Search Results (42 total)

We study an impedance due to coherent synchrotron radiation (CSR) generated by a short bunch of charged particles passing through a dipole magnet of finite length in a vacuum chamber of a given cross section. In our method we decompose the electromagnetic field of the beam over the eigenmodes of the toroidal chamber and derive a system of equations for the expansion coefficients in the series. The general method is further specialized for a toroidal vacuum chamber of a rectangular cross section where the eigenmodes can be computed analytically. We also develop a computer code that calculates the CSR impedance for a toroid of rectangular cross section. Numerical results obtained with the code are presented in the paper.

We propose and analyze a scheme to generate enhanced narrow-band terahertz (THz) radiation through down-conversion of the frequency of optical lasers using laser-modulated electron beams. In the scheme the electron beam is first energy modulated by two lasers with wave numbers k₁ and k₂, respectively. After passing through a dispersion section, the energy modulation is converted to density modulation. Because of the nonlinear conversion process, the beam will have density modulation at wave number k=nk₁+mk₂, where n and m are positive or negative integers. By properly choosing the parameters for the lasers and dispersion section, one can generate density modulation at THz frequency in the beam using optical lasers. This density-modulated beam can be used to generate powerful narrow-band THz radiation. Since the THz radiation is in tight synchronization with the lasers, it should provide a high temporal resolution for the optical-pump THz-probe experiments. The central frequency of the THz radiation can be easily tuned by varying the wavelength of the two lasers and the energy chirp of the electron beam. The proposed scheme is in principle able to generate intense narrow-band THz radiation covering the whole THz range and offers a promising way towards the tunable intense narrow-band THz sources.

We propose a scheme that combines the echo-enabled harmonic generation technique with the bunch compression and allows one to generate harmonic numbers of a few hundred in a microbunched beam through up-conversion of the frequency of an ultraviolet seed laser. A few-cycle intense laser is used to generate the required energy chirp in the beam for bunch compression and for selection of an attosecond x-ray pulse. Sending this beam through a short undulator results in an intense isolated attosecond x-ray pulse. Using a representative realistic set of parameters, we show that 1 nm x-ray pulse with peak power of a few hundred MW and duration as short as 20 attoseconds (FWHM) can be generated from a 200 nm ultraviolet seed laser. The proposed scheme may enable the study of electronic dynamics with a resolution beyond the atomic unit of time (∼24 attoseconds) and may open a new regime of ultrafast sciences.

In order to reach the high peak current required for an x-ray free electron laser, two separate magnetic dipole chicanes are used in the Linac Coherent Light Source accelerator to compress the electron bunch length in stages. In these bunch compressors, coherent synchrotron radiation (CSR) can be emitted either by a short electron bunch or by any longitudinal density modulation that may be on the bunch. In this paper, we report detailed measurements of the CSR-induced energy loss and transverse emittance growth in these compressors. Good agreement is found between the experimental results and multiparticle tracking studies. We also describe direct observations of CSR at optical wavelengths and compare with analytical models based on beam microbunching.

By analyzing the pulse to pulse intensity fluctuations of the radiation emitted by a charge particle in the incoherent part of the spectrum, it is possible to extract information about the spatial distribution of the beam. At the Advanced Light Source of the Lawrence Berkeley National Laboratory, we have developed and successfully tested a simple scheme based on this principle that allows for the absolute measurement of the rms bunch length. A description of the method and the experimental results are presented.

In this paper, we systematically study the echo-enabled harmonic generation (EEHG) free electron laser (FEL). The EEHG FEL uses two modulators in combination with two dispersion sections that allow one to generate in the beam a high harmonic density modulation starting with a relatively small initial energy modulation of the beam. After presenting an analytical theory of the phenomenon, we address several practically important issues, such as the effect of incoherent synchrotron radiation in the dispersion sections, and the beam transverse size effect in the modulator. Using a representative realistic set of beam parameters, we show how the EEHG scheme enhances the FEL performance and allows one to generate a fully (both longitudinally and transversely) coherent radiation. As an example, we demonstrate that 5 nm coherent soft x rays with GW peak power can be generated directly from the 240 nm seeding laser using the proposed EEHG scheme.

We propose to use the mechanism of an echo effect previously observed in hadron accelerators for up-frequency conversion of density modulation in an electron beam. We show that, for generation of high harmonics, this method is much more efficient in comparison with the currently used approach. A one-dimensional model of the effect is developed which allows us to optimize the amplitude of the modulation for a given harmonic number.

It is usually assumed that the space charge effects in relativistic beams scale with the energy of the beam as γ^-2, where γ is the relativistic factor. We show that for a beam accelerated in the longitudinal direction there is an additional space charge effect in free space that scales as E/γ, where E is the accelerating field. This field has the same origin as the “electromagnetic mass of the electron” discussed in textbooks on electrodynamics. It keeps the balance between the kinetic energy of the beam and the energy of the electromagnetic field of the beam. We then consider the effect of this field on a beam generated in an rf gun and calculate the energy spread produced by this field in the beam.

We study the impedance of a tapered transition at small frequencies for an arbitrary shape of the transition cross section. Our approach does not require a symmetry axis in the system (unlike round geometry). We show that the calculation of the impedance reduces to finding a few auxiliary potential functions that satisfy two-dimensional Poisson equations with Dirichlet boundary conditions. In simple cases such solutions can be obtained analytically; for more complicated geometries they can easily be found numerically. We apply our method to axisymmetric geometry and reproduce results known from the literature. We then calculate the impedance of a taper with rectangular cross section in which the vertical dimension of the cross section is a slowly changing function of the longitudinal coordinate. Finally, we find a transverse kick experienced by a beam passing near a conducting wall with a variable distance from the beam to the wall.

In a companion report, we have derived a method for finding the impedance at high frequencies of vacuum chamber transitions that are short compared to the catch-up distance, in a frequency regime that—in analogy to geometric optics for light—we call the optical regime. In this report we apply the method to various nonaxisymmetric geometries such as irises/short collimators in a beam pipe, step-in transitions, step-out transitions, and more complicated transitions of practical importance. Most of our results are analytical, with a few given in terms of a simple one-dimensional integral. Our results are compared to wakefield simulations with the time-domain, finite-difference program ECHO, and excellent agreement is found.

In this paper we introduce an optical approximation into the theory of impedance calculation, one valid in the limit of high frequencies. This approximation neglects diffraction effects in the radiation process, and is conceptually equivalent to the approximation of geometric optics in electromagnetic theory. Using this approximation, we derive equations for the longitudinal impedance for arbitrary offsets, with respect to a reference orbit, of source and test particles. With the help of the Panofsky-Wenzel theorem, we also obtain expressions for the transverse impedance (also for arbitrary offsets). We further simplify these expressions for the case of the small offsets that are typical for practical applications. Our final expressions for the impedance, in the general case, involve two-dimensional integrals over various cross sections of the transition. We further demonstrate, for several known axisymmetric examples, how our method is applied to the calculation of impedances. Finally, we discuss the accuracy of the optical approximation and its relation to the diffraction regime in the theory of impedance.

We report on a recent set of measurements of the transverse wakefields from longitudinally tapered collimators. The measurements were performed with a low-emittance 1.19 GeV beam in the SLAC linac by inserting a collimator aperture into the beam path and reconstructing the vertical deflection of the beam as a function of the vertical position of the aperture. Each collimator in the experiment was designed to present a relatively large transverse impedance and to minimize the impedance from other contributions such as resistivity. In addition, the collimator parameters were chosen to provide some insight into the scaling of the transverse geometric wakefield as a function of the collimator’s geometry. A description of the experimental apparatus and the aperture design, the method of data collection and analysis, and a comparison to theoretical and numerical predictions are presented.

We numerically study properties of primary dark currents in an X-band accelerating structure. For the H60VG3 structure considered for the Next Linear Collider (NLC) we first perform a fairly complete (with some approximations) calculation of dark-current trajectories. These results are used to study properties of the dark current leaving the structure. For example, at accelerating gradient of 65  MV/m, considering two very different assumptions about dark-current emission around the irises, we find that the fraction of emitted current leaving the structure to be a consistent ∼1%. Considering that ∼1  mA outgoing dark current is seen in measurement, this implies that ∼100  mA (or 10 pC per period) is emitted within the structure itself. Using the formalism of the Liénard-Wiechert potentials, we then perform a systematic calculation of the transverse kick of dark currents on a primary linac bunch. The result is ∼1   V kick per mA (or per 0.1  pC per period) dark current emitted from an iris. For an entire structure we estimate the total kick on a primary bunch to be ∼15   V. For the NLC linac this translates to a ratio of (final) vertical beam offset to beam size of about 0.2. However, with the assumptions that needed to be made—particularly the number of emitters and their distribution within a structure—the accuracy of this result may be limited to the order of magnitude.

The standard theoretical formulas for resistive wall impedance are usually derived in a model which assumes an infinitely long pipe. In practice, one often has to deal with resistive inserts with a conductivity different from the rest of the pipe. To address this case, we calculate the resistive wall impedance when the wall conductivity varies along the axis of the pipe. We show that at not very high frequencies the impedance of an insert per unit length is given by the same formulas as for an infinitely long pipe.

A self-consistent theory of a free electron laser (FEL) with slowly varying beam and undulator parameters is developed using the WKB approximation. The theory is applied to study the performance of a self-amplified spontaneous emission (SASE) FEL when the electron beam energy varies along the undulator as would be caused by vacuum pipe wakefields and/or when the undulator strength parameter is tapered in the small signal regime before FEL saturation. We find that a small energy gain or an equivalent undulator taper slightly reduces the power gain length in the exponential growth regime and can increase the saturated SASE power by about a factor of 2. Power degradation away from the optimal performance can be estimated based upon knowledge of the SASE bandwidth. The analytical results, which agree with numerical simulations, are used to optimize the undulator taper and to evaluate wakefield effects.

A microbunching instability driven by longitudinal space charge, coherent synchrotron radiation, and linac wakefields is studied for the linac coherent light source (LCLS) accelerator system. Since the uncorrelated (local) energy spread of electron beams generated from a photocathode rf gun is very small, the microbunching gain may be large enough to significantly amplify rf-gun generated modulations or even shot-noise fluctuations of the electron beam. The uncorrelated energy spread can be increased by an order of magnitude to provide strong Landau damping against the instability without degrading the free-electron laser performance. We study different damping options in the LCLS and discuss an effective laser heater to minimize the impact of the instability on the quality of the electron beam.

In the x-ray, free-electron laser project, the Linac Coherent Light Source (LCLS), a proposal has been made to generate a shorter light pulse by placing a spoiler foil in the middle of a compressor chicane: The foil has a small slot, which selects out the small fraction of particles passing through it (“target particles”) to lase. In this report, using the method of field matching, we obtain longitudinal and transverse impedances and wakefields for several models of the proposed LCLS spoiler foil. We consider the model of a pencil beam and of a cylindrically symmetric, bi-Gaussian beam that is wider than it is long. Third, we generate a Green function that allows us to consider asymmetric beams also. For target particles of the tilted, tri-Gaussian beam that is found at the LCLS spoiler location we obtain approximate analytical formulas and numerical results for wakefield kicks in the three directions. We find that the kicks, after correction using a simple dipole and quadrupole, are all within tolerances.

We propose a novel method to generate femtosecond and subfemtosecond photon pulses in a free-electron laser by selectively spoiling the transverse emittance of the electron beam. Its merits are simplicity and ease of implementation. When the system is applied to the Linac Coherent Light Source, it can provide x-ray pulses the order of 1 fs in duration containing about 10¹⁰ transversely coherent photons.

Extraordinarily high fields generated by focused lasers are envisioned to accelerate particles to high energies. In this paper, we develop a new method to calculate laser acceleration in vacuum based on the energy exchange arising from the interference of the laser field with the radiation field of the particle. We apply this method to a simple accelerating structure, a perfectly conducting screen with a round hole, and show how to optimize the energy gain with respect to the hole radius, laser angle, and spot size, as well as the transverse profile of the laser. Limitations and energy scaling of this acceleration method are also discussed.

Coherent synchrotron radiation (CSR) can play an important role by not only increasing the energy spread and emittance of a beam, but also leading to a potential instability. Previous studies of the CSR induced longitudinal instability were carried out for the CSR impedance due to dipole magnets. However, many storage rings include long wigglers where a large fraction of the synchrotron radiation is emitted. This includes high-luminosity factories such as DAPHNE, PEP-II, KEK-B, and CESR-C as well as the damping rings of future linear colliders. In this paper, the instability due to the CSR impedance from a wiggler is studied assuming a large wiggler parameter K. The primary consideration is a low-frequency microwavelike instability, which arises near the pipe cutoff frequency. Detailed results are presented on the growth rate and threshold for the damping rings of several linear collider designs. The different scaling between the wiggler CSR impedance and the dipole CSR impedance suggests an optimization for the damping ring design.

The microwave instability driven by the coherent synchrotron radiation (CSR) has been previously studied [S. Heifets and G. V. Stupakov, Phys. Rev. ST Accel. Beams 5, 054402 (2002)] neglecting effect of the shielding caused by the finite beam pipe aperture. In practice, the unstable mode can be close to the shielding threshold where the spectrum of the radiation in a toroidal beam pipe is discrete. In this paper, the CSR instability is studied in the case when it is driven by a single synchronous mode. A system of equations for the beam-wave interaction is derived and its similarity to the 1D free-electron laser theory is demonstrated. In the linear regime, the growth rate of the instability is obtained and a transition to the case of continuous spectrum is discussed. The nonlinear evolution of the single-mode instability, both with and without synchrotron damping and quantum diffusion, is also studied.

Most studies of coherent synchrotron radiation (CSR) have considered only the radiation from independent dipole magnets. However, in the damping rings of future linear colliders, a large fraction of the radiation power will be emitted in damping wigglers. In this paper, the longitudinal wakefield and impedance due to CSR in a wiggler are derived in the limit of a large wiggler parameter K. After an appropriate scaling, the results can be expressed in terms of universal functions, which are independent of K. Analytical asymptotic results are obtained for the wakefield in the limit of large and small distances, and for the impedance in the limit of small and high frequencies.

Several ideas have been proposed to “condition” an electron beam prior to the undulator of a free-electron laser (FEL) by increasing each particle’s energy in proportion to the square of its transverse betatron amplitude. This conditioning enhances FEL gain by reducing the axial velocity spread within the electron bunch. We demonstrate that for symplectic beam lines, and independent of the method, this conditioning is always accompanied by a large head-tail focusing variation which, for short-wavelength FELs, is so severe as to make conditioning completely impractical. We furthermore find that any system added to correct the head-tail focusing variation will also remove the conditioning. As an example, a new method for conditioning is presented and shown to generate exactly the same head-tail focusing problems as in previously published work.

We develop a new approach to the calculation of the synchrotron radiation in a toroidal vacuum chamber. Using a small parameter ϵ=sqrt[a/R], where a is the characteristic size of the cross section of the toroid and R is the bending radius, we simplify Maxwell’s equations assuming that the characteristic frequency of the modes ω∼c/aϵ and neglect terms of higher order in ϵ. For a rectangular cross section of the waveguide, we find an analytical solution of the equations and analyze their asymptotics at very high frequency. We then obtain an equation which gives radiation into each synchronous mode. We demonstrate the flexibility of the new method by calculating the frequencies and the loss factors for the lowest modes in square and round waveguides.

We consider the impedance of a structure with rectangular, periodic corrugations on two opposing sides of a rectangular beam tube. Using the method of field matching, we find the modes in such a structure. We then limit ourselves to the case of small corrugations, but where the depth of corrugation is not small compared to the period. For such a structure we generate analytical approximate solutions for the wave number k, group velocity v_g, and loss factor κ for the lowest (the dominant) mode which, when compared with the results of the complete numerical solution, agreed well. We find if w∼a, where w is the beam pipe width and a is the beam pipe half-height, then one mode dominates the impedance, with k∼1/sqrt[wδ] (δ is the depth of corrugation), (1-v_g/c)∼δ, and κ∼1/(aw), which (when replacing w by a) is the same scaling as was found for small corrugations in a round beam pipe. Our results disagree in an important way with a recent paper of Mostacci et al. [A. Mostacci , Phys. Rev. ST Accel. Beams 5, 044401 (2002)], where, for the rectangular structure, the authors obtained a synchronous mode with the same frequency k, but with κ∼δ. Finally, we find that if w is large compared to a then many nearby modes contribute to the impedance, resulting in a wakefield that Landau damps.