Resistive Wall Wake Research Articles

Multi-Bunch Resistive Wall Wake Field Tracking via Pseudomodes in the ALS-U Accumulator Ring

Multi-Bunch Resistive Wall Wake Field Tracking via Pseudomodes in the ALS-U Accumulator Ring

Resistive-wall wake for nonrelativistic beams revisited

In this paper, we derive the longitudinal and transverse resistive wall impedance for a beam traveling in a round pipe with $vlc$. We argue that from the general formulas for the impedance obtained from the solution of the Maxwell equations one has to subtract the space charge component. After such subtraction, we find that the classical expressions for the impedance derived in the ultrarelativistic limit are also applicable for long bunches even when they are nonrelativistic---in contrast to the conclusion of Zimmermann and Oide [Phys. Rev. Accel. Beams 7, 044201 (2004)]. We also calculate the resistive wall Green-function wake for $vlc$ at small distances and show that the jump at the origin in the longitudinal wake and in the derivative of the transverse wake are smeared out and the wake propagates in front of the source charge.

Numerical investigations of resistive wall wake potentials

The aim of this Letter is to examine and identify longitudinal resistive wall wake potential behaviours of medium- β long bunches and ultra-relativistic short bunches using different beam and pipe properties for particle accelerator applications. The lack of detailed analysis in current literature for the chosen set of parameters ignites this work. Since computations of wake potentials for the considered beam parameters by particle-in-cell codes are extremely difficult the author uses an analytical approach. Numerical integrations are evaluated for large domains with fine discretisations. The author observes that conductivity of beam pipe has a larger impact on medium- β long bunches, variation of beam velocity effects wakes of short bunches more significantly, beam radii changes may have a contribution to instability for low energy short bunches. Interesting numerical results are presented and their physical explanations are discussed in this Letter.

Single bunch transverse instability in a circular accelerator with chromaticity and space charge

The transverse instability of a bunch in a circular accelerator is elaborated in this paper. A new tree-modes model is proposed and developed to describe the most unstable modes of the bunch. This simple and flexible model includes chromaticity and space charge, and can be used with any bunch and wake forms. The dispersion equation for the bunch eigentunes is obtained in form of a third-order algebraic equation. The known head-tail and TMCI modes appear as the limiting cases which are distinctly bounded at zero chromaticity only. It is shown that the instability parameters depend only slightly on the bunch model but they are rather sensitive to the wake shape. In particular, space charge effects are investigated in the paper and it is shown that their influence depends on sign of wake field enhancing the bunch stability if the wake is negative. The resistive wall wake is considered in detail including a comparison of single and collective effects. A comparison of the results with earlier publications is carried out.

WAKEFIELDS OF SUB-PICOSECOND ELECTRON BUNCHES

We discuss wakefields excited by short bunches in accelerators. In particular, we review some of what has been learned in recent years concerning diffraction wakes, roughness impedance, coherent synchrotron radiation wakes, and the resistive wall wake, focusing on analytical solutions where possible. As examples, we apply formulas for these wakes to various parts of the Linac Coherent Light Source (LCLS) project. The longitudinal accelerator structure wake of the SLAC linac is an important ingredient in the LCLS bunch compression process. Of the wakes in the undulator region, the dominant one is the resistive wall wake of the beam pipe.

Resistive-wall wake and impedance for nonultrarelativistic beams

The usual formulas for the resistive-wall wake field are derived considering ultrarelativistic beams, traveling at the speed of light. This simplifies the calculation, and it leads to a cancellation between electric and magnetic fields. However, for proton beams below 10 GeV and for many heavy-ion beams, the velocities may significantly differ from the speed of light. In this paper, we compute the longitudinal and transverse wake fields for velocities smaller than $c$ and examine under which conditions nonrelativistic effects become important. We illustrate our results by a few examples.

Cumulative beam breakup due to resistive-wall wake

The cumulative beam breakup problem excited by the resistive-wall wake is formulated. An approximate analytic method of finding the asymptotic behavior for the transverse bunch displacement is developed and solved. Comparison between the asymptotic analytical expression and the direct numerical solution is presented. Good agreement is found. The criterion of using the asymptotic analytical expression is discussed.