FEL Theory

MOCOS03 Backward Wave Excitation and Generation of Oscillations in Distributed Gain Media and Free-Electron Lasers in the Absence of Feedback
Yosef Pinhasi, Yuri Lurie, Gad A. Pinhasi, Asher Yahalom (The College of Judea and Samaria, Ariel)

Quantum and free-electron lasers (FELs) are based on distributed interactions between electromagnetic radiation and gain media. In an amplifier configuration, a forward wave is amplified while propagating in a polarized medium. Formulating a coupled mode theory for excitation of both forward and backward waves, we identify conditions for phase matching, leading to efficient excitation of backward wave without any mechanism of feedback or resonator assembly. The excitations of incident and reflected waves are described by a set of coupled differential equations expressed in the frequency domain. The induced polarization is given in terms of an electronic susceptibility tensor. In quantum lasers the interaction is described by two first order differential equations, while in high-gain free-electron lasers, the differential equations are of the third order each. Analytical solutions of reflectance and transmittance for both quantum lasers and FELs are presented. It is found that when the solutions become infinite, the device operates as an oscillator, producing radiation at the output with no field at its input, entirely without any localized or distributed feedback.

MOCOS05 CSRtrack: Faster Calculation of 3-D CSR Effects
Martin Dohlus, Torsten Limberg (DESY, Hamburg)

CSRtrack is a new code for the simulation of Coherent Synchrotron radiation effects on the beam dynamics of linear accelerators. It incorporates the physics of our previous code, TraFiC4, and adds new algorithms for the calculation of the CSR fields. A one-dimensional projected method allows quick estimates and a greens function method allows 3D calculations about ten times faster than with the `direct' method. The tracking code is written in standard FORTRAN77 and has its own parser for comfortable input of calculation parameters and geometry. Phase space input and the analysis of the traced particle distribution is done with MATLAB interface programs.

MOPOS08 A 3D Self-Consistent, Analytical Model for Longitudinal Plasma Oscillation in a Relativistic Electron Beam
Gianluca Geloni, Evgeny L. Saldin, Evgeny A. Schneidmiller, Mikhail V. Yurkov (DESY, Hamburg)

Longitudinal plasma oscillations are becoming a subject of great interest for XFEL physics in connection with LSC microbunching instability [1] and certain pump-probe synchronization schemes [2]. In the present paper we developed the first exact analytical treatment for longitudinal oscillations within an axis-symmetric, (relativistic) electron beam, which can be used as a primary standard for benchmarking space-charge simulation codes. Also, this result is per se of obvious theoretical relevance as it constitutes one of the few exact solutions for the evolution of charged particles under the action of self-interactions.

MOPOS09 Benchmark of ASTRA with Analytical Solution for the Longitudinal Plasma Oscillation Problem
Gianluca Geloni, Evgeny L. Saldin, Evgeny A. Schneidmiller, Mikhail V. Yurkov (DESY, Hamburg)

During the design of X-FELs, space-charge codes are required to simulate the evolution of longitudinal plasma oscillation within an electron beam in connection with LSC microbunching instability [1] and certain pump-probe synchronization schemes [2]. In the paper [3] we presented an analytical solution to the initial value problem for longitudinal plasma oscillation in an electron beam. Such a result, besides its theoretical importance, allows one to benchmark space-charge simulation programs against a self-consistent solution of the evolution problem. In this paper we present a comparison between our results [3] and the outcomes of the simulation code ASTRA.

MOPOS22 Off-Axis Orbits in Realistic Helical Wigglers: Fixed Points and Time Averaged Dynamical Variables
John Thomas Donohue (CENBG, Gradignan), Jean-Luc Rullier (CESTA, Le Barp)

Many years ago Fajans, Kirkpatrick and Bekefi studied off-axis orbits in a realistic helical wiggler, both experimentally and theoretically. They found that as the distance from the axis of symmetry to the guiding center increased, both the mean axial velocity and the precession frequency of the guiding center varied. . They proposed a clever semi-empirical model which yielded an excellent description of both these variations. We point out that a approximate model proposed by us several years ago can be made to predict these delicate effects correctly, provided we extend our truncated quadratic Hamiltonian to include appropriate cubic terms. We develop an argument similar to the virial theorem to compare time averaged and fixed-point values of dynamical variables. Illustrative comparisons of our model with numerical calculation are presented.

MOPOS23 Analytic Electron Trajectories in an Extremely Relativistic Helical Wiggler: an Application to the Proposed SLAC E166 Experiment.
John Thomas Donohue (CENBG, Gradignan)

The proposed experiment SLAC E166 intends to generate circularly polarized gamma rays of energy 10 MeV by passing a 15 GeV electron beam through a meter long wiggler with approximately 400 periods. Using an analytic model formulated by Rullier and me, I present calculations of electron trajectories. At this extremely high energy the trajectories are described quite well by the model, and an extremely simple picture emerges, even for trajectories that that fail to encircle the axis of the wiggler. Our calculations are successfully compared with standard numerical integration of the Lorentz force equations of motion. In addition, the calculation of the spectrum and angular distribution of the radiated photons is easily carried out.

MOPOS26 Harmonic Generation and Linewidth Narrowing in Seeded FELs
Luca Giannessi (ENEA C.R. Frascati, Frascati - Roma)

The process of harmonic generation in a seeded single pass Free Electron Laser are studied in the time/frequency domain. The linewidth narrowing of the fundamental harmonic is correlated to the amplitude of the input seed. The spectral evolution of the harmonics is studied within a self consistent time dependent model.

MOPOS29 Analytical Solution of Phase Space Evolution of Electrons in a SASE FEL
Nobuyuki Nishimori (JAERI/FEL, Ibaraki-ken)

The phase space evolution of electrons in a self-amplified spontaneous emission (SASE) FEL operating in the linear regime before saturation is solved analytically from the one dimensional (1D) FEL equaiton. The analytical solution agrees well with a time-dependent numerical simulation which solves the 1D FEL equation in an exact manner and includes a shot-noise effect. The radiation field reaches saturation when the optimum bunching of the electrons is formed on the scale of the resonant wavelength. The optimum bunching leads to the well known saturation condition ρ Nw ~ 1.

MOPOS32 Behaviour of Electron Beam in Combined a Self-Generated Field and a Reversed Guide Field in the Helical Wiggler
Soon-Kwon Nam, Ki-Bum Kim (Kangwon National University, Kangwon-Do)

We have studied behaviour of electron beam in combined a self-generated field and a reversed axial-guide field in the tapered helical wiggler. The divergence of electron beam is caused by a three-dimensional effect on the off-axis electrons and self-generated fields. In order to reduce the electron beam loss, we employ a tapered and reversed axial-guide magnetic field. Evolution of energy spread and emittance of electron beam are investigated using three dimensional simulation. Beam cross-section, transverse momentum variation and cross-section view of electron beam are calculated along the z axis. The electron beam loss is reduced by optimizing the magnetic field strength and tapering parameter of reversed axial guide field.

MOPOS33 Evolution of Electron Beam in the Tapered Planar Wiggler
Soon-Kwon Nam, Ki-Bum Kim (Kangwon National University, Kangwon-Do)

We have investigated the evolution of electron beam in the tapered planar wiggler field with a axial-guide field, self-electric fields, and self-magnetic fields. In order to suppress the divergence of emittance and energy spread of the electron beam by the three-dimensional effects on the off-axis electrons and a self-generated field effect,the wiggler field was tapered and the reversed axial-guide magnetic field was applied. We calculate the emittance, transverse trajectories and Fourier transfomation of electron beam using three dimensional simulation by optimizing the magnetic field strength, a tapering parameter and self-field parameters. This method could be expected to enhance the gain and efficiency compared to those of a uniform axial-guide field and a untapered wiggler in a free-electron laser.

MOPOS39 The Effect of Liner Induced Phase Fluctuations on the Gain of a Cerenkov FEL
Isabel de la Fuente, Klaus Boller, Peter van der Slot (UTWENTE, Enschede)

It is well known that wiggler errors can degrade the gain of a FEL. A similar process takes places in a Cerenkov FEL where the phase velocity of the amplified EM wave is determined by parameters of the dielectric liner. Thus deviations in the inner radius (Rd) of the liner will result in fluctuations of the phase velocity of the EM wave. E.g., for a quartz liner (εr=4.4) with Rd = 1.5 mm and outer radius of 4 mm, the derivative of the longitudinal wavenumber with respect to Rd is about 105 m-2 for a frequency of 50 GHz. Thus fluctuations in the Rd induce phase fluctuations that may degrade the gain of a Cerenkov FEL. In contrast to the undulator FEL, where the relative phase fluctuations are a result from deviations in the electron trajectories, the phase fluctuations are a result of pertubations in the radiation field for a Cerenkov FEL. As an example of the influence of pertubations in the inner radius of the liner on the gain we will present results of an analysis for a 100 kV Cerenkov FEL operating at a frequency of 50 GHz.

MOPOS40 Simulation Investigation of the Detuning Curve
Xiaojian Shu, Yuhuan Dou, Yuanzhang Wang (IAP, Beijing)

The detuning curves of free-electron laser oscillators are calculated with the help of our three-dimensional code, which are compared with those from one-dimensional simulations and supermode theory, and the experiments. The influence of the optical guiding and other three-dimensional effects on the detuning curve is studied. It is found that the length of the detuning curve from three-dimemsional simulations is shorter than that from one-dimensional simulations and supermode theroy.

MOPOS41 Harmonic Amplifier Free Electron Laser
Qika Jia (USTC/NSRL, Hefei, Anhui)

The evolution of the optical field for an optical klystron(OK) free electron laser is described analytically for both low gain case and high gain case. The harmonic optical klystron (HOK) in which the second undulator is resonant on the higher harmonic of the first undulator is analysed as a harmonic amplifier. The optical field evolution equation of the HOK is derived analytically for both CHG mode (Coherent Harmonic Generation, the quadratic gain regime) and HGHG mode (High Gain Harmonic Generation, the exponential gain regime), the effects of energy spread, energy modulation and dispersion in the whole process are considered. For the quadratic gain regime, the analytical formula of CHG mode is given and compared with that of OK case. For the exponential gain regime, the linear theory of HGHG mode is given and discussed.

MOPOS42 Parameter Analysis For A High-Gain Harmonic Generation FEL By Numerical Calculation Based On 1D Theory
Yuhui Li, Qika Jia, Shancai Zhang (USTC/NSRL, Hefei, Anhui)

The high-gain harmonic generation (HGHG) free-electron laser (FEL) is an important candidate for a fourth-generation light source. Lots of theoretical work has been performed. Recently a further 1D theory about HGHG FEL has been developed. It considers the effects of different parameters for the whole process. An initial program based on this theory has been made. In this paper, a brief comparison of the results from this 1D program and from TDA (3D code) is discussed. It also analyses the parameters for Shanghai deep ultra violate free-electron laser source (SDUV-FEL), including electron beam energy spread, seed laser power, strength of dispersion section etc.

MOPOS49 Improving Selectivity of 1D Bragg Resonator Using Coupling of Propagating and Trapped Waves
Naum Samuilovich Ginzburg, Andrey Malkin, Nikolay Peskov, Alexander Sergeevich Sergeev (IAP RAS, Nizhny Novgorod), Artem Elzhov, Alim Kaminsky, Sergey Sedykh, Anatoly Sergeev (JINR, Dubna, Moscow Region)

A novel 1D Bragg resonator based on coupling propagated and locked (quasi cut-off) modes should be tested in a JINR- IAP FEM-oscillator to improve selectivity over the transverse mode index. In this scheme the electron beam interacts with only propagating wave, and the latter is coupled with a quasi cut-off mode. This coupling can be realized by either helical or azimuthally-symmetric corrugation. The quasi cut-off mode provides the feedback in the system leading to the absolute instability and the self-excitation of the whole system while efficiency in the steady-state regime of generation is almost completely determined by the propagating mode, synchronous to the beam. Analytical consideration and numerical simulation show that the efficiency of such an FEM can be rather high. The main advantage of this scheme is provision of higher selectivity over the transverse mode index than traditional scheme of Bragg FEL that encourage increasing operating frequency for fixed transverse size of the interaction space.

MOPOS57 Analytic Model of Harmonic Generation in the Low-Gain FEL Regime
Gregory Penn (LBNL/CBP, Berkeley, California), Matthias Reinsch (LBNL, Berkeley, California), Jonathan Wurtele (LBNL, Berkeley, California; UC Berkeley, Berkeley)

Harmonic generation using free electron lasers (FELs) requires two undulators: the first generates energy modulation through the inverse FEL effect; the second undulator uses the subsequently bunched beam to radiate at a higher harmonic. These processes are currently evaluated using extensive calculations or simulation codes which can be slow to evaluate and difficult to set up. We describe a simple algorithm to predict the output of a harmonic generation beamline in the low-gain FEL regime based on trial functions for the output radiation. Full three-dimensional effects are included. This method has been implemented as a Mathematica script which runs rapidly and can be generalized to include effects such as asymmetric beams and misalignments. This method is compared with simulation results using the FEL code GENESIS, both for single stages of harmonic generation and to model the design of LUX, a proposed facility for ultra-short X-ray pulses, where multiple stages upshift the input laser frequency by factors of up to 200.

MOPOS65 Short Rayleigh Length Free Electron Laser Simulations in Expanding Coordinates
Robert L. Armstead, Joseph Blau, William B. Colson (NPS, Monterey, CA)

For compact short-Rayleigh length FELs, the area of the optical beam can be thousands of times greater at the mirrors than at the beam waist. A fixed numerical grid of sufficient resolution to represent the narrow mode at the waist and the broad mode at the mirrors would be prohibitively large. To accommodate this extreme change of scale with no loss of information, we employ a coordinate system that expands with the diffracting optical mode. The simulation using the new expanding coordinates has been validated by comparison to analytical cold-cavity theory, and is now used to simulate short-Rayleigh length FELs.

MOPOS66 Optical Mode Distortion in a Short Rayleigh Length Free Electron Laser
Joseph Blau, William B. Colson, Robb P. Mansfield, Sean P. Niles, Brett W. Williams (NPS, Monterey, CA)

A short-Rayleigh length FEL will operate primarily in the fundamental mode with a Gaussian profile that is narrow at the waist and broad at the mirrors. The gain medium will distort the optical mode profile and produce higher-order modes that will expand more rapidly than the fundamental. Wavefront propagation simulations are used to study the higher-order modes, as the cavity length, Rayleigh length, electron beam current and radius, undulator taper, and the focus positions of the optical mode and electron beam are varied.

MOPOS69 Wiggler Effects on the Growth Rate of a Raman Free-electron Laser with Axial Magnetic Field or Ion-Channel Guiding
Behrouz Maraghechi (IPM, Tehran; AUT, Tehran), Hossein Aghahosseini (AUT, Tehran), Amir Kordbacheh (AUT, Tehran; IPM, Tehran)

A relativistic theory for Raman backscattering in the beam frame of electrons is presented and is used to find the growth rate of a free-electron laser (FEL), in the Raman regime. A one dimensional helical wiggler and an axial magnetic field are considered. The effects of static self-electric and self-magnetic fields, induced by the steady-state charge density and currents of the non-neutral electron beam, are taken into account to find the steady-state trajectories. The wiggler effects on the linear dispersion relations of the space-charge wave and radiation are included in the analysis. A numerical computation is conducted to compare the growth rate of the excited waves with nonrelativistic treatment. It was found that self-field effects increase the growth rate in the group II orbits and decrease it in the group I orbits. However, the wiggler effects on growth rate are stronger and increase the growth rate on both group I and group II orbits. The discontinuity, due to the cyclotron resonance with the radiation, is removed by including the self-fields or wiggler effects.