Search Results (12 total)

The beam coupling impedances of small discontinuities of an accelerator vacuum chamber have been calculated [e.g., Kurennoy, Gluckstern, and Stupakov, Phys. Rev. E 52, 4354 (1995)] for ultrarelativistic beams using the Bethe diffraction theory. Here we extend the results to an arbitrary beam velocity. The vacuum chamber is assumed to have an arbitrary, but uniform along the beam path, cross section. The longitudinal and transverse coupling impedances are derived in terms of series over cross-section eigenfunctions, while the discontinuity shape enters via its polarizabilities. Simple explicit formulas for two important particular cases—circular and rectangular chamber cross sections—are presented. The impedance dependence on the beam velocity exhibits some unusual features: for example, the reactive impedance, which dominates in the ultrarelativistic limit, can vanish at a certain beam velocity, or its magnitude can exceed the ultrarelativistic value many times. In addition, we demonstrate that the same technique, the field expansion into a series of cross-section eigenfunctions, is convenient for calculating the space-charge impedance of uniform beam pipes with arbitrary cross section.

We studied the electrostatic field due to a charged-particle beam with uniform particle density propagating inside an rf-shielding cage (rf cage) constructed from evenly spaced conducting wires. The beam and the rf cage are surrounded by a ceramic beam pipe positioned inside a conducting pipe concentric with the beam and the rf cage. The space-charge impedances in the long wavelength regime are investigated by considering the electrostatic fields due to the longitudinal and transverse perturbations on the density of the charged-particle beam. Shielding effects due to the rf cage are discussed and simple formulas are derived for estimating the space-charge impedances. Numerical examples are given for illustration. Comparisons between analytical estimates and the results produced by the field-solver computer program MAFIA show good agreement.

The fields produced by a long beam with a given transverse charge distribution in a homogeneous vacuum chamber are studied. Signals induced by a displaced finite-size beam on electrodes of a beam position monitor (BPM) are calculated and compared to those produced by a pencil beam. The nonlinearities and corrections to BPM signals due to a finite transverse beam size are calculated for an arbitrary chamber cross section. Simple analytical expressions are given for a few particular transverse distributions of the beam current in a circular or rectangular chamber. Of particular interest is a general proof that in an arbitrary homogeneous chamber the beam-size corrections vanish for any axisymmetric beam current distribution.

Beam energy loss in a cavity can be easily computed for a relativistic bunch using time-domain codes like MAFIA or ABCI. However, for nonrelativistic beams the problem is more complicated because of difficulties with its numerical formulation in the time domain. We calculate the cavity loss factors for a bunch in frequency domain as a function of its velocity and compare results with the relativistic case.

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.

The beam coupling impedances of small axisymmetric obstacles having a semielliptical cross section along the beam in the vacuum chamber of an accelerator are calculated at frequencies for which the wavelength is large compared to a typical size of the obstacle. Analytical results are obtained for both the irises and the cavities with such a shape, which allows simple estimates of their broadband impedances.

The beam coupling impedances of small obstacles protruding inside the vacuum chamber of an accelerator are calculated at frequencies for which the wavelength is large compared to a typical size of the obstacle. Formulas for a few important particular cases including both essentially three-dimensional objects like a post or a mask and axisymmetric irises, are presented. These results allow simple practical estimates of the broadband impedance contributions from such discontinuities.

An analysis of the stability and halo formation is presented for a breathing axisymmetric beam of uniform density [Kapchinsky-Vladimirsky (KV) beam] in a uniform focusing channel. Theoretical results are obtained for the form of modes involving nonuniform charge density. In particular, the mismatch-tune depression space is explored, both analytically and by numerical particle-in-cell simulations, to determine the stability limits and growth rates of the most unstable modes. The implications for halo formation are then explored. Halo parameters obtained by simulations are compared with predictions of an analytical model for halo formation from the breathing KV beam developed earlier. The practical applications of the results for high-current linear accelerators are discussed.

A general theory of the beam interaction with small discontinuities of the vacuum chamber of an accelerator is developed taking into account the reaction of radiated waves back on the discontinuity. The reactive impedance calculated earlier is reproduced as the first order and the resistive one as the second order of a perturbation theory based on this general approach. The theory also gives, in an easy and natural way, the analytical results for the frequencies and coupling impedances of the trapped modes due to small discontinuities on the vacuum chamber of a general cross section. Formulas for two important particular cases—a circular and a rectangular chamber—are presented.

It has been demonstrated recently [G. V. Stupakov and S. S. Kurennoy, Phys. Rev. E 49, 794 (1994)] that a single small discontinuity (such as an enlargement or a hole) on a smooth waveguide can result in the appearance of trapped electromagnetic modes with frequencies slightly below the waveguide cutoff frequencies. The present paper studies a similar phenomenon for a waveguide with many small discontinuities, which is a good model for the vacuum chamber of large accelerators. Frequencies of trapped modes and their contributions to the coupling impedance are calculated. The frequencies for the cases of a few discontinuities or a periodic structure coincide well with those from numerical simulations. The trapped modes produce sharp resonance peaks of the coupling impedance near the cutoff frequencies. The magnitude of these peaks, as well as the existence itself of a trapped mode, strongly depends on the distribution of discontinuities, or on the distance between them if a regular array is considered. The impedance in the extreme case can be as large as N³ times that for a single discontinuity, where N is the number of discontinuities.

We demonstrate that a small discontinuity (such as an enlargement or a hole) on a smooth waveguide can result in the appearance of trapped modes localized in the vicinity of the discontinuity. The frequencies of these modes lie slightly below the cutoff frequencies of the corresponding propagating modes in the waveguide. We find the distribution of the electromagnetic field in the modes and calculate their damping rate due to a finite conductivity of the walls. The contribution of the trapped modes to the longitudinal impedance is calculated.