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Stupakov, G V

Publications and source records attributed to Stupakov, G V.

Coupling Impedance of a Periodic Array of Diaphragms (Erratum)

A method is presented for calculating the high-frequency longitudinal and transverse coupling impedances in a periodic array of diaphragms in a circular perfectly conducting pipe. The method is based on Weinstein's theory of diffraction of a plane electromagnetic wave on a stack of halfplanes. Using Weinstein's solution, it is shown that the problem of finding the beam field in the pipe reduces to an effective boundary condition at the radius of the diaphragms that couples the longitudinal electric field with the azimuthal magnetic one. Solving Maxwell's equations with this boundary condition leads to simple formulae for Z{sub long} and Z{sub tr}. A good agreement with a numerical solution of the problem found by other authors is demonstrated.

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Ideas for a Future PEP-X Light Source

SLAC is developing a long-range plan to transfer the evolving scientific programs at SSRL from the SPEAR3 light source to a much higher performing synchrotron source -- PEP-X -- a new storage ring that would occupy the existing PEP-II tunnel and support two experimental halls, each containing 16 x-ray beam lines. Operating at 4.5 GeV and 1.5 A with a horizontal emittance of 0.14 nm-rad, reached using 90 m of damping wigglers, PEP-X would have an order of magnitude higher average brightness and flux in the 1-{angstrom} x-ray range than any existing or planned future storage ring sources. Higher brightness in the soft x-ray regime might be reached with partial lasing in long undulators, and high peak brightness could be reached with seeded FEL emission. The status of preliminary studies of PEP-X is presented.

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A Study of Single Pass Ion Effects at the ALS

We report the results of experiments on a 'fast beam-ion instability' at the Advanced Light Source (ALS). This ion instability, which can arise even when the ions are not trapped over multiple beam passages, will likely be important for many future accelerators. In our experiments, we filled the ALS storage ring with helium gas, raising the pressure approximately two orders of magnitude above the nominal pressure. With gaps in the bunch train large enough to avoid conventional (multi-turn) 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. Ion trapping has long been recognized as a potential limitation in electron storage rings. The ions, generated by beam-gas collisions, become trapped in the negative potential of the beam and accumulate over multiple beam passages. The trapped ions are then observed to cause a number of deleterious effects such as an increasing beam phase space, a broadening and shifting of the beam transverse oscillation frequencies (tunes), collective beam instabilities, and beam lifetime reductions. All of these effects are of concern for the next generation of accelerators, such as the B-factories or damping rings for future linear colliders, which will store high beam currents with closely spaced bunches and ultra-low beam emittances. One of the standard solutions used to prevent ion trapping is to include a gap in the bunch train which is long compared to the bunch spacing. In this case, the ions are first strongly-focused by the passing electron bunches and then over-focused in the gap. With a sufficiently large gap, the ions can be driven to large amplitudes where they form a diffuse halo and do not affect the beam. In this paper, we describe experiments that study a new regime of transient ion instabilities predicted to arise in future electron storage rings, and linacs with bunch trains. These future rings and linacs, which will be operated with higher beam currents, small transverse beam emittances, and long bunch trains, will use ion clearing gaps to prevent conventional ion trapping. But, while the ion clearing gap may suppress the conventional ion instabilities, it will not suppress a transient beam-ion instability where ions generated and trapped during the passage of a single train lead to a fast instability. While both conventional and transient ion instabilities have the same origin, namely ions produced by the beam, they have different manifestations and, more importantly, the new transient instability can arise even after the conventional ion instability is cured. This new instability is called the 'Fast Beam-Ion Instability' (FBII). In many future rings, the FBII is predicted to have very fast growth rates, much faster than the damping rates of existing and proposed transverse feedback systems, and thus is a potential limitation. To study the FBII, we performed experiments at the ALS, a 1.5 GeV electron storage ring. At the nominal ALS pressure of about 0.24 nTorr, the FBII is not evident. To study the instability, we intentionally added helium gas to the storage-ring vacuum system until the residual gas pressure was increased about 80 nTorr. This brought the predicted growth rate of the instability at least an order of magnitude above the growth rate of conventional multibunch instabilities driven by the RF cavities and above the damping rate of the transverse feedback system (TFB) in the ALS and, thereby, established conditions very similar to those in a future storage ring. We then filled the ring with a relatively short train of bunches, suppressing conventional ion instabilities. In the following, we will first briefly describe This paper describes the experiment and results in more detail.

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Geometrical Wake of a Smooth Flat Collimator

A transverse geometrical wake generated by a beam passing through a smooth flat collimator with a gradually varying gap between the upper and lower walls is considered. Based on generalization of the approach recently developed for a smooth circular taper we reduce the electromagnetic problem of the impedance calculation to the solution of two much simpler static problems - a magnetostatic and an electrostatic ones. The solution shows that in the limit of not very large frequencies, the impedance increases with the ratio h/d where h is the width and d is the distance between the collimating jaws. Numerical results are presented for the NLC Post Linac collimator.

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Nonlinear Dynamics of Single Bunch Instability

A nonlinear equation is derived that governs the evolution of the amplitude of unstable oscillations with account of quantum diffusion effects due to the synchrotron radiation. Numerical solutions to this equation predict a variety of possible scenarios of nonlinear evolution of the instability some of which are in good qualitative agreement with experimental observations. Microwave single bunch instability in circular accelerators has been observed in many machines. The instability usually arises when the number of particles in the bunch exceeds some critical value, Nc, which varies depending on the parameters of the accelerating regime. Recent observations on the SLC damping rings at SLAC with a new low-impedance vacuum chamber revealed new interesting features of the instability. In some cases, after initial exponential growth, the instability eventually saturated at a level that remained constant through the accumulation cycle. In other regimes, relaxation-type oscillations were measured in nonlinear phase of the instability. In many cases, the instability was characterized by a frequency close to the second harmonic of the synchrotron oscillations. Several attempts have been made to address the nonlinear stage of the instability based on either computer simulations or some specific assumptions regarding the structure of the unstable mode. An attempt of a more general consideration of the problem is carried out in this paper. We adopt an approach recently developed in plasma physics for analysis of nonlinear behavior of weakly unstable modes in dynamic systems. Assuming that the growth rate of the instability is much smaller than its frequency, we find a time dependent solution to Vlasov equation and derive an equation for the complex amplitude of the oscillations valid in the nonlinear regime. Numerical solutions to this equation predict a variety of possible scenarios of nonlinear evolution of the instability some of which are in good qualitative agreement with experimental observations.

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Fast Ion Instability in Real Lattice

The ionization of residual gas by an electron beam in an accelerator generates ions that can resonantly couple to the beam through a wave propagating in the beam-ion system. The original theory of the Fast Ion Instability was developed assuming both a constant external focusing and the beam size. The theory predicts an instability in which an initial perturbation grows as {approx} exp({alpha}{radical}t). In the present paper we consider a more realistic model that takes into account variation of the beta function in the lattice and associated with it variation of the beam size. We find that, in combination with ion decoherence effect, the spatial inhomogeneity can result in (1) purely exponential growth, {approx} exp({Lambda}t); and (2) typically smaller growth rates. Detailed calculations are performed for the lattice of the Advanced Light Source at the LBL.

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Effect of Diffusion on Bunched Beam Echo

When a beam receives a dipole kick, its centroid signal decoheres due to the betatron tune spread in the beam. Long after the signal has decohered, however, a followup quadrupole kick to the beam brings a pronounced echo back to the centroid signal. This echo effect has been analyzed for the case of a bunched beam in Ref. [1]. In this work, the perturbation calculation of Ref. [1] is extended to include a diffusion in betatron amplitude. The effect of diffusion on the magnitude of the echo is then parameterized and studied.

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Spectral Fluctuations of Incoherent Radiation And Measurement of Longitudinal Bunch Profile

A method for measurement of ultrashort beam current profile I{sub b}(t) is proposed that is based on detecting fluctuations of the spectral intensity P ({omega}) of single bunch incoherent radiation. We show that the variance of the Fourier transform of the spectrum is proportional to the convolution function of the beam current. After the convolution function is found, using phase retrieval technique one can restore the shape of the pulse in many practical cases.

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Synchrotron Radiation Wake in Free Space

In this paper, we derive the transverse radiation force of a bunch of ultrarelativistic charged particles coherently radiating in free space assuming that the bending radius is much larger than the beam dimensions. In contrast to a similar recent study, where the authors decompose the total transverse force and find only a part that is responsible for the distortion of the beam orbit, we derive a full expression for the force and leave the issues of the beam dynamics for a separate consideration. Another approach to the calculation of the transverse force has been previously developed. In many cases considered in this paper, the calculations are extremely cumbersome; they were systematically performed with the use of symbolic engine of the computer program MATHEMATICA.

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