Parabolic Pole Research Articles

Three-dimensional and nonlinear analysis of efficiency enhancement in the E × B drifting electron laser with a prebunched electron beam and a planar wiggler

AbstractA nonlinear simulation of the E × B drifting electron laser (DEL) and the free-electron laser (FEL), in three dimensions, is presented for a prebunched electron beam to study efficiency enhancement. For the planar wiggler with flat pole faces, prebunching considerably shortens the saturation length, which favors the DEL compared to the FEL. Operation of the DEL with the planar wiggler with parabolic pole faces was not found to be possible due to the modulation of the E × B drift by the wiggler. However, simulation results of the FEL with this type of wiggler are reported.

Simulation of the effect of wiggler imperfections on harmonic generation in two-beam free-electron lasers

A three-dimensional simulation of a free-electron laser (FEL) with two beams is used to study the sensitivity of the third harmonic due to wiggler imperfections. In the two-beam FEL, for a fundamental wavelength of 107.5 nm, the power will be converted to the third harmonic at a shorter wavelength, in this case in the extreme ultraviolet at 35.8 nm. In this arrangement, the fundamental resonance of the higher energy beam coincides with the third harmonic of the lower energy beam, for this energy conversion to take place. For enhanced focusing, a planar wiggler with parabolic pole face is considered. Investigation of the effect of wiggler errors on the efficiencies of harmonic and fundamental resonance of the two-beam and the one-beam FEL shows that the average efficiency for the third harmonic in the two-beam FEL is decreased by 36% while the reduction of average efficiency for the fundamental of the two-beam is 55% and for the third harmonic of the one-beam is 48%. This shows that the third harmonic radiation in the two-beam FEL is less sensitive to wiggler imperfection compared to its fundamental as well as the third harmonic in the one-beam FEL. The reason is that the energy that transfers to the third harmonic of the two-beam FEL comes from both electron beams. It was also found that, for almost all cases, standard deviation increases with an increasing level of wiggler imperfection while, for the two-beam FEL, saturation length of the fundamental resonance decreases and the third harmonic increases with increasing wiggler imperfection.

Robust H/sub /spl infin// filter design with variance constraints and parabolic pole assignment

In this letter, we consider a multiobjective filtering problem for uncertain linear continuous time-invariant systems subject to error variance constraints. A linear filter is used to estimate a linear combination of the system states. The problem addressed is the design of a filter such that, for all admissible parameter uncertainties, the following three objectives are simultaneously achieved: 1) the filtering process is P-stable, i.e., the poles of the filtering matrix are located inside a parabolic region; 2) the steady-state variance of the estimation error of each state is not more than the individual prespecified value; and 3) the transfer function from exogenous noise inputs to error state outputs meets the prespecified H/sub /spl infin// norm upper-bound constraint. An effective algebraic matrix inequality approach is developed to derive both the existence conditions and the explicit expression of the desired filters. An illustrative example is used to demonstrate the usefulness of the proposed design approach.

A pure permanent magnet — two plane focusing — tapered wiggler for a high average power FEL

A high-average power FEL is under construction at Los Alamos. The FEL will have aspects of both an oscillator and a SASE (self-amplified spontaneous emission) device. That is, a high-gain and high-extraction efficiency wiggler will be used with a very low- Q optical resonator. FEL simulations reveal that a tapered wiggler with two-plane focusing is required to obtain desired performance. The wiggler is comprised of a 1 m long untapered section followed by a 1 m tapered section. The taper is achieved with the magnetic gap and not the wiggler period which is constant at 2 cm. The gap is tapered from 5.9 to 8.8 mm. The gap, rather than the period, is tapered to avoid vignetting of the 16 μm optical beam. Two-plane focusing is necessary to maintain high current density and thus high gain through out the 2 m long wiggler. Several magnetic designs have been considered for the wiggler. The leading candidate approach is a pure permanent wiggler with pole faces that are cut to roughly approximate the classical parabolic pole face design. Focusing is provided by the sextupole component of the wiggler magnetic field and is often called “natural” or “betatron” focusing. Details of the design will be presented.

Microwave FEL experiments at CESTA

At CESTA the EUPHROSYNE pulsed generator was used for Ondine I, our first FEL experiment at 35 GHz. The work was focused on beam creation and propogation first with an oxide cathode and then with a cold cathode. Typically 1 kA at 2.5 MeV was propagated in single shot operation. A lot of calculations have been done on these problems and we have also developed simulation codes on FEL interaction in both Compton and Raman regimes, taking into account 3D wiggler field, guiding field, waveguide modes, and electron beam injection, to obtain trajectories, gain and efficiency. Good agreement with some previous experiments and codes has been found. In the frame of a preliminary superradiant experiment using a bifilar helical wiggler, we obtained an amplification of the spontaneous emission up to 1 MW in the Kα band and 0.2 MW in the 33–36 GHz band. A microwave apparatus has been completed to work in an amplifier configuration: injection magnetron tube (100 kW), amplification line and diagnostics. All these components are compatible of the new Ondine II experiment designed for operation with the LELIA induction linac. This experiment is to start at 0.1 Hz with the induction injector (1.3 MeV, 1 kA, 50 ns) using the same wiggler technology as Ondine 1. In the future we plan to carry out the 35 GHz experiment at 3 MeV by adding an accelerating module to the LELIA injector. An hybrid planar wiggler with parabolic pole faces is being studied for further experiments.

Development of a focusing wiggler magnet with parabolic pole faces

A focusing wiggler magnet which consists of permanent magnets with parabolic pole faces has been developed. A magnet with parabolic pole faces gives an additional sextupole contribution to the conventional wiggler field, and generates a focusing force in both directions on an electron beam. Furthermore, it can give the FEL resonance properties as well as a helical wiggler. The shape of the magnet pole faces has been optimized using the TOSCA code. The alloy NdFeB was chosen as the magnetic material for a peak field of more than 0.43 T with a gap of 23 mm on the wiggler axis. Magnetic field errors could be substantially reduced using thin iron shimming plates attached to the permanent magnets. The results of the magnetic field measurements are in good agreement with the values obtained by TOSCA. Numerical simulation of the electron trajectory using a measured magnetic field is performed and it verified that the wiggler with parabolic pole faces has enough focusing force in the x direction in addition to the y direction.

Relativistic beam transport in a focusing wiggler

The transport of a relativistic electron beam was studied experimentally and numerically in a magnetic field configuration which consists of a focusing wiggler as well as an additional axial guide field. A new beam divergence was found for the lower side of the magnetoresonance. It was identified as due to the effect of the second harmonic mode of the cyclotron frequency in the resonance, determined by nΩ ‖=k w ν ‖ for n = 2 . The experimental observation shows good agreement with the numerical calculation, where the motions of the electrons are traced in a planar wiggler having parabolic pole faces and an axial uniform guide field, in the limit of low density beam. The formalism for the calculation is given and discussed. The harmonic resonance was detected for the planar wiggler first, and it could appear also for the helical one.

Nonlinear theory of slow-wave ubitrons/free electron lasers

A three-dimensional nonlinear formulation of a slow-wave ubitron/free electron laser is presented. The configuration is that of an electron beam propagating through a dielectric-lined rectangular waveguide in the presence of a planar wiggler field. The wiggler field model describes parabolic pole faces for enhanced beam focussing. The electromagnetic field is described in terms of a multimode ensemble of the normal modes of the vacuum waveguide. In this case, the dielectric liner is imposed along the y-axis of the guide (which is also the principal orientation of the wiggler) and there are no orthogonal TE or TM modes. Instead, we deal with modes which are transverse electric (LSE) or magnetic (LSM) to the y-axis. Equations are derived which describe the evolution of the amplitude and phase of these modes in terms of the microscopic particle currents. These equations are solved in conjunction with the complete Lorentz force equations for the electron trajectories. The essential purpose of employing a slow-wave structure is to reach shorter wavelengths at relatively low beam energies, and numerical results will be presented to demonstrate the potentialities of this concept.

Electron-beam quality degradation in a long undulator

Under the influence of space charge or longitudinal wake fields, transporting an electron beam through a long undulator can cause a degradation of beam quality. Using the PARMELA code, including longitudinal wake-field and space-charge contributions, we simulate a beam bunch that travels through the undulator. The electron beam is focused in both planes with the parabolic pole faces of the undulator. The effect of space charge on the beam envelope is also calculated using the K-V (Kapchinskij-Vladimirskij) envelope equation.

Nonlinear theory and design of a harmonic Ubitron/Free Electron Laser

A fully three-dimensional nonlinear analysis of the harmonic Ubitron/Free Electron Laser is discussed which is valid for arbitrary harmonic number. The analysis has been performed for a configuration consisting of a beam propagating through a loss-free rectangular waveguide in the presence of a planar wiggler field. The wiggler model includes an adiabatic entry taper to model the injection of the beam into the wiggler, parabolic pole pieces to provide additional focussing in the plane normal to the wiggler, and an amplitude taper downstream from the entry region for efficiency enhancement. The advantage of harmonic operation is that relatively high operating frequencies may be obtained with relatively modest beam energies; however, this occurs at the expense of a greater sensitivity to beam thermal effects. In addition to enhancing the extraction efficiency, a tapered wiggler has been shown to reduce the sensitivity of the interaction to thermal effects. Thus, the tapered wiggler is designed to counter the increased thermal sensitivity of the harmonic interaction. Specific design criteria for a third harmonic experiment operating at 15 GHz with a 55 keV electron beam are discussed.

Harmonic content in a planar wiggler based free electron laser amplifier

Amplification at harmonics of the fundamental frequency of the free electron laser (FEL) is studied for a configuration utilizing a planar wiggler with parabolically shaped pole pieces. The analysis employs a fully three-dimensional FEL simulation code, which treats the propagation of the electron beam and radiation through a rectangular waveguide. Substantial power is found at odd harmonics of the fundamental resonance frequency. In addition, the three-dimensional nature of the wiggler field produced by the parabolic pole pieces introduces a low frequency component to the electron motion which results in emission in the vicinity of the even harmonics as well. The physical basis for this is investigated by analytic and numerical solution of the single-particle trajectories. In general, the results indicate that the effect of the wiggle plane focussing can act to enhance the harmonic content of the output spectrum.

Eine charakteristische eigenschaft des symmetrischen schleifschiebers

The symmetrical double slider mechanism, also known as mechanism number 6, exhibits a symmetrical motion with parabolic pole curves. For this mechanism it is well known that there exists only one finite point as a Burmester point. In this paper it is shown that this condition is a characteristics property.