Very short range wake in strongly tapered disk loaded waveguide structures

1. Very short range wake in strongly tapered disk loaded waveguide structures Grudiev 2/05/2012

2. Outline • Introduction • Karl Bane (KB) model for const impedance and tapered structures • Comparison of KB model with ECHO2D simulations • Corrected KB model for const impedance structure • Model for Strongly Tapered structures • Examples

3. Introduction: Short range wake In order to estimate critical number off cells: To calculate the wake of infinitely long periodic structure at w we need more than Ncrit cells Image courtesy of R.B. Palmer, Particle Accelerators, v25, 1990

4. Karl Bane model: WL K.Bane et al., ‘Calculation of the short-range longitudinal wakefields in the NLC linac’, ICAP98, 1998 Const impedance of periodic structure: NLC structure at 1998 was tapered over 206 cells. On the other hand, for this structure: Ncrit ≈ amax2/2Lσz ≈ 14 << Nc = 206, what justifies averaging the wake of periodic structure over the 206 cells However in CLIC_G for nominal CLIC σz = 44um , Ncrit ≈ amax2/2Lσz ≈ 14 is comparable to Nc = 26, Furthermore taking shorter bunch like for example in X-FELs: σz = 10 or 2 um Ncrit => ~60 or ~300 which is bigger or much bigger than Nc. (2) cannot be used In the extreme case,

5. Wakefield simulation using ECHO2D Zagorodnov I.A, Weiland T., ‘TE/TM Field Solver for Particle Beam Simulations without Numerical Cherenkov Radiation’, PRST-AB, 8 (2005) 042001 Geometry of the tapered structure: L=10mm, g=9mm, a=4->2mm, Nc=26 Number of structures Ns was increased by x2 till the loss factor change δkL < 1e-3: For σz = 10um, Ns = 32 For σz = 5um, Ns = 200 For σz = 2um, too long for simulations σz = 5um kLKB/kLE2D 30 % σz = 10um kLKB/kLE2D 20%

6. Applicability of KB model for periodic structure It is applicable for 0.34 < a/L < 0.69 0.54 < g/L < 0.9 In the case where only the amin irises are affecting the bunch L’ -> Ls =NcL, For our example structure, a/L’ = 2/260 = 0.0077, (1) cannot be used uncorrected For a = 2 mm; solid line – KB model, dashed lines – ECHO2D simulations σz = 10 um σz = 5 um

7. Correction of KB model for periodic structure KB model solid line; KB’ model dashed line Corrected KB model (KB’ model) is based on fitting the ECHO2D results for a=1-2 mm and σz = 10-5 um For a = 2 mm; solid line – (corrected) KB’ model, dashed lines – ECHO2D simulations σz = 10 um σz = 5 um

8. New model for very short range wake in strongly tapered structures m Iris on the left Iris on the right Model 1: Model 2: Model 3:

9. Comparing new model(s) and simulations δ-wake Model 3 shows the best agreement both for 5 and 10 um; loss factors [V/pC/m] σz = 10 um σz = 5 um

10. Short range wake in CLIC_G Geometry of CLIC_G: L=8.332mm, g=L-(1.66->1)mm, a=3.15->2.35mm, Nc=26+2 δ-wake σz = 5 um

11. Effect on the loss factor Loss factor [V/pC/m] in CLIC_G Loss factor [V/pC/m] in the example structure: a=4->2mm

12. Karl Bane model: Wx K.Bane , ‘Short-range dipole wakefields in accelerating structure for the NLC’, SLAC-PUB-9663, 2003 [8] A. V. Fedotov, R.L. Gluckstern, M. Venturini , PRST-AB 2, (1999), 064401

13. Dipole wake in the example structure σz = 5 um

14. Dipole wake in CLIC_G σz = 5 um ECHO2D simulations are ongoing