Electro-optic techniques for longitudinal electron bunch diagnostics

Electro-optic techniques are becoming increasingly important in ultrafast electron bunch longitudinal diagnostics and have been successfully implemented at various accelerator laboratories. The longitudinal bunch shape is directly obtained from a single-shot, non-intrusive measurement of the temporal electric field profile of the bunch. Further- more, the same electro-optic techniques can be used to measure the temporal profile of terahertz / far-infrared opti- cal pulses generated by a CTR screen, at a bending magnet (CSR), or by an FEL. This contribution summarizes the re- sults obtained at FELIX and FLASH

Electro-optic time profile monitors for femtosecond electron bunches at the soft x-ray free-electron laser FLASH

Precise measurements of the temporal profile of ultrashort electron bunches are of high interest for the optimization and operation of ultraviolet and x-ray free-electron lasers. The electro-optic (EO) technique has been applied for a single-shot direct visualization of the time profile of individual electron bunches at FLASH. This paper presents a thorough description of the experimental setup and the results. An absolute calibration of the EO technique has been performed utilizing simultaneous measurements with a transverse-deflecting radio-frequency structure that transforms the longitudinal bunch charge distribution into a transverse streak. EO signals as short as 60 fs (rms) have been observed using a gallium-phosphide (GaP) crystal, which is a new record in the EO detection of single electron bunches and close to the physical limit imposed by the EO material properties. The data are in quantitative agreement with a numerical simulation of the EO detection process

Single-shot longitudinal bunch profile measurements at FLASH using electro-optic detection:experiment, simulation, and validation

At the superconducting linac of FLASH at DESY, we have installed an electro-optic (EO) experiment for single- shot, non-destructive measurements of the longitudinal electric charge distribution of individual electron bunches. The time profile of the electric bunch field is electro- optically encoded onto a chirped titanium-sapphire laser pulse. In the decoding step, the profile is retrieved either from a cross-correlation of the encoded pulse with a 30 fs laser pulse, obtained from the same laser (electro- optic temporal decoding, EOTD), or from the spectral intensity of the transmitted probe pulse (electro-optic spectral decoding, EOSD). At FLASH, the longitudinally compressed electron bunches have been measured during FEL operation with a resolution of better than 50 fs. The electro-optic process in gallium phosphide was numerically simulated using as input data the bunch shapes determined with a transverse-deflecting RF structure. In this contribution, we present electro-optically measured bunch profiles and compare them with the simulation

Single shot longitudinal bunch profile measurements by temporally resolved electro-optical detection

For the high gain operation of a SASE FEL, extremely short electron bunches are essential to generate sufficiently high peak currents. At the superconducting linac of FLASH at DESY, we have installed an electro- optic measurement system to probe the time structure of the electric field of single ~100 fs electron bunches. In this technique, the field induced birefringence in an electro-optic crystal is encoded on a chirped picosecond laser pulse. The longitudinal electric field profile of the electron bunch is then obtained from the encoded optical pulse by a single shot cross correlation with a 35 fs laser pulse using a second harmonic crystal (temporal decoding). An electro-optical signal exhibiting a feature with 118 fs FWHM was observed, and this is close to the limit of resolution due to the material properties of the particular electro-optic crystal used. The measured electro-optic signals are compared to bunch shapes simultaneously measured with a transverse deflecting cavity

Phase separation in coupled chaotic maps on fractal networks

The phase ordering dynamics of coupled chaotic maps on fractal networks are investigated. The statistical properties of the systems are characterized by means of the persistence probability of equivalent spin variables that define the phases. The persistence saturates and phase domains freeze for all values of the coupling parameter as a consequence of the fractal structure of the networks, in contrast to the phase transition behavior previously observed in regular Euclidean lattices. Several discontinuities and other features found in the saturation persistence curve as a function of the coupling are explained in terms of changes of stability of local phase configurations on the fractals.Comment: (4 pages, 4 Figs, Submitted to PRE

Complete Solution of the Kinetics in a Far-from-equilibrium Ising Chain

The one-dimensional Ising model is easily generalized to a \textit{genuinely nonequilibrium} system by coupling alternating spins to two thermal baths at different temperatures. Here, we investigate the full time dependence of this system. In particular, we obtain the evolution of the magnetisation, starting with arbitrary initial conditions. For slightly less general initial conditions, we compute the time dependence of all correlation functions, and so, the probability distribution. Novel properties, such as oscillatory decays into the steady state, are presented. Finally, we comment on the relationship to a reaction-diffusion model with pair annihilation and creation.Comment: Submitted to J. Phys. A (Letter to the editor

High-precision laser master oscillators for optical timing distribution systems in future light sources

An ultra-stable timing and synchronization system for linac-driven FELs has been designed providing 10 fs precision over distances of several kilometers. Mode-locked fiber lasers serve as master oscillators. The optical pulse train is distributed through length-stabilized fiber links. The layout of the optical synchronization system and its phase noise properties are described. A prototype system has been tested in an accelerator environment and has achieved the required stability

Non-equilibrium stationary state of a two-temperature spin chain

A kinetic one-dimensional Ising model is coupled to two heat baths, such that spins at even (odd) lattice sites experience a temperature $T_{e}$ ($$). Spin flips occur with Glauber-type rates generalised to the case of two temperatures. Driven by the temperature differential, the spin chain settles into a non-equilibrium steady state which corresponds to the stationary solution of a master equation. We construct a perturbation expansion of this master equation in terms of the temperature difference and compute explicitly the first two corrections to the equilibrium Boltzmann distribution. The key result is the emergence of additional spin operators in the steady state, increasing in spatial range and order of spin products. We comment on the violation of detailed balance and entropy production in the steady state.Comment: 11 pages, 1 figure, Revte

Probability currents as principal characteristics in the statistical mechanics of non-equilibrium steady states

One of the key features of non-equilibrium steady states (NESS) is the presence of nontrivial probability currents. We propose a general classification of NESS in which these currents play a central distinguishing role. As a corollary, we specify the transformations of the dynamic transition rates which leave a given NESS invariant. The formalism is most transparent within a continuous time master equation framework since it allows for a general graph-theoretical representation of the NESS. We discuss the consequences of these transformations for entropy production, present several simple examples, and explore some generalizations, to discrete time and continuous variables.Comment: 39 pages, 5 figures. Invited article for JSTAT Special Issue on 'Principles of Dynamics of Nonequilibrium Systems', held at the Newton Institute, Cambridge, UK, in 200

Phase transition and correlation decay in Coupled Map Lattices

For a Coupled Map Lattice with a specific strong coupling emulating Stavskaya's probabilistic cellular automata, we prove the existence of a phase transition using a Peierls argument, and exponential convergence to the invariant measures for a wide class of initial states using a technique of decoupling originally developed for weak coupling. This implies the exponential decay, in space and in time, of the correlation functions of the invariant measures