Search Results (39 total)

We study the transverse geometric impedance of elliptical cross-section tapers in the low-frequency “inductive regime.” We have followed a dual approach: computer simulations have been carried out using the finite element electromagnetic code GDFIDL and analytic results for the dipolar and quadrupolar components of the impedance have been derived extending a perturbation technique introduced by Stupakov. Our work provides new insight into the behavior of the impedance of axially asymmetric tapered structures at low frequency. In particular, we clarify the frequency range characterizing the inductive regime, suggesting new criteria relating the extent of the inductive regime for dipolar and quadrupolar components of the impedance to the dimensions of the minimal cross section of a tapered transition.

A method for producing short electron bunches in an electron storage ring using pulsed phase modulation has been demonstrated. A simple theoretical model was validated using the particle tracking code elegant, and the bunch compression process was observed experimentally in the Advanced Photon Source storage ring using a visible light streak camera. Compression to 54% of the initial bunch length was achieved.

We use Rice’s theory of shot noise random processes to provide a statistical analysis of the evolution of the amplitude and phase of the chaotic optical field from a high-gain, self-amplified, spontaneous-emission (SASE) free-electron laser. The theoretical framework developed is compared with recent frequency-resolved optical-gating measurements of the SASE output at the LEUTL facility at Argonne National Laboratory.

We determine the low frequency transverse impedance of axially symmetric tapered structures. Higher-order perturbation theory is used to improve previous estimates due to Yokoya and Stupakov. For linear tapers, accurate numerical results are obtained using the ABCI electromagnetic simulation code. Based upon insight gained from the perturbation calculations, we introduce a simple parametrization that provides an excellent fit to all of our ABCI data—including cases with gradual and steep tapers as well as large and small change in cross section.

Stupakov has used a perturbation method to estimate the transverse impedance at zero frequency of a rectangular collimator having characteristic taper length ℓ, half-width w, and average vertical half-aperture b₀, under the condition b₀≪w≪ℓ. We use the boundary perturbation method to approximate the transverse impedance of a flat, slowly tapered chamber in the complementary limit, w=∞.

We determine the impedance of a cylindrical metal tube (resistor) of radius a, length g, and conductivity σ attached at each end to perfect conductors of semi-infinite length. Our main interest is in the asymptotic behavior of the impedance at high frequency (k≫1/a). In the equilibrium regime, ka²≪g, the impedance per unit length is accurately described by the well-known result for an infinite length tube with conductivity σ. In the transient regime, ka²≫g, where the contribution of transition radiation arising from the discontinuity in conductivity is important, we derive an analytic expression for the impedance and compute the short-range wakefield. The analytic results are shown to agree with numerical evaluation of the impedance.

We introduce a simplified model for the saturation of a self-amplified spontaneous-emission free-electron laser. Within this model, we determine the effect of nonlinearity upon the statistical properties of the output radiation. Comparing our results with the computer simulations of Saldin, Schneidmiller, and Yurkov [The Physics of Free Electron Lasers (Springer-Verlag, Berlin, 2000)], we find that the model provides a good description of the average intensity, field correlation function, and coherence time, but underestimates the intensity fluctuation. Asymmetric spectral broadening phenomena are not included in the model.

Saturation of a high-gain harmonic-generation free-electron laser (HGHG-FEL) at 266 nm has been accomplished at the Brookhaven National Laboratory/Deep Ultra Violet Free Electron Laser Facility (BNL/DUV-FEL) by seeding with an 800 nm Ti:sapphire laser. We describe the diagnostics used to characterize the electron beam and the FEL output. Analytic and simulation calculations of the HGHG output are presented and compared with the experimental data. We also discuss the chirped pulse amplification of a frequency chirped seed by an energy chirped electron beam. The third harmonic at 88 nm accompanying the 266 nm fundamental has been used in an ion pair imaging experiment in chemistry, the first application of the BNL/DUV-FEL.

We report on a characterization of the chaotic optical field from a high-gain, self-amplified spontaneous-emission (SASE) free-electron laser. The temporal structure of the amplitude and phase are measured in a single-shot mode, with a resolution well below the coherence length, and the statistics over multiple pulses is determined. The measurement is in excellent quantitative agreement with the prediction based on analysis of random noise, and further verifies the chaotic nature of the SASE optical field.

We report the first experimental results on a high-gain harmonic-generation (HGHG) free-electron laser (FEL) operating in the ultraviolet. An 800 nm seed from a Ti:sapphire laser has been used to produce saturated amplified radiation at the 266 nm third harmonic. The results confirm the predictions for HGHG FEL operation: stable central wavelength, narrow bandwidth, and small pulse-energy fluctuation.

We present a statistical analysis of the temporal and spectral properties of self-amplified spontaneous emission from an energy-chirped electron beam passing through a long undulator. It is found that the coherence time is independent of the chirp, while the range of spectral coherence is linearly proportional to it. We consider the use of a monochromator to pick out a small temporal slice of the radiation output. For the filtered radiation pulse, we determine the pulse duration, the number of modes, and the energy fluctuation. We apply our analysis to schemes proposed to generate short x-ray pulses at the Linac Coherent Light Source.

The narrow band chaotic output of the self-amplified spontaneous-emission free-electron laser exhibits intensity spikes. In the linear regime before saturation, we use an approach developed by Rice to determine probability distributions for the peak values of intensity in both the time and frequency domains. We also find the average number of spikes per unit time or frequency. In addition, we derive joint probabilities for the intensity in the output pulse to have values I₁ and I₂ at times t₁ and t₂, and for the spectral intensity to have values I˜₁ and I˜₂ at frequencies ω₁ and ω₂.

The coherent synchrotron radiation of a bunch in a bunch compressor may lead to the microwave instability producing longitudinal modulation of the bunch with wavelengths small compared to the bunch length. It can also be a source of an undesirable emittance growth in the compressor. We derive and analyze the equation that describes linear evolution of the microwave modulation taking into account incoherent energy spread and finite emittance of the beam. Numerical solution of this equation for the Linac Coherent Light Source bunch compressor gives the amplification factor for different wavelengths of the beam microbunching.

We report on an experimental investigation characterizing the output of a high-gain harmonic-generation (HGHG) free-electron laser (FEL) at saturation. A seed CO₂ laser at a wavelength of 10.6 μm was used to generate amplified FEL output at 5.3 μm. Measurement of the frequency spectrum, pulse duration, and correlation length of the 5.3 μm output verified that the light is longitudinally coherent. Investigation of the electron energy distribution and output harmonic energies provides evidence for saturated HGHG FEL operation.

In the linear regime before saturation, we solve the one-dimensional, classical free-electron laser equations, maintaining the longitudinal discreteness of the electrons throughout the analysis. We then take the limit in which the beam of discrete electrons is approximated by a continuum fluid. In the continuum limit, we recover the Green function used by Wang and Yu in their treatment of self-amplified spontaneous emission (SASE). For a bunched electron beam, we discuss both incoherent and coherent SASE. We also discuss the field radiated from a bunch whose length is short compared to the radiation wavelength.

In the exponential regime before saturation, we present a variational calculation of the gain of a free electron laser (FEL), with alternating-gradient focusing used to supplement the natural focusing of the wiggler. The longitudinal velocity modulation due to the quadrupole focusing is properly taken into account and it is found that it does not prevent quadrupole focusing from efficiently increasing the gain. Our analytic calculation agrees with computer simulation to a few percent, and it provides rapid computation facilitating FEL design optimization.

We study the saturated state of an untapered free-electron laser (FEL) in the Compton regime, arising after exponential amplification of an initially low level of radiation by an initially monoenergetic, unbunched electron beam. The saturated state of the FEL is described by oscillations about an equilibrium state. Using the two invariants of the motion and certain assumptions motivated by computer simulations we provide approximate analytic descriptions of the radiation field and electron distribution in the saturation regime. We first consider a one-dimensional approximation and later extend our approach to treat an electron beam of finite radial extent. Of note is a result on the radiated power in the case of an electron beam with a small radius.

For free-electron laser (FEL) operating in the exponential regime before saturation, we present an analytic description of the effect on the gain of longitudinal velocity variations arising from wigger field errors. The average gain reduction and the width of the output power distribution are expressed in terms of the mean-square average of the ponderomotive phase shift per gain length. A scheme for correcting the electron trajectory using position monitors and dipole correctors is analyzed. Our work is directly applicable to the design of FEL amplifiers, and the results are encouraging for their feasibility.

We present a variational calculation of free-electron-laser gain the exponential regime before saturation using a dispersion relation incorporating the energy spread, emittance, and focusing of the electron beam, and the diffraction and guiding of the radiation. Rapid computation facilitates free-electron-laser design optimization. Results are expressed in a universal scaled form.

Treating diffraction effects within the paraxial approximation, we solve the initial-value problem determining the start-up of a single-pass free-electron laser from shot noise in the electron beam. Linearized Vlasov-Maxwell equations are used to derive an equation for the three-dimensional slowly varying envelope function of the radiated electric field. In the high-gain regime before saturation, the output power is expressed in terms of Moore’s exponentially growing guided modes. For a cylindrical monoenergetic electron beam with step-function profile, explicit numerical and analytical calculations have been performed, determining the power in the guided modes. The condition for the dominance of the fundamental mode is discussed. Our solution of the initial-value problem is based upon a Green’s-function technique, and our results are derived despite the lack of orthogonality and completeness of the guided modes. The Green’s function is expanded in terms of an orthonormal set of eigenfunctions of a two-dimensional Schrödinger equation with non-self-adjoint Hamiltonian. In the limit of a long wiggler, the asymptotic representation of the Green’s function is found to be dominated by the contribution of the guided modes. The radiated electric field, and hence the output power, is determined with use of the Green’s function.

For a classical oscillator subject to a time-dependent perturbation, the average change in the action variable 〈ΔJ〉=〈J-J₀〉 is related to its fluctuation 〈(ΔJ)²〉 by 〈ΔJ〉=(1/2)∂〈(ΔJ)²〉/∂J₀, where J₀ is the initial value of J and the average is over the initial value θ₀ of the angle variable. In this paper, the quantum-mechanical generalization of this relation is derived, and we discuss the correspondence between our work and the usual treatment of the fluctuation-dissipation theorem for a system which initially is described by a canonical distribution.

We suggest that the Monte Carlo renormalization group, when combined with the type of cell-spin transformation introduced by van Leeuwen, should be a powerful tool in the study of Ising models with n>~2. Numerical results are presented for the Baxter model and the Ising model with nearest- and next-nearest-neighbor interactions on a square lattice.

The dimensionality of the order parameters of several spin 1/2 Ising models with competing interactions is discussed. It is argued that many such models are described by n>~2 component order parameters.

In the preceding paper, we derived n≥4-component Landau-Ginzburg-Wilson Hamiltonians describing phase transitions in certain physical systems. Here, we use Wilson's ε expansion to study the phase transitions associated with these Hamiltonians. Although the n=4 systems TbAu₂, DyC₂, and NbO₂ have different symmetries, they are predicted to have the same critical exponents. Similarly, although the n=6 systems TbD₂, Nd, and K₂IrCl₆ have different symmetries, their critical exponents are predicted to be equal, but different from those of an isotropic n=6 model. We suggest these predictions be tested experimentally. Three of the Hamiltonians we have considered possess no stable fixed points. Two of the materials UO₂ (n=6) and MnO (n=9) described by these Hamiltonians are known to have first-order transitions. We suggest that experiments should be performed to test whether or not the transitions in the n=8 systems ErSb, MnSe, NiO, and in the n=4 systems TbAs, TbP, TbSb are first order.