Muon Collider

1
FERMI NATIONAL ACCELERATOR
LABORATORY US
DEPARTMENT OF ENERGY
f
Muon Collider Ionization Cooling Issues Y.
Alexahin
FNAL Accelerator Advisory Committee meeting
December 5, 2006
2
Plan of the talk

• Overview of basic ideas
• low emittance MC
• 6D ionization cooling
• PIC and REMEX
• Ongoing work
• Questions to answer
• FY07 plan
• FY08 plan and beyond
• Summary

Muon Collider Ionization Cooling Issues - Y.
Alexahin, FNAL December 5,
2006
3
Muon Collider parameters

• Low emittance option (advanced) owing to ideas
  by Yaroslav Derbenev (HCC, PIC) much lower 6D
  emittances seem to be feasible than previously
  thought of.
• High emittance option (baseline) conceptually
  follows 1999 PRSTAB Muon Collider Collaboration
  report

Low Emitt. High Emitt. Energy (TeV)
0.750.75 (?7098.4) Average Luminosity
(1e34/cm2/s) 2.7 1 Average bending field
(T) 10 8.33 Mean radius (m) 361.4 363.8 Number
of IPs 4 (350m/2 each) 2 (200m each) P-driver
rep.rate (Hz) 65 60 Beam-beam parameter/IP,
? 0.052 0.1 ?? (cm) 0.5 3 Bunch length (cm),
?z 0.5 2 Number of bunches/beam,
nb 10 1 Number of muons/bunch (1e11),
N? 1 12 Norm.transverse emittance (?m),
??N 2.1 13 Energy spread () 1
0.1 Norm.longitudinal emittance (m), ?N 0.35
0.14 Total RF voltage (GV) at 800MHz 406.6
?103?c 0.26?103?c RF bucket height
() 23.9 0.6 Synchrotron tune 0.723 ?103?c
0.02?103?c ? ?- in collision / proton 0.15
/2 0.15 8GeV proton beam power (MW) 1.1 0.6
Muon Collider Ionization Cooling Issues - Y.
Alexahin, FNAL December 5,
2006
4
Low emittance option for MC

• 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 Ionization Cooling Issues - Y.
Alexahin, FNAL December 5,
2006
5
The roadmap to low emittance
Ionization cooling very similar to SR cooling
in e-damping rings The longitudinal damping
partition number is naturally negative at p ?
lt300MeV/c
How to make it positive see next slide. The
normalized equilibrium emittance (r.m.s.)
(overestimation for H and He)
With Z4 (Be) and the natural value of glt0 (the
final cooling stage)
so that to achieve ??2?m ??lt0.2mm is required
(for ??1). Is it feasible? Another possibility
(D.Neuffer) decelerate muons to very low ?.
Muon Collider Ionization Cooling Issues - Y.
Alexahin, FNAL December 5,
2006
6
Basic 6D Cooling

• Two ways to get ggt0
• generate large dispersion and use wedge
  absorbers
• generate large momentum compaction ?c gt0 in a
  homogeneous absorber
• The first method is realized in two schemes
• "Guggenheimed" RFOFO channel (helical or spiral
  with reducing radius), estimated emittances
  ??N5?102 ?m , ? N1mm
• straight FOFO channel with tilted solenoids,
  ??N5?102 ?m , ? N0.5mm
• The second method in
• Helical Cooling Channel (HCC) , ??N2?102 ?m ,
  ? N 0.3mm
• HCC is the most attractive scheme, however, it
  has inherent difficulties

Muon Collider Ionization Cooling Issues - Y.
Alexahin, FNAL December 5,
2006
7
PIC REMEX

• Basic idea of the Parametric resonance Ionization
  Cooling (Y. Derbenev)
• form a structure with 180? phase advance/cell
• resonantly excite beta-beating with special
  lenses to obtain very small ?? at absorber plates

Lattice magnets and RF cavities not shown

• Reverse EMittance EXchange
• obtain very small ?? as described above
• enhance transverse damping by making g lt0 as
  large by the absolute value as possible by
  reversing the wedge angle and generating maximum
  dispersion at the wedges

Muon Collider Ionization Cooling Issues - Y.
Alexahin, FNAL December 5,
2006
8
Guggenheim RFOFO structure (R.Palmer)
- modification of the initially proposed by
V.Balbekov RFOFO ring
Muon Collider Ionization Cooling Issues - Y.
Alexahin, FNAL December 5,
2006
9
Guggenheim 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 include 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 Ionization Cooling Issues - Y.
Alexahin, FNAL December 5,
2006
10
HCC Simulations (K.Yonehara)

• 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!

6D cooling factor in the series of HCC is 50,000
Muon Collider Ionization Cooling Issues - Y.
Alexahin, FNAL December 5,
2006
11
HCC issues
Vladimir Kashikhin found a brilliant solution
helical solenoid! Magically, the dipole and
quadrupole components have the right values,
while the orbit goes through the centers of the
coils!

• Still a number of problems to be solved
• how far down this helix can be scaled? Is helix
  period of 20cm (with Bs15T) technically
  feasible?
• a principal solution for the RF structure which
  can fit inside the HCC has yet to be found
• segmented HCC with RF cavities between solenoid
  sections was proposed but not demonstrated to
  provide adequate cooling

Muon Collider Ionization Cooling Issues - Y.
Alexahin, FNAL December 5,
2006
12
REMEX with HTS solenoids (R.Palmer)
It is possible to obtain ??N10 ?m in a
solenoidal focusing channel with LH2 absorber
Simulations of cooling in a channel with 6
solenoids (no RF yet) gave ??N25 ?m . To achieve
emittances for the low emittance MC option this
channel must be followed by a stronger focusing
channel with short solid absorbers.
Muon Collider Ionization Cooling Issues - Y.
Alexahin, FNAL December 5,
2006
13
Mixed Lattice for PIC/REMEX channels (A.Bogacz)
absorber
10T solenoid
quads
dipoles
This mixed quadrupole-solenoid focusing lattice
provides ?? 1.4cm at the absorber center. Large
dispersion function gives the possibility of
chromatic correction (not demonstrated yet). By
reducing dimensions and increasing field strength
one may hope to get ?? in the mm range.
Muon Collider Ionization Cooling Issues - Y.
Alexahin, FNAL December 5,
2006
14
Questions to answer

• Collider ring
• correction of chromatic perturbations
  (chromatic beta-beating, nonlinear chromaticity
  and momentum compaction factor)
• radiation shielding necessary to protect the
  superconducting magnets and detectors at specific
  for the particular design beam intensity and
  sizes
• field quality of the magnets which have the
  required aperture and field strength (magnets
  being developed for the LHC luminosity upgrade is
  a good first approximation)
• dynamic aperture with realistic field and
  alignment errors
• beam-beam effects
• suppression of coherent instabilities at given
  bunch intensity, length, momentum compaction and
  lattice functions.
• 6D cooling channel
• scalability of the proposed by V.Kashikhin HCC
  technical solution to the helix period of 20cm
  (with Bs15T)
• principal solution for the RF structure which
  can fit inside the HCC

Muon Collider Ionization Cooling Issues - Y.
Alexahin, FNAL December 5,
2006
15
Questions to answer

• 6D cooling channel (continued)
• ability of gas-filled cavities to support
  high-gradient RF field in the presence of
  ionizing beam
• end-to-end simulation of the "Guggenheimed"
  RFOFO channel to prove its competitiveness
• proof-of-principle study of the FOFO channel
  with tilted solenoids followed by cooling
  simulations.
• PIC / REMEX
• optics design for different stages (solenoidal
  vs quadrupole and mixed focusing)
• compensation of chromatic and spherical
  aberrations
• space charge effects
• Proton driver, Pion production, Muon RF capture,
  Bunch coalescing, Acceleration
• There is little doubt in feasibility of these
  elements of the complex,
• there are a number of options for each of them
  which should be studied and compared,
• but only after the principal solution for the
  collider ring and the cooling channel is chosen.

Muon Collider Ionization Cooling Issues - Y.
Alexahin, FNAL December 5,
2006
16
FY07 plan

• Physics analysis and computer simulations of
  different schemes for the basic 6D cooling
  channel and PIC/REMEX channel.
• Side-by-side comparison of the obtained results
  with the aim of choosing the 6D cooling channel
  baseline scheme compatible with the chosen
  collider option.
• Analysis of implications of different options
  for the muon collider (low emittance vs. high
  emittance, electrostatic separation in one ring
  vs. double ring) resulting in a presumably
  optimal choice of parameters.
• Collider ring optics design for the chosen
  option.
• Preliminary analysis of the technical
  feasibility and physical validity of the proposed
  design (momentum acceptance, medium-term dynamic
  aperture, coherent stability).
• Formulating requirements to the proton driver
  and other systems of the complex.
• Consistent scheme(s) of the muon collider
  complex.

Muon Collider Ionization Cooling Issues - Y.
Alexahin, FNAL December 5,
2006
17
FY08 plan and beyond

• Upgrade of the muon production and RF capture
  systems design
• Analysis, selection and preliminary design of
  muon acceleration systems (RLA vs. FFAG for the
  first stage, RLA vs. fast ramping synchrotrons
  for subsequent stages)
• Extensive simulation studies and design
  optimization of all essential systems of the
  collider complex.
• Analysis of radiological issues for appropriate
  choice of the collider orientation and depth
• Cost estimates
• Draft conceptual design report
• Optimistically, the conceptual design will be
  finished in 2009

Muon Collider Ionization Cooling Issues - Y.
Alexahin, FNAL December 5,
2006
18
Summary

• The Muon Collider for c.o.m. energy 1.5-2TeV
  seems doable with present day technology and can
  be accomodated on the Fermilab site
• Extensive design and simulation work is
  necessary for all parts of the complex with the
  1999 PRSTAB Muon Collider Collaboration report
  being a good first approximation

• The requested funding for this work seems
  adequate taking into account heavy contribution
  from other labs especially BNL, JLab and MuonsInc.

Muon Collider Ionization Cooling Issues - Y.
Alexahin, FNAL December 5,
2006
19
Backup slides Emittance diagram
Emittance evolution in R.Palmers muon cooling
scheme
Muon Collider Ionization Cooling Issues - Y.
Alexahin, FNAL December 5,
2006
20
Backup slides straight FOFO channel (Y.Alexahin)
tilted solenoids
straight solenoids
RF cavities
y/L
z/L
x/L
Closed orbit at ? 0.01 (dispersion follows the
same pattern)

• Phase advance over the 4-solenoid period is
  above 2? ? resonant dispersion generation
• Cooling by combination of GH2 and Li wedges in
  high-dispersion locations for damping repartition
• The scheme requires RF cavities operation in
  high magnetic field (hopefully GH2 will help)

Muon Collider Ionization Cooling Issues - Y.
Alexahin, FNAL December 5,
2006
21
Backup slides collider ring optics

• Two optics designs so far
• prepared for 1999 PRSTAB Muon Collider
  Collaboration report by Carol Johnstone et al.
  ? 3mm, peak ?max1.5 ?105m, ?c - 9.2?10-5.
  Requires further work on chromatic correction,
  the momentum acceptance is just (- 1.2?10-4,
  1.6?10-4).
• more conventional design by A.Bogacz ? 1cm,
  peak ?max4.8 ?103m (but with the distance from
  IP to the first quad just 2m), ?c 2?10-4

IR and a few arc cells in the design by A.Bogacz
Muon Collider Ionization Cooling Issues - Y.
Alexahin, FNAL December 5,
2006