Resistive wall wake with ac conductivity Karl Bane

Resistive wall wake with ac conductivity Karl Bane and Gennady Stupakov August 3, 2004

Introduction • resistive wall wake is a limiting effect in the LCLS undulator, with the induced ΔE~ , the Pierce parameter • can add effects of ac conductivity and anomalous skin effect to resistive wall model • will show ac conductivity effect; anomalous skin effect is weak at room temperature (can show another time)

Ac conductivity (see K. Bane and M. Sands, SLAC-PUB-95 -7074) • ac conductivity: parameter = c /s 0. with the relaxation time; new • for Cu with beam pipe radius a= 2. 5 mm, s 0= 8 m, c = 8 m, = 1. 0; for Al, s 0= 9. 3 m, c = 2. 4 m, = 0. 26. • impedance: with • for ac conductivity replace with transform of Z(k) ; for wake, take inverse Fourier

• wake Wz(z) is composed of a resonator and a diffusion component • for 1, can approximate with the plasma frequency impedance

for the resonator component of the wake: the frequency r, damping factor αr, and amplitude fr; the large analytical formula is given by dashes (from K. Bane and M. Sands).

s 0= 8 m ac wake with high approximation

Point charge wake

Induced energy change for rectangular bunch with full length of 65 m charge— 1 n. C, energy— 14 Ge. V, tube radius— 2. 5 mm, tube length— 130 m Induced energy change (top) for LCLS bunch shape (bottom).