Ionization Cooling for a Factory or Collider

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Ionization Cooling for a ?-Factory or ?????
Collider

• David Neuffer
• Fermilab
• 7/15/06

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Outline

• Cooling Requirements
• ?-Factory
• ????? Collider
• Ionization Cooling
• Cooling description
• Heating Longitudinal Cooling
• Emittance Exchange- Partition Number
• Helical wiggler-PIC-REMEX
• Low-Energy Cooling
• Emittance exchange
• Li lens
• Solenoid
• Cooling Scenarios

3
References

• A. N. Skrinsky and V.V. Parkhomchuk, Sov. J.
  Nucl. Physics 12, 3(1981).
• D. Neuffer, Particle Accelerators 14, 75 (1983)
• D. Neuffer, ??- Colliders, CERN report 99-12
  (1999).
• D. Neuffer, Introduction to Muon Cooling, NIM
  A532,p. 26 (2004).
• C. X. Wang and K. J. Kim, Linear Theory of 6-D
  Ionization Cooling, (PRL) MuCOOL Note 240, April
  2002. (also COOL03), NIM A532, p. 260 (2004)
• Y. Derbenev and R. Johnson, Phys. Rev. ST Accel.
  Beams 8, E041002 (2005) COOL05 proc.
• Simulation tools
• R. Fernow, ICOOL http//pubweb.bnl.gov/users/ferno
  w/www/icool/readme.html
• T. Roberts, G4BeamLine (Muons, Inc.)
  http//www.muonsinc.com/

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????? ColliderOverview
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????? Collider Parameters
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Overview of ?-Factory

• Proton Driver (1-4 MW) proton bunches on target
  produce ??s
• Front-end ? decay ? ? ? collect and cool
  ??s (phase rotation
  ionization cooling)
• Accelerator - to full energy (
  linac RLAs to 2050 GeV)
• ? - Storage ring
• Store ?s until decay (300 B turns)
• ?? e ?? ??e decays produce
  neutrino beams directed toward
• Long base line neutrino detector (20008000 km
  away )
• 1020 to 1021(?e, ??) /SS/year

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Producing and Capturing ???

• Collaboration baseline
• 10GeV p-beam on
• Target (Hg-jet) immersed in
• 20?1.75 T solenoid, taking
• 300 MeV/c ???

?-Factory Rf 200 MHz, 12 MV/m Capture in
string Of 50 bunches
µ-Collider Rf 200 MHz, Capture string of 20
bunches- Recombine after cooling
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Cooling Requirements

• Beam from target has
• ??,rms ? 210-2 m-rad ?,rms ? 1m
• ?-Storage Ring ?-Factory
• Goal is to collect maximum number of ? and/or
  ?- that fit within accelerator / storage
  ring acceptances
• Transverse cooling by 10? is sufficient
• ??,rms ? 0.2 to 0.810-2m-rad ?,rms ? 0.06
  m-rad/bunch
• ????? Collider
• Goal is maximal cooling of maximum number of both
  ? AND ?- high luminosity needed.
• Cooling by gt 100? in each of ?x, ?y, ?z is
  required
• ??,rms ? 0.5 to 0.02510-4m-rad ?,rms ? 0.04
  m-rad

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Cooling Summary
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Muon Cooling-general principle

• Transverse cooling
• Particle loses momentum P(? ? and ?) in
  material
• Particle regains P? (only) in RF
• Multiple Scattering in material increases rms
  emittance

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Ionization Cooling Principle
Loss of transverse momentum in absorber
Heating by multiple scattering
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Combining Cooling and Heating

• Low-Z absorbers (H2, Li, Be, ) to reduce
  multiple scattering
• High Gradient RF
• To cool before ?-decay (2.2? ?s)
• To keep beam bunched
• Strong-Focusing at absorbers
• To keep multiple scattering
• less than beam divergence
• ? Quad focusing ?
• ? Li lens focusing ?
• ? Solenoid focusing?

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Transverse cooling limits

• Transverse Cooling equilibrium emittance

equilibrium scattering angle

• Want materials with small multiple scattering
  (large LR),
• but relatively large dE/ds, density (?)
• Want small ?? at absorbers gt strong focusing
• - equilibrium emittances (/??) smallest for low-Z
  materials

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Ionization Cooling problems

• Must focus to very small ß?
• ß? 1m ? 1mm
• Intrinsic scattering of beam is large
• ?rms gt 0.1 radians
• Intrinsic momentum spread is large
• sP/P gt 0.03
• Cooling must occur within muon lifetime
• ?? 2.2? ?s or L? 660 ß? m pathlength
• Does not (directly) cool longitudinally

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Longitudinal Cooling

• Energy cooling occurs if the derivative
• ?(dE/ds)/?E gL(dp/ds)/p gt 0
• gL(E) is negative for E lt 0.2 GeV
• and only weakly positive for
• E gt 0.2 GeV
• Ionization cooling does not
• effectively cool longitudinally

Energy straggling increases energy spread
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Emittance exchange enables longitudinal cooling

• Cooling derivative is changed by use of
  dispersion wedge
• (Dependence of energy loss on energy can be
  increased)

(if due to path length)
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Partition Numbers, dE-dt cooling
With emittance exchange the longitudinal
partition number gL changes
But the transverse cooling partition number
decreases
The sum of the cooling partition numbers (at P
P? ) remains constant
Sg gt 0
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Cooling Energy straggling ...
Energy spread (sE) cooling equation
Equilibrium sp
Longitudinal Emittance Cooling equation

• Longitudinal Cooling requires
• Positive gL (?, wedge), Strong bunching (ßct
  small)
• Large Vrf, small ?rf

Energy loss/recovery Before decay requires
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µ Cooling Regimes

• Efficient cooling requires
• Frictional Cooling (lt1MeV/c) Sg3
• Ionization Cooling (0.3GeV/c) Sg2
• Radiative Cooling (gt1TeV/c) Sg4
• Low-et cooling Sg2ß2
• (longitudinal heating)

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Focusing for Cooling

• Strong focussing needed magnetic quads,
  solenoids, Li lens ?
• Solenoids have been used in most (recent) studies
• Focus horizontally and vertically
• Focus both ? and ?-

• Strong focussing possible
• ß? 0.13m for B10T, p? 200 MeV/c
• ß? 0.0027m for B50T, p? 20 MeV/c
• But
• Solenoid introduces angular motion
• L damped by cooling field flips
• No chromatic correction (yet)
• B within rf cavities ?

?? ? ??(? ??)
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Solenoidal Focusing and Angular Momentum

• Angular motion with focusing complicates cooling
• Energy loss in absorbers reduces P?, including P?
  Orbits cool to Larmor centers, not r
  0

Solution Flip magnetic fields new Larmor
center is near r0
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More complete coupled cooling equations
Wang and Kim, (MuCOOL 240) have developed
coupled cooling equations including dispersion,
wedges, solenoids, and symmetric focussing (ßx
ßy ßT)
Scattering terms
?D, ?W are dispersion, wedge angles
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Cooling with ?? ? exchange and solenoids (Wang
and Kim)
Example rms Cooling equations with dispersion
and wedges (at ????) in x-plane
The additional correlation and heating terms are
small in well-designed systems.
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Study 2 Cooling Channel (for MICE)
108 m cooling channel consists of 16 2.75m cells
40 1.65m cells Focusing increases along
channel Bmax increases from 3 T to 5.5 T
sFOFO 2.75m cells

• Cell contains
• Rf for acceleration/bunching
• H2 absorbers
• Solenoidal magnets

Simulation Results
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Study2 cooling channel

• Focusing function at absorbers 0.5m?0.2m
• Total length of channel 100m
• Cools to ?? 0.002m

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Study 2A cooling channel

• Lattice is weak-focusing
• Bmax 2.5T, solenoidal
• ß? ? 0.8m
• Cools transversely
• ? ? from 0.018 to 0.007m
• in 70m

Before
After cooling
-0.4m
0.4m
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RFOFO ring cooler performance
Transverse before and after

• Example cools longitudinally more than
  transversely
• Can be adjusted for more transverse cooling

E-ct before and after
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RF Problem cavity gradient in magnetic field is
limited?

• Rf breakdown field decreases in magnetic fields?
• Solenoidal focussing gives large B at cavities
• But gas in cavity suppresses breakdown

Muons, Inc. results 50 MV/m no change with B
Vacuum Cavities 800 MHz results 40MV/m?13MV/m
10 of liquid H2
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Helical 6-D Cooler (Derbenev)

• Magnetic field is solenoid B0 dipole quad
• System is filled with H2 gas, includes rf
  cavities
• Cools 6-D (large E means longer path length)

Key parameters a, k2p/?, solenoid field B0,
transverse field b(a)
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Comments on Helical Wiggler parameters

• 1/?T2 ? 0.67 for equal cooling at ?g2
• Energy loss at liquid H2 density is 30MV/m
  (800atm-e gas)
• Typical simulations have used 15MV/m energy
  loss
• Need more rf gradient 22MV/m
• (could use less if needed)

Typical case
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Helical Wiggler 3-D Cooling (Pµ250MeV/c)
l1.0
l0.8
l0.6
l0.4
Cooling factor 50,000
Yonehara, et al.
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Helical wiggler RD

• Need Magnet design
• Solenoid, dipole quad
• Displaced solenoid coils can provide needed field
• Matching in/out

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?-?? Collider Cooling Scenarios

• ?-?? Collider
• requires energy cooling and emittance exchange
  (and anti-exchange) to obtain small ?L, ex, ey
  emittances required for high-luminosity
• Start with large beam from target, compress and
  cool, going to stronger focussing and bunching as
  the beam gets smaller

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Updated Scenario (Palmer-5-1-06)
Guggenheim 6D cooler
Low Emttance Muon Collider
REMEX?
PIC?
800 MHz 6D cooler
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Palmer scenario to do

• Matching from section to section
• Buncher/Wiggler 3D dynamics
• Reoptimization
• Phase rotation buncher is ?-Factory case (not
  Collider optimum)
• Tapered Guggenheims
• Final cooler
• Matching in/out
• Rf match in/out
• realistic field models
• Reacceleration scenario from low-emittance
• Lower frequency rf buncher
• Can PIC/REMEX or get us to smaller emittance?

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• PIC-Parametric-resonance Ionization Cooling
• (JLab, Y. Derbenev) (also Balbekov, 1997)
• Excite ½ integer parametric resonance (in Linac
  or ring)
• Similar to vertical rigid pendulum or ½-integer
  extraction
• Elliptical phase space motion becomes hyperbolic
• Use xxconst to reduce x, increase x'
• Use Ionization Cooling to reduce x'
• Detuning issues being addressed (chromatic and
  spherical aberrations, space-charge tune spread).
  Simulations underway.

First
Then
IC reduces x
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PIC/REMEX cooling (Derbenev)

• PIC ??,eff 0.6cm ? 0.1cm
• Transverse longitudinal cooling
• Reverse emittance exchange to reduce transverse
  emittance
• (REMEX)
• Chromaticity correction a problem
• Depth of focus a problem
• Labsorber lt ß?
• No realistic simulations

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PIC/REMEX examples (Bogacz, Beard, Newsham,
Derbenev)

• Example
• Solenoids quads dipolesrf
• 2m cells
• ß? 1.4cm, ?x 0.0m
• Problems
• Large sp/p (3)
• Large s? (gt0.1)
• Short absorber
• 1cm Be 3MeV
• Solution approach
• Use simulations to tune this as a resonant beam
  line

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Cooling scenario (Muons, Inc.)
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Low-Energy CoolingREMEX without wedges

• At Pµ 10 to 200 MeV/c, energy loss heats the
  beam longitudinally
• Transverse cooling can occur
• emittance exchange
• Equilibrium transverse emittance decreases
• dE/ds scales as 1/ß2
• ßt scales as ß
• Solenoid ßt ? p/B
• eN,rms ? Pµ2 ???
• Decrease eN,transverse while elong increases
• wedgeless emittance exchange
• eN,rms 1/30, elong 300 ???

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Low-Energy cooling-emittance exchange

• dPµ/ds varies as 1/ß3
• Cooling distance becomes very short
• 
  for H at Pµ10MeV/c
• Focusing can get quite strong
• Solenoid
• ß?0.002m at 30T, 10MeV/c
• eN,eq 1.510-4 cm at 10MeV/c
• Small enough for low-emittance collider

100 cm
Lcool
0.1 cm
200 MeV/c
10
Pµ
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Emittance exchange solenoid focusing

• Solenoid focusing(30T)
• ??? 0.002m
• Momentum (30?10 MeV/c)
• L 5cm
• R lt 1cm
• Liquid Hydrogen (or gas)

Lcool

• eN,eq 1.510-4 cm at 10MeV/c

0.1cm
Use gas H2 if cooling length too short
-Will need rf to change ?p to ?z
200 MeV/c
10
Pµ
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Li-lens cooling

• Lithium Lens provides strong-focusing and low-Z
  absorber in same device
• Liquid Li-lens may be needed for highest-field,
  high rep. rate lens
• BINP (Silvestrov) was testing prototype liquid Li
  lens for FNAL
• But FNAL support was stopped - and prototypes
  were not successful ...

ß? 0.026m (200 MeV/c, 1000 T/m) ß? 0.004m (40
MeV/c, 8000 T/m)
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Summary

• Cooling for neutrino factory is practical
• Collider cooling scenario needs considerable
  development
• Longitudinal cooling by large factors
• Transverse cooling by very large factors
• Final beam compression with reverse emittance
  exchange
• Reacceleration and bunching from low energy

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Linac-area MuCool Test Area

• Test area for bench test and beam-test of Liquid
  H2 absorbers
• Enclosure complete in October 2003
• Can test 200 and 805 MHz rf for MuCOOL and also
  for Fermilab
• Assemble and beam test cooling modules
• (absorber rf cavity solenoid)

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MTA experimental program

• Rf 805, 201 MHz, gas-filled
• 201MHz just reached 16 MV/m
• 805 MHz 3T, gas-cavity test
• H2 absorbers

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MICE beam line (Drumm, ISS)

• MICE (International Muon Ionization Cooling
  Experiment)
• To verify ionization cooling (for a neutrino
  factory) with a test of a
  complete cooling module in a muon beam
• Muon beam line and test area in RAL-ISIS (Oxford)
• Installation Jan. Oct. 1 2007
• Experiment occurs in 2007-2009 time frame

MICE beam line and experimental area (RAL)
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10 cooling of 200 MeV muons requires 20 MV of
RF single particle measurements gtD ( e out/e in
) 10-3
Coupling Coils 12
Spectrometer solenoid 1
Matching coils 12
Spectrometer solenoid 2
Matching coils 12
Focus coils 1
Focus coils 2
Focus coils 3
m
Beam PID TOF 0 Cherenkov TOF 1
RF cavities 1
RF cavities 2
Downstream particle ID TOF 2 Cherenkov Calorimet
er
Diffusers 12
Liquid Hydrogen absorbers 1,2,3
Incoming muon beam
Trackers 1 2 measurement of emittance in and
out
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MICE Experiment
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Last Slide
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Postdoc availability Front end Optimization