Landau damping | EPFL Graph Search

In physics, Landau damping, named after its discoverer, Soviet physicist Lev Davidovich Landau (1908–68), is the effect of damping (exponential decrease as a function of time) of longitudinal space charge waves in plasma or a similar environment. This phenomenon prevents an instability from developing, and creates a region of stability in the parameter space. It was later argued by Donald Lynden-Bell that a similar phenomenon was occurring in galactic dynamics, where the gas of electrons interacting by electrostatic forces is replaced by a "gas of stars" interacting by gravitational forces. Landau damping can be manipulated exactly in numerical simulations such as particle-in-cell simulation. It was proved to exist experimentally by Malmberg and Wharton in 1964, almost two decades after its prediction by Landau in 1946. Wave–particle interactions Landau damping occurs because of the energy exchange between an electromagnetic wave with phase velocity v_\text{ph}

Development of a musculoskeletal model of the knee joint to predict articular contact patterns during a loaded squat movement

Alexandra Stephanie Krause

Computational models are a current way to study specific behavior of healthy or pathological tissue or the mechanics of joints. Simulating the native anatomical structures and kinematics are two of the most important tasks to achieve reliable results. It is especially challenging for the knee as it is one of the most complex joint in the human body. It consists of two articulations, one between femur and tibia and one between femur and patella. This thesis estimates the patellofemoral and tibiafemoral contact pattern during a simulated squat movement. This is achieved by using a musculoskeletal, loaded knee model controlled by muscle activation. The flexion is performed by the elongation of the rectus femoris muscle. The knee model consists of femural, patellar and tibial articular cartilage, the menisci, anterior and posterior cruciate ligaments and the medial and lateral collateral ligaments. Contours of all soft tissues were segmented on the magnetic resonance imaging slides and imported into Solidworks (SolidWorks Corp., Concord, MA, United States) to build up the 3D geometry. A previous thesis already reconstructed the tibia, femur, fibula and patella bone geometry from Computed tomography images, so cartilage and menisci were done during this study. Abaqus (Dassault Systèmes Simulia Corp., Rhode Island, USA) was used for finite element modeling. The cartilage and menisci were meshed with hexahedral elements and bones were modeled as rigid bodies. An explicit solver was chosen for the numerical simulation and the squat movement should be performed quasi static. Mass scaling was required to reduce computational time and a global damping was used to minimize the oscillations. But sill, the squat movement could not be performed.

2010

Longitudinal intensity effects in the CERN Large Hadron Collider

Juan Federico Esteban Müller

This PhD thesis provides an improved knowledge of the LHC longitudinal impedance model and a better understanding of the longitudinal intensity effects. These effects can limit the LHC performance and lead to a reduction of the integrated luminosity. The LHC longitudinal impedance was measured with beams. Results obtained using traditional techniques are consistent with the expectations based on the impedance model, although the measurement precision was proven insufficient for the low impedance of the LHC. Innovative methods to probe the LHC reactive impedance were successfully used. One of the methods is based on exciting the beam with a sinusoidal rf phase modulation to estimate the synchrotron frequency shift from potential-well distortion. In the second method, the impedance is estimated from the loss of Landau damping threshold, which is also found to be in good agreement with analytical estimations. Beam-based impedance measurements agree well with estimations using the LHC impedance model. Macroparticle simulations of loss of Landau damping reproduce the measurements precisely and are used to determine the current stability limits. The single-bunch stability is analyzed for the HL-LHC, for a bunch intensity almost twice higher than the nominal LHC intensity. The effect of an additional rf system installed for double rf operation provides an increased stability margin in the absence of a wideband longitudinal damper system. The differences between the bunch-shortening and bunch-lengthening operation modes are presented, as well as the effect of an error in the phase synchronization between both rf systems. Several options for the rf parameters are considered, and their advantages and drawbacks under different circumstances are analyzed. A novel diagnostic tool for e-cloud monitoring based on bunch phase measurements has been fully developed. An advanced post-processing was implemented to improve the measurement accuracy up to the required level by reducing systematic and random errors. The tool is available at the CERN Control Room and shows the e-cloud build-up structure along the bunch trains and the total beam power loss due to e-cloud. Phase shift measurements are in good agreement with simulations of the e-cloud buildup and can be used to estimate the heat load in the cryogenic system. The use of this method in operation has been proven to ease the scrubbing run optimization and can eventually be used as an additional input for the cryogenic system.

EPFL2016

Beam Transfer Function measurements and transverse beam stability studies for the Large Hadron Collider and its High Luminosity upgrade

Claudia Tambasco

The motion of high energetic particle beams in accelerators is influenced by their interactions with the accelerator environment through electromagnetic fields induced by the particle passages. Traveling with a speed close to the speed of light, the particles induce image charge and currents in the surroundings generating wake-fields that act back on the beams. Destabilizing effects may arise from the coupled motion between the circulating particles and the induced wake fields compromising the accelerator performances. The stability of the beams is ensured by the Landau damping of coherent motions generated by the diversity of oscillation frequencies of the particles in the beams. Under the effect of non linear forces produced by machine non linearities or beam-beam interactions the particles oscillate with slightly different frequencies depending on their amplitudes in the beams (tune spread). At the Large Hadron Collider (LHC) transverse instability thresholds are evaluated via the computation of the dispersion integral that depends on the tune spread in the beams as well as on the particle distribution. A large tune spread is beneficial for the Landau damping as long as no diffusive mechanism is present. In the presence of diffusive mechanisms, caused by resonance excitations or noise, the stability diagram can be deformed due to the modification of the particle distribution inside the beam leading to a possible lack of Landau damping of the impedance coherent modes previously damped by lying within the unperturbed stability area. This work aims to experimentally explore the transverse stability of the beams by means of Beam Transfer Function measurements at the LHC. They provide direct measurements of the stability diagrams and are sensitive to particle distribution changes. First measurements of the Landau stability diagrams at the LHC are presented and compared to model expectations. Experimental studies have been carried out in the presence of different sources of non linear effects such as octupole magnets and beam-beam interactions and compared to the model expectations. Limitations deriving from transverse coherent instabilities in the LHC are analysed and possible explanations for the observed LHC instabilities are discussed. In the perspective of the High-Luminosity LHC upgrade (HL-LHC), transverse stability studies for different beam-beam interactions and machine configurations are presented together with possible solutions to compensate reductions of the Landau damping during the operational phases of the HL-LHC.

EPFL2017