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Study of Bunch Instabilities By the Nonlinear Vlasov-Fokker-Planck Equation

Description: Instabilities of the bunch form in storage rings may be induced through the wake field arising from corrugations in the vacuum chamber, or from the wake and precursor fields due to coherent synchrotron radiation (CSR). For over forty years the linearized Vlasov equation has been applied to calculate the threshold in current for an instability, and the initial growth rate. Increasing interest in nonlinear aspects of the motion has led to numerical solutions of the nonlinear Vlasov equation, augmented with Fokker-Planck terms to describe incoherent synchrotron radiation in the case of electron storage rings. This opens the door to much deeper studies of coherent instabilities, revealing a rich variety of nonlinear phenomena. Recent work on this topic by the author and collaborators is reviewed.
Date: July 11, 2006
Creator: Warnock, Robert L.
Partner: UNT Libraries Government Documents Department

MATRIX N/D METHOD WITH ABSORPTION AND THE UNITARITY PROBLEM IN COUPLED-CHANNEL REGGE THEORY

Description: In a crossing-symmetric Regge theory with several coupled two-particle channels, there are many-particle absorptive effects due to crossed two-particle processes. Also, some of the partial-wave amplitudes have overlapping left-hand and right-hand cuts in the s-plane, To enforce unitarity in such a theory, one needs a coupled-channel N/D method allowing arbitrary absorption parameters and overlapping cuts. These requirements lead to a nonlinear marginally singular N/D equation, which is proposed as part of a scheme to construct a coupled-channel Regge theory with exact crossing symmetry.
Date: November 1, 1979
Creator: Warnock, Robert Lee
Partner: UNT Libraries Government Documents Department

A Vlasov Solver for Longitudinal Dynamics in Beam Delivery Systems for X-Ray FELs

Description: Direct numerical methods for solving the Vlasov equationoffer some advantages over macroparticle simulations, as they do notsuffer from the consequences of the statistical fluctuations inherent inusing a number of macroparticles smaller than thebunch population.Unfortunately these methods are more time-consuming and generallyconsidered impractical in a full 6D phase space. However, in alower-dimension phase space they may become attractive if the beamdynamics is sensitive to the presence of small charge-densityfluctuations and a high resolution is needed. In this paper we present a2D Vlasov solverfor studying the longitudinal beam dynamics insingle-pass systems of interest for X-Ray FELs, where characterization ofthe microbunching instability stemming from self-field amplified noise isof particular relevance.
Date: May 9, 2007
Creator: Venturini, Marco; Warnock, Robert & Zholents, Alexander
Partner: UNT Libraries Government Documents Department

Evolving bunch and retardation in the impedance formalism

Description: The usual expression for the longitudinal wake field in terms of the impedance is exact only for the model in which the source of the field is a rigid bunch. To account for a deforming bunch one has to invoke the complete impedance, a function of both wave number and frequency. A computation of the corresponding wake field would be expensive, since it would involve integrals over frequency and time in addition to the usual sum over wave number. We treat the problem of approximating this field in an example of current interest, the case of coherent synchrotron radiation (CSR) in the presence of shielding by the vacuum chamber.
Date: May 22, 2003
Creator: Warnock, Robert & Venturini, Marco
Partner: UNT Libraries Government Documents Department

Simulations of the microbunching instability in beam deliverysystems for free electron lasers

Description: In this paper, we examine the growth of the microbunchinginstability in the electron beam delivery system of a free electron laser(FEL). We present the results of two sets of simulations, one conductedusing a direct Vlasov solver, the other using a particle-in-cell codeImpact-Z with the number of simulation macroparticles ranging up to 100million. Discussion is focused on the details of longitudinal dynamicsand on numerical values of uncorrelated (slice) energy spread atdifferent points in the lattice. In particular, we assess the efficacy oflaser heater in suppression of the instability, and look at the interplaybetween physical and numerical noise in particle-basedsimulations.
Date: June 29, 2007
Creator: Pogorelov, Ilya; Qiang, Ji; Ryne, Rob; Venturini, Marco; Zholents, Alexander & Warnock, Robert
Partner: UNT Libraries Government Documents Department

Development of a 2D Vlasov Solver for Single-Pass Systems

Description: Direct numerical methods for solving the Vlasov equationoffer some advantages over macroparticle simulations, as they do notsuffer from the numerical noise inherent in using a number ofmacroparticles smaller than the bunch population. Unfortunately thesemethods are more time-consuming and generally considered impractical in afull 6D phase space. However, in a lower-dimension phase space they maybecome attractive if the beam dynamics is sensitive to the presence ofsmall charge-density fluctuations and a high resolution is needed. Inthis paper we present a 2D Vlasov solver for studying the longitudinalbeam dynamics in single-pass systems of interest for X-FEL's, wherecharacterization of the microbunching instability is of particularrelevance. The solver includes a model to account for the smearing effectof a finite horizontal emittance on microbuncing. We explore the effectof space charge and coherent synchrotron radiation (CSR). The numericalsolutions are compared with results from linear theory and good agreementis found in the regime where linear theory applies.
Date: July 31, 2006
Creator: Venturini, Marco; Warnock, Robert & Zholents, Alexander
Partner: UNT Libraries Government Documents Department

Microbunching Instability in a Chicane: Two-Dimensional Mean Field Treatment

Description: We study the microbunching instability in a bunch compressor by a parallel code with some improved numerical algorithms. The two-dimensional charge/current distribution is represented by a Fourier series, with coefficients determined through Monte Carlo sampling over an ensemble of tracked points. This gives a globally smooth distribution with low noise. The field equations are solved accurately in the lab frame using retarded potentials and a novel choice of integration variables that eliminates singularities. We apply the scheme with parameters for the first bunch compressor system of FERMI{at}Elettra, with emphasis on the amplification of a perturbation at a particular wavelength. Gain curves agree with those of the linearized Vlasov model at long wavelengths, but show some deviation at the smallest wavelengths treated.
Date: January 27, 2009
Creator: Bassi, G.; Ellison, James A.; Heinemann, Klaus & Warnock, Robert
Partner: UNT Libraries Government Documents Department

Construction of Large Period Symplectic Maps by Interpolative Methods

Description: The goal is to construct a symplectic evolution map for a large section of an accelerator, say a full turn of a large ring or a long wiggler. We start with an accurate tracking algorithm for single particles, which is allowed to be slightly non-symplectic. By tracking many particles for a distance S one acquires sufficient data to construct the mixed-variable generator of a symplectic map for evolution over S, given in terms of interpolatory functions. Two ways to find the generator are considered: (1) Find its gradient from tracking data, then the generator itself as a line integral. (2) Compute the action integral on many orbits. A test of method (1) has been made in a difficult example: a full turn map for an electron ring with strong nonlinearity near the dynamic aperture. The method succeeds at fairly large amplitudes, but there are technical difficulties near the dynamic aperture due to oddly shaped interpolation domains. For a generally applicable algorithm we propose method (2), realized with meshless interpolation methods.
Date: December 17, 2009
Creator: Warnock, Robert; Cai, Yunhai; /SLAC; Ellison, James A. & U., /New Mexico
Partner: UNT Libraries Government Documents Department

Impedance and Single Bunch Instability Calculations for the ILCDamping Ring

Description: An important action item for the damping rings of theInternational Linear Collider (ILC) is to compute the broad-bandimpedance and, from it, the threshold to the microwave instability. Wereport on the status of our study and provide a preliminary estimate ofthe instability threshold based on impedance models developed sofar.
Date: June 29, 2007
Creator: Venturini, Marco; Bane, Karl; Heifets, Sam; Li, Zhenhai; Ng, Cho; Novokhatski, Alexander et al.
Partner: UNT Libraries Government Documents Department

Stable CSR in storage rings: A model

Description: A comprehensive historical view of the work done on coherent synchrotron radiation (CSR) in storage rings is given in reference [1]. Here we want just to point out that even if the issue of CSR in storage rings was already discussed over 50 years ago, it is only recently that a considerable number of observations have been reported. In fact, intense bursts of coherent synchrotron radiation with a stochastic character were measured in the terahertz frequency range, at several synchrotron light source storage rings [2-8]. It has been shown [8-11], that this bursting emission of CSR is associated with a single bunch instability, usually referred as microbunching instability (MBI), driven by the fields of the synchrotron radiation emitted by the bunch itself. Of remarkably different characteristics was the CSR emission observed at BESSY II in Berlin, when the storage ring was tuned into a special low momentum compaction mode [12, 13]. In fact, the emitted radiation was not the quasi-random bursting observed in the other machines, but a powerful and stable flux of broadband CSR in the terahertz range. This was an important result, because it experimentally demonstrated the concrete possibility of constructing a stable broadband source with extremely high power in the terahertz region. Since the publication of the first successful experiment using the ring as a CSR source [14], BESSY II has regular scheduled user s shifts dedicated to CSR experiments. At the present time, several other laboratories are investigating the possibility of a CSR mode of operation [15-17] and a design for a new ring optimized for CSR is at an advanced stage [18]. In what follows, we describe a model that first accounts for the BESSY II observations and then indicates that the special case of BESSY II is actually quite general and typical when relativistic ...
Date: January 3, 2005
Creator: Sannibale, Fernando; Byrd, John M.; Loftsdottir, Agusta; Venturini, Marco; Abo-Bakr, Michael; Feikes, Jorge et al.
Partner: UNT Libraries Government Documents Department

Linear Vlasov analysis for stability of a bunched beam

Description: We study the linearized Vlasov equation for a bunched beam subject to an arbitrary wake function. Following Oide and Yokoya, the equation is reduced to an integral equation expressed in angle-action coordinates of the distorted potential well. Numerical solution of the equation as a formal eigenvalue problem leads to difficulties, because of singular eigenmodes from the incoherent spectrum. We rephrase the equation so that it becomes non-singular in the sense of operator theory, and has only regular solutions for coherent modes. We report on a code that finds thresholds of instability by detecting zeros of the determinant of the system as they enter the upper-half frequency plane, upon increase of current. Results are compared with a time-domain integration of the nonlinear Vlasov equation with a realistic wake function for the SLC damping rings. There is close agreement between the two calculations.
Date: June 30, 2004
Creator: Warnock, Robert; Stupakov, Gennady; Venturini, Marco & Ellison, James A.
Partner: UNT Libraries Government Documents Department

Coherent synchrotron radiation and bunch stability in a compactstorage ring

Description: We examine the effect of the collective force due to coherent synchrotron radiation (CSR) in an electron storage ring with small bending radius. In a computation based on time-domain integration of the nonlinear Vlasov equation, we find the threshold current for a longitudinal microwave instability induced by CSR alone. The model accounts for suppression of radiation at long wave lengths due to shielding by the vacuum chamber. In a calculation just above threshold, small ripples in the charge distribution build up over a fraction of a synchrotron period, but then die out to yield a relatively smooth but altered distribution with eventual oscillations in bunch length. The instability evolves from small noise on an initial smooth bunch of r.m.s.length much greater than the shielding cutoff. The paper includes a derivation and extensive analysis of the complete impedance function Z for synchrotron radiation with parallel plate shielding. We find corrections to the lowest approximation to the coherent force which involve ''off-diagonal'' values of Z, that is, fields with phase velocity not equal to the particle velocity.
Date: April 9, 2004
Creator: Venturini, Marco; Warnock, Robert; Ruth, Ronald & Ellison, James A.
Partner: UNT Libraries Government Documents Department