Search Results (16 total)

In this paper we report on large-scale high resolution simulations of beam dynamics in electron linacs for the next-generation x-ray free electron lasers (FELs). We describe key features of a parallel macroparticle simulation code including three-dimensional (3D) space-charge effects, short-range structure wakefields, coherent synchrotron radiation (CSR) wakefields, and treatment of radio-frequency (rf) accelerating cavities using maps obtained from axial field profiles. We present a study of the microbunching instability causing severe electron beam fragmentation in the longitudinal phase space which is a critical issue for future FELs. Using parameters for a proposed FEL linac at Lawrence Berkeley National Laboratory (LBNL), we show that a large number of macroparticles (beyond 100 million) is generally needed to control the numerical macroparticle shot noise and avoid overestimating the microbunching instability. We explore the effect of the longitudinal grid on simulation results. We also study the effect of initial uncorrelated energy spread on the final uncorrelated energy spread of the beam for the FEL linac.

In this paper, we present a three-dimensional quasistatic model for high brightness beam dynamics simulation in rf/dc photoinjectors, rf linacs, and similar devices on parallel computers. In this model, electrostatic space-charge forces within a charged particle beam are calculated self-consistently at each time step by solving the three-dimensional Poisson equation in the beam frame and then transforming back to the laboratory frame. When the beam has a large energy spread, it is divided into a number of energy bins or slices so that the space-charge forces are calculated from the contribution of each bin and summed together. Image-charge effects from conducting photocathode are also included efficiently using a shifted-Green function method. For a beam with large aspect ratio, e.g., during emission, an integrated Green function method is used to solve the three-dimensional Poisson equation. Using this model, we studied beam transport in one Linac Coherent Light Sources photoinjector design through the first traveling wave linac with initial misalignment with respect to the accelerating axis.

We investigate the phenomenon of space-charge driven emittance growth in a three-dimensional mismatched anisotropic charged particle beam with relevance to high-intensity linear accelerators. The final emittance growth can be understood as a superposition of the contributions from the mismatch-induced halo formation and from the anisotropy-induced energy exchange. The averaged emittance growth per degree of freedom is bounded from above by the so-called “free energy limit” extended by the contributions from energy exchange. The partition of the growth into longitudinal or transverse is, however, a strong function of the tune ratio including the possibility that an initially equipartitioned beam is even driven substantially away from equipartition. The growth of the beam halo extent is dominated by the effect of mismatch, whereas anisotropy itself generates practically no halo.

The theory and simulation of coherent resonant coupling due to space charge in coasting or bunched anisotropic equilibrium beams is presented. Our work confirms that analytical results on coherent oscillations and instabilities of anisotropic KV (Kapchinskij-Vladimirskij) distributions are a valid tool to interpret the findings from 2D and 3D self-consistent particle-in-cell simulations for both KV and waterbag distributions. With reference to rings we discuss space charge coherent tune shifts up to fourth order and introduce a coherent coupled mode coefficient, which enables us to resolve the issue of KV anomalies by relating them to negative energy modes. The second emphasis of this study is with reference to linacs and a detailed discussion of “stability charts” describing resonant regions where approach to equipartition may occur.

In this paper we present a new approach, based on a shifted Green function, to evaluate the electromagnetic field in a simulation of colliding beams. Unlike a conventional particle-mesh code, we use a method in which the computational mesh covers only the largest of the two colliding beams. This allows us to study long-range parasitic collisions accurately and efficiently. We have implemented this algorithm in a new parallel strong-strong beam-beam simulation code. As an application, we present a study of a beam sweeping scheme for the LBNL luminosity monitor of the Large Hadron Collider.

Macroparticle simulation plays an important role in modern accelerator design and operation. Most linear rf accelerators have been designed based on macroparticle simulations using longitudinal position as the independent variable. In this paper, we have done a systematic comparison between using longitudinal position as the independent variable and using time as the independent variable in macroparticle simulations. We have found that, for an rms-matched beam, the maximum relative moment difference for second, fourth moments and beam maximum amplitudes between these two types of simulations is 0.25% in a 10 m reference transport system with physical parameters similar to the Spallation Neutron Source linac design. The maximum z-to- t transform error in the space-charge force calculation of the position dependent simulation is about 0.1% in such a system. This might cause a several percent error in a complete simulation of a linac with a length of hundreds of meters. Furthermore, the error may be several times larger in simulations of mismatched beams. However, if such errors are acceptable to the linac designer, then one is justified in using position dependent macroparticle simulations in this type of linac design application.

Energy exchange between the longitudinal and transverse degrees of freedom of nonequipartitioned bunched beams (non-neutral plasmas) is investigated by means of 3D simulation. It is found that collective instability may lead to energy transfer in the direction of equipartition, without full progression to it, in certain bounded regions of parameter space where internal resonance conditions are satisfied, in good agreement with stability charts from an earlier derived 2D Vlasov analysis. Nonequipartitioned stable equilibria, however, exist in relatively wide regimes of parameter space. This provides evidence that such regimes may be safely used in the design of future high-intensity linacs.

In this paper we present a study of beam halo based on a three-dimensional particle-core model of an ellipsoidal bunched beam in a constant focusing channel including the effects of nonlinear rf focusing. For an initially mismatched beam, three linear envelope modes—a high frequency mode, a low frequency mode, and a quadrupole mode—are identified for an azimuthally symmetric bunched beam. The high frequency mode has three components all in phase; the low frequency mode has the transverse components in phase and the longitudinal component 180° out of phase; the quadrupole mode has no longitudinal component, and the two transverse components in the mode are 180° out of phase. We also study the case of an ellipsoidal bunched beam without azimuthal symmetry and find that the high frequency mode and the low frequency mode are still present but the quadrupole mode is replaced by a new mode with transverse components 180° out of phase and a nonzero longitudinal component. Previous studies, which generally addressed the situation where the longitudinal-to-transverse focusing strength is roughly 0.6 or less, conclude that the oscillation of the high frequency mode is predominantly transverse, and that of the low frequency mode is predominantly longitudinal. In this paper we present a systematic study of the features of the modes as a function of the longitudinal-to-transverse focusing strength ratio. We find that, when the ratio is greater than unity, the high frequency mode may contain a significant longitudinal component. Thus, excitation of the high frequency mode in this situation can be responsible for the formation of longitudinal beam halo. Furthermore, while previous studies have observed halo amplitudes roughly 2–3 times the matched beam edge, for the present parameters we observe much larger amplitudes (5 times or more). This is due to the fact that the longitudinal-to-transverse focusing ratio used here is greater than that of previous studies. The finding of large transverse halo amplitude can have significant impact on the design of high-intensity ion accelerators where the longitudinal-to-transverse focusing ratio is slightly greater than unity in some parts of the linac.

In this paper, we describe in detail a method of computing Lyapunov exponents for a continuous-time dynamical system and extend the method to discrete maps. Using this method, a partial Lyapunov spectrum can be computed using fewer equations as compared to the computation of the full spectrum, there is no difficulty in evaluating degenerate Lyapunov spectra, the equations are straightforward to generalize to higher dimensions, and the minimal set of dynamical variables is used. Explicit proofs and other details not given in previous work are included here.

A realistic treatment of halo formation must take into account 3D beam bunches and 6D phase space distributions. We recently constructed, analytically and numerically, a new class of self-consistent 6D phase space stationary distributions, which allowed us to study the halo development mechanism without being obscured by the effect of beam redistribution. In this paper we consider nonstationary distributions and study how the halo characteristics compare with those obtained using the stationary distribution. We then discuss the effect of redistribution on the halo development mechanism. In contrast to bunches with a large aspect ratio, we find that the effect of coupling between the r and z planes is especially important as the bunch shape becomes more spherical.

We present a new method for the computation of Lyapunov exponents utilizing representations of orthogonal matrices applied to decompositions of M or MM̃ where M is the tangent map. This method uses a minimal set of variables, does not require renormalization or reorthogonalization, can be used to efficiently compute partial Lyapunov spectra, and does not break down when the Lyapunov spectrum is degenerate.

Dynamical chaos has recently been shown to exist in the Gaussian approximation in quantum mechanics and in the self-consistent mean field approach to studying the dynamics of quantum fields. In this study, we first note that any variational approximation to the dynamics of a quantum system based on the Dirac action principle leads to a classical Hamiltonian dynamics for the variational parameters. Since this Hamiltonian is generically nonlinear and nonintegrable, the dynamics thus generated can be chaotic, in distinction to the exact quantum evolution. We then restrict our attention to a system of two biquadratically coupled quantum oscillators and study two variational schemes, the leading order large-N (four canonical variables) and Hartree (six canonical variables) approximations. The chaos seen in the approximate dynamics is an artifact of the approximations: this is demonstrated by the fact that its onset occurs on the same characteristic time scale as the breakdown of the approximations when compared to numerical solutions of the time-dependent Schrödinger equation.

The Lyapunov exponents of a chaotic system quantify the exponential divergence of initially nearby trajectories. For Hamiltonian systems the exponents are related to the eigenvalues of a symplectic matrix. We make use of this fact to develop a new method for the calculation of Lyapunov exponents of such systems. Our approach avoids the renormalization and reorthogonalization of usual techniques. It is also easily extendible to damped systems. We apply our method to two examples of physical interest: a model system that describes the beam halo in charged particle beams and the driven van der Pol oscillator.

We have used relativistic klystron technology to extract 290 MW of peak power at 11.4 GHz from an induction linac beam, and to power a short 11.4-GHz high-gradient accelerator. We have measured rf phase stability, field emission, and the momentum spectrum of an accelerated electron beam. An average accelerating gradient of 84 MV/m has been achieved with 80 MW of relativistic klystron power.