Longitudinal impedance and shielding effectiveness of a resistive beam pipe for arbitrary energy and frequency

Abstract

The longitudinal coupling impedance of a cylindrical beam pipe for arbitrary relativistic gamma(0) and mode frequency is obtained analytically for finite wall conductivity and finite wall thickness. Closed form expressions for the electromagnetic fields excited by a beam perturbation are derived analytically. General expressions for the resistive-wall impedance in the presence of a metallic shield and for the rf shielding effectiveness of the beam pipe have been obtained and then compared with approximate expressions. The results are applied to the GSI synchrotron SIS, where the thickness of the vacuum chamber in the dipole magnets is much smaller than the skin depth at injection energy.

Analysis of the longitudinal space charge impedance of a round uniform beam inside parallel plates and rectangular chambers

“…The superscript "rd" on the left hand side stands for "round chamber". The above equation gives the wellknown LSC impedance per unit length of a round uniform beam inside a round beam chamber [13][14][15][16] ( )…”

“…On the other hand, the LSC, as a positive factor, increases the current modulation and can be used as an amplifier for FEL [6].Various LSC field models have been proposed and studied extensively by different methods in the existing literatures, such as Refs. [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. The LSC impedances in the entire wavelength spectrum of a beam in free space [8] and inside a round chamber [13][14][15][16] have been intensively studied.…”

“…[7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. The LSC impedances in the entire wavelength spectrum of a beam in free space [8] and inside a round chamber [13][14][15][16] have been intensively studied. The LSC impedance of a beam inside a round chamber in the long-wavelength limit is also well-known [17][18][19][20][21].In many accelerators, the configurations of the real beam and chamber system can be simplified as a field model consisting of a round beam moving inside a rectangular chamber.…”

Resistive-wall impedance of two-layer tube

“…Here we have adopted a cylindrical coordinate system r; '; s, where r, ', and s are radial, azimuthal, and longitudinal coordinates, respectively. The beam pipe can be divided into four regions as sketched in Fig I vacuum a 1 < r < a 2 ; II 1st layer a 2 < r < a 3 ; III 2nd layer a 3 < r < a 4 ;…”

“…The resistive-wall impedance of a vacuum chamber for v < c has been derived for a single layer tube with infinite [1,2] and finite wall thickness [3,4]. In Refs.…”