The Existence of a Static Solution for the Haissinski Equation with

The equilibrium longitudinal distribution of electrons in circular accelerators is discussedfor the case of the 8\u27 wake function. Contrary to the well known fact that the solution does not exist in this case beyond a threshold, it is strongly suggested that the solution actually exists when we regularize the singularity of the 8\u27 wake function in a physical way, therefore the non-existence of the solution has no physical consequence

Theoretical study of a waveguide THz free electron laser and comparisons with simulations

In a so-called waveguide free electron laser (FEL) for THz radiations, an extremely small aperture (∼mm) waveguide is used to confine angularly wide spread radiation fields from a low energy electron beam into a small area. This confinement increases the interaction between the electron beam and the radiation fields to achieve a much higher FEL gain. The radiation fields propagate inside the waveguide as waveguide modes, not like a light flux in a free space FEL. This characteristic behavior of the radiation fields makes intuitive understanding of the waveguide FEL difficult. We developed a three-dimensional waveguide FEL theory to calculate a gain of THz waveguide FEL including the effects of the energy spread, the beam size and the betatron oscillations of an electron beam, and effects of a rectangular waveguide. The FEL gain can be calculated as a function of frequency by solving the dispersion relation. Theoretical gains are compared with simulation results for a waveguide FEL with a planar undulator similar to the KAERI one. Good agreements are obtained

Optimization of electrode shape for stripline beam position monitors

The exponentially tapered beam position monitor has been proposed by Linnecar to produce a flat and wideband frequency response for beam position signals. However, it still has a large ringing fluctuation on the amplitude of the transfer function. This paper aims at improving the overall characteristics of the transfer function. With the help from the window function theory, we investigate the correlation between the shape of the electrode and the resulting transfer function. Finally, we propose a polynomial shape for the electrode that provides a much flatter response function. Three-dimensional results using the cst studio are also presented to demonstrate the validity of the polynomial shape even in more realistic conditions

Analytical method for the evaluation of field modulation inside the rf-shielded chamber with a time-dependent dipole magnetic field

A ceramic chamber with Cu stripes is usually used as the vacuum chamber in a rapid cycling synchrotron. The Cu stripes terminate at either end as capacitors, and provide the low impedance for the circulating beam, and the high impedance for the induced current with the frequency components of the external time-dependent magnetic field (for example, injection bump magnets, bending magnets, etc.). It is important to be able to precisely estimate the field modulations inside the chamber when the field is excited, because any such field modulations can cause the beam characteristics to deteriorate. In this paper a theoretical approach to evaluate the field modulations in a quick and precise manner is developed

Generalized Napoly integral to compute wake potentials in axisymmetric structure

The Napoly integral is the very useful method for calculations of wake potentials in structures where parts of the boundary extend below the beam pipe radius or the radii of the two beam pipes at both ends are unequal. It reduces CPU time a lot by deforming the integration path so that the integration contour is confined to the finite length over the gap of the structures. However, the original Napoly method cannot be applied to the transverse wake potentials in a structure where the two beam tubes on both sides have unequal radii . In this case, the integration path needed to be a straight line and the integration is stretched out to an infinite, in principle. We generalize the Napoly integrals so that integrals are always confined in a finite length even when the two beam tubes have unequal radii, for both longitudinal and transverse wake potential calculations. The extended method has been successfully implemented to the ABCI code

Impedance of a ceramic break and its resonance structures

A new theory is developed to evaluate longitudinal and transverse impedances of any size of ceramic break that is sandwiched between metal chambers. The theory has been numerically compared with the codes ABCI and CST studio. Excellent agreements are obtained with both codes, in particular with ABCI. The theory successfully reproduces resonance structures of the impedance due to trapped modes inside the ceramic break, which are enhanced by the difference of the dielectric constants between the ceramic and the surrounding space. Moreover, the theory can evaluate the impedance of the ceramic break with titanium nitride coating. We discuss several characteristics of the impedances, especially the difference between the impedances of the ceramic break covered with and without a conductive wall on its outer surface

Coupling impedances of a resistive insert in a vacuum chamber

We have developed a theory to calculate both longitudinal and transverse impedances of a resistive short (typically shorter than the chamber radius) insert with cylindrical symmetry, sandwiched by perfectly conductive chambers on both sides. It is found that unless the insert becomes extremely thin (typically a few nm for a metallic insert) the entire image current runs on the thin insert, even in the frequency range where the skin depth exceeds the insert thickness, and therefore the impedance increases drastically from the conventional resistive-wall impedance. In other words, the wakefields do not leak out of the insert unless it is extremely thin. Formulas of the impedance valid for various cases of the insert are categorized in summary

Coupling impedances of a gap in vacuum chamber

A gap in the vacuum chamber stands between a beam and the outside world, and the theoretical elucidation of the interaction mechanism between the gap and the beam is of great importance to understand the interaction of any device with the beam. In this paper, we will present the formulas for the longitudinal and transverse impedances due to a gap in the beam chamber. In this process, we will derive the complete solutions of electromagnetic fields effective in the entire region, including the inside and the outside of the chamber, in a form that they can be easily numerically evaluated. The newly developed technique can provide new methods of solutions of electromagnetic fields also for a rather broad class of structures such as cavities. The numerical results of impedances are consistent with the ABCI results and their behavior in high frequency agrees well with the prediction of the diffraction theory. Our theory can also accurately reproduce the behavior of the impedance near and above the cutoff frequencies. In addition, our theory is applicable even to the impedances for nonrelativistic beams. We found that the broadband impedance of the small cavitylike structure can be estimated from the gap size and the chamber radius only, regardless of the exact shape of the structure. We also found that the transverse impedance of a gap has a large resonance peak at the frequency where the wavelength is equal to the chamber circumference. This resonance peak appears around 1–2 GHz in most of the cases, and we should be careful to design a ceramic break so that this transverse mode will not leak out to interact with nearby devices