Investigation of Wake Fields in The RF Couplers of SC Linacs Nawin Juntong

Purpose: Investigate effect from rf couplers (fundamental and HOMs) to the beam dynamics.

Impact: The issue of the rf coupler kick on the beam dynamics is considered to be extremely important as if left unsuppressed it is likely to cause severe emittance dilution or possibly a beam break up instability (BBU).Physics: Each cell of cavity is considered as the resonant RLC circuit coupling together with the coupling constant, k. Here we study SC cavity, so R=0. We investigate the mode frequencies, which can be excited in the cavity from circuit model. The extended circuit model to represent the HOM frequencies and kick factors is studied.

The rf coupler kick is defined as the ratio of the change in the transverse momentum to the change in the longitudinal momentum inside cavity. These momentums can be obtained by integration of Lorentz force from the e.m. fields inside the cavity, which is obtained by simulation the standing wave solution with different boundary condition at the coupler end and combination together.

The Inclusion of rf couplers breaks cavity symmetry, so it causes the transverse fields inside cavity. These fields affect particle beams in such the way that they influence on beams emittance and beams shape.Future directions: The study of the inclusion of HOM coupler will be carry on. The beam dynamics effect from the rf coupler kick will be studied by the tracking code, PLACET. The extended version of circuit model included the couplers is also in focus.

E.M. fields along the cavity axis between 2 boundary conditions at the coupler end; a) PEC, b) PMC.

(a) (b)

Results: The tuned Double band circuit model is provide the consistent of dipole frequency results with the HFSS simulation results on the TESLA 9 cell structure and it delivered well prediction of dipole kick factor.

The wake fields simulation of the cavity in term of loss factors are consistent, less than 5% difference, between two codes; ECHO 2D, ABCI. These results are validate on 3 structures; TESLA, ICHIRO, RE-ENTRANT.

σz = 1 mm σz = 0.7 mm σz = 0.3 mm

ECHO 2D

ABCIΔ

(%)ECHO

2DABCI

Δ (%)

ECHO 2D

ABCIΔ

(%)

TESLAkL [V/pC] 9.89 10.04 1.52 11.56 11.82 2.25 17.72 18.46 4.18

kT [V/pC/m] 18.36 18.52 0.87 15.41 15.61 1.30 10.38 10.57 1.83

ICHIROkL [V/pC] 12.89 13.03 1.09 15.32 15.57 1.63 25.19 25.77 2.30

kT [V/pC/m] 28.14 28.26 0.43 23.94 24.06 0.50 17.03 17.12 0.53

RE-ENTRANT

kL [V/pC] 11.01 11.15 1.27 13.08 13.34 1.99 21.25 21.91 3.11

kT [V/pC/m] 21.17 21.30 0.61 17.96 18.14 1.00 12.70 12.85 1.18

The rf coupler kick from the fundamental mode coupler is obtained from the combination of 2 standing wave solutions. The study is based on ILC cavity shape and TTF-III type coupler and the result rf kick of this coupler is (19.74+91.03i)x10-6.