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A method for producing narrow-band THz radiation proposes passing an ultra-relativistic beam through a metallic pipe with small periodic corrugations. We present results of a measurement of such an arrangement at Brookhaven's Accelerator Test Facility (ATF). Our pipe was copper and was 5 cm long; the aperture was cylindrically symmetric, with a 1 mm (radius) bore and a corrugation depth (peak-to-peak) of 60 um. In the experiment we measured both the effect on the beam of the structure wakefield and the spectral properties of the radiation excited by the beam. We began by injecting a relatively long beam compared to the wavelength of the radiation to excite the structure, and then used a downstream spectrometer to infer the radiation wavelength. This was followed by injecting a shorter bunch, and then using an interferometer (also downstream of the corrugated pipe) to measure the spectrum of the induced THz radiation., Comment: 3 pages, 4 figures

We develop analytical models of the longitudinal and transverse wakes, on and off axis for realistic structures, and then compare them with numerical calculations, and generally find good agreement. These analytical "first order" formulas approximate the droop at the origin of the longitudinal wake and of the slope of the transverse wakes; they represent an improvement in accuracy over earlier, "zeroth order" formulas. In example calculations for the RadiaBeam/LCLS dechirper using typical parameters, we find a 16\% droop in the energy chirp at the bunch tail compared to simpler calculations. With the beam moved to 200~$\mu$m from one jaw in one dechiper section, one can achieve a 3~MV transverse kick differential over a 30~$\mu$m length., Comment: 28 pages, 13 figures

We consider the calculation of electromagnetic fields generated by an electron bunch passing through a vacuum chamber structure that, in general, consists of an entry pipe, followed by some kind of transition or cavity, and ending in an exit pipe. We limit our study to structures having rectangular cross-section, where the height can vary as function of longitudinal coordinate but the width and side walls remain fixed. For such structures, we derive a Fourier representation of the wake potentials through one-dimensional functions. A new numerical approach for calculating the wakes in such structures is proposed and implemented in the computer code ECHO(2D). The computation resource requirements for this approach are moderate and comparable to those for finding the wakes in 2D rotationally symmetric structures. Numerical examples obtained with the new numerical code are presented., Comment: 31 pages, 10 figures

In LCLS-II, after acceleration and compression and just before entering the undulator, the beam passes through 2.5 km of 24.5 mm (radius) stainless steel pipe. The bunch that passes through the pipe is extremely short---with an rms of 8 um for the nominal 100 pC case. Thus, even though the pipe has a large aperture, the wake that applies is the {\it short-range} resistive wall wakefield. The bunch distribution is approximately uniform, and therefore the wake induced voltage is characterized by a rather linear voltage chirp. It turns out that the wake supplies needed dechirping to the LCLS-II beam before it enters the undulator. In this note we calculate the wake, discuss the confidence in the calculation, and investigate how to improve the induced chirp linearity and/or strength. Finally, we also study the strength and effects of the transverse (dipole) resistive wall wakefield., Comment: 5 pages, 4 figures, presented at the 27th Linear Accelerator Conference, Geneva, Switzerland, held August 31--September 5, 2014

The superconducting cavities in the continuous wave (CW) linacs of LCLS-II are designed to operate at 2 K, where cooling costs are very expensive. One source of heat is presented by the higher order mode (HOM) power deposited by the beam. Due to the very short bunch length--especially in L3 the final linac--the LCLS-II beam spectrum extends into the terahertz range. Ceramic absorbers, at 70 K and located between cryomodules, are meant to absorb much of this power. In this report we perform two kinds of calculations to estimate the effectiveness of the absorbers and the amount of beam power that needs to be removed at 2 K., Comment: 6 pages, 4 figures, presented at 27th Linear Accelerator Conference, Linac14, held in Geneva, Switzerland on 31 August-- September, 2014

We investigate the effect of wall roughness on the wakefield-induced energy variation in the undulator beam pipe of LCLS-II. We find that a wall roughness equivalent to an rms surface slope of 30 mr increases the total induced energy variation within the bunch (due to the resistive wall wake) by a modest 20%., Comment: 16 pages, 7 figures

For LCLS-II we estimate the power of radiated wakefields generated in the SRF cavities (including the 3rd harmonic cavities) and in the end transitions. Much of this power will pass through and reflect in the strings of cryomodules that comprise linacs L1, L2, or L3. Presumably, some of it will be absorbed by the higher order mode (HOM) couplers, or by the absorbers at warmer temperatures situated between the cryomodules. We investigate where such power gets generated, but not where it ends up. As such the results can serve as a pessimistic calculation of the extra power that needs to be removed by the cryosystem. Finally, we also estimate---under the assumption that all the wake power ends up in the SRF walls---the wall heating and the extent of Cooper pair breaking in L3, where the bunch is most intense. Note that all calculations here are of single bunch effects; thus resonant interactions are not included., Comment: 16 pages, 1 figure

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 non-axisymmetric 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., Comment: 29 pages, 20 figures

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., Comment: 10 pages, 5 figures

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 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 $\kappa$ for the lowest (the dominant) mode which, when compared with the results of the complete numerical solution, agreed well. We find: if $w\sim a$, where $w$ is the beam pipe width and $a$ is the beam pipe half-height, then one mode dominates the impedance, with $k\sim1/\sqrt{w\delta}$ ($\delta$ is the depth of corrugation), $(1-v_g/c)\sim\delta$, and $\kappa\sim1/(aw)$, which (when replacing $w$ by $a$) is the same scaling as was found for small corrugations in a {\it round} beam pipe. Our results disagree in an important way with a recent paper of Mostacci {\it et al.} [A. Mostacci {\it et al.}, Phys. Rev. ST-AB, {\bf 5}, 044401 (2002)], where, for the rectangular structure, the authors obtained a synchronous mode with the same frequency $k$, but with $\kappa\sim\delta$. 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., Comment: 18 pages, 6 figures, 1 bibliography file

In the NLC project multiple bunches of electrons and positrons will be accelerated initially to a centre of mass of 500 GeV and later to 1 TeV or more. In the process of accelerating 192 bunches within a pulse train, wakefields are excited which kick the trailing bunches off axis and can cause luminosity dilution and BBU (Beam Break Up). Several structures to damp the wakefield have been designed and tested at SLAC and KEK and these have been found to successfully damp the wakefield [1]. However, these 2pi/3 structures suffered from electrical breakdown and this has prompted us to explore lower group velocity structures operating at higher fundamental mode phase advances. The wakefield partitioning amongst the bands has been found to change markedly with increased phase advance. Here we report on general trends in the kick factor and associated wakefield band partitioning in dipole bands as a function of phase advance of the synchronous mode in linacs. These results are applicable to both TW (travelling wave) and SW (standing wave) structures [1] R.M. Jones et al, PAC99, also SLAC-PUB-8103, Comment: 4 pages including title page. This is SLAC-PUB-9467 and has been submitted to The XXI International Linear Accelerator Conference (LINAC2002), Korea

We derive a simple relation for estimating the relative emittance growth in x and y due to intrabeam scattering (IBS) in electron storage rings. We show that IBS calculations for the ATF damping ring, when using the formalism of Bjorken-Mtingwa, a modified formalism of Piwinski (where eta squared divided by beta has been replaced by the dispersion invariant), or a simple high-energy approximate formula all give results that agree well. Comparing theory, including the effect of potential well bunch lengthening, with a complete set of ATF steady-state beam size vs. current measurements we find reasonably good agreement for energy spread and horizontal emittance. The measured vertical emittance, however, is larger than theory in both offset (zero current emittance) and slope (emittance change with current). The slope error indicates measurement error and/or additional current-dependent physics at the ATF; the offset error, that the assumed Coulomb log is correct to within a factor of 1.75., Comment: 17 pages, 6 figures, .bbl file

At the Accelerator Test Facility (ATF) at KEK intrabeam scattering (IBS) is a strong effect for an electron machine. It is an effect that couples all dimensions of the beam, and in April 2000, over a short period of time, all dimensions were measured as functions of current. In this report we derive a simple relation for the growth rates of emittances due to IBS. We apply the theories of Bjorken-Mtingwa, Piwinski, and a formula due to Raubenheimer to the ATF parameters, and find that the results all agree (if in Piwinski's formalism we replace the dispersion squared over beta by the dispersion invariant). Finally, we compare theory, including the effect of potential well bunch lengthening, with the April 2000 measurements, and find reasonably good agreement in the energy spread and horizontal emittance dependence on current. The vertical emittance measurement, however, implies that either: there is error in the measurement (equivalent to an introduction of 0.6% x-y coupling error), or the effect of intrabeam scattering is stronger than predicted (35% stronger in growth rates)., Comment: 4 pages, 3 figures, Presented at IEEE Particle Accelerator Conference

We present energy spread and bunch length measurements at the Accelerator Test Facility (ATF) at KEK, as functions of current, for different ring rf voltages, and with the beam both on and off the coupling resonance. We fit the on-coupling bunch shapes to those of an impedance model consisting of a resistor and an inductor connected in series. We find that the fits are reasonably good, but that the resulting impedance is unexpectedly large., Comment: 9 pages, 5 figures, presented at 10th International Symposium on Applied Electromagnetics and Mechanics (ISEM2001)

In April 2000 the single bunch energy spread, bunch length, horizontal emittance, and vertical emittance were measured as functions of current in KEK's ATF damping ring. In this report the measurement results are analyzed in light of intrabeam scattering theory. The measurements are found to be relatively consistent with theory, although the measured effects appear to be stronger than theory. In addition, the factor of 3 growth in vertical emittance at a current of 3 mA does not seem to be supported., Comment: 16 pages, 7 figures, SLAC-AP-135

This report presents bunch length and energy spread measurements performed in April 2000 at the ATF Damping Ring, at KEK. Measurements were performed with the beam on and then off the linear (difference) coupling resonance. Due to strong intra-beam scattering in the ATF ring, the results depended strongly on the coupling., Comment: 15 pages, 13 figures

We show that scattering matrix calculations for dipole modes between 23-43 GHz for the 206 cell detuned structure (DS) are consistent with finite element calculations and results of the uncoupled model. In particular, the rms sum wake for these bands is comparable to that of the first dipole band. We also show that for RDDS1 uncoupled wakefield calculations for higher bands are consistent with measurements. In particular, a clear 26 GHz signal in the short range wake is found in both results., Comment: 3 pages, 7 figures, submitted to LINAC2000 as TUA18, 21-28 August, Monterey, CA

In accelerator projects involving the use of very short bunches, such as the Linac Coherent Light Source (LCLS)-where the rms bunch length in the undulator section is 30 micron-, it appears that even submicron imperfections in the beam tube surface can generate an impedance that is unacceptably large. We consider two periodic models of an imperfect, rough surface, one with small rectangular corrugations, the other with smooth sinusoidal oscillations. We compare the impedance of these two models., Comment: 3 pages, 4 figures, for LINAC2000 paper MOA21

The injector linacs of the JLC/NLC comprise the e+ booster, the e- drive linac, the e+ booster, and the two prelinacs. These four systems together transport the two types of beams from the 80 MeV point at the end of their respective bunchers up to the storage rings, and then from the storage rings to the 10 GeV point at the beginning of the bunch compressors. Nominally, the e+ booster structure will be L-band and the others S-band. In transport through these linacs it is important that the emittances and particle losses stay within specified tolerances. In particular, the effects of the dipole wakefield-especially the long-range dipole wakefield-need to be carefully considered. We present designs of the injector linac structures that employ simple mode detuning, without damping, and that allow us to satisfy our tolerance requirements, for both the nominal (2.8 ns) and alternate (1.4 ns) bunch spacing options., Comment: 3 pages, 4 figures, 1 cls file