Transcript Tune and time of flight

Orbit distortion due to lumped rf cavities
- 14 vs 19 (=21-2) rf cavities Shinji Machida
ASTeC/CCLRC/RAL
17 January, 2007
http://hadron.kek.jp/~machida/doc/nufact/
ffag/machida_20070117.ppt & pdf
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Purpose
• Whether we should put rf cavities every 2 cells (total
21 rf cavities) or every 3 cells (total 14 rf cavities)?
• If we put cavities every 2 cells, we need to remove 2
of them to make space for injection and extraction. In
such case, symmetry is broken and the total number
of cavities becomes 19.
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rf parameters
• a=1/6, b=1/4
– Voltage = 46.027 kV/cell
– ToF = 55.3535 ns
c.f. Previous study assumes
(http://hadron.kek.jp/~machida/doc/nufact/ffag/machida_20070104.pdf)
– a=1/12, b=1/5
• Two way of acceleration
– Constant energy gain
– Outside buckets acceleration
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21 rf with constant energy gain (1)
• To make a beam explore larger tune range, start from
9.5 MeV/c and assume energy gain per turn is
constant.
• Orbit distortion is negligible with 21 rf cavities, even
with one missing cavity.
21 rf
21 rf-#21
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21 rf with constant energy gain (2)
• Two missing cavities make larger oscillations.
However, it is still small.
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14 rf with constant energy gain (1)
• (3Qx)-Qs=1 resonance is manifest. (6Qx)-Qs=1
becomes visible when two cavities are missing.
14 rf
14 rf-#14
14 rf-#12,#14
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Outside buckets acceleration
with perfect symmetry
• Acceleration starts just below Qx=0.33.
• 14rf makes larger oscillations, but still within 1mm.
• There is droop in both cases.
21 rf
14 rf
• The droop can be cured by 1% increase of rf voltage.
21 rf, +1%
21 rf, +2%
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14rf with outside buckets acceleration
• Ignore the droop because it can be cured.
• Missing cavities make larger oscillations.
all 14 rf alive
14rf-#14
14rf-#12,#14
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21rf with outside buckets acceleration (1)
• Oscillation amplitude is smaller than 14 rf case.
all 21 rf
w/o #21
w/o #11 and #21
w/o #20 and #21
w/o #19 and #21
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21rf with outside buckets acceleration (2)
• 21 rf without #11 and #21 cavities.
• Droop can be cured by increased rf voltage (2 or 5%).
• Large amplitude oscillations around x=30x103 may
correspond to (4Qx)-Qs=1.
V=V0
V=1.02xV0
V=1.05xV0
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Summary
• 14 rf has larger oscillations and is more sensitive to
synchro-beta coupling: (3Qx)-Qs=1 and (6Qx)-Qs=1.
• 21 rf with missing cavities shows some increase of
oscillations, but not much.
• Outside buckets acceleration with new rf parameters
introduces droop. However, it can be cures.
• I prefer 21 rf with 2 missing cavities because
– 3 consecutive long straight sections for injection and extraction.
– In early stage of commissioning, we may have to stay around
injection momentum where coupling is sensitive: Qx=0.333.
– Muon ring does not have symmetric configuration anyway.
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Another rf pattern: series of rf + series of empty (1)
• Based on discussions with Chris.
21 rf
21 rf
24 rf
20 rf
18 rf
21 rf
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Another rf pattern: series of rf + series of empty (2)
• rf cavities are not necessarily distributed evenly.
• Because the wave-guide of 1.3 GHz is not small, it
may have advantage to squeeze cavities into
consecutive cells.
• It may be good to have a group of 2 or 4 cavities from
a view point of splitting rf power from the source.
• Among the pattern we tested, 24 rf with the pattern of
6x( 4rf + 3empty cell) is the best.
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Appendix
• Momentum and tune
– It is slightly different from Berg’s value.
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