This paper describes a semianalytical hysteresis model for hard superconductors. The model is based on the critical state model considering the dependency of the critical current density on the varying local field in the superconducting filaments. By combining this hysteresis model with numerical field computation methods, it is possible to calculate the persistent current multipole errors in the magnet taking local saturation effects in the magnetic iron parts into consideration. As an application of the method, the use of soft magnetic iron sheets (coil protection sheets mounted between the coils and the collars) for partial compensation of the multipole errors during the ramping of the magnets is investigated.

Electron bunches of high charge (up to 10 nC) are compressed in length in the Compact Linear Collider Test Facility magnetic chicane to less than 0.4 mm rms. The short bunches radiate coherently in the chicane magnetic field, and the horizontal and longitudinal phase space density distributions are affected. This paper reports the results of beam emittance and momentum measurements. Horizontal and vertical emittances and momentum spectra were measured for different bunch compression factors and bunch charges. In particular, for 10 nC bunches, the mean beam momentum decreased by about 5% while the rms momentum spread increased from 2% to 8%. The experimental results are compared with simulations made with the code TraFiC4.

Tomography is now a very broad topic with a wealth of algorithms for the reconstruction of both qualitative and quantitative images. In an extension in the domain of particle accelerators, one of the simplest algorithms has been modified to take into account the nonlinearity of large-amplitude synchrotron motion. This permits the accurate reconstruction of longitudinal phase space density from one-dimensional bunch profile data. The method is a hybrid one which incorporates particle tracking. Hitherto, a very simple tracking algorithm has been employed because only a brief span of measured profile data is required to build a snapshot of phase space. This is one of the strengths of the method, as tracking for relatively few turns relaxes the precision to which input machine parameters need to be known. The recent addition of longitudinal space charge considerations as an optional refinement of the code is described. Simplicity suggested an approach based on the derivative of bunch shape with the properties of the vacuum chamber parametrized by a single value of distributed reactive impedance and by a geometrical coupling coefficient. This is sufficient to model the dominant collective effects in machines of low to moderate energy. In contrast to simulation codes, binning is not an issue since the profiles to be differentiated are measured ones. The program is written in Fortran 90 with high-performance Fortran extensions for parallel processing. A major effort has been made to identify and remove execution bottlenecks, for example, by reducing floating-point calculations and recoding slow intrinsic functions. A pointerlike mechanism which avoids the problems associated with pointers and parallel processing has been implemented. This is required to handle the large, sparse matrices that the algorithm employs. Results obtained with and without the inclusion of space charge are presented and compared for proton beams in the CERN protron synchrotron booster. Comparisons of execution times on different platforms are presented and the chosen solution for our application program, which uses a dual processor PC for the number crunching, is described.

Residual vertical dispersion can be a significant performance limitation for the LEP collider because the associated vertical emittance increase reduces the luminosity of the machine. To make the search for orbits yielding small vertical emittances fast and deterministic, a simultaneous correction of the closed orbit and the residual dispersion was implemented at LEP. The principle of the correction and the resulting performance gains are discussed.

Air-core printed-circuit (PC) quadrupoles and dipoles have been developed for the University of Maryland electron ring, currently under construction. The quadrupoles and dipoles are characterized by very small magnetic fields (about 15 G at the aperture edge) and small aspect ratios (length/diameter $<1$). We review the theory behind the design of the PC lenses and bending elements, and present general expressions for estimating the values of integrated field and integrated field gradient as functions of design parameters. The new quadrupole magnet represents an improvement over an earlier version which was based on an empirical approach. Further, we summarize the results of multipole content of the magnet fields as measured with a rotating coil apparatus of special construction. The results are compared with calculations with an iron-free magnetics code and are related to different types of errors in the manufacture and assembly of the PC magnets.

A cw high power linear accelerator can only work with very low particle losses and structure activation. At low energy, the radio frequency quadrupole (RFQ) is an accelerator element that is very sensitive to losses. To design this structure, a good understanding of the beam dynamics is required. Generally, the reference code PARMTEQM is enough to design the accelerator. TOUTATIS has been written with the goals of cross-checking results and obtaining more reliable dynamics. This paper relates the different numerical methods used in the code. It is time based, using multigrids methods and adaptive mesh for a fine description of the forces without being time consuming. The field is calculated through a Poisson solver and the vanes are fully described, allowing it to properly simulate the coupling gaps and the RFQs extremities. Theoretical and experimental tests are also described and show a good agreement between simulations and reference cases.

Recently there has been renewed interest in the influence of fringe fields on particle dynamics, due to studies that revealed their importance in some cases, as, for example, the proposed Neutrino Factory and muon colliders. In this paper, we present a systematic study of generic fringe field effects. Using as an example a lattice of the proposed Neutrino Factory, we show that fringe fields influence the dynamics of particles at all orders, starting with the linear motion. It is found that the widely used sharp cutoff approximation leads to divergences regardless of the specific fall-off shape of the fields. The results suggest that a careful consideration of fringe field effects in the design stage of small machines for large emittances is always recommended.

The soft-Gaussian approximation is often employed in computer simulations of strong-strong beam-beam interactions in storage rings. Its defect on the coherent oscillation frequency is pointed out and a possible remedy using Hermitian polynominals is discussed.

In this paper the validity of coupling impedance bench measurements is theoretically demonstrated for the standard model of a uniformly distributed wall impedance. Integral equations expressing the magnetic field at the wall are found for the two cases where the device is excited either by a beam or a central wire. The integral equations are solved by a perturbation method with the coupling impedance as the expansion parameter, leading to expressions for the coupling impedance of the beam and the forward scattering coefficient in the bench measurement. Conditions for the validity of bench measurements are indicated, and the interpretation of wire measurements via the scattering coefficient by the conventional formulas is discussed.

A new method for the measurement of loss factor for an rf cavity is presented. The method consists of measuring the above quantity by means of the detection of both the rf voltage induced by an electron bunch in the device under test and the bunch charge. The device to be investigated is a copper reentrant T-shaped cavity. The experimental results and their comparison with analytical and numerical results are presented.

A novel approach for modeling high-current, charged particle beams in a three-dimensional manner is introduced. While the integration of beam motion equations is done as in completely 3D particle-in-cell codes, the space charge forces are found by an approximately self-consistent inclusion of the transverse and longitudinal fields. The algorithm is dramatically faster than fully 3D algorithms with computational times comparable to 2D field solvers. In addition, a sparser spatial grid and fewer required macroparticles provide significantly reduced memory demands. The proposed sub-3D technique has been verified with good agreement with other independent algorithms.

Macroparticle tracking is a direct and attractive approach to following the evolution of a longitudinal phase space distribution. When the particles interact through short-range wake fields or when the interparticle force is included, calculations of this kind require a large number of macroparticles. However, it is possible to reduce both the number of macroparticles required and the number of tracking steps per unit simulated time by employing a simple scaling. It is demonstrated that the Vlasov equation is unchanged by introduction of the scaled quantities. It is further shown that under rather general conditions the speed of calculation improves with the fourth power of the scaling constant. Two examples comparing scaled and original cases illustrate the effectiveness of the approach. Limitations to the amount of rescaling are discussed.

The presence of quadrupole errors in a storage ring will lead to errors in the Twiss parameters and/or errors in the horizontal-vertical coupling. This in turn can lead to degradation of machine performance, such as a decrease in the luminosity. At the Cornell Electron/Positron Storage Ring, the measurement of the betatron phase along with the horizontal-vertical coupling has led to the ability to locate the position of any quadrupole errors and to calculate its strength. This is analogous to using orbit data to locate the source of a kick. Once the source of the error is known, steps can be taken to remove it or to nullify its effect.

We recently used an rf dipole magnet to study the spin flipping of a 120 MeV horizontally polarized proton beam stored in the presence of a nearly full Siberian snake in the Indiana University Cyclotron Facility Cooler Ring. We flipped the spin by ramping the rf dipole's frequency through an rf-induced depolarizing resonance. After optimizing the frequency ramp parameters, we used multiple spin flips to measure a spin-flip efficiency of $86.5\pm 0.5\%$. The spin-flip efficiency was apparently limited by the field strength in the rf dipole. This result indicates that spin flipping a stored polarized proton beam should be possible in high energy rings such as the Brookhaven Relativistic Heavy Ion Collider and HERA where Siberian snakes are certainly needed and only dipole rf-flipper magnets are practical.

A recent study on a high energy accelerator system which involves multistage laser wakefield acceleration shows that the system is very sensitive to jitters due to misalignment between the beam and the wakefield. In particular, the effect of jitters in the presence of a strong focusing wakefield and initial phase space spread of the beam leads to severe emittance degradation of the beam. One way to improve the emittance control is to mitigate the wakefield by working with a plasma channel. However, there are limitations in this approach. Our present investigation does not involve a plasma channel. Instead of averaging over the full phase range of the quarter-wave acceleration, we treat the phase range as a variable. We have found that, for a fixed final acceleration energy and a small phase slip, the final emittance is inversely proportional to the total number of stages. This leads us to consider an accelerator system which consists of superunits, where each superunit consists of closely spaced short tubes, or chips, with the wakefield of each chip being created by an independent laser pulse. There is a relatively large gap between adjacent superunits. With this arrangement the beam electrons are accelerated with a small phase slip; i.e., the phase of the beam is approximately synchronous with respect to the wakefield. This system is designed to have resilience against jitters. It has its practical limitations. We also consider a “horn model” with an exact synchronous acceleration based on a scheme suggested by Katsouleas. Computer simulation of both the chip model and the horn model confirms an expected $(\sin \psi {)}^{3/2}$ law for emittance degradation in the small phase angle region. Thus the choice of a small loading phase together with a small phase slip provides another important ingredient in controlling emittance degradation.

We report on the experimental demonstration of a novel wakefield acceleration technique where a short electron bunch excites a broadband harmonic frequency spectrum, in a cylindrical dielectric structure, to synthesize an accelerating waveform. The structure is designed to have its ${\mathrm{TM}}_{0n}$ modes nearly equally spaced so that the modes generated by a single short electron bunch constructively interfere in the neighborhood of integral multiples of the fundamental wavelength producing large acceleration gradients. Realization of a harmonic multimode structure requires more stringent design considerations than a single-mode structure, since the permittivity and loss tangent of the material should not change substantially over the bandwidth of the structure. In this experiment, a bunch train of four 5 nC electron bunches, separated by 760 ps (one net wavelength), were passed through a 60 cm long dielectric-lined cylindrical harmonic structure. Use of a train of drive bunches spaced by one wavelength reinforced the accelerating wakefield; observation of the energy loss of each bunch via a magnetic spectrometer served as a diagnostic of the wakefield. The measured energy spectrum of the four beams after passing through the waveguide was found to be in excellent agreement with the predictions of the analytic model. This result demonstrates that a dielectric can be fabricated which can synthesize the required wakefield. We also discuss potential advantages of this harmonic approach over conventional single-mode wakefield accelerators.

Accelerating structures with damped higher-order modes (HOMs) have been the focus of many studies over the past decade. This report compares the results of numerical simulations of damping of HOMs using a new calculation technique applied to the case of the PEP-II rf cavity. We compare these results using this technique, which was not yet developed at the time of the original design, with bench and beam-based measurements of the HOM damping. These results show agreement with bench measurements of the shunt impedances of the strongest HOMs as well as measurements of the beam-induced signals on cavities installed in PEP-II.

Advanced storage ring concepts for intense ion beams often require operation far outside the stability boundaries provided by Landau damping. Whether a machine can be operated in such a regime depends on the phase space dilution after saturation of the microwave instability. A Vlasov simulation model is employed to analyze the saturation mechanisms in space charge dominated coasting beams. The stabilizing effect of space charge [I. Hofmann, Laser Part. Beams 3, 1 (1985)] is addressed to fluidlike mode coupling effects.

An analytical method for calculating nonlinear envelopes in beam expanders is presented. It is illustrated by implementation in a matrix transport code and accompanied with various considerations on expander line design and transverse beam tail confinement effects.