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Coupling impedance of a long slot and an array of slots in a circular vacuum chamber

Description: We find the real part of the longitudinal impedance for both a small hole and a long slot in a beam vacuum chamber with a circular cross section. The slot can be arbitrarily long; the only requirement on the dimensions of the slots is that its width be much smaller than c/w. Regular array of N slots periodically distributed along the pipe is also considered.
Date: June 1, 1995
Creator: Stupakov, G.V.
Partner: UNT Libraries Government Documents Department

Coupling impedance of a periodic array of diaphragms

Description: A method is presented for calculating the high-frequency longitudinal and transverse coupling impedances in a periodic array of diaphragms in a circular perfectly conducting pipe. The method is based on Weinstein`s theory of diffraction of a plane electromagnetic wave on a stack of halfplanes. Using Weinstein`s solution, it is shown that the problem of finding the beam field in the pipe reduces to an effective boundary condition at the radius of the diaphragms that couples the longitudinal electric field with the azimuthal magnetic one. Solving Maxwell`s equations with this boundary condition leads to simple formulae for Z{sub long} and Z{sub tr}. A good agreement with a numerical solution of the problem found by other authors is demonstrated.
Date: June 1, 1995
Creator: Stupakov, G.V.
Partner: UNT Libraries Government Documents Department

Emittance growth due to power ripple in a hadron collider

Description: Emittance growth of the beam caused by power supply ripple in the Superconducting Super Collider (SSC) is studied. We find that due to nonlinear terms in the equation of the betatron oscillations, the emittance grows only during an initial transient period, after which its increase saturates at some level. An analytical formula is derived that gives the fractional increase of the emittance as a function of the amplitude of the ripple. Numerical estimates for the SSC are presented.
Date: May 1, 1993
Creator: Stupakov, G.V.
Partner: UNT Libraries Government Documents Department

Using Beam Echo Effect for Generation of Short-Wavelength Radiation

Description: We propose to use 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 to optimize the amplitude of the modulation for a given harmonic number.
Date: October 31, 2008
Creator: Stupakov, G.
Partner: UNT Libraries Government Documents Department

Transient Resistive Wall Wake for Very Short Bunches

Description: The catch up distance for the resistive wall wake in a round pipe is approximately equal to the square of the pipe radius divided by the bunch length. The standard formulae for this wake are applicable at distances much larger than the catch up distance. In this paper, we calculate the resistive wall wake at distances compared with the catch up distance assuming a constant wall conductivity.
Date: May 13, 2005
Creator: Stupakov, G.
Partner: UNT Libraries Government Documents Department

Impedance Scaling for Small-angle Tapers and Collimators

Description: In this note I will prove that the impedance calculated for a small-angle collimator or taper, of arbitrary 3D profile, has a scaling property that can greatly simplify numerical calculations. This proof is based on the parabolic equation approach to solving Maxwell's equation developed in Refs. [1, 2]. We start from the parabolic equation formulated in [3]. As discussed in [1], in general case this equation is valid for frequencies {omega} >> c/a where a is a characteristic dimension of the obstacle. However, for small-angle tapers and collimators, the region of validity of this equation extends toward smaller frequencies and includes {omega} {approx} c/a.
Date: February 11, 2010
Creator: Stupakov, G.
Partner: UNT Libraries Government Documents Department

Echo-Enabled Harmonic Generation for Seeded FELs

Description: In the x-ray wavelengths, the two leading FEL concepts are the self-amplified spontaneous emission (SASE) configuration and the high-gain harmonic generation (HGHG) scheme. While the radiation from a SASE FEL is coherent transversely, it typically has rather limited temporal coherence. Alternatively, the HGHG scheme allows generation of fully coherent radiation by up-converting the frequency of a high-power seed laser. However, due to the relatively low up-frequency conversion efficiency, multiple stages of HGHG FEL are needed in order to generate x-rays from a UV laser. The up-frequency conversion efficiency can be greatly improved with the recently proposed echo-enabled harmonic generation (EEHG) technique. In this work we will present the concept of EEHG, and address some practically important issues that affect the performance of the seeding. We show how the EEHG can be incorporated in the FEL scheme and what is the expected performance of the EEHG seeded FEL. We will then briefly describe the first proof-of-principle EEHG experiment carried out at the Next Linear Collider Test Accelerator (NLCTA) at SLAC. We will also discuss latest advances in the echo-scheme approach, and refer to subsequent modifications of the original concept.
Date: May 19, 2011
Creator: Stupakov, G.
Partner: UNT Libraries Government Documents Department

Effect of Centrifugal Transverse Wakefield for Microbunch in Bend

Description: We calculate centrifugal force for a short bunch in vacuum moving in a circular orbit and estimate the emittance growth of the beam in a bend due to this force. Many of the basic features of the coherent synchrotron radiation (CSR) of short bunches and its effect on beam dynamics in accelerators are now well established. The effect is usually described in terms of the longitudinal force, or wakefield, that causes the energy loss in the beam, and also redistributes the energy between the particles by accelerating the head and decelerating the tail of the bunch. Coherent radiation becomes most important for short bunches and high currents. More subtle features of CSR such as transition effect due to the entrance to and exit from the bend, CSR force in the undulator, and shielding due to the close metallic boundaries have been also studied. Much less is known about the transverse force in a short bunch moving on a circular orbit. The problem has been treated in several papers beginning from R. Talman's work, who pointed out that the centrifugal force of a rotating bunch can result in a noticeable tune shift of betatron oscillations. Later, an important correction to the Talman paper has been added, where it was shown that due to the energy variation in the bunch, the effect of the transverse force proportional to R{sup -1} is canceled, and the residual effect is of the order of R{sup -2}, that is much smaller than originally predicted. Recently, however, Derbenev and Shiltsev found the centrifugal force of the order of R{sup -1} that differs from Talman's result by a logarithmic factor only. Taking into account the existing controversy in the literature, in this paper, we consider the transverse force in a bunch based on simple physical arguments, starting from ...
Date: March 22, 2006
Creator: Stupakov, G. V.
Partner: UNT Libraries Government Documents Department

Fast Ion Instability in Real Lattice

Description: The ionization of residual gas by an electron beam in an accelerator generates ions that can resonantly couple to the beam through a wave propagating in the beam-ion system. The original theory of the Fast Ion Instability was developed assuming both a constant external focusing and the beam size. The theory predicts an instability in which an initial perturbation grows as {approx} exp({alpha}{radical}t). In the present paper we consider a more realistic model that takes into account variation of the beta function in the lattice and associated with it variation of the beam size. We find that, in combination with ion decoherence effect, the spatial inhomogeneity can result in (1) purely exponential growth, {approx} exp({Lambda}t); and (2) typically smaller growth rates. Detailed calculations are performed for the lattice of the Advanced Light Source at the LBL.
Date: September 9, 2011
Creator: Stupakov, G.V.
Partner: UNT Libraries Government Documents Department

Geometrical Wake of a Smooth Flat Collimator

Description: A transverse geometrical wake generated by a beam passing through a smooth flat collimator with a gradually varying gap between the upper and lower walls is considered. Based on generalization of the approach recently developed for a smooth circular taper we reduce the electromagnetic problem of the impedance calculation to the solution of two much simpler static problems - a magnetostatic and an electrostatic ones. The solution shows that in the limit of not very large frequencies, the impedance increases with the ratio h/d where h is the width and d is the distance between the collimating jaws. Numerical results are presented for the NLC Post Linac collimator.
Date: September 9, 2011
Creator: Stupakov, G.V.
Partner: UNT Libraries Government Documents Department

Beam Echo Effect for Generation of Short-Wavelength Radiation

Description: The Echo-Enabled Harmonic Generation (EEHG) FEL uses two modulators in combination with two dispersion sections to generate a high-harmonic density modulation starting with a relatively small initial energy modulation of the beam. After presenting the concept of the EEHG, we address several practically important issues, such as the effect of coherent and incoherent synchrotron radiation in the dispersion sections. 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. We then discuss application of the echo modulation for generation of attosecond pulses of radiation, and also using echo for generation of terahertz radiation. We present main parameters of a proof-of-principle experiment currently being planned at SLAC for demonstration of the echo modulation mechanism.
Date: December 9, 2009
Creator: Stupakov, G.
Partner: UNT Libraries Government Documents Department

ADVANCES IN IMPEDANCE THEORY

Description: We review recent progress in the following areas of the impedance theory: calculation of impedance of tapers and small angle collimators; optical approximation and parabolic equation for the high-frequency impedance; impedance due to resistive inserts in a perfectly conducting pipe.
Date: June 5, 2009
Creator: Stupakov, G.
Partner: UNT Libraries Government Documents Department

Study of the trapped modes at the vacuum ports

Description: Pumping ports in PEP-II vacuum chamber will be shielded with slots cut in the walls of the beam pipe. The number of slots n{sub s}, their length l, and width w are defined by the required pumping conductance. The present design has 40 slots around the stainless steel round pipe in the straight sections, and, for the rectangular copper chamber of the arcs, there are 18 slots placed in upper and lower decks. Here we want to address two potential problems related to the slots: radiation of the TE HOM-s through the slots, and generation of the trapped modes.
Date: January 1, 1995
Creator: Heifets, S. & Stupakov, G.
Partner: UNT Libraries Government Documents Department

Study of beam decoherence in the presence of head-tail instability using a two-particle model

Description: The decoherence behavior of a beam centroid motion after a kick is studied using a two-particle model. A simple theory based on averaging of the governing equation is developed. The effects of a finite chromaticity and synchrotron motion are taken into account. Increasing the tune spread in the beam, a transition from a head-tail instability to a stable decay of an initial kick is explicitly demonstrated.
Date: June 1, 1995
Creator: Stupakov, G.V. & Chao, A.W.
Partner: UNT Libraries Government Documents Department

Coupling impedance of a periodic array of diaphragms

Description: A method is presented for calculating the high-frequency longitudinal and transverse coupling impedances in a periodic array of diaphragms in a circular perfectly conducting pipe. The method is based on Weinstein`s theory of diffraction of a plane electromagnetic wave on a stack of halfplanes. Using Weinstein`s solution, it is shown that the problem of finding the beam field in the pipe reduces to an effective boundary condition at the radius of the diaphragms that couples the longitudinal electric field with the azimuthal magnetic one. Solving Maxwell`s equations with this boundary condition leads to simple formulae for Z(long) and Z(tr). A good agreement with a numerical solution of the problem found by other authors is demonstrated.
Date: June 1, 1995
Creator: Stupakov, G.V.
Partner: UNT Libraries Government Documents Department

CALCULATING POINT-CHARGE WAKEFIELDS FROM FINITE LENGTH BUNCH WAKE-POTENTIALS

Description: Starting from analytical properties of high frequency geometric impedance we show how one can accurately calculate short bunch wake-potentials (and even point-charge wakefields) from time domain calculations performed with a much longer bunch. In many practical instances this drastically reduces the need for computer resources, speeds up the calculations, and improves their accuracy. To illustrate this method we give examples for 2D accelerator structures of various complexities. We describe preliminary results of a new method that allows us to accurately obtain longitudinal wakefields of short bunches by adding a long-bunch result from an EM solver and a singular analytical wake model. In the future this work will be generalized to 3D geometries as well. Similarly, the method should be equally applicable to the calculations of transverse wakefields. Periodic structures with a significant number of periods (2 {ge} a{sup 2}/{sigma}L, where L is the period length) have not been considered so far. They have asymptotic wakefields that differ from the examples described above. We believe this method is applicable to such geometries as well, as long as correct asymptotic solutions are used.
Date: March 28, 2011
Creator: Podobedov, B. & Stupakov, G.
Partner: UNT Libraries Government Documents Department

A new method for calculation of low-frequency coupling impedance

Description: In high-energy proton accelerators and storage rings the bunch length is typically at least a few times larger than the radius of the vacuum chamber. For example, the SSC will have an rms bunch length above 6 cm and a beam-pipe radius below 2 cm. The main concern for beam stability in such a machine is the low-frequency impedance, i.e., the coupling impedance at frequencies wen below the cut-off frequency of the vacuum chamber. In the present paper we develop a new analytical approach for calculation of the low-frequency impedance of axisymmetric structures that allows us to give quick and reliable estimates of contributions to the impedance from various chamber discontinuities. Simple formulae for the longitudinal impedance of some typical discontinuities are obtained.
Date: May 1, 1993
Creator: Kurennoy, S.S. & Stupakov, G.V.
Partner: UNT Libraries Government Documents Department

Emittance Limitation of a Conditioned Beam in a Strong Focusing FEL Undulator

Description: Various methods have been proposed to condition an electron beam in order to reduce its emittance effect and to improve the short-wavelength free electron laser (FEL) performance. In this paper, we show that beam conditioning does not result in a complete elimination of the emittance effect in an alternating-gradient focusing FEL undulator. Using a one-dimensional model and a three-dimensional simulation code, we derive a criteria for the emittance limitation of a perfectly conditioned beam that depends on the focusing structure.
Date: March 24, 2006
Creator: Huang, Z.; Stupakov, G. & Reiche, S.
Partner: UNT Libraries Government Documents Department

Coherent Soft X-Ray Generation in the Water Window with the EEHG Scheme

Description: Recently a scheme entitled echo-enabled harmonic generation (EEHG) was proposed for producing short wavelength FEL radiation that allows far higher harmonic numbers to be accessed as compared with the normal limit arising from incoherent energy spread. In this paper we study the feasibility of a single EEHG stage to generate coherent radiation in the 'water window' (2--4 nm wavelength) directly from a UV seed laser at 190-nm wavelength. We present time-dependent simulation results which demonstrate that the single-stage EEHG FEL can generate high power soft x-ray radiation in the water window with narrow bandwidth close to Fourier transform limit directly from a UV seed laser. The schemes to generate short x-ray pulse from femtosecond to attosecond using EEHG FEL are also discussed.
Date: May 26, 2009
Creator: Xiang, D. & Stupakov, G.
Partner: UNT Libraries Government Documents Department

Free Electron Lasers with Slowly Varying Beam and Undulator Parameters

Description: The performance of a free electron lasers (FEL) is affected when the electron beam energy varies alone the undulator as would be caused by vacuum pipe wakefields and/or when the undulator strength parameter is tapered in the small signal regime until FEL saturation. In this paper, we present a self-consistent theory of FELs with slowly-varying beam and undulator parameters. A general method is developed to apply the WKB approximation to the beam-radiation system by employing the adjoint eigenvector that is orthogonal to the eigenfunctions of the coupled Maxwell-Vlasov equations. This method may be useful for other slowly varying processes in beam dynamics.
Date: May 25, 2005
Creator: Huang, Z. & Stupakov, G.
Partner: UNT Libraries Government Documents Department

Running Shanghai Soft x-ray FEL with the EEHG scheme

Description: With the nominal beam parameters (beam energy: 0.84 GeV, slice energy spread: 168 keV, peak current: 600 A, normalized emittance: 2 mm mrad) of the Shanghai soft X-ray Free Electron Laser (SXFEL) project, we show that using the echo-enabled harmonic generation (EEHG) scheme, 9 nm coherent soft x-ray with peak power exceeding 400 MW can be generated directly from the 270 nm seeding laser.
Date: December 18, 2008
Creator: Xiang, D. & Stupakov, G.
Partner: UNT Libraries Government Documents Department

Model of CSR Induced Bursts in Slicing Experiments

Description: We suggest a model describing the CSR bursts observed in recent experiments at the Advanced Light Source at the LBL. The model is based on the linear theory of the CSR instability in electron rings. We describe how an initial perturbation of the beam generated by the laser pulse evolves in time when the beam is unstable due to the CSR wakefield.
Date: May 16, 2006
Creator: Stupakov, G. & Heifets, S.
Partner: UNT Libraries Government Documents Department

Corrugated Pipe as a Beam Dechirper

Description: We have studied the use of a metallic pipe with small corrugations for the purpose of passively dechirping, through its wakefield, a short, intense electron bunch. The corrugated pipe is attractive for this purpose because its wake: (i) has near maximal possible amplitude for a given aperture and (ii) has a relatively large oscillation wave length, even when the aperture is small. We showed how the corrugated structure can satisfy dechirping requirements encountered in the NGLS project at LBNL. We found that a linear chirp of -40 MeV/mm can be induced by an NGLS-like beam, by having it pass through a corrugated, metallic pipe of radius 3 mm, length 8.2 m, and corrugation parameters full depth 450 {mu}m and period 1000 {mu}m. This structure is about 15 times as effective in the role of dechirper as an S-band accelerator structure used passively.
Date: April 20, 2012
Creator: Bane, K. L. F. & Stupakov, G.
Partner: UNT Libraries Government Documents Department