707 research outputs found
Calculation of wakefields in 2D rectangular structures
We consider the calculation of electromagnetic fields generated by an
electron bunch passing through a vacuum chamber structure that, in general,
consists of an entry pipe, followed by some kind of transition or cavity, and
ending in an exit pipe. We limit our study to structures having rectangular
cross-section, where the height can vary as function of longitudinal coordinate
but the width and side walls remain fixed. For such structures, we derive a
Fourier representation of the wake potentials through one-dimensional
functions. A new numerical approach for calculating the wakes in such
structures is proposed and implemented in the computer code ECHO(2D). The
computation resource requirements for this approach are moderate and comparable
to those for finding the wakes in 2D rotationally symmetric structures.
Numerical examples obtained with the new numerical code are presented.Comment: 31 pages, 10 figure
Impedance of a Rectangular Beam Tube with Small Corrugations
We consider the impedance of a structure with rectangular, periodic
corrugations on two opposing sides of a rectangular beam tube. Using the method
of field matching, we find the modes in such a structure. We then limit
ourselves to the the case of small corrugations, but where the depth of
corrugation is not small compared to the period. For such a structure we
generate analytical approximate solutions for the wave number , group
velocity , and loss factor for the lowest (the dominant) mode
which, when compared with the results of the complete numerical solution,
agreed well. We find: if , where is the beam pipe width and is
the beam pipe half-height, then one mode dominates the impedance, with
( is the depth of corrugation),
, and , which (when replacing by
) is the same scaling as was found for small corrugations in a {\it round}
beam pipe. Our results disagree in an important way with a recent paper of
Mostacci {\it et al.} [A. Mostacci {\it et al.}, Phys. Rev. ST-AB, {\bf 5},
044401 (2002)], where, for the rectangular structure, the authors obtained a
synchronous mode with the same frequency , but with .
Finally, we find that if is large compared to then many nearby modes
contribute to the impedance, resulting in a wakefield that Landau damps.Comment: 18 pages, 6 figures, 1 bibliography fil
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