Transcript UKNFPlenary09062010WP1BL

Beam loading in the muon accelerator
(for details see IPAC paper WEPE060)
J. Pozimski
UKNF plenary meeting @ RAL. 09th June 2010
Beam Loading and beam parameters
 Energy transfer:
Wparticle=e*U
Wcav,after=Wcav,before-Wparticle
Wcav,before=Wcav,after+PRFgen*T
Stored energy scales with volume and EM field strength.
Power transferred from generator to cavity is Q factor dependent
 NF Numbers :
1021/year of 107 sec and a DR eff of 0.37, at 50 Hz = 5.4*1012 muons at 50 Hz
201.25 MHz – 88 bunches per train = 6.2*1010 p / bunch
(number of bunches in the bunch train has practically no effect on
beam loading over bunchtrain, numbers scale with number of proton
bunches 2.07*10910 p/bunch for 3 proton bunches,.... )
Definition of accelerators components and initial
parameters
•
f=201.25 MHz, initial energy 244 ± 24 MeV
Linac consists of 66 cavitiy cells (6 modules with 1 cell, 8 modules with 2 cells,
11 modules with 4 cells = 9.93 MeV/cell average)
RLA1 - 4.5 passes - 600 MeV / pass - 48 cells (2 * 12 modules with 2 cells= 12.5
MeV/cell average)
RLA2 - 4.5 passes - 2000 MeV / pass - 160 cavities (2 * 20 modules with
4 cells= 12.5 MeV/cell average)
FFAG
FDFCC
of beam
expected average
gain per cell
12.71 MeV. FDFCC might
longer
fitting 3
would then
required number
again.
FCDC least problems with
beam loading and
largest influence
loading
energy
be favoured due to
drift sections, but
cells in one drift
reduce the
of turns
Energy gain of particles &
stored energy
• NF linac - worst case – one proton pulse:
• 10 MV / 12.5 (12.75) MV
• ~ 1.6 pJ per particle and cavity, ~ 100 mJ per bunch, ~ 8.6 J per
bunch train
For 10 MV energy gain 1kJ and for 12.5 MV
1.5 kJ seems quite independent of the geometry.
Beam loading results behind
FDFCC – FFAG
Beam Loading - conclusions
• Only an issue for several bunch trains per 50 Hz and short (<60
s bunch train spacing) for all other cases beam loading is not
a serious problem compared to other sources of energy
spread.
• 3 Proton bunch scenario & 100 s bunch (train) spacing will
reduce the energy spread by a factor of ~3 and allow to refill
cavity (~1 MW / cell) sufficiently until next bunch train arrives
for all reasonable scenarios and keep the additional energy
spread at 3 times the initial energy spread and is far below the
energy spread induced by the FFAG (~150 / 1250 MeV) .
• Fast active phase shifters or more RF could reduce this further.
• But cavities (energy gain per cell) are the main issue !
• Required gradient seem very ambitious and was not reached
so far.