Orbit distortion due to lumped rf cavities - 14 vs 19 (=21-2) rf cavities -

1
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

• a1/6, b1/4
• 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)
• a1/12, b1/5
• 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)-Qs1 resonance is manifest. (6Qx)-Qs1
  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 Qx0.33.
• 14rf makes larger oscillations, but still within
  1mm.
• There is droop in both cases.
• The droop can be cured by 1 increase of rf
  voltage.

14 rf
21 rf
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 19 and 21
w/o 20 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 x30x103 may
  correspond to (4Qx)-Qs1.

VV0
V1.02xV0
V1.05xV0
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Summary

• 14 rf has larger oscillations and is more
  sensitive to synchro-beta coupling (3Qx)-Qs1
  and (6Qx)-Qs1.
• 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 Qx0.333.
• 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 Bergs value.