1. Tolerances coming from RF Alexej Grudiev 24 Nov 2014 X-band accelerating structure review

2. RF design as it is defined in EDMS

3. Undamped Cell and Iris parameters Beam axis a b r d sbe ae l e=ae/be

4. Additional parameters for a damped cell Beam axis b c ac bc bc = (b-c-idw/sqrt(2))/(sqrt(1+eow*eow)-1) ac = eow*bc rdw = (adw/sqrt(2)-b+c-bc+ac)/(sqrt(2)-1) idw/2 adw/2 ldw 45 o rdw

5. Parameter table for TD26_vg1.8_R05_CC Iris parameters Iris #a [mm]d [mm] 1 3.151.67 2 3.11921.6442 3 3.08851.6185 4 3.05771.5927 5 3.02691.5669 6 2.99621.5412 7 2.96541.5154 8 2.93461.4896 9 2.90381.4638 10 2.87311.4381 11 2.84231.4123 12 2.81151.3865 13 2.78081.3608 14 2.751.335 15 2.71921.3092 16 2.68851.2835 17 2.65771.2577 18 2.62691.2319 19 2.59621.2062 20 2.56541.1804 21 2.53461.1546 22 2.50381.1288 23 2.47311.1031 24 2.44231.0773 25 2.41151.0515 26 2.38081.0258 27 2.351.00 Cell parameters0.5 Cell #b [mm]c [mm]l [mm]eow 0 8.7560.656.663.4 1 8.61540.62696.67493.3962 2 8.60350.62086.70073.3885 3 8.59170.61466.72643.3808 4 8.58010.60856.75223.3731 5 8.56870.60236.7783.3654 6 8.55750.59626.80373.3577 7 8.54650.596.82953.35 8 8.53570.58386.85533.3423 9 8.52510.57776.8813.3346 10 8.51470.57156.90683.3269 11 8.50450.56546.93263.3192 12 8.49450.55926.95833.3115 13 8.48480.55316.98413.3038 14 8.47530.54697.00993.2962 15 8.46590.54087.03573.2885 16 8.45670.53467.06143.2808 17 8.44770.52857.08723.2731 18 8.43880.52237.1133.2654 19 8.43010.51627.13873.2577 20 8.42150.517.16453.25 21 8.41320.50387.19033.2423 22 8.4050.49777.2163.2346 23 8.3970.49157.24183.2269 24 8.38920.48547.26763.2192 25 8.38160.47927.29333.2115 26 8.37420.47317.31913.2038 27 8.695750.56.663.2 Other parameters: r_pipe = 4 mm rr_pipe = 1mm l_pipe > 12 mm N = 26 – regular cell number h = 8.332 mm - period r = 0.5 mm s = 0.1 *d e = 1+(d/h)/(a/2.625mm) idw = 8 mm adw = 11 mm ldw = 40 mm apw = 22.86 mm lpw = 60 mm b1 = b c1 = c epw = eow ipw_in = 7.77 mm ipw_out = 7.29 mm

6. Shape accuracy

7. Shape accuracy as it is defined in the drawings

8. Materials Riccardo Zennaro, “Study of the machining and assembly tolerances for the CLIC accelerating structures”, EUROTeV-Report- 2008-081, (2008) Jiaru Shi, Alexej Grudiev, Walter Wuensch, “Tuning of X-band traveling-wave accelerating structures”, NIMA 704 (2013)

9. Geometry P – structure period B – cell radius A – iris radius D – iris thickness Field distribution along the CLIC_G

10. Geometrical errors

11. Systematic errors

12. Most critical is the cell diameter 2B. Systematic error of 1um in the diameter of all cells results in ~2.5% reduction of the accelerating gradient. Sub micron precision is required if no tuning is applied and no temperature correction is allowed (which is the current CLIC baseline ?)

13. Random errors Obviously random errors are much less (~sqrt(Ncells) = 5) critical It also depends on the error distribution Good model of the machining error distribution could give us better way to make tolerance specifications

14. Mismatch

15. “Bookshelf” effect

17. Tolerances with tuning Frequency errors of ±10 MHz can be accepted with the current tuning procedure This gives a more relaxed tolerances for the cell diameter 2B: ±20 um

18. Conclusions Sub-micron tolerances are required for a structure without tuning Tuning allows to relax tolerances on certain dimensions related to cell frequency. For example, up to ±20 um on the cell diameter That does not mean that we can relax all tolerances if we have tuning. Certain errors cannot be corrected by tuning: – Iris diameter and thickness influence also cell-to-cell coupling. Too big error will result to internal reflections and standing wave pattern inside the structure – Disk tilt or halves misalignment result in vertical kick – Too loose tolerances on shape accuracy can potentially results in step and/or sharp edge formation which is within tolerances but may compromise the high gradient performance More detailed studies are necessary if we would like to refine our tolerance specifications for CLIC_G