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Dependence of the breakdown rate on the pulse shape

Dependence of the breakdown rate on the pulse shape. 5.03.2008 Alexej Grudiev. Pulse shape dependences. P in /P in load = 0.9. p l = P out load /P out unload. t r. t f. t f. t b. t r. η : t p = t b + t f + t r. ∆T~(t T p ) 1/2 : t T p = t p -[t f ●(1-p l )/2+ t r ●(1-p l /2)].

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Dependence of the breakdown rate on the pulse shape

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  1. Dependence of the breakdown rate on the pulse shape 5.03.2008 Alexej Grudiev

  2. Pulse shape dependences Pin/Pinload= 0.9 pl=Poutload/Poutunload tr tf tf tb tr η: tp = tb + tf + tr ∆T~(tTp)1/2: tTp = tp-[tf●(1-pl)/2+ tr●(1-pl/2)] P/C*(tPp)1/3: tPp = time when Pin/Pinload> 0.9=Pth

  3. Pulsed surface heating For rect. pulse:

  4. Pulsed heating of breakdown site BDR=const means ∆T=const Using power loss expressed as

  5. Pulsed heating of breakdown site Simulation of T53vg3MC experiment For βE0 = 10 GV/m Pth= 84% ------> βE0 = 5 GV/m Pth= 89%

  6. Pulsed heating of breakdown site Simulation of NLC structure experiment 30%, 115ns 50%, 100ns For βE0 = 10 GV/m Pth= 84% βE0 = 5 GV/m Pth= 89% For βE0 = 10 GV/m Pth= 83% βE0 = 5 GV/m Pth= 89%

  7. Pulsed heating of breakdown site CLIC pulse shape For βE0 = 10 GV/m Pth= 83% βE0 = 5 GV/m Pth= 89% In conclusion, based on the model the threshold power level Pth is somewhere between 83 and 89 % of the flat top power level depending on βE0.

  8. P t tf tb Effective pulse length for breakdown Rect-pulse => NLC-pulse 65 MV/m => 67.5 MV/m Assuming: Ea*tp1/6 = const 400ns => 320ns 0.1Pin 0.5Pin 20ns NLC: tf = 100 ns; tb = 300 ns

  9. More details on NLC pulse shape From: Adolphsen, Chris [mailto:star@slac.stanford.edu]Sent: Mon 12/3/2007 10:48 AMTo: Alexej GrudievSubject: RE: NLC design pulse shapeThe shape of course depends on the beam loading we assumed, but if I remember correctly, the ramp we used was roughly linear in power and started at the 30-50% power level (it was not easy to set given the SLED manipulations, so it was never exactly the same run to run). The fill (ramp) times were typically 100 to 115 ns. 320ns 90% 78%

  10. Recent experiment in T53vg3MC 130ns At BDR=10-6 Effective pulse length: tpP = 130ns predicted Rect. Pulse of 100ns: Ea =105 MV/m measured Ramped Pulse of 100+100ns: Ea = 105*(100/130)1/3 = 100.5 MV/m 85% From Chris: The T53 data with the ramped pulsed was taken after the system was vented to install a new mode converter after the sled system - the data points shown in this case do not follow a straight line like the 100 ns square pulse data because the structure was being processed along the way. The important point is the last (red) one where the structure ran at 100 MV/m for 70 hrs with a roughly 1e-7 bkd rate (only 2 bkds so the error is fairly large) - this is as good as the original 100 ns square pulse data, but reflects additional processing (this structure ran a total of about 2300 hours). We did not run with a 100 ns square pulse after this - we are 'saving' the modulator for the T18 structure, which will run in mid-March (sorry we cannot give you a clean measure of the effect of the ramp - this would be hard to measure because of the low statistics - better to build structures that do not break down :)

  11. Recent experiment in T53vg3MC USHG-2008: C. Adolphsen L. Laurent

  12. A theoretical model based on the pulsed heating of field emission sites has been proposed to determine the threshold power level. It is found that Pth varies from 83 to 89 % depending on the local electric field βE0 , from 10 to 5 GV/m, respectively. Pth is weakly dependent on the pulse shape (in the range of reasonable pulse shapes which can be used for acceleration) It is also found that the time when power decreases from flat-top value down to threshold value does not contribute to the effective pulse length Modified model for effective pulse length definition is proposed. To take the flat-top time tb plus the time when the power exceeds 85% of the flat-top level only during ramping up. The model predictions agree well with available experimental results on pulse shape dependence of the breakdown rate. Conclusions

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