Muon Collider Design

1
FERMI NATIONAL ACCELERATOR
LABORATORY US DEPARTMENT
OF ENERGY
f
Muon Collider Design Simulations Plan Y.
Alexahin
NFMCC meeting, UCLA
January 31- February 1, 2007
2
MCTF Accelerator Physics Studies Goals

• 2007
• Choice of the baseline Ionization Cooling scheme
• Decision on prototyping the Helical Solenoid (6D
  MANX)
• Collider ring optics design, requirements to the
  magnets
• 2008
• Choice of the proton driver and muon
  acceleration schemes
• Choice of the collider orientation and depth
  from radiological considerations
• Cost estimates
• Draft conceptual design report

Muon Collider Design Simulations Plans - Y.
Alexahin, FNAL February 1, 2007
3
Ionization Cooling Schemes
Muon Collider Design Simulations Plans - Y.
Alexahin, FNAL February 1, 2007
4
R.Palmers way
Guggenheimed RFOFO cooling simulations
(R.Palmer, A.Klier)

• Adding 804 MHz section would allow to achieve
  ??N7.5?102 ?m , but
• no matching section designed yet (may further
  increase losses surpassing 50 already)
• high magnetic field may drastically limit RF
  voltage (would GH2 filling help?)
• shown reduction in emittances includes both
  cooling and initial shaving
• the merit factor of the 2-stage RFOFO channel
  is just (N? /?6D)fin/ (N? /?6D)ini 800

Muon Collider Design Simulations Plans - Y.
Alexahin, FNAL February 1, 2007
5
R.Palmers way
Final 6D Cooling
Muon Collider Design Simulations Plans - Y.
Alexahin, FNAL February 1, 2007
6
Final 6D Cooling, R.Palmers way
No field reversal in simulations? - trajectories
are different which may affect transmission in
nonlinear fields
Muon Collider Design Simulations Plans - Y.
Alexahin, FNAL February 1, 2007
7
R.Palmers way
REMEX in 50T solenoids
Muon Collider Design Simulations Plans - Y.
Alexahin, FNAL February 1, 2007
8
R.Palmers way

• To choose this way would be helpful to know
• How to reduce the total length of the RFOFO
  channel?
• How to improve the transmission through the
  Guggenheimed RFOFO channel ? - Helical
  RFOFO?
• How the LiH container walls in Fernows new
  channel will contribute to the emittance?
• How field reversals will affect transmission
  through the new channel?
• Momentum acceptance in a channel with 50T
  solenoids with RF in and matching between the
  solenoids?
• Space charge effects in a bunch of 2?1012 muons?

Muon Collider Design Simulations Plans - Y.
Alexahin, FNAL February 1, 2007
9
R.Johnsons way

• Initial proposal
• RF cavities packed inside solenoid
• additional helical coils create rotating dipole
  and quadrupole fields
• As R.Palmer noted the transverse field on the
  coils would exceed 103T at the last stage!

K.Yonehara obtained the 6D cooling factor in the
series of HCC of 50,000
Muon Collider Design Simulations Plans - Y.
Alexahin, FNAL February 1, 2007
10
R.Johnsons way

• Slinky helical solenoid (Vlad. Kashikhin)
• solves the problem with unrealistically high
  field, however, a number of problems remains
• Is the helical solenoid with period of lt 30cm
  and Bs gt15T technically feasible?
• How to fit the RF structure into the solenoid?
• Segmented HCC with RF cavities between solenoid
  sections was proposed but not demonstrated yet to
  work.

• PIC / REMEX
• The proposed scheme not demonstrated yet to work
• Previous efforts by V.Balbekov to implement the
  PIC idea failed due to strong nonlinear
  aberrations - is there understanding why the new
  scheme will be better?

Muon Collider Design Simulations Plans - Y.
Alexahin, FNAL February 1, 2007
11
How to make the choice?

• It would be wonderful to have end-to-end
  simulations with matching between all sections
  but
• may be not realistic due to time constraints
• may be not necessary since the different parts
  of the two schemes can be chosen and combined
  (e.g. HCC for 6D cooling and 50T solenoids for
  REMEX)
• new (or forgotten old) ideas may emerge and
  prove advantageous 2mm
• It would be enough to design and simulate two
  pieces of the channel with necessary matching,
  realistically placed RF, windows (if needed) for
  the two essential cooling ranges
• ??N 2.0 mm ? 0.4 mm (HCC, RFOFO, straight
  FOFO)
• ?N 2.5 mm ? 0.5 mm
• ??N 0.1 mm ? 25 ?m
• ?N ? ? lt40 mm (50T solenoid), lt40 mm /
  Nb (PIC), Nb number of bunches to coalesce
• Important to check the results with the same
  software!
• Timeframe end of August

Muon Collider Design Simulations Plans - Y.
Alexahin, FNAL February 1, 2007
12
Strawman Muon Collider parameters

• Low emittance option (Rol Johnson) owing to new
  ideas (HCC, PIC, gas-filled cavities) much lower
  6D emittances seem to be feasible than previously
  thought of.
• High emittance option (Bob Palmer) conceptually
  follows 1999 PRSTAB Muon Collider Collaboration
  report

Low Emitt. High Emitt. Energy
(TeV) 0.750.75 (?7098.4) 11 Average
Luminosity (1e34/cm2/s) 2.7 0.7 (corr) ?
1.4 Average bending field (T) 10 5.18 Mean
radius (m) 361.4 652.5 Number of IPs 4 (350m
for 2) ? P-driver rep.rate (Hz) 65 6 Beam-beam
parameter/IP, ? 0.052 (corr) 0.043 ? 0.086 ??
(cm) 0.5 0.3 Bunch length (cm),
?z 0.5 0.3 Number of bunches/beam,
nb 10 1 Number of muons/bunch (1e11),
N? 1 20 Norm.transverse emittance (?m),
??N 2.1 50 ? 25 Energy spread () 1
0.12 Norm.longitudinal emittance (m), ?N
0.35 0.036 Total RF voltage (GV) at
800MHz 406.6 ?103?c - RF bucket height
() 23.9 - Synchrotron tune 0.723 ?103?c - ?
?- in collision / proton 0.15 /2 - 8GeV proton
beam power (MW) 1.1 1.5
Muon Collider Design Simulations Plans - Y.
Alexahin, FNAL February 1, 2007
13
LEMC Issues
f
?z / ??
Hourglass factor

• Low emittance pros smaller ?? ? smaller total
  number of particles nbN? ?
• ? relaxed coherent stability requirements
• ? low proton driver power
• ? low neutrino radiation
• Low emittance cons
• bb-effect limits N? ? larger nb is required ?
  electrostatic separation or crossing angle
• smaller ?? ? strong IR chromaticity
• ? smaller ?z is required ?
• ? small ?c ?
  strong arc cell chromaticity
• ? higher
  ?p/p for the same long. emittance

problems with momentum acceptance
Muon Collider Design Simulations Plans - Y.
Alexahin, FNAL February 1, 2007
14
Muon Collider Ring Design
Carols design ? 3mm ? ?max150km, ?c lt 0,
?c 10-5
Eliana Gianfelice improved the momentum
acceptance by a factor of 5, but at a cost of
shifting the tunes to unfavorable for beam-beam
effect values. Probably it can be increased
further, but not too much. Alex Bogacz proposed a
more conservative approach using 60º/60º FODO
lattice and ? 1cm. However, he placed quads too
close to IP (2m) and have not looked at chromatic
aberrations (should not be a problem in his case
though) Now we are trying FODO lattice in the
arcs but with larger phase advance per cell, up
to 108º (successfully tried in LEP in the
horizontal plane) - no viable solution insofar
Muon Collider Design Simulations Plans - Y.
Alexahin, FNAL February 1, 2007
15
Requirements to the Muon Collider Ring Lattice
Design

• So we may announce a competition for the lattice
  design with following properties
• ? ? 1cm
• 2 IPs
• distance of the first quad from IP ? 6.5m (is
  really necessary for E0.75TeV?)
• momentum compaction ?c ? 10-4
• momentum acceptance ? 0.5
• transverse acceptance ? 10 ??(geo) (for high
  emittance) 60nm ? agt4cm at ?25km
• possibility of electrostatic separation of 10
  bunches/beam
• tunability in a wide particle energy range (
  starting maybe from where LEP stopped 100GeV)
• Have P.Snopok and C.Johnstone already done this?
  - Lets ask Oprah for the prize!
• Timeframe April, then
• Dynamic aperture study with realistic multipole
  field errors
• (long term tracking for the p-? option needed)
• Analysis of coherent instabilities
• Beam-beam simulations
• Beam collimation energy deposition

Muon Collider Design Simulations Plans - Y.
Alexahin, FNAL February 1, 2007
16
MCTF Accelerator Physics Group
FNAL C.Ankenbrandt, Y.Alexahin, V.Balbekov,
C.Bhat, A.Burov, A.Drozhdin, D.Finley, N.Gelfand,
E.Gianfelice-Wendt, C.Johnstone, J.Johnstone,
V.Lebedev, N.Mokhov, A.Moretti, D.Neuffer,
K.-Y.Ng, M.Popovich, I.Rakhno, P.Spentsouris,
A.Striganov, A.Valishev, A.Van Ginneken,
K.Yonehara MuonsInc R.Johnson, M.Cummings,
S.Kahn, T.Roberts, R.Sah BNL J.S.Berg,
J.Gallardo, R.Gupta, H.Kirk, R.Palmer,
R.Fernow Jlab K.Beard, A.Bogacz, Y.-C.Chao,
Y.Derbenev, B.Rimmer ANL J.Norem
My apologies for this list being obviously
incomlete!
Muon Collider Design Simulations Plans - Y.
Alexahin, FNAL February 1, 2007