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Abstract Landau damping is the suppression of an instability by a spread of frequencies in the beam. It is treated here from an experimental point of view. To introduce the concept we consider a set of oscillators having a spread in resonant frequencies !r and calculate the response of their there center-of-mass to an external driving force. A pulse excitation gives each oscillator the same initial velocity but, due to their different frequencies, the center-of-mass motion will decay with time. A harmonic excitation with a frequency ! being inside the distribution in !r results in oscillators responding with different phases and only a few of them having !r ! will grow to large amplitudes and absorb energy. The oscillator response to a pulse excitation, called Green function, and the one to a harmonic excitation, called transfer function, serve as a basis to calculate Landau damping which suppresses an instability at infinitesimal level before any large amplitudes are reached. This is illustrated by a negative feed-back system acting on the center-ofmass of the oscillators. In the absence of a frequency spread this leads in an exponential growth, but a sufficiently large spread will provide stability. Landau damping is then applied to the transverse motion of a coasting (un-bunched) beam. The dependence of revolution frequency and betatron tune on momentum establishes a spread of the frequencies contained in the upper and lower betatron side-band. A transverse impedance present in the ring gets excited by the beam and acts back on it, causing an instability. For a given frequency distribution a maximum value of this impedance, being still conform with stability, is calculated and plotted in a stability diagram. Finally, longitudinal instabilities in a coasting beam are investigated. They can be stabilized by a spread of revolution frequencies caused by an energy distribution of the particles in the beam.
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A generation of neutrino experiments have established that neutrinos mix and probably have mass. The mixing phenomenon points to processes beyond those of the Standard Model, possibly at the Grand Unification energy scale. A extensive sequence of of experiments will be required to measure precisely all the parameters of the neutrino mixing matrix, culminating with the discovery and study of leptonic CP violation. As a first step, extensions of conventional pion/kaon decay beams, such as off-axis beams or low-energy super-beams, have been considered. These could yield first observations of $\nu_\mu \to \nu_e$ transitions at the atmospheric frequency, which have not yet been observed, and a first measurement of $\theta_{13}$. Experiments with much better flux control can be envisaged if the neutrinos are obtained from the decays of stored particles. One such possibility is the concept of beta beams provided by the decays of radioactive nuclei, that has been developed within the context of these studies. These would provide a pure (anti-)electron-neutrino beam of a few hundred MeV, and beautiful complementarity with a high-intensity, low-energy conventional beam, enabling experimental probes of T violation as well as CP violation. Ultimately, a definitive and complete set of measurements would offered by a Neutrino Factory based on a muon storage ring. This powerful machine offers the largest reach for CP violation, even for very small values of $\theta_{13}$.
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We begin by giving a description of the radio-frequency generator-cavity-beam coupled system in terms of basic quantities. Taking beam loading and cavity detuning into account, expressions for the cavity impedance as seen by the generator and as seen by the beam are derived. Subsequently methods of beam-loading compensation by cavity detuning, radio-frequency feedback and feedforward are described. Examples of digital radio-frequency phase and amplitude control for the special case of superconducting cavities are also given. Finally, a dedicated phase loop for damping synchrotron oscillations is discussed.
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A system for bunch-by-bunch detection of transverse proton and antiproton coherent oscillations in the Fermilab Tevatron collider is described. It is based on the signal from a single beam-position monitor located in a region of the ring with large amplitude functions. The signal is digitized over a large number of turns and Fourier-analyzed offline with a dedicated algorithm. To enhance the signal, band-limited noise is applied to the beam for about 1 s. This excitation does not adversely affect the circulating beams even at high luminosities. The device has a response time of a few seconds, a frequency resolution of $1.6\times 10^{-5}$ in fractional tune, and it is sensitive to oscillation amplitudes of 60 nm. It complements Schottky detectors as a diagnostic tool for tunes, tune spreads, and beam-beam effects. Measurements of coherent mode spectra are presented and compared with models of beam-beam oscillations.
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The T2K (Tokai-to-Kamioka) experiment is a long baseline neutrino oscillation experiment in Japan. A near detector, located at 280m of the production target, is used to characterize the beam. One of its key elements is a tracker, made of three Time Projection Chambers (TPC) read by Micromegas endplates. A new readout system has been developed to collect, amplify, condition and acquire the data produced by the 124,000 detector channels of these detectors. The front-end element of this system is a a new 72-channel application specific integrated circuit. Each channel includes a low noise charge preamplifier, a pole zero compensation stage, a second order Sallen-Key low pass filter and a 511-cell Switched Capacitor Array. This electronics offers a large flexibility in sampling frequency, shaping time, gain, while taking advantage of the low physics events rate of 0.3 Hz. We detail the design and the performance of this ASIC and report on the deployment of the frond-end electronics on-site.
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RF electronics deals with the generation, acquisition and manipulation of high-frequency signals. In particle accelerators signals of this kind are abundant, especially in the RF and beam diagnostics systems. In modern machines the complexity of the electronics assemblies dedicated to RF manipulation, beam diagnostics, and feedbacks is continuously increasing, following the demands for improvement of accelerator performance. However, these systems, and in particular their front-ends and back-ends, still rely on well-established basic hardware components and techniques, while down-converted and acquired signals are digitally processed exploiting the rapidly growing computational capability offered by the available technology. This lecture reviews the operational principles of the basic building blocks used for the treatment of high-frequency signals. Devices such as mixers, phase and amplitude detectors, modulators, filters, switches, directional couplers, oscillators, amplifiers, attenuators, and others are described in terms of equivalent circuits, scattering matrices, transfer functions; typical performance of commercially available models is presented. Owing to the breadth of the subject, this review is necessarily synthetic and non-exhaustive. Readers interested in the architecture of complete systems making use of the described components and devoted to generation and manipulation of the signals driving RF power plants and cavities may refer to the CAS lectures on Low-Level RF.
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The handling of weak networks with asymmetric loads and disturbances implies the accurate handling of the second-harmonic component that appears in an unbalanced network. This paper proposes a classic vector control approach using a PI-based controller with superior decoupling capabilities for operation in weak networks with unbalanced phase voltages. A synchronization method for weak unbalanced networks is detailed, with dedicated dimensioning rules. The use of a double-frame controller allows a current symmetry or controlled imbalance to be forced for compensation of power oscillations by controlling the negative current sequence. This paper also serves as a useful reminder of the proper way to cancel the inherent coupling effect due to the transformation to the synchronous rotating reference frame, and of basic considerations of the relationship between switching frequency and control bandwidth.
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FE-I4 is the 130 nm ATLAS pixel IC currently under development for upgraded Large Hadron Collider (LHC) luminosities. FE-I4 is based on a low-power analog pixel array and digital architecture concepts tuned to higher hit rates [1]. An integrated Phase Locked Loop (PLL) has been developed that locally generates a clock signal for the 160 Mbit/s output data stream from the 40 MHz bunch crossing reference clock. This block is designed for low power, low area consumption and recovers quickly from loss of lock related to single-event transients in the high radiation environment of the ATLAS pixel detector. After a general introduction to the new FE-I4 pixel front-end chip, this work focuses on the FE-I4 output blocks and on a first PLL prototype test chip submitted in early 2009. The PLL is nominally operated from a 1.2V supply and consumes 3.84mW of DC power. Under nominal operating conditions, the control voltage settles to within 2% of its nominal value in less than 700 ns. The nominal operating frequency for the ring-oscillator based Voltage Controlled Oscillator (VCO) is fVCO = 640MHz. The last sections deal with a fabricated demonstrator that provides the option of feeding the single-ended 80MHz output clock of the PLL as a clock signal to a digital test logic block integrated on-chip. The digital logic consists of an eight bit pseudo-random binary sequence generator, an eight bit to ten bit coder and a serializer. It processes data with a speed of 160 Mbit/s. All dynamic signals are driven off-chip by custommade pseudo-LVDS drivers.
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