should the warm BPMs in LHC be coated with a 100 micron copper layer? (question by Gerhard Schneider)

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Moris Sharp
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1 shoud the warm BPMs in LHC be coated with a micron copper ayer? (question by Gerhard Schneider) 46 BPMs per beam (6 BPMSW, 8 BPMW, 4 BPMWA, 8 BPMWB) Average beta Injection Top Horizonta beta Vertica beta 9.9 m 5. m 38. m 36.5 m Each BPM is 85 mm ong. The inner bore radius b is typicay 3 mm. The thickness d is mm stainess stee. The tota ength is 3. m. I assume a stainess stee conductivity of σ=.4x 6 Ω - m -, which might however increase with temperature, if the beam pipe heats up. Skin depth of copper is.7 mm at 8 khz, and 5 µm at MHz. st response by Francesco: a Cu coating is wecome to reduce beam induced ohmic heating and resistive wa impedance at very ow frequency (down to ~ khz), but a thin coating is not very effective at room temperature, where you need a Cu thickness in the mm range to shied the outer SS. I have aso the foowing two naive remarks: - the Cu coating shoud remain compatibe with the BPM functionaity, - the Cu coating may be counter-productive in case of resonant modes with a Q-factor that woud be enhanced by such a ow resistivity coating.

2 resistive wa impedance π π ρ π ) sgn( L i L i b c c b i t = = CERN formua (L. Vos, E. Metra) inductive bypass ony active in the transverse pane; derivation uncear, independent of chamber thickness ( ) ( ) )) sgn( ( tanh tanh σ µ π i d b b d b b i t = = FNAL formua (Burov, Lebedev) soution of Maxwe s equation; chamber thickness enters; Burov/Lebedev s resut agrees with formua in otter/kheifets book in some cases and extends it in many others

3 Burov and Lebedev aso give a resut for -ayer chamber, where inner ayer, e.g., d= micron copper, is surrounded by another materia, e.g., by an infinite amount of stainess stee t, = i πb + + b + = ( i sgn( )) µ σ, tanh ( d) + b tanh ( d)

4 Normaize the beta function to 7 m. Use definition of the transverse effective impedance of LHC Design Report. Effective ongitudina transverse impedance is obtained by integration over the bunch spectrum. uncoated (ong/n)eff (Ω).6 (injection). (top) (ong/n)eff (Ω).38 (injection).5 (top) eff [8 khz] (MΩ/m) i (injection) i (top energy) factor ~ difference! eff [8 khz] (MΩ/m).83-. i (injection) I (top energy) eff [ MHz] (MΩ/m).-. i (injection).4-.4 i (top) eff [ MHz] (MΩ/m).4-.4 i (injection).3-.3 i (top) L. Vos Burov/ Lebedev tota impedance from design report (sign probem) (ong/n)eff (Ω).7.76 eff [8 khz] (MΩ/m) -45- i (injection) -9-4 i (top energy) eff [ MHz] (MΩ/m) -3-9 i (injection) -5-5 i (top) for ongit. impedance I assumed the standard resistive-wa reation = t ( b /( c). Resistive-wa contribution from the BPMs is ess than % of the tota. for a coated chamber (σ=5.9x 7 Ω - m - ) I find from Burov/Lebedev (ong/n)eff (Ω).34 (injection).8 (top) eff [8 khz] (MΩ/m) i (injection) i (top energy) eff [ MHz] (MΩ/m).-. i (injection).-. i (top)

5 concusion on BPMs different formuae give resuts that differ by a factor even in the worst case the tota impedance for the uncoated BPMs is % or ess of the tota LHC impedance Fritz tes me that none of the formuae can be trusted since the rea probem is 3-dimensiona he recommends cacuation with HFSS nevertheess -dim. estimates shoud give an upper bound at ~khz frequencies my tentative concusion is that no coating woud be needed

6 Touschek modue in MADX C. Miardi, F. Schmidt, F. immermann impemented genera formua from Piwinski (Chao-Tigner handbook) impementation faciitated by simiarities with IBS modue new modue wi give growth rate for each beamine eement bunch ength and energy spread are at the moment frozen around the ring (not a good approximation for strong rf focusing at DAFNE)

7 atest e-coud predictions for LHC: heat oad vs deta_max for nomina bunch popuation at injection and top energy

8 e-coud in DAFNE news from Mikhai obov: Last year DAFNE was substantiay changed: modified wiggers, two new interaction regions, some optics modifications etc. Now we can observe a strong horizonta instabiity which have many features that can be attributed to e-coud: ) ampitude of horizonta osciations grows aong the train; ) the betatron ine is spitted in severa ines... On the other hand, the same behaviour is observed for the e- ring, but at much higher currents and threshods. But in case of e-ring, it can be due to the horizonta ion instabiity ike that at KEKB. Yet another observation - different tune shifts versus mutibunch currents in e- and e+ rings. It seems that in the e+ring there is some additiona positive tune shift in both transverse panes...

9 Mikhai s news cont d. Now we have a possibiity to measure betatron ampitudes turn-by-turn on the bunch-bybunch basis. What you can see is grow-damp measurements: for a very short time we switched off the transverse feedback and ook at the ampitudes. In the shown exampe there were 9 bunches + 3 bunch gap.. Tune shift measurements were performed in singe bunch and mutibunch regimes in October (for DEAR experiment) and in January 4 (for FINUDA experiment). Summarizing: a) Singe bunch -- tunes shift is negigibe for both rings; b) Mutibunch -- tune shifts have opposite sign sopes and can be cacuated anayticay for e- ring (strong asymmetry due to wigger vacuum chamber) c) In the e+ ring -- the vertica tune shift is amost zero, but the horizonta one is positive and by a factor of higher with respect to the e-ring (Oct. ) and amost by a factor of 4 higher now (January). Respectivey, the instabiity threshod is by a factor of ower now. Cure: certainy, beam-beam. Yet another strange thing - the instabiity threshod grows from 5 ma to A by changind the RF frequence by - khz (dispersive orbit?, impedance? Energy?) (the orbit changes by 3 mm at maximum inside the wigger vacuum chambers having sizes 3 x cm. No (sight) tune changes, no chromaticity changes. No noninearity changes - we have measured the decoherence at different RF frequencies).

10 9 consecutive bunches + bucket gap Bunches 5, 5, 7, 9 Bunches at the train end:75, 8, 85,9

11 Tune Shifts of Bunch Trains due to Resistive Was without Circuar Symmetry PRSTAB,5, () (Chao, Heifets, otter) dq x, y di π = ± R L b + 48Qx, y E / e b C d b - horizonta vacuum chamber size; d - vertica vacuum chamber size; L vacuum chamber ength; R machine radius; 376 Ω; DAΦNE, Oct. Qx, n e-, Qx, Qy, bunches I, ma Qy, on dq, y di x = ±.4/ A Good agreement with experimenta data!!

12 Tune Shift Measurements in e+ Ring (important not ony for the instabiity, but aso for beam-beam coisions!) Qx Horizonta tune e+ bunches Qx, on Qx, on Qx, off Qx, off I, ma f, khz - Factor of instabiity threshod increase Qx (SB) Qx 5 ma. 7.8 Qx DAΦNE, Oct. DAΦNE, //4

(Refer Slide Time: 2:34) L C V

(Refer Slide Time: 2:34) L C V Microwave Integrated Circuits Professor Jayanta Mukherjee Department of Eectrica Engineering Indian Intitute of Technoogy Bombay Modue 1 Lecture No 2 Refection Coefficient, SWR, Smith Chart. Heo wecome