also reduced by about a factor two, clearly different from charged correlations. The trigger particles are a mixture of photon pairs from the decays of neutral pions and single photons, mainly from photon-jet events, with small contributions from other hadron decays and fragmentation photons. Pythia simulations predict a ratio of neutral pions to prompt photons of 3.5:1 in p+p collisions with the same cuts as in the presented analysis. Single particle suppression further reduces this ratio in central Au_Au collisions, down to about 0.8:1, indicating that the majority of trigger particles in central Au+Au collisions are prompt photons. The increasing fraction of prompt photon triggers without an accompanying jet and therefore zero associated yield reduces the average yield per trigger particle. The magnitude of the observed effect agrees well with the expectation from Pythia simulations and the assumption of a single particle suppression by a factor 4-5. An analysis of away-side correlations is more difficult, because both photon-jet and di-jet events contribute. The aim is the separation of these two contributions. As a clear separation is not possible with the available dataset, a comparison with two different scenarios is given, where a surprisingly small suppression by only a factor of about 5 is favoured for both dijet- and photon-jet-correlations. A separate measurement of both contributions will be possible by a shower-shape analysis with the EM calorimeter or a comparison with charged correlations in the same kinematic region.
This work gives a detailed introduction into a fully new experimental method to investigate the quantum crystal behavior of solid Helium-4. It has been found that a fascinating new effect occurs in the expansion of solid Helium-4 into a vacuum through pinhole orifices with diameters between 1 and 5 µm. It is observed that the beam flux intensity shows a periodic behavior for source conditions corresponding to the solid phase of Helium-4. The period is in the range of seconds up to minutes. It shows a strong dependence on temperature and source pressure. The oscillating part of the beam flux intensity amounts several percent of the total flux. This new phenomenon has been studied for temperatures between 2.1 K and 1.3 K and pressures up to 30 bar above the melting pressure. The beam flux intensity has been recorded by the vacuum pressure in a pitot vacuum chamber. The jet velocity in the range of 200 m/sec indicates that surprisingly the beam is a liquid jet, whereas the conditions in the source correspond to the solid state. In this work mainly the behavior of the flux modulation has been studied as a function of pressure and temperature and the influence of the isotope Helium-3. Furthermore geometrical aspects such as the influence of the nozzle diameter d0 have been investigated. In order to explain this novel phenomenon a kinetic model based on the injection of excess vacancies into the solid is proposed. According to this model the vacancies are generated at a solid/liquid interface. Forced by drift and diffusion they accumulate at some distance from the orifice, leading to the collapse of the solid. With the subsequent re-injection of vacancies the effect repeats and turns out to be periodical. The reproducibility of the time dependent beam flux intensity is demonstrated for a wide range of temperatures and pressures and gives direct access to values such as the temperature and pressure dependence of the vacancy diffusion coefficient Dv in the range of 10 high -5 cm high 2/sec, the recombination time of vacancies with interstitials T r near 1-20 sec and the vacancy activation energy f near 20 K. The good agreement with former experimental results by Zuev et al. [131] confirms the applicability of the theoretical model. As a result from the kinetic model the vacancy concentration is increased above the equilibrium vacancy concentration, caused by the injection of excess vacancies. Therefore, the most important discovery is the possibility of generating a non-equilibrium quantum solid. The investigation of this non-equilibrium solid leads to the discovery of a fluid-like regime in the solid phase of Helium-4 at temperatures below T = 1.58 K. The result gives a strong indication for the supersolid state, especially because the fluid-like behavior of the solid can be eliminated with smallest concentrations of Helium-3.
Studies and measurements of linear coupling and nonlinearities in hadron circular accelerators
(2006)
In this thesis a beam-based method has been developed to measure the strength and the polarity of corrector magnets (skew quadrupoles and sextupoles) in circular accelerators. The algorithm is based on the harmonic analysis (via FFT) of beam position monitor (BPM) data taken turn by turn from an accelerator in operation. It has been shown that, from the differences of the spectral line amplitudes between two consecutive BPMs, both the strength and the polarity of non-linear elements placed in between can be measured. The method has been successfully tested using existing BPM data from the SPS of CERN, since presently the SIS-18 is not equipped with the necessary hardware. The magnet strength of seven SPS extraction sextupoles was measured with a precision of about 10%. The polarities have been unambiguously measured. This method can be used to detect polarity errors and wrong power supply connections during machine commissioning, as well as for a continuous monitoring of the "nonlinearity budget" in superconducting machines. A second beam-based method has been studied for a fast measurement and correction of betatron coupling driven by skew quadrupole field errors and tilted focusing quadrupoles. Traditional methods usually require a time-consuming scan of the corrector magnets in order to minimize the coupling stop band |C|. In this thesis it has been shown how the same correction can be performed in a single machine cycle from the harmonic analysis of multi-BPM data. The method has been successfully applied to RHIC. It has been shown that the stop band |C| (also known in the American literature as Delta-Qmin) measured in a single machine cycle with the new algorithm is compatible with the value obtained by traditional methods. The measurement of the resonance phase Theta defines automatically the best corrector setting, which was found in agreement with the one obtained with a traditional scan. A third theoretical achievement is a new description of the betatron motion close to the difference resonance in presence of linear coupling. Compared to the matrix formalism the motion is parametrized as a function of the resonance driving term f1001 only (which is proven to be an observable), whereas making use of the matrix approach four parameters need to be measured. Formulae describing the exchange of RMS emittances when approaching the resonances have been already derived in the 70s in the smooth approximation. New formulae have been derived here making use of Lie algebra providing a better description of the emittance behavior. The emittance exchange curves are predicted by new formulae with excellent agreement with multi-particle simulations and the counter-intuitive emittance variation along the ring of the emittance is proven to be related to the variation of f1001. A new way to decouple the equations of motion and explicit expressions for the individual single particle invariants have been found. For the first time emittance exchange studies have been carried out in the SIS-18 of GSI. Transverse RMS emittances have been measured during 2005 from rest gas monitor (RGM) data. Crossing the linear coupling resonance, the transverse emittances exchange completely. It has been observed that this effect is reversible. Applications of this manipulation are: emittance equilibration under consideration for future operations of the SIS-18 as booster for the SIS-100; emittance transfer during multi-turn injection to improve the eficiency and to protect the injection septum in high intensity operations, by shifting part of the horizontal emittance into the vertical plane. The emittance exchange curves obtained experimentally have been compared with analytic formulae providing a fast measurement (in few machine cycles only) of the linear coupling stop band |C|. Technical problems prevented the use of the eight skew quadrupoles installed in the SIS-18 to compensate the linear coupling resonance. It has been observed that the emittance exchange curve is highly sensitive to the beam intensity. Multi-particle simulations with 2D PIC space-charge solver have been run to infer heuristic scaling laws able to quantify the observable stop band, to be used for the resonance compensation. The analysis of BPM and RGM data has been performed making use of new software applications developed for this purpose. The bpm2rdt code for the harmonic analysis of BPM data has been written and tested with real data. The software reads the BPM turn-by-turn data and the Twiss parameters. Then it performs the FFT of these data, finds the peaks of the Fourier spectra and infers the RDT fjklm, the strengths ^hjklm and the local terms lambda-jklm. All these observables are printed out together with the corresponding values of the model, computed from the nominal values of strengths and the Twiss parameters. From the FFT of dual-plane BPM data the linear optics (beta functions and phase advances Delta phi) at the corresponding location is also inferred. From the measurement of f1000, the linear coupling coeffcient C (amplitude and phase) is also computed. The code has been tested by using existing SPS data and new RHIC data. For the on-line analysis of RGM data the rgm2emitt code has been written. The application reads in input the raw data files from the RGM and the beam loss monitor (BLM) respectively, the latter created by the RGM on-line software itself. From the RGM data the transverse beam sizes and emittances are inferred and used together with the BLM data to compute the tune shift during the machine cycle.
The focus of this thesis is on quantum Heisenberg magnets in low dimensions. We modify the method of spin-wave theory in order to address two distinct issues. In the first part we develop a variant of spin-wave theory for low-dimensional systems, where thermodynamic observables are calculated from the Gibbs free energy for fixed order parameter. We are able to go beyond linear spin-wave theory and systematically calculate two-loop correction to the free energy. We use our method to determine the low-temperature physics of Heisenberg ferromagnets in one, two and three spatial dimensions. In the second part of the thesis, we treat a two-dimensional Heisenberg antiferromagnet in the presence of a uniform external magnetic field. We determine the low-temperature behavior of the magnetization curve within spin-wave theory by taking the absence of the spontaneous staggered magnetization into account. Additionally, we perform quantum Monte Carlo simulations and subsequently show that numerical findings are qualitatively comparable to spin-wave results. Finally, we apply our method to an experimentally motivated case of the distorted honeycomb lattice in order to determine the strength of the exchange interactions.