It is possible to associate a topological space to the category of modules over any ring. This space, the Ziegler spectrum, is based on the indecomposable pure-injective modules. Although the Ziegler ...spectrum arose within the model theory of modules and plays a central role in that subject, this book concentrates specifically on its algebraic aspects and uses. The central aim is to understand modules and the categories they form through associated structures and dimensions, which reflect the complexity of these, and similar, categories. The structures and dimensions considered arise particularly through the application of model-theoretic and functor-category ideas and methods. Purity and associated notions are central, localisation is an ever-present theme and various types of spectrum play organising roles. This book presents a unified, coherent account of material which is often presented from very different viewpoints and clarifies the relationships between these various approaches.
An intense positron sources is a demanding element in the design of future lepton colliders. A crystal-based hybrid positron source could be an alternative to a more conventional scheme based on the ...electron conversion into positron in a thick amorphous target. The conceptual idea of the hybrid source is to have two separate objects, a photon radiator and a photon-to-positron converter target. In such a scheme an electron beam crosses a thin axially oriented crystal with the emission of a channeling radiation, characterized by a considerably larger amount of photons if compared to Bremsstrahlung. The net result is an increase in the number of produced positrons at the converter target. In this paper we present the results of a beam test conducted at the DESY TB 21 with 5.6 GeV electron beam and a crystalline tungsten radiator. Experimental data clearly highlight an increased production of photons and they are critically compared with the outcomes of novel method to simulate the number of radiated photons, showing a very good agreement. Strong of this, the developed simulation tool has been exploited to design a simple scheme for a positron source based on oriented crystal, demonstrating the advantages in terms of reduction of both deposited energy and the peak energy deposition density if compared to conventional sources. The presented work opens the way for a realistic and detailed design of a hybrid crystal-based positron source for future lepton colliders.
We report on the measurements of the spectra of gamma radiation generated by 855 MeV electrons in bent silicon and germanium crystals at MAMI (MAinzer MIkrotron). The crystals were 15
μ
m
thick ...along the beam direction to ensure high deflection efficiency. Their (111) crystalline planes were bent by means of a piezo-actuated mechanical holder, which allowed to remotely change the crystal curvature. In such a way it was possible to investigate the radiation emitted under planar channeling and volume reflection as a function of the curvature of the crystalline planes. We showed that, using volume reflection, intense gamma radiation can be produced – with intensity comparable to that obtained in channeling but with higher angular acceptance. We studied the trade-off between radiation intensity and angular acceptance at different values of the crystal curvature. The measurements of radiation spectra have been carried out for the first time in bent germanium crystals. In particular, the intensity of radiation in the germanium crystal is higher than in the silicon one due to the higher atomic number, which is important for the development of the X-ray and gamma radiation sources based on higher-Z deformed crystals, such as crystalline undulators.
Systematic measurements of the annihilation cross sections of low energy antinucleons were performed at CERN in the 80's and 90's. However the antiproton data on medium-heavy and heavy nuclear ...targets are scarce. The ASACUSA Collaboration at CERN has measured the antiproton annihilation cross section on carbon at 5.3 MeV: the value is (1.73 ± 0.25) barn. The result is compared with the antineutron experimental data and with the theoretical previsions.
We have observed a significant enhancement in the energy deposition by 25–
100
GeV
photons in a
1
cm
thick tungsten crystal oriented along its
⟨
111
⟩
lattice axes. At
100
GeV
, this enhancement, ...with respect to the value observed without axial alignment, is more than twofold. This effect, together with the measured huge increase in secondary particle generation is ascribed to the acceleration of the electromagnetic shower development by the strong axial electric field. The experimental results have been critically compared with a newly developed Monte Carlo adapted for use with crystals of multi-
X
0
thickness. The results presented in this paper may prove to be of significant interest for the development of high-performance photon absorbers and highly compact electromagnetic calorimeters and beam dumps for use at the energy and intensity frontiers.
We report the observation of the steering of 855 MeV electrons by bent silicon and germanium crystals at the MAinzer MIkrotron. Crystals with 15
μ
m of length, bent along (111) planes, were exploited ...to investigate orientational coherent effects. By using a piezo-actuated mechanical holder, which allowed to remotely change the crystal curvature, it was possible to study the steering capability of planar channeling and volume reflection vs. the curvature radius and the atomic number, Z. For silicon, the channeling efficiency exceeds 35%, a record for negatively charged particles. This was possible due to the realization of a crystal with a thickness of the order of the dechanneling length. On the other hand, for germanium the efficiency is slightly below 10% due to the stronger contribution of multiple scattering for a higher-Z material. Nevertheless this is the first evidence of negative beam steering by planar channeling in a Ge crystal. Having determined for the first time the dechanneling length, one may design a Ge crystal based on such knowledge providing nearly the same channeling efficiency of silicon. The presented results are relevant for crystal-based beam manipulation as well as for the generation of e.m. radiation in bent and periodically bent crystals.
We observed reduction of multiple Coulomb scattering of 855 MeV electrons within a Si crystalline plate w.r.t. an amorphous plate with the same mass thickness. The reduction owed to complete or ...partial suppression of the coherent part of multiple scattering in a crystal vs crystal orientation with the beam. Experimental data were collected at Mainz Mikrotron and critically compared to theoretical predictions and Monte Carlo simulations. Our results highlighted maximal 7% reduction of the r.m.s. scattering angle at certain beam alignment with the 100 crystal axes. However, partial reduction was recorded over a wide range of alignment of the electron beam with the crystal up to 15
∘
. This evidence may be relevant to refine the modelling of multiple scattering in crystals for currently used software, which is interesting for detectors in nuclear, medical, high energy physics.
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