The Vlasov technique is used to model the electron cooling force. Limitations of the applicability of the method is obtained by considering the perturbations of the electron plasma. Analytical expressions of the electron cooling force, valid beyond the Coulomb logarithm approximation, are derived and compared to numerical calculations using adaptive Monte Carlo integration. The calculated longitudinal cooling force is verified with measurements in CELSIUS. Transverse damping rates of betatron oscillations for a nonlinear cooling force is explored. Experimental data of the transverse monochromatic instability is used to determine the rms angular spread due to solenoid field imperfections in CELSIUS. The result, θrms= 0.16 ± 0.02 mrad, is in agreement with the longitudinal cooling force measurements. This verifies the internal consistency of the model and shows that the transverse and longitudinal cooling force components have different velocity dependences. Simulations of electron cooling with applications to HESR show that the momentum reso- lution ∆p/p smaller than 10−5 is feasible, as needed for the charmonium spectroscopy in the experimental program of PANDA. By deflecting the electron beam angle to make use of the monochromatic instability, a reasonable overlap between the circulating antiproton beam and the internal target can be maintained. The simulations also indicate that the cooling time is considerably shorter than expected.

No description available.

The topic of this thesis concerns the LHC, the next large particle accelerator at CERN which will start operating in 2007. Being based on superconductivity, the LHC needs to operate at very low temperatures, which makes great demands on the cryogenic system of the accelerator. To cope with the heat loads induced by the particle beam, a beam screen cooled with forced flow of supercritical helium is used. There is an interest in upgrading the energy and luminosity of the LHC in the future and this would require a higher heat load to be extracted by the beam screen cooling system. The objective of this thesis is to quantify different ways to upgrade this system by mainly studying the effects of different pressure and temperatures levels as well as a different cooling medium, neon. For this a numerical program which simulates one-dimensional pipe flow was constructed. The frictional forces were accounted for by the empirical concept of friction factor. For the fluid properties, software using empirically made correlations was used. To validate the numerical program, a comparison with previous experimental work was done. The agreement with experimental data was good for certain flow configurations, worse for others. From this it was concluded that further comparisons with experimental data must be made in order to tell the accuracy of the mathematical model and the correlations for fluid properties used. When using supercritical helium, thermo-hydraulic instabilities may arise in the cooling loop. It was of special interest to see how well a numerical program could simulate and predict this phenomenon. It was found that the numerical program did not function for such unstable conditions; in fact it was much more sensitive than what reality is. For the beam screen cooling system we conclude that to cope with the increased heat loads of future upgrades, an increase in pressure level is needed regardless if the coolant remains helium, or is changed to neon. Increasing the pressure level also makes that the problems with thermo-hydraulic instabilities can be avoided. Of the two coolants, helium gave the best heat extraction capacity. Unlike neon, it is also possible to keep the present temperature level when using helium.

The field of inverse problems is an area in applied mathematics that is of great importance in several scientific and industrial applications. Since an inverse problem is typically founded on non-linear and ill-posed models it is a very difficult problem to solve. To find a regularized solution it is crucial to have a priori information about the solution. Therefore, general theories are not sufficient considering new applications. In this thesis we consider the inverse problem to determine the beam bending stiffness from measurements of the transverse dynamic displacement. Of special interest is to localize parts with reduced bending stiffness. Driven by requirements in the wood-industry it is not enough considering time-efficient algorithms, the models must also be adapted to manage extremely short calculation times. For the developing of efficient methods inverse problems based on the fourth order Euler-Bernoulli beam equation and the second order string equation are studied. Important results are the transformation of a nonlinear regularization problem to a linear one and a convex procedure for finding parts with reduced bending stiffness.

Concrete is a very weak and brittle material in tension. It has been shown in previous researches that the addition of steel fibers to a concrete matrix can improve this behavior. The ability of fibers to control and redistribute stresses after cracking results in a number of improvements in the structural behaviour of concrete. A review of existing literature shows that the addition of steel fibers enhances concrete’s tensile resistance, crack control properties, ductility and damage tolerance. In beams, fibers can transform brittle shear response into a flexural response and promote ductility, thereby allowing for a full or partial replacement of traditional shear reinforcement. The enhanced shear capacity, ductility and damage tolerance of Steel Fiber Reinforced Concrete (SFRC) can also potentially be used to relax seismic detailing requirements in frames by partially replacing the required transverse reinforcement in the plastic hinge regions of RC beams. One of the drawbacks associated with SFRC is that the addition of steel fibers to a traditional concrete mix at high fiber contents can result in workability problems. The combined use of Self-Consolidating Concrete (SCC) and fibers can solve this problem and facilitate placement for a wider range of structural applications. Although several studies have been conducted on the behaviour of SFRC beams subjected to monotonic loading, there is limited research on the behaviour of SFRC beams under cyclic or reverse-cyclic loading. This thesis presents the results of an experimental and analytical study conducted on nine SFRC beam specimens tested under load reversals. The main objective of this research program was to investigate the effect of fibers on structural behaviour and to examine the ability of steel fibers to replace transverse reinforcement. The experimental and analytical results show that use of fibers results in several improvements in behaviour, including enhanced damage tolerance and post-peak ductility. The results also show that steel fibers can potentially be used to allow for a reduction of transverse reinforcement in beams, however further research is required.

CERN's Large Hadron Collider (LHC) is the largest machine ever built, with a total circumference of 26.7 km; and it is the most powerful accelerator ever, both in beam energy and beam intensity. The main magnets are superconducting, keeping the particles into two counter circulating beams, which collide in four interaction points. CERN and the LHC will be described in chap. 1. The superconducting magnets of the LHC have to be protected against particle losses. Depending on the number of lost particles, the coils of the magnets will become normal conducting and/or will be damaged. To avoid these events a beam loss monitoring (BLM) system was installed to measure the particle loss rates. If the predefined safe thresholds of loss rates are exceeded, the beams are directed out of the accelerator ring towards the beam dump. The detectors of the BLM system are mainly ionization chambers located outside of the cryostats. In total, about 3500 ionisation chambers are installed. Further challenges include the high dynamical range of losses (chamber currents ranging between 2 pA and 1 mA). The BLM system will be further described in chap. 2. The subject of this thesis is to study the loss patterns and find the origin of the losses in a deterministic way, by comparing measured losses to well understood loss scenarios. This is done through a case study: different techniques were used on a restrained set of loss scenarios, as a proof of concept of the possibility to extract information from a loss profile. Finding the origin of the losses should allow acting in response. A justification of the doctoral work will be given at the end of chap. 2. Then, this thesis will focus on the theoretical understanding and the implementation of the decomposition of a measured loss profile as a linear combination of the reference scenarios; and the evaluation of the error on the recomposition and its correctness. The principles of vector decomposition are developed in chap. 3. An ensemble of well controlled loss scenarios (such as vertical and horizontal blow-up of the beams or momentum offset during collimator loss maps) has been gathered, in order to allow the study and creation of reference vectors. To achieve the Vector Decomposition, linear algebra (matrix inversion) is used with the numeric algorithm for the Singular Value Decomposition. Additionally, a specific code for vector projection on a non-orthogonal basis of a hyperplane was developed. The implementation of the vector decomposition on the LHC data is described in chap. 4. After this, the use of the decomposition tools systematically on the time evolution of the losses will be described: first as a study of the variations second by second, then by comparison to a calculated default loss profile. The different ways to evaluate the variation are studied, and are presented in chap. 5. The next chapter (6) describes the gathering of decomposition results applied to beam losses of 2011. The vector decomposition is applied on every second of the ''stable beans'' periods, as a study of the spatial distribution of the loss. Several comparisons of the results given by the decompositions with measurements from other LHC instruments allowed different validations. Eventually, a global conclusion on the interest of the vector decomposition is given. Then, the extra chapter in Appendix A describes the code which was developed to access the BLM data, to represent them in a meaningful way, and to store them. This included connecting to different databases. The whole instrument uses ROOT objects to send SQL queries to the databases, as well as java API, and is coded in Python. A short glossary of the acronyms used here can be found at the end, before the bibliography.

Graduation date: 1993

Piezoelectric actuators (PEA) hold the most promise for precision positioning applications due to their capability of producing extremely small displacements down to 10 pm (1 pm = 10-12 m) as well as their high stiffness and force output. The piezoelectric-driven stick-slip (PDSS) actuator, working on the friction-inertia concept, has the capacity of accomplishing an unlimited range of motion. It also holds the promises of simple configuration and low cost. On the other hand, the PDSS actuator has a relatively low efficiency and low loading capability, which greatly limits its applications. The purpose of this research is to improve the performance of the PDSS actuators by employing specially-designed working surfaces.<p> The working surfaces, referred as anisotropic friction (AF) surfaces in this study, can provide different friction forces depending on the direction of relative motion of the two surfaces, and are used in this research to accomplish the aforementioned purpose. To fabricate such surfaces, two nanostructure technologies are employed: hot filament chemical vapour deposition (HFCVD) and ion beam etching (IBE). The HFCVD is used to deposit diamond on silicon substrates; and the IBE is used to etch the diamond crystalloid with a certain angle with respect to the coating surface to obtain an unsymmetrical-triangle microstructure. <p> A PDSS actuator prototype containing the AF surfaces was developed in this study to verify the function of the AF surfaces and characterize the performance of PDSS actuators. The designed surfaces were mounted on the prototype; and the improvement in performance was characterized by conducting a set of experiments with both the normal isotropic friction (IF) surfaces and the AF surfaces, respectively. The results illustrate that the PDSS actuator with the AF surface has a higher efficiency and improved loading capability compared to the one with the IF surfaces.<p> A model was also developed to represent the displacement of the novel PDSS actuator. The dynamics of the PEA and the platform were approximated by using a second order dynamic system. The pre-sliding friction behaviour involved was investigated by modifying the LuGre friction model, in which six parameters (Note that three parameters are used in the LuGre model) were employed to represent the anisotropic friction. By combining the PEA mechanism model, the modified friction model, and the dynamics of end-effector, a model for the PDSS actuator with the AF surface was developed. The model with the identified parameters was simulated in MATLAB Simulink and the simulation results obtained were compared to the experimental results to verify the model. The comparison suggests that the model developed in this study is promising to represent the displacement of the novel PDSS actuators with AF surfaces.

No description available.

Thin and slender structures are widely occurring both in nature and in human creations. Clever geometries of thin structures can produce strong constructions while requiring a minimal amount of material. Computer modeling and analysis of thin and slender structures have their own set of problems, stemming from assumptions made when deriving the governing equations. This thesis deals with the derivation of numerical methods suitable for approximating solutions to problems on thin geometries. It consists of an introduction and four papers. In the first paper we introduce a thread model for use in interactive simulation. Based on a three-dimensional beam model, a corotational approach is used for interactive simulation speeds in combination with adaptive mesh resolution to maintain accuracy. In the second paper we present a family of continuous piecewise linear finite elements for thin plate problems. Patchwise reconstruction of a discontinuous piecewise quadratic deflection field allows us touse a discontinuous Galerkin method for the plate problem. Assuming a criterion on the reconstructions is fulfilled we prove a priori error estimates in energy norm and L2-norm and provide numerical results to support our findings. The third paper deals with the biharmonic equation on a surface embedded in R3. We extend theory and formalism, developed for the approximation of solutions to the Laplace-Beltrami problem on an implicitly defined surface, to also cover the biharmonic problem. A priori error estimates for a continuous/discontinuous Galerkin method is proven in energy norm and L2-norm, and we support the theoretical results by numerical convergence studies for problems on a sphere and on a torus. In the fourth paper we consider finite element modeling of curved beams in R3. We let the geometry of the beam be implicitly defined by a vector distance function. Starting from the three-dimensional equations of linear elasticity, we derive a weak formulation for a linear curved beam expressed in global coordinates. Numerical results from a finite element implementation based on these equations are compared with classical results.