Search Results (47 total)

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.

Resonance-driven collective instabilities of charged-particle beams were extensively studied in connection with high-current transport systems, leading to restrictions imposed on the zero-current phase advance. In this paper, we discuss application of such parametric instabilities to circular machines. This effect is directly related to the space-charge limit in rings and its understanding is of crucial importance. Its relation to the coherent resonance condition of an integer type is explained. Practical application of such resonant responses to both structural and imperfection driven harmonics is addressed.

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.

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.

Space charge presents a fundamental limitation to high intensity circular accelerators. Its effects are especially important in the latest designs for high-intensity proton rings, which require beam losses much smaller than presently achieved in existing facilities. It is therefore necessary to understand the major space-charge effects which could lead to emittance growth and associated beam loss. In this paper, we explore the excitation of high-order collective beam modes and associated instabilities driven by space-charge coupling resonances. Such studies help us to understand energy exchange and emittance growth driven by space-charge coupling. They also have direct application to the choice of a good working point in a high-intensity machine. The studies are performed using an earlier version of the Spallation Neutron Source lattice, which was used as a generic example of a circular machine. In this way, we explore the nature of the observed space-charge coupling effect and its applicability to high-intensity rings in general.

We use the linearized Vlasov-Poisson equations to study the response of a Kapchinskij-Vladimirskij beam to magnetic multipole errors in a circular lattice. This work extends the calculation of Gluckstern [Proceedings of the Linac Conference, 1970 (Fermilab, Batavia, IL, 1970), p. 811] to the case of nonideal periodic lattices. The smooth approximation is assumed. We determine the resonance conditions as well as the amplitude of the excited collective modes as a function of the error size outside the stopbands. We find that the frequencies associated with lattice resonances are a subset of the beam natural eigenfrequencies. The result is used to study the motion of test particles crossing the boundary of the beam core. Close to resonance the model predicts the emergence of a halo if sufficiently large gradient errors are present. Application is made to the University of Maryland Electron Ring.

We examine the transverse impedance of a periodic array of cavities in a beam pipe at high frequency. The calculation is an extension of a previous one for the longitudinal impedance of a periodic array of azimuthally symmetric pillboxes, for which only TM modes were needed. In the present case, we must include TE modes as well. In addition, we extend the applicability of the previous calculation by including an extra term in the coupling kernel so that the results are valid for all values of the ratio of the cavity length to the period of the structure (all values of the ratio of iris thickness to structure period). In spite of the presence of TE modes, we find that the high frequency limit of the transverse impedance is simply (2/ka²) times the corresponding limit of the longitudinal impedance, just as it is for the resistive wall impedances, a relation which occurs frequently for azimuthally symmetric structures. Finally, we present numerical results as well as approximate expressions for the impedance per period, valid for all ratios of cavity length to structure period.

Beam halo formation issues are important for the design of high current linear ion accelerators. Various mechanisms can potentially cause beam halo. Some recent studies suggested that Coulomb collisions in the beam bunch can contribute significantly to beam bunch growth and halo development in linear accelerators. Despite the general belief that collisions are not important, it is clear that a rigorous treatment of this question is needed. In an effort to explore this issue in detail we have undertaken an analysis of the effects of Coulomb scattering between ions in a self-consistent spherical bunch.

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 have constructed, analytically and numerically, a class of self-consistent six-dimensional (6D) phase space stationary distributions. Stationary distributions allow us to study the halo development mechanism without it being obscured by beam redistribution and its effect on halo formation. The beam is then mismatched longitudinally and/or transversely, and we explore the formation of longitudinal and transverse halos in 3D axisymmetric beam bunches. We find that the longitudinal halo forms first for comparable longitudinal and transverse mismatches because the longitudinal tune depression is more severe than the transverse one for elongated bunches. Of particular importance is the result that, due to the coupling between longitudinal and transverse motion, a longitudinal or transverse halo is observed for a mismatch less than 10% if the mismatch in the other plane is large.

We recently developed a general analysis for an azimuthally asymmetric rectangular slot in the inner conductor of a coaxial liner, which allowed us to investigate the coupling impedance numerically. In the present paper we obtain analytic expressions for a small hole of arbitrary shape. Specifically, we go beyond the quasistatic (Bethe) approximation to explore and understand the structure of the impedance in the frequency region near the cutoffs of the inner beam pipe and outer coaxial structure. Finally, we extend our analytic analysis to a hole in a wall of finite thickness.

Beam pipes in high-energy superconducting colliders require a shielding tube (liner) with pumping slots to screen cold chamber walls from synchrotron radiation. Earlier we developed a general analysis, based on a variational formulation, which includes both the realistic coaxial structure of the beam pipe with a liner and the effect of finite wavelength in the calculation of the coupling impedance of a rectangular slot in a liner wall of zero thickness. In the present paper we use this analysis to study the frequency dependence of the coupling impedance of a longitudinal rectangular slot, which is of great interest as a shape of pumping slot. Resonant effects in the coupling impedance involving the ratio of the slot length to the wavelength are explored. We also present the analytic results for the real part of the impedance at low frequencies for a liner wall of both negligible and finite thickness.

Beam pipes of high-energy superconducting colliders require a shielding tube (liner) with pumping slots to screen cold chamber walls from synchrotron radiation. Pumping slots in the liner walls are required to keep high vacuum inside the beam pipe and provide for a long beam lifetime. As previously discussed [Fedotov and Gluckstern, Phys. Rev. E 54, 1930 (1996)], for a long narrow slot whose length may be comparable with the wavelength, the usual static approximation for the polarizability and susceptibility that enter into the impedance is a poor one. Therefore, finding semianalytic expressions for the impedance of a rectangular slot in a broad frequency range is highly desirable. We develop a general analysis based on a variational formulation, which includes both the realistic coaxial structure of the beam-pipe and the effect of finite wavelength, in order to calculate the coupling impedance of a rectangular slot in a liner wall of zero thickness. We then present a numerical study of the frequency dependence of the coupling impedance of a transverse rectangular slot. Numerical results for a small square hole are presented for frequencies above and below cutoff, and compared with the results of other calculations.

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.

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.

The static approximation suggests that, for a given hole area, the use of a long narrow slot in a beam pipe gives a reduced coupling impedance. But for a long slot the slot length may be comparable with the wavelength, making the static approximation a poor one. In this paper we derive expressions for the generalized polarizability and susceptibility [Cheng, Fedotov, and Gluckstern, Phys. Rev. E 52, 3127 (1995)] of an elliptical hole in a thin plane metallic screen, as a function of hole dimensions and wavelength. In particular, we construct a variational form that allows us to obtain an approximate analytic result for the resonant frequency of a cavity with such a hole. In the calculations we include the effects of finite wavelength, but still confine our attention to reduced wavelengths no smaller than the primary hole dimensions. We then use these results to estimate the coupling impedance of a long narrow elliptical slot in a beam pipe, and show that the effect of finite wavelength is important. © 1996 The American Physical Society.

An analysis of the stability of a breathing beam of uniform density and circular cross section is presented. Theoretical results are obtained for the form of the modes involving nonuniform charge density. In particular, the mismatch-tune depression space is explored to determine the limits beyond which exponential growth is predicted, and the corresponding growth rates. These results for what is believed to be the most unstable modes are confirmed in detail by numerical particle-in-cell simulations. Their practical implications with regard to beam halo formation for high current linacs 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.

We calculate a generalized polarizability and susceptibility for a circular hole in a thick metallic plate as a function of hole dimensions and wavelength. In particular, we construct a variational form that allows us to obtain accurate numerical results for the resonant frequency of a cavity with such a hole with a minimum of computational effort. Numerical results are obtained for a variety of hole dimensions relative to the wavelength. Results are also obtained analytically which are valid to second order in the ratio of the hole dimension to the wavelength for a vanishingly thin wall. These results are confirmed by the numerical calculations.

The transverse stability of bunches in a bunch train is determined by solving the equations of betatron motion for macroparticles circulating in a high energy storage ring. We ignore multibunch modes that are more likely to be serious with equal bunch spacing, and find that a nonexponential beam breakup instability may develop, which would not be found by the usual instability analysis with an exponential ansatz. In the absence of radiation or other damping mechanisms, the amplitudes of the trailing bunches would grow with a power law and would soon be lost if the first bunches perform a betatron oscillation about the closed orbit. Experimental observations on a large electron-positron collider are also discussed.

We construct an azimuthally symmetric 2D model for halo formation in high current ion linacs. The driving term, a "breathing" oscillation caused by a transverse mismatch along the linac, leads to growth of ion amplitudes in the core through the parametric resonance. As the ion amplitude grows, its wave number increases, enhancing the resonance. This leads to the formation of a halo surrounding the core. We explore the dependence of this mechanism on the tune depression and the size of the mismatch. The model agrees well with simulations at Los Alamos, but does not yet include the effects of chaos observed in the simulations as the tune depression becomes severe.

The use of iris loaded cavities to accelerate high current bunched beams makes it important to understand the impedance and wake fields caused by an iris in a beam pipe. In this paper we present a method to calculate both the longitudinal and transverse impedance of a circular iris of radius b and thickness g in a circular beam pipe of radius a for ultrarelativistic particles. An integral equation is derived for the transverse electric field at the junction between the iris and the beam pipe and a variational expression is obtained for the impedance, using the transverse field as a trial function. Accurate numerical results are obtained for the longitudinal and transverse impedances using a trial function with only a few adjustable parameters. By invoking causality we confirm the analytic behavior of the impedances in the complex frequency plane and obtain the corresponding wake functions. We particularly explore the limit b→∞ to compare with previous studies of the impedance of a circular hole in a transverse metallic plane.

Simultaneous longitudinal and transverse focusing can be obtained in a drift tube linac by alternating the sign of the synchronous phase. It is found both theoretically and numerically that, in the alternating-phase-focused (APF) linac with a symmetric synchronous phase sequence, the lowest-order resonance due to the synchrobetatron coupling naturally occurs, causing significant emittance transfer between the longitudinal and transverse motions. Equations for the averaged APF motion are derived to investigate the coupling effect. Two approximate invariants are obtained. Results from computer simulations based on a modified parmila code yield good agreement with the formulas for the invariant and tune shift derived from the theory. We then suggest a way to move the parameters away from the lowest-order resonance. Simulation results for the effect of space charge on the emittance exchange along with the synchrobetatron coupling are briefly discussed.

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.