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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.

Effect of Finite Pulse Length and Laser Frequency Chirp on HGHG and EEHG Seeding

Description: Theoretical studies of high-gain harmonic generation (HGHG) and echo-enabled harmonic generation (EEHG) often start from a simplified model in which the beam is assumed infinitely long and longitudinally uniform and the laser induced energy modulation is perfectly sinusoidal and of infinite duration. In such a model the resulting seed has a spectrum consisting of a collection of delta-functions (of zero width) located at the harmonics of the laser frequency. Being a useful tool for study of the seed bunching amplitudes, such a model cannot be used for realistic analysis the spectral properties of the seed. In this paper we take into account the finite duration of the laser pulse as well as some possible laser phase errors to study their effect on the spectrum of the seed.
Date: November 18, 2011
Creator: Stupakov, G.

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.

Luminosity dilution due to random offset beam-beam interaction

Description: We consider beam-beam interaction in a collider in the case when the beams randomly displace around the equilibrium orbit at the interaction point. Due to the random part of the interaction, particles diffuse over the betatron amplitude causing an emittance growth of the beam. A Fokker-Planck equation is derived in which a diffusion coefficient is related with the spectral density of the noise. Estimations for the Superconducting Super Collider parameters give a tolerable level of the high-frequency beam offset at the interaction point. 2 refs.
Date: November 1, 1991
Creator: Stupakov, G.

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.

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.

Surface Impedance Formalism for a Metallic Beam Pipe with Small Corrugations

Description: A metallic pipe with wall corrugations is of special interest in light of recent proposals to use such a pipe for the generation of terahertz radiation and for energy dechirping of electron bunches in free electron lasers. In this paper we calculate the surface impedance of a corrugated metal wall and show that it can be reduced to that of a thin layer with dielectric constant {epsilon} and magnetic permeability {mu}. We develop a technique for the calculation of these constants, given the geometrical parameters of the corrugations. We then calculate, for the specific case of a round metallic pipe with small corrugations, the frequency and strength of the resonant mode excited by a relativistic beam. Our analytical results are compared with numerical simulations, and are shown to agree well.
Date: August 30, 2012
Creator: Stupakov, G. & Bane, K. L. F.

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.

Using Nonlinear RF Acceleration for FEL Beam Conditioning

Description: We consider a new approach to condition an electron beam using nonlinear effects in the RF field. We demonstrate that such effects can generate a desirable--for the FEL interaction--radial variation of the particle's energy in the beam, and calculate the induced energy spread in the limit of weak field.
Date: December 14, 2005
Creator: Stupakov, G. & Huang, Z.

Coupling Impedance of a Periodic Array of Diaphragms (Erratum)

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: May 24, 2012
Creator: Stupakov, G. V.

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.

CSR IMPEDANCE DUE TO A BEND MAGNET OF FINITE LENGTH WITH A VACUUM CHAMBER OF RECTANGULAR CROSS SECTION

Description: We study the 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. Our method represents a further development of the previous studies: 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. We illustrate our general method by calculating the CSR impedance of a beam moving in a toroidal vacuum chamber of rectangular cross section.
Date: June 5, 2009
Creator: Stupakov, G.; /SLAC; Kotelnikov, I.A. & U., /Novosibirsk State

Impedance Scaling for Small Angle Transitions

Description: Based on the parabolic equation approach to Maxwell's equations we have derived scaling properties of the high frequency impedance/short bunch wakefields of structures. For the special case of small angle transitions we have shown the scaling properties are valid for all frequencies. Using these scaling properties one can greatly reduce the calculation time of the wakefield/impedance of long, small angle, beam pipe transitions, like one often finds in insertion regions of storage rings. We have tested the scaling with wakefield simulations of 2D and 3D models of such transitions, and found that the scaling works well. In modern ring-based light sources one often finds insertion devices having extremely small vertical apertures (on the order of millimeters) to allow for maximal undulator fields reaching the beam. Such insertion devices require that there be beam pipe transitions from these small apertures to the larger cross-sections (normally on the order of centimeters) found in the rest of the ring. The fact that there may be many such transitions, and that these transitions introduce beam pipe discontinuities very close to the beam path, means that their impedance will be large and, in fact, may dominate the impedance budget of the entire ring. To reduce their impact on impedance, the transitions are normally tapered gradually over a long distance. The accurate calculation of the impedance or wakefield of these long transitions, which are typically 3D objects (i.e. they do not have cylindrical symmetry), can be quite a challenging numerical task. In this report we present a method of obtaining the impedance of a long, small angle transition from the calculation of a scaled, shorter one. Normally, the actual calculation is obtained from a time domain simulation of the wakefield in the structure, where the impedance can be obtained by performing a Fourier transform. We shall ...
Date: October 27, 2010
Creator: Stupakov, G.; Bane, Karl; /SLAC; Zagorodnov, I.; /DESY & ,

Calculation of the Beam Field in the LCLS Bunch Length Monitor

Description: Maintaining a stable bunch length and peak current is a critical step for the reliable operation of a SASE based x-ray source. In the LCLS, relative bunch length monitors (BLM) right after both bunch compressors are proposed based on the coherent radiation generated by the short electron bunch. Due to its diagnostic setup, the standard far field synchrotron radiation formula and well-developed numerical codes do not apply for the analysis of the BLM performance. In this paper, we develop a calculation procedure to take into account the near field effect, the effect of a short bending magnet, and the diffraction effect of the radiation transport optics. We find the frequency response of the BLM after the first LCLS bunch compressor and discuss its expected performance.
Date: June 7, 2006
Creator: Stupakov, G.; Ding, Y.; Huang, Z. & /SLAC

FEL and Optical Klystron Gain for an Electron Beam with Oscillatory Energy Distribution

Description: If the energy spread of a beam is larger then the Pierce parameter, the FEL gain length increases dramatically and the FEL output gets suppressed. We show that if the energy distribution of such a beam is made oscillatory on a small scale, the gain length can be considerably decreased. Such an oscillatory energy distribution is generated by first modulating the beam energy with a laser via the mechanism of inverse FEL, and then sending it through a strong chicane. We show that this approach also works for the optical klystron enhancement scheme. Our analytical results are corroborated by numerical simulations.
Date: December 9, 2009
Creator: Stupakov, G.; Ding, Y.; Huang, Z. & /SLAC

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.

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.

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.

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.