Berkeley Lab Generic Presentation

1
TeV Scale RLA Based Muon Acceleration
Alex Bogacz
in collaboration with Guimei Wang, Kevin
Beard and Rol Johnson
2
LEMC Scenario
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RLA for Muons (MC)

• Dogbone (Single Linac) RLA has advantages over
  the Racetrack
• FODO linac Optics is superior to Triplet
  focusing - more passes transported.
• Bisected linac Optics mirror symmetric quad
  gradient along the linac
• Pulsed linac Optics. even larger number of
  passes is possible if the quadrupole focusing can
  be increased as the beam energy increases
• Flexible Momentum Compaction (FMC) return arc
  Optics to accommodate two passes (two neighboring
  energies) NS-FFAG like Optics based on the
  opposing bend combined function magnets (proposed
  by Dejan Trbojevic)
• Pulsed arcs? ramping arc magnets to further
  reuse the arcs (Kevin Beard)

4
Racetrack vs Dogbone RLA (both m and m- )
DE

• better orbit separation at linacs end energy
  difference between consecutive passes (2DE)
• allows both charges to traverse the Linac in the
  same direction (more uniform focusing profile
• the droplets can be reduced in size according to
  the required energy
• both charge signs can be made to follow a
  Figure-8 path (suppression of depolarization
  effects)

5
Dogbone RLA with FODO Focusing

• Beam dynamics challenges - RLA Optics solutions
• Phase slippage in the linacs
• Multi-pass linac optics
• Droplet arc lattice
• Orbit separation switchyard
• Longitudinal compression
• 8-pass Dogbone RLA - Linear Optics/Lattices
  designed
• 400 MHz RF, 25 MV/m gradient
• SBIR study with Muons, Inc.

6
Multi-pass bisected linac Optics
half pass , 3-5 GeV
initial phase adv/cell 90 deg. scaling quads with
energy
quad gradient
1-pass, 5-9 GeV
mirror symmetric quads in the linac
quad gradient
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Multi-pass linac Optics
4-pass, 17-21 GeV
quad gradient
7-pass, 29-33 GeV
quad gradient
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Linac-to-Arc Beta Match
E 5 GeV

• Matched by design
• 900 phase adv/cell maintained across the
  junction
• No chromatic corrections needed

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Mirror-symmetric Droplet Arc Optics
(bout bin and aout -ain , matched to the
linacs)
E 5 GeV
2 cells out
transition
2 cells out
transition
10 cells in
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Droplet Arc multi-pass beam separation
(bout bin and aout -ain , matched to the
linacs)
E 5 GeV
2 cells out
transition
2 cells out
transition
10 cells in
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Mirror-symmetric Droplet Arc Optics
Arc1 (E 5 GeV)
10 cells in
2 cells out
2 cells out
Arc2 (E 9 GeV)
15 cells in
3 cells out
3 cells out
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Mirror-symmetric Droplet Arc Optics
Arc3 (E 13 GeV)
20 cells in
4 cells out
4 cells out
Arc4 (E 17 GeV)
25 cells in
5 cells out
5 cells out
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Pulsed linac Dogbone RLA (8-pass)

• Quad pulse would assume 500 Hz cycle ramp with
  the top pole field of 1 Tesla.
• Equivalent to maximum quad gradient of Gmax 2
  kGauss/cm (5 cm bore radius) ramped over t 10-3
  sec from the initial gradient of G0 0.1
  kGauss/cm (required by 900 phase advance/cell
  FODO structure at 3 GeV). G8 13 G0 1.3
  kGauss/cm
• These parameters are based on similar
  applications for ramping corrector magnets such
  as the new ones for the Fermilab Booster
  Synchrotron that have 1 kHz capability

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Pulsed linac RLA quad ramping

• For simplicity, we consider a linear ramp
  according to the following formula
• A single bunch traveling with a speed of light
  along the Linac with quads ramped as above
  sees the following quad gradient passing
  through i-th cell along the Linac (i 1,20)
• where is the cell length
  and i defines the bunch position along the Linac.
• For multiple passes through the Linac (the index
  n defines the pass number) the above formula can
  be generalized as follows
• where is the full Linac length and
  is the length of the lowest energy droplet arc.
  Here we also assume that the energy gain per
  linac is much larger than the injection energy.

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Fixed vs Pulsed linac Optics (8-pass)
Fixed
Pulsed
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Fixed vs Pulsed linac Optics (12-pass)
Fixed
Pulsed
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Pulsed Dogbone ILC - example
number of passes
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Prototype Arc design NS-FFAG
NS-FFAG (Non-Scaling Fixed Field Alternating
Gradient)

• Racetrack RLA to accommodate large momentum
  range (60)

Dejan Trbojevic

• Large energy acceptance
• Very small orbit offsets
• Reduce number of arcs
• Very compact structure

Basic cell structure in ARC (combined function
magnet with extremely strong focusing )
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Multi-pass Droplet Arc

• FMC Optics (NS-FFAG-line)
• Compact triplet cells based on opposed bend
  combined function magnets
• Middle magnet high gradient bend (QD) having a
  strong central field and negative gradient at the
  center
• Flanked by a pair of negative bending magnets QF
  that are horizontally focusing

,
20
Flexible Momentum Compaction Cells
Guimei Wang
,

• Strong focusing (middle magnet) yields very small
  beta functions and dispersion
• Momentum offset of 60 corresponds to the orbit
  displacement of about 4.3 cm.

21
NS-FFAG multi-pass Droplet Arc
,
600 outward
600 outward
3000 inward

• MADX-PT - Polymorphic Tracking Code is used to
  study multi-pass beam dynamics for different pass
  beams path length difference, optics mismatch
  between linac and arcs, orbit offset and tune
  change is being studied.

22
Large Momentum Acceptance Arc

• Lattice requirements
• Mirror symmetry arc structure for both m m-
  acceleration
• Large momentum acceptance (factor of two?)
• Achromat Optics at both energies
• Optics match between Linac and Arc, mismatch
  sensitivity
• Path length control to match beam phase in the
  linac

23
Beta functions vs. Energy
Outward bending cell
Inward bending cell
For different energy spread, the same beta
function in opposite bending cell.
With MADX- Polymorphic Tracking Code. Energy
spread changes from -30 to 90
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Dispersion vs. Energy
Outward bending cell
Inward bending cell

• For different energy spread, opposite offset and
  dispersion in opposite bending cell.
• Beam offset lt10cm, dispersion lt 0.1 m.

Possible solution (1) Matching cell with I
matrix in x plane, and /- I matrix in y plane.
25
Analysis with multipoles components
Same bending raduis, same optics, same
chromaticity
Beam offset vs energy spread
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Momentum compaction
The path length changes as a parabolic function
of energy rather than linearly, which allows the
relative RF phase change to be limited to a small
range. (Minus ds means the path length is longer
than that of the reference particle.)
27
Conclusions

• Dogbone RLA preferred configuration
• better orbit separation for higher passes
• offers symmetric solution for simultaneous
  acceleration of m and m-
• FODO bisected linac Optics - large number of
  passes supported
• 8-pass RLA example
• Pulsed linac Optics Dogbone RLA - looks very
  encouraging
• Increase from 8-pass (Fixed Optics) to 12-pass
  (Pulsed Optics) for 500 m long 4 GeV pass example
  
• Flexible Momentum Compaction (FMC) return arc
  Optics allowing to accommodate two passes (two
  neighboring energies) under studies