Search Results (15 total)

We report on a successful implementation of a three-dimensional wavelet-based solver for the Poisson equation with Dirichlet boundary conditions, optimized for use in particle-in-cell (PIC) simulations. The solver is based on the operator formulation of the conjugate gradient algorithm, for which effectively diagonal preconditioners are available in wavelet bases. Because of the recursive nature of PIC simulations, a good initial approximation to the iterative solution is always readily available, which we demonstrate to be a key advantage in terms of overall computational speed. While the Laplacian remains sparse in a wavelet representation, the wavelet-decomposed potential and density can be rendered sparse through a procedure that amounts to simultaneous compression and denoising of the data. We explain how this procedure can be carried out in a controlled and near-optimal way, and show the effect it has on the overall solver performance. After testing the solver in a stand-alone mode, we integrated it into the IMPACT-T beam dynamics particle-in-cell code and extensively benchmarked it against the IMPACT-T with the native FFT-based Poisson solver. We present and discuss these benchmarking results, as well as the results of modeling the Fermi/NICADD photoinjector using IMPACT-T with the wavelet-based solver.

The longitudinal charge distribution of electron bunches in the Fermilab/NICADD photoinjector was determined using the coherent transition radiation produced by electrons passing through a thin metallic foil. The autocorrelation of the transition radiation signal was measured with a Michelson-type interferometer. The response function of the interferometer was determined from measured and simulated intensity spectra for low electron bunch charge and maximum longitudinal compression. Both pyroelectric and Golay detectors were used for these measurements. A Kramers-Kronig technique was used to determine longitudinal charge distribution. Measurements were performed for electron bunch lengths in the range from 0.3 to 2 ps (rms). To test the accuracy of this interferometric method, the longitudinal charge distribution was measured for double-peaked electron bunches with known distance between the two pulses. The agreement between measured bunch length and simulation is within 30%.

We investigate how collective modes and colored noise conspire to produce a beam halo with much larger amplitude than could be generated by either phenomenon separately. The collective modes are lowest-order radial eigenmodes calculated self-consistently for a configuration corresponding to a direct-current, cylindrically symmetric, warm-fluid Kapchinskij-Vladimirskij equilibrium. The colored noise arises from unavoidable machine errors and influences the internal space-charge force. Its presence quickly launches statistically rare particles to ever-growing amplitudes by continually kicking them back into phase with the collective-mode oscillations. The halo amplitude is essentially the same for purely radial orbits as for orbits that are initially purely azimuthal; orbital angular momentum has no statistically significant impact. Factors that do have an impact include the amplitudes of the collective modes and the strength and autocorrelation time of the colored noise. The underlying dynamics ensues because the noise breaks the Kolmogorov-Arnol’d-Moser tori that otherwise would confine the beam. These tori are fragile; even very weak noise will eventually break them, though the time scale for their disintegration depends on the noise strength. Both collective modes and noise are therefore centrally important to the dynamics of halo formation in real beams.

We investigate the validity of the Vlasov-Poisson equations for calculating properties of systems of N charged particles governed by time-independent Hamiltonians. Through numerical experiments we verify that there is a smooth convergence toward a continuum limit as N→∞ and the particle charge q→0 such that the system charge Q=qN remains fixed. However, in real systems N and q are always finite, and the assumption of the continuum limit must be questioned. We demonstrate that Langevin simulations can be used to assess the importance of discreteness effects, i.e., granularity, in systems for which the physical particle number N is too large to enable orbit integrations based on direct summation of interparticle forces. We then consider a beam bunch in thermal equilibrium and apply Langevin techniques to assess whether the continuum limit can be safely applied to this system. In the process we show, especially for systems supporting a sizable population of chaotic orbits that roam globally through phase space, that for the continuum limit to be valid, N must sometimes be surprisingly large. Otherwise the influence of granularity on particle orbits cannot be ignored.

The formation of beam halos has customarily been described in terms of a particle-core model in which the space-charge field of the oscillating core drives particles to large amplitudes. This model involves parametric resonance and predicts a hard upper bound to the orbital amplitude of the halo particles. We show that the presence of colored noise due to space-charge fluctuations and/or machine imperfections can eject particles to much larger amplitudes than would be inferred from parametric resonance alone.

Phase mixing of chaotic orbits exponentially distributes these orbits through their accessible phase space. This phenomenon, commonly called “chaotic mixing,” stands in marked contrast to phase mixing of regular orbits which proceeds as a power law in time. It is operationally irreversible; hence, its associated e-folding time scale sets a condition on any process envisioned for emittance compensation. A key question is whether beams can support chaotic orbits, and if so, under what conditions? We numerically investigate the parameter space of three-dimensional thermal-equilibrium beams with space charge, confined by linear external focusing forces, to determine whether the associated potentials support chaotic orbits. We find that a large subset of the parameter space does support chaos and, in turn, chaotic mixing. Details and implications are enumerated.

This paper uses the assumptions of ergodicity and a microcanonical distribution to compute estimates of the largest Lyapunov exponents in lower-dimensional Hamiltonian systems. That the resulting estimates are in reasonable agreement with the actual values computed numerically corroborates the intuition that chaos in such systems can be understood as arising generically from a parametric instability and that this instability may be modeled by a stochastic-oscillator equation [cf. Casetti, Clementi, and Pettini, Phys. Rev. E 54, 5969 (1996)], linearized perturbations of a chaotic orbit satisfying a harmonic-oscillator equation with a randomly varying frequency.

An analytic theory of cumulative multibunch beam breakup in linear colliders is developed. Included is a linear variation of transverse focusing across the bunch train as might be applied, e.g., by chirping the radio frequency power sources or by using radio frequency quadrupole magnets. The focusing variation saturates the exponential growth of the beam breakup and establishes an algebraic decay of the transverse bunch displacement versus bunch number. A closed-form expression for the transverse bunch displacement is developed. It is used to quantify the total normalized emittance and thereby isolate the region of parameter space corresponding to high multibunch luminosity.

Jefferson Laboratory's kW-level infrared free-electron laser utilizes a superconducting accelerator that recovers about 75% of the electron-beam power. In achieving first lasing, the accelerator operated “straight ahead” to deliver 38-MeV, 1.1-mA cw current for lasing near 5 μm. The waste beam was sent directly to a dump while producing stable operation at up to 311 W. Utilizing the recirculation loop to send the electron beam back to the linac for energy recovery, the machine has now recovered cw average currents up to 5 mA, and has lased cw with up to 1720 W output at 3.1 μm.

A semianalytic formalism is constructed for investigating the transverse dynamics of intense, mismatched charged-particle beams which are centered on, and propagate through, focusing channels. It uses the Fokker-Planck equation to account for the rapid evolution of the coarse-grained distribution function in the phase space of a single beam particle. It also incorporates the space-charge potential, which is calculated from Poisson’s equation using the coarse-grained density. A simple phenomenological model of dynamical friction and diffusion represents the effects of turbulence triggered by charge redistribution. Sheet beams and fully two-dimensional beams are both considered in detail. In addition, closed-form solutions are presented for beams in which the space charge is negligible and noise arises from other stochastic processes.

The transverse dynamics of a nonrelativistic, mismatched charged-particle beam propagating through a continuous, linear focusing channel is calculated using the Fokkker-Planck equation to represent the evolution of a coarse-grained distribution function in the phase space of a single beam particle. The relaxation rate and diffusion coefficient are determined from a simple model of turbulence resulting from charge redistribution. The solution for the distribution function enables calculation of all transverse beam properties as a function of time, including the halo.

An analytic formalism of cumulative beam breakup in linear accelerators is developed. This formalism is applied to both low-velocity ion accelerators and high-energy electron accelerators. It includes arbitrary velocity, acceleration, focusing, initial conditions, beam-cavity resonances, finite bunch length, and arbitrary charge distribution within the bunches, and variable cavity geometry and spacing along the accelerator. For both direct-current beams and beams comprised of δ-function bunches, both the steady-state and transient displacements of the beam are calculated, and scaling laws are determined for the transient beam breakup. The steady-state transverse displacement of particles between bunches is also calculated since, if allowed to impinge on the accelerating structures, these particles could cause activation over long periods of continuous-wave operation. The formalism is then applied to high-current ion accelerators by studying the effects of finite bunch length and arbitrary charge distribution within the bunches. The role of focusing in controlling cumulative beam breakup is quantified in each of these cases. Additionally, the effects of random initial conditions and a distribution of deflecting-mode frequencies in the cavities are also quantified.

The rf surface resistance of a single bulk polycrystalline YBa₂Cu₃O_7-x sample was measured with TEM resonant cavities as a function of temperature from 4.2 to 100 K, rf field amplitude from 0 to 640 G, and frequency from 175 to 1050 MHz. The surface resistance increased monotonically with rf field amplitude, saturating at a value approximately 5% of the normal-state surface resistance. The surface resistance is strongly frequency and temperature dependent below the saturation region and weakly frequency and temperature dependent above. Low-field surface resistances as small as ≲1.1 μΩ (at 175 MHz) were observed at T=4.2 K. The superconducting state did not break down, even at the highest field achieved (∼640 G).