Calculation Of Wake Potentials Research Articles

A new Green's function for the wake potential calculation of the SLAC S-band constant gradient accelerating section

The behavior of the longitudinal wake fields excited by a very short bunch in the SLAC S-band constant gradient accelerating structures has been studied. Wake potential calculations were performed for a bunch length of 10μm using the author's code to obtain a numerical solution of Maxwell's equations in the time domain. We have calculated six accelerating sections in the series (60-ft) to find the stationary solution. While analyzing the computational results we have found a new formula for Green's function. Wake potentials, which are calculated using this Green's function are in amazingly good agreement with numerical results over a wide range of bunch lengths. Green's function simplifies the wake potential calculations and can be easily incorporated into the tracking codes. This is very useful for beam dynamics studies of the linear accelerators of LCLS [1] and FACET [2].

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.

The short-range wakefields in the BTW accelerating structure of the ELETTRA LINAC

Future FEL operations in the ELETTRA LINAC require a high quality beam with an ultra short bunch. The knowledge of the short-range wakefields in the backward traveling wave (BTW) accelerating structure is needed to predict the beam quality in term of the single bunch energy spread and emittance. To calculate the effect of the longitudinal and transverse wakefields we have used the time domain numerical approach with a new implicit scheme for calculation of wake potential of short bunches in long structure [A. Novokhatski, M. Timm, T. Weiland, Transition dynamics of the wake fields of ultra short bunches, Proceeding of the ICAP California, USA, 1998, I. Zagorodnov, T. Weiland, Calculation of transverse wake potential for short bunches, ICAP, 2002]. The wake potentials of the BTW structure are calculated numerically for very short bunches and analytical approximations for wake functions in short and long ranges are obtained by fitting procedures based on analytical estimations.

A generalized method for calculating wake potentials

We describe a generalized method to compute wake potentials created in axisymmetric structures. It relies on expressing the wake potentials, of any multipole order, as integrals over the e.m. fields along an arbitrary one-dimensional contour spanning the structure longitudinally. For perfectly conducting structures, the integration along the axis can then be replaced by choosing a contour beginning and ending on the beam tubes. Thus it generalizes the former method of calculating the wake potentials by integrating along a straight line at the beam tube radius. Its usefulness is illustrated with the computer code ABCI which permits calculation of wake potentials in structures extending to the inside of the beam tube radius, or having unequal beam tube radii at the two sides.

Wake Potentials of a Relativistic Point Charge Crossing a Beam-Pipe Gap: An Analytical Approximation

Although much work has been devoted recently to the numerical calculation of wake potentials, there is at present no analytical expression for the wake of a point charge crossing a gap in a beam-pipe of finite diameter. For a relativistic charge the wake potential can be computed in a simple manner from an integral over the electric field at the radius of the beampipe. In the case of a pill-box cavity, our basic assumptions are that the resonant frequencies and the field at the radius of the beam-pipe are essentially the same as in a cavity without beam hole. The summation over the infinity of modes can still be carried out as far as reflections from the outer cavity wall do not contribute; this is sufficient to compute the total loss for short bunches.