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Beamloading status

Beamloading status. Energy gain of particles. NF linac - worst case – one proton pulse: 17 MV/m , 0.75 m, transit time factor ~ 0.636* ~ 10 MV ~ 1.6 pJ per particle and cavity, ~ 37 mJ per bunch, ~ 3.2 J per bunch train

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Beamloading status

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  1. Beamloadingstatus

  2. Energy gain of particles • NF linac - worst case – one proton pulse: • 17 MV/m , 0.75 m, transit time factor ~ 0.636* ~ 10 MV • ~ 1.6 pJ per particle and cavity, ~ 37 mJ per bunch, ~ 3.2 J per bunch train * values taken before simulation of cavities assuming a “closed” pillbox cavity, for elliptical cavity the transit time factor is higher (~0.72) but ratio of maximum field to average field will drop. Also the stored energy was assumed to be 460.6 J for 10 MV energy gain, in result the energy spread due to beam loading will drop

  3. Cavities study 2a

  4. Study 2 cavity parameters Scott : “The Cornell folks seemed to think that the gradients in question were achievable (they failed to do so due to an unexpectedly high Q-slope in the cavities), but I have no other support for that assertion.” Results published in 2009 on 1.3 GHz 9 cell cavities (niobium bulk, accelerating gradient)

  5. Definition of accelerators and initial parameters • 201 MHz one proton bunch (Energy spread 244+- 24 MeV) Linac consists of 66 cavities – 6 short (1 cell, 1 cav), 8 medium (2 cell, 1 cav), 11 long (4 cell, 2 cav) RLA1 - 4.5 passes - 600 MeV / pass - 48 cavities RLA2 - 4.5 passes - 2000 MeV / pass - 160 cavities FFAG - 8 passes - 1.56 MeV / pass - 124 cavities 500 kW RF couplers (SC at 800 MHz) available – lower frequency (201 MHz) allows in the “P 20 (=20 s)” and “P200 (=200 s)” named scenarios one 500 kW coupler per two cavities was assumed, in the “P25 (=20 s)” scenario one P=500 kW coupler per cavity was assumed. (in study 2) two 500 kW per cavity (=2 cells)).The amount of energy that can be recovered in the time between the bunch trains  is given by

  6. Cryo modules in Linac (Study 2a)

  7. Beam loading results - summary

  8. Beam loading results behind FFAG

  9. Energy spread E1 is the energy shift of the first bunch in relation to the reference energy, E2 is the energy spread with in one bunch train, E3 is the energy shift between two bunch trains, and E4 is the energy spread between the first and the last bunch. The value given for E4 without beam loading is the energy spread caused by the FFAG.

  10. Discussions with Scott & Alex • The synchrotron oscillations in the RLAs should provide some mitigation to the beam loading effect; this should be studied.  Unfortunately in the FFAG, there are no synchrotron oscillations to help.  However, one may be able to remove the slope with a small amount of wrong-frequency RF just after (or before!) the FFAG. • I believe in the end that we will do better than the 5% energy spread after the FFAG that we found.  If we don’t I would probably suggest dropping the FFAG!  We had some earlier simulations indicating that we could do better, so we need to reconcile the results (and see if we can do better).  Thus while you are right to compare to energy spreads from other sources, I’m not sure that we are ready to use 5% as a point of comparison.  However, it is hard to imagine the beam not having a 1% energy spread, and many of your scenarios have spreads smaller than that.  However, I would also suggest that having bunch trains with significantly different beam characteristics in the storage ring would likely lead to undesirable experimental systematic.

  11. Beam Loading – conclusions & next steps • No issue for muon front end • Small (invisible) influence in Linac • In RLA and FFAG BL causes increase of energy spread and (slight) decrease of acceleration. (Is this acceptable ?) • 3 Proton bunch scenario & 100 s bunch (train) spacing will reduce the effect within a bunchtrain by a factor of ~3.4 and allow to refill cavity until next bunchtrain (~100 kW / cavity)) • Fast active phase shifters ? • Rerun code with latest values for cavities and accelerator set up = > getting a consistent data set…. • Discussion on how sensitive NF results on energy spread • Presentation of results at IPAC

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