Search Results (14 total)

In this paper we report on large-scale high resolution simulations of beam dynamics in electron linacs for the next-generation x-ray free electron lasers (FELs). We describe key features of a parallel macroparticle simulation code including three-dimensional (3D) space-charge effects, short-range structure wakefields, coherent synchrotron radiation (CSR) wakefields, and treatment of radio-frequency (rf) accelerating cavities using maps obtained from axial field profiles. We present a study of the microbunching instability causing severe electron beam fragmentation in the longitudinal phase space which is a critical issue for future FELs. Using parameters for a proposed FEL linac at Lawrence Berkeley National Laboratory (LBNL), we show that a large number of macroparticles (beyond 100 million) is generally needed to control the numerical macroparticle shot noise and avoid overestimating the microbunching instability. We explore the effect of the longitudinal grid on simulation results. We also study the effect of initial uncorrelated energy spread on the final uncorrelated energy spread of the beam for the FEL linac.

A 1D model of space-charge impedance, assuming a transversely uniform beam with circular cross section, has been proposed and is being extensively used in the modeling of the microbunching instability of relevance for the beam delivery systems of x-ray free-electron lasers. In this paper we investigate the limitation of the model when applied to studying the effect of shot noise—one of the sources of the microbunching instability. We make comparison with a fully 3D calculation and identify the upper end of the frequency spectrum for applicability of the 1D model. Relaxation of the assumptions regarding axis symmetry and uniformity of the transverse density is also reviewed.

We apply a recently developed Vlasov solver to the study of the microbunching instability generated by shot noise in the beam delivery systems of x-ray free electron lasers (FELs). We discuss two lattices presently under consideration for the FEL Fermi project at Elettra and show that at least one of the two lattices appears capable of delivering a beam with the desired quality in the longitudinal phase space.

Direct numerical methods for solving the Vlasov equation offer some advantages over macroparticle simulations, as they do not suffer from the consequences of the statistical fluctuations inherent in using a number of macroparticles smaller than the bunch population. Unfortunately, these methods are more time consuming and generally considered impractical in a full 6D phase space. However, in a lower-dimension phase space they may become attractive if the beam dynamics is sensitive to the presence of small charge-density fluctuations and a high resolution is needed. In this paper we present a 2D Vlasov solver for studying the longitudinal beam dynamics in single-pass systems of interest for x-ray FELs, where characterization of the microbunching instability stemming from self-field amplified noise is of particular relevance.

We are concerned with coherent longitudinal motion in a storage ring, especially with situations in which coherent synchrotron radiation (CSR) can influence stability of the beam. The collective force from CSR is usually described by an impedance or a wake function in such a way that the force depends only on the charge distribution at the present time. This description is exact only for a rigid bunch, since causality demands that the force depend on the prior history of the bunch. We show how to treat a deforming bunch by applying the “complete impedance” Z(n,ω), a function of wave number and frequency. We derive this impedance and study its analytic properties for a special model: radiation from circular orbits shielded by parallel plates representing the metallic vacuum chamber. We analyze the corresponding collective force, obtaining the usual formula as a first approximation, plus easily computed corrections that depend on present and prior values of the time derivative of the charge density. In related papers we have applied these results in numerical simulations of instabilities induced by CSR.

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 wavelengths 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 rms length much greater than the shielding cutoff.

We present a model describing high power stable broadband coherent synchrotron radiation (CSR) in the terahertz frequency region in an electron storage ring. The model includes distortion of bunch shape from the synchrotron radiation (SR), which enhances higher frequency coherent emission, and limits to stable emission due to an instability excited by the SR wakefield. It gives a quantitative explanation of several features of the recent observations of CSR at the BESSY II storage ring. We also use this model to optimize the performance of a source for stable CSR emission.

Evidence of coherent synchrotron radiation has been reported recently at the electron storage rings of several light source facilities. The main features of the observations are (i) a radiation wavelength short compared to the nominal bunch length, and (ii) a coherent signal showing recurrent bursts of duration much shorter than the radiation damping time, but with spacing equal to a substantial fraction of the damping time. We present a model of beam longitudinal dynamics that reproduces these features.

In the presence of rf focusing and a purely inductive impedance bunch, equilibria in the form of Haïssinski distributions—when they exist—are linearly stable. This is the case whether the potential well distortion associated with the impedance causes bunch lengthening or shortening. We provide a general proof of this fact using Hamiltonian methods and energy principles. In the presence of bunch shortening our analysis indicates that there is a critical current for linear stability. However, this threshold is identical to the critical current defining the condition for the very existence of a Haïssinski equilibrium.

Air-core printed-circuit (PC) quadrupoles and dipoles have been developed for the University of Maryland electron ring, currently under construction. The quadrupoles and dipoles are characterized by very small magnetic fields (about 15 G at the aperture edge) and small aspect ratios (length/diameter < 1). We review the theory behind the design of the PC lenses and bending elements, and present general expressions for estimating the values of integrated field and integrated field gradient as functions of design parameters. The new quadrupole magnet represents an improvement over an earlier version which was based on an empirical approach. Further, we summarize the results of multipole content of the magnet fields as measured with a rotating coil apparatus of special construction. The results are compared with calculations with an iron-free magnetics code and are related to different types of errors in the manufacture and assembly of the PC magnets.

We use the linearized Vlasov-Poisson equations to study the response of a Kapchinskij-Vladimirskij beam to magnetic multipole errors in a circular lattice. This work extends the calculation of Gluckstern [Proceedings of the Linac Conference, 1970 (Fermilab, Batavia, IL, 1970), p. 811] to the case of nonideal periodic lattices. The smooth approximation is assumed. We determine the resonance conditions as well as the amplitude of the excited collective modes as a function of the error size outside the stopbands. We find that the frequencies associated with lattice resonances are a subset of the beam natural eigenfrequencies. The result is used to study the motion of test particles crossing the boundary of the beam core. Close to resonance the model predicts the emergence of a halo if sufficiently large gradient errors are present. Application is made to the University of Maryland Electron Ring.

We examine the transverse impedance of a periodic array of cavities in a beam pipe at high frequency. The calculation is an extension of a previous one for the longitudinal impedance of a periodic array of azimuthally symmetric pillboxes, for which only TM modes were needed. In the present case, we must include TE modes as well. In addition, we extend the applicability of the previous calculation by including an extra term in the coupling kernel so that the results are valid for all values of the ratio of the cavity length to the period of the structure (all values of the ratio of iris thickness to structure period). In spite of the presence of TE modes, we find that the high frequency limit of the transverse impedance is simply (2/ka²) times the corresponding limit of the longitudinal impedance, just as it is for the resistive wall impedances, a relation which occurs frequently for azimuthally symmetric structures. Finally, we present numerical results as well as approximate expressions for the impedance per period, valid for all ratios of cavity length to structure period.

The matching of charged particle beams into transport lines is usually done by using the rms envelope equations. The usual rms envelope equations, however, do not apply in the presence of bending magnets and a longitudinal momentum spread. A new set of equations is needed that simultaneously describes the rms envelopes of the beam and the dispersion function. A derivation is outlined in this paper. The new equations will make it possible to achieve proper matching of the rms envelopes and dispersion in the regime of highly space charge dominated beams.

The interplay between dispersion and space charge in circular accelerators or storage rings is investigated by looking for self-consistent, stationary solutions of the Vlasov-Poisson equation in the form of generalized Kapchinsky-Vladimirsky (KV) distributions. The smooth approximation is assumed. The results show a growth of the rms quantities describing the beam distribution with the longitudinal momentum spread, and the tune depression. This growth, however, is modest for realistic values of these parameters in strong focusing systems.