Search Results (24 total)

Detection of the field induced by a beam outside of the beam pipe can be used as a beam diagnostic. Wires placed in longitudinal slots in the outside wall of the beam pipe can be used as a beam pickup. This has a very small beam-coupling impedance and avoids complications of having a feedthrough. The signal can be reasonably high at low frequencies. We present a field waveform at the outer side of a beam pipe, obtained as a result of calculations and measurements. We calculate the beam-coupling impedance due to a long longitudinal slot in the resistive wall and the signal induced in a wire placed in such a slot and shielded by a thin screen from the beam. These results should be relevant for impedance calculations of the slot in an antechamber and for slots in the PEP-II distributed ion pump screens. The design of the low-frequency beam position monitor is very simple. It can be used in storage rings, synchrotron light sources, and free electron lasers, like LINAC coherent light source.

The paper describes a method for calculating the longitudinal and transverse impedances of the laminated round pipe with many layers of different materials. The charge is moving along the pipe axis with arbitrary constant velocity. The study is based on the field-matching technique applied for the arbitrary harmonic of the electromagnetic field. The matrix formalism has been developed to describe the field transitions through the subsequent layers that allow coupling the electromagnetic fields inside and outside the pipe. The number of equations to be solved is then reduced to four algebraic equations. The solutions and ultrarelativistic limits for the field harmonics in the inner and outer regions of the pipe are derived.

A general formalism for treating simultaneously the transverse coupled-bunch and transverse coupled-mode instabilities is presented. In this approach, the equations of motion of a coupled multibunch beam are expanded to yield a system of equations involving correlation moments of the transverse and longitudinal motions. After a proper truncation, the system of equations is closed and can be solved. This approach allows us to formulate within one framework several known instability mechanisms including the single-bunch mode-coupling instability, the coupled-bunch instability, the mode-coupling instability, and the coupled-mode coupled-bunch instability as particular cases.

The Pedersen analysis of the low-level rf feedback system assumes that all bunches oscillate in phase which corresponds to the lowest coupled-bunch mode. This analysis is extended here to take into account all other coupled-bunch modes what might be important for the strongly detuned cavities in large storage rings such as PEP-II.

Wakefields defining beam stability affect also the beam optics and beam properties in high current machines. In this paper we present observations and analysis of the optical effects in the PEP-II Stanford Linear Accelerator Center B Factory, which has the record in achievement of high electron and positron currents. We study the synchronous phase and the bunch length variation along the train of bunches, overall bunch lengthening, and effects of the wakes on the tune and on the Twiss parameters. This analysis is being used in upgrades of PEP-II and may be applied to future B factories and damping rings for linear colliders.

The beam dynamics for a quasi-isochronous lattice differs from that in the usual case of a lattice with a large positive momentum compaction factor. In particular, the quasi-isochronous lattice allows us to double the number of bunches which may be an attractive option for colliders. However, microwave instability and, as we show, longitudinal head-tail instability set the threshold for the beam current.

In this paper the results of the experimental measurements at Berlin electron storage ring for synchrotron radiation (BESSY-II) are presented. Grow/damp measurements of the transverse coupled-bunch instabilities were performed using a multibunch feedback system and a synchronized time-domain bunch motion recorder. The results of these experiments are described and explained by the beam-ion instability. Simplified simulations and revised theory of the instability extended to a nonlinear regime are used for the interpretation of the results.

The sudden drop of the beam lifetime and bursts of the background radiation were detected in many machines and associated with microscopic dust particles. We present the model of the dust particle dynamics explaining the long time of the dust events observed in the PEP-II B-factory and BEPC-II machines.

The coherent synchrotron radiation instability may be driven at the shielding threshold by a single mode excited in the beam pipe. Such a problem may have general interest for other one-mode dominated problems arising in plasma, free-electron laser theory, and microwave instability. The problem may have practical interest if the steady state exists but requires the study of the nonlinear regime of instability. The results of the study, both analytic and numerical, are presented in the coasting beam approximation and for a bunched beam.

The microwave instability driven by the coherent synchrotron radiation (CSR) has been previously studied [S. Heifets and G. V. Stupakov, Phys. Rev. ST Accel. Beams 5, 054402 (2002)] neglecting effect of the shielding caused by the finite beam pipe aperture. In practice, the unstable mode can be close to the shielding threshold where the spectrum of the radiation in a toroidal beam pipe is discrete. In this paper, the CSR instability is studied in the case when it is driven by a single synchronous mode. A system of equations for the beam-wave interaction is derived and its similarity to the 1D free-electron laser theory is demonstrated. In the linear regime, the growth rate of the instability is obtained and a transition to the case of continuous spectrum is discussed. The nonlinear evolution of the single-mode instability, both with and without synchrotron damping and quantum diffusion, is also studied.

We present an explanation for the opposite signs of the horizontal and vertical tune shifts of bunch trains which have been observed recently in several high-energy storage rings. This result can be understood in terms of the long-range quadrupolar wakes of noncircular vacuum chambers with finite resistivity. In vacuum chambers with circular cross section, the dominant transverse wake driven by a leading particle and seen by a trailing test particle is dipolar and is proportional only to the transverse offset of the driving particle. The contributions of preceding bunches or previous turns tend to cancel, as they add with oscillatory factors. On the other hand, quadrupolar wakes are independent of the offset of the driving particle, and thus the contributions of preceding bunches and turns are strictly additive. Since quadrupole fields are focusing in one plane and defocusing in the plane orthogonal to it, their effects on tune shifts in these planes have opposite signs. Their cumulative effect also explains the large values of the tune shifts measured in PEP-II, which exceeded estimates from other impedance sources by factors of 3 to 4. Our analysis also offers a connection to the familiar Laslett tune shift.

The coherent synchrotron radiation of a bunch in a bunch compressor may lead to the microwave instability producing longitudinal modulation of the bunch with wavelengths small compared to the bunch length. It can also be a source of an undesirable emittance growth in the compressor. We derive and analyze the equation that describes linear evolution of the microwave modulation taking into account incoherent energy spread and finite emittance of the beam. Numerical solution of this equation for the Linac Coherent Light Source bunch compressor gives the amplification factor for different wavelengths of the beam microbunching.

A relativistic electron beam moving in a circular orbit in free space can radiate coherently if the wavelength of the synchrotron radiation exceeds the length of the bunch. In accelerators coherent synchrotron radiation of the bunch is usually suppressed by the shielding effect of the conducting walls of the vacuum chamber. However an initial density fluctuation with a characteristic length much shorter than the bunch length can radiate coherently. If the radiation reaction force results in the growth of the initial fluctuation, one can expect an instability which leads to microbunching of the beam and an increased coherent radiation at short wavelengths. Such an instability is studied theoretically in this paper.

Quantum theory of optical stochastic cooling is presented. Results include a full quantum analysis of the interaction of the beam with radiation in the undulators and in the quantum amplifier. A density matrix of the whole system is constructed and the cooling rate is evaluated. It is shown that quantum fluctuations change classical results of stochastic cooling at low bunch population and set a limit on the cooling rate.

Evolution of the density matrix in a quantum amplifier is described for initial conditions corresponding to superposition of the coherent states. The approach developed in the paper is also applicable for an arbitrary initial condition allowing the inverse Mellin transform. As such an example, we consider the evolution of the squeezed state.

The nonlinear regime of the beam-beam instability for flat beams is considered. Excitation of coherent modes and mode interaction is studied above the threshold of instability. It is shown that the exponential growth of the linear approximation may saturate, leading to a finite growth of transverse emittance.

We study single bunch stability with respect to monopole longitudinal oscillations in electron storage rings. Our analysis is different from the standard approach based on the linearized Vlasov equation. Rather, we reduce the full nonlinear Fokker-Planck equation to a Schrödinger-like equation which is subsequently analyzed by perturbation theory. We show that the Haissinski solution [Nuovo Cimento Soc. Ital. Fis. 18B, 72 (1973)] may become unstable with respect to monopole oscillations and derive a stability criterion in terms of the ring impedance. We then discuss this criterion and apply it to a broadband resonator impedance model.

We report the results of observations of a new regime of ion instabilities at the Advanced Light Source (ALS). With artificially increased pressure and gaps in the bunch train large enough to avoid multiturn ion trapping, we observed a factor of 2–3 increase in the vertical beam size along with coherent beam oscillations which increased along the bunch train. The observations are qualitatively consistent with the “fast beam-ion instability” [T. O. Raubenheimer and F. Zimmermann, Phys. Rev. E 52, 5487 (1995); G. V. Stupakov et al., Phys. Rev. E 52, 5499 (1995)], which can arise even when the ions are not trapped over multiple beam passages. This effect may be important for many future accelerators.

Stability of the steady-state bunch distribution described by the Haissinski solution [J. Haissinski, Nuovo Cimento 18B, 72 (1973)] is studied above the threshold of microwave instability. It is shown that instability may lead to a new self-consistent state corresponding to particles trapped in a separatrix of an unstable mode. The free energies of the two solutions are compared. The relaxation oscillations between the new and Haissinski solutions are possible and may be related to the sawtooth instability observed recently in the experiments [P. Krejcik et al., (unpublished)]. © 1996 The American Physical Society.

A systematic review of theoretical results for the longitudinal and transverse impedances obtained by different methods is presented. Definitions, general theorems, modal analysis, diffraction model, and analytical results comprise the content of the paper. Several new results are included. In particular, necessary and sufficient conditions for the independence of the impedance on the beam longitudinal direction are given. The impedances of two basic simple structures—that of a cavity and that of a step—are studied in detail. The transition from the regime of a cavity to the regime of a step is explained, an approximate formula describing this transition is given, and the criterion for determining the applicability of each regime is established. The asymptotic behavior of the impedance for a finite number M of periodically arranged cavities as a function of M is studied. The difference in the behavior of the impedance for a single cavity and that for an infinite number of cavities is explained as the result of the interference of the diffracted waves. A criterion for determining the transition in the impedance behavior from small M to large M is presented.

High-frequency diffraction can be described by iterations based on an approximate formulation of the boundary conditions. The method formulated is analogous to the Born series of scattering theory. It is used to study the interaction of short bunches with the beam environment in terms of the impedances. The impedances of typical elements of an accelerator structure are obtained. The crosstalk between elements, the impedance of a periodic array, and the effect of a taper are discussed. The method can be applied to a cavity of an arbitrary shape.

The longitudinal impedance of an array of cylindrically symmetric cavities connected by side pipes is estimated in the high-frequency limit. The expression for the impedance is obtained for an arbitrary number of cavities. The transition from the case of a single cavity to a periodic structure is studied. The impedance per cell decreases with frequency ω as ω^-1/2 for a small number of cells. For a large number of cells the impedance decreases as ω^-1/2 or as ω^-3/2 depending on a certain relation between the frequency and the number of cells. The parameter which governs the transition from one regime to the other is found. In particular, for the infinite periodic structure there is only the second regime and the impedance decreases as ω^-3/2 for all frequencies.