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

RF design as it is defined in EDMS

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

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

Parameter table for TD26_vg1.8_R05_CC Iris parameters Iris #a [mm]d [mm] Cell parameters0.5 Cell #b [mm]c [mm]l [mm]eow Other parameters: r_pipe = 4 mm rr_pipe = 1mm l_pipe > 12 mm N = 26 – regular cell number h = 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 = mm lpw = 60 mm b1 = b c1 = c epw = eow ipw_in = 7.77 mm ipw_out = 7.29 mm

Shape accuracy

Shape accuracy as it is defined in the drawings

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

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

Geometrical errors

Systematic errors

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 ?)

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

Mismatch

“Bookshelf” effect

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

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