ALTERNATING WAKE FORCE IN RECTANGULAR WAVEGUIDE WITH PERIODIC PERTURBED WALLS

A. Opanasenkoª

National Science Center Kharkov Institute of Physics and Technology, Kharkov, Ukraine

Abstract

The wake field excited by a relativistic charged bunch in a periodic waveguide can be expressed as a spatial harmonic Floquet series. Usually spatial harmonics of the wake force synchronous with the bunch are of interest due to their action on particles that results in the well known beam loading and beam break up effects in rf structures. However, an alternating transverse wake force which consists of nonsynchronous harmonics can give rise to undulating the particles with alternating transverse velocity that can result in no less important effect such as the wake field undulator radiation [1]. Therefore there exist an interest in developing of methods of calculation of alternating wake forces in a periodic rf structures. In this work a perturbation method for calculation of wake field in rectangular periodic waveguides was considered. A possible usage of the wake field excited by an electron bunch passing through a sub-millimeter planar periodic waveguide for both ultra-high gradient acceleration and generation of the hard wake field undulator radiation is discussed.

ª – corresponding author

Paper 

31

CORRECTION TERMS TO PANOFSKY-WENZEL FORMULA AND WAKE POTENTIAL

A. Opanasenkoª

National Science Center Kharkov Institute of Physics and Technology, Kharkov, Ukraine

Abstract

In their 1956 article [1] Panofsky and Wenzel derived a relation for the net transverse kick experienced by a fast charge particle crossing a closed cavity excited in a single rf mode. Later this relation, usually referred to the Panofsky-Wenzel theorem, was generalized for cavity containing wake field induced by a driving charge. This theorem has played very important role in accelerator physics. One well-known conclusion of this paper was that in a TE mode the deflecting impulse of the electric field always cancels the impulse of the magnetic fields. In our presentation we more exactly rederive Panofsky and Wenzel's result and obtain correction terms to the transverse kick. We show that in a TE mode the net transverse kick is not zero. Using the given approach we find correction terms to wake potentials which turn out to be inversely proportional to the relativistic factor. Practical implications of our results are discussed.

ª – corresponding author

Paper 

34