Ionization Cooling Introduction

1
Ionization CoolingIntroduction

• David Neuffer
• Fermilab
• 4/20/08

2
Outline

• Ionization Cooling
• Cooling description
• Heating Longitudinal Cooling
• Emittance Exchange - Partition Numbers
• Solenoidal focusing
• Helical Cooler-PIC-REMEX
• Low-Energy Cooling
• Cooling Scenarios
• Other Applications
• Nuclear physics, stopped ?s
• Experimental Studies

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, MuCOOL Note 240 (2002).
  
• Y. Derbenev and R. Johnson, Phys. Rev. ST Accel.
  Beams 8, E041002 (2005)
• 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/
• Collaboration Efforts
• Muon Collaboration http//www.cap.bnl.gov/mumu/mu
  _home_page.html
• Muon Collider Task Force https//mctf.fnal.gov/
• MICE Collaboration http//hep04.phys.iit.edu/cool
  demo/
• UKNF group (RAL)

4
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 toward
• Long base line neutrino detector (20008000 km
  away )
• 1020 to 1021(?e, ??) /SS/year

5
Overview of ????? Collider

• 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 TeV)
• ? - Collider Ring
• Store ?s until decay (300 B turns)
• ?- ?- ? X
• high-energy collisions

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????? Collider Parameters
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Producing and Capturing ???

• Target is immersed in high field solenoid
• Particles are trapped in Larmor orbits
• B 20T -gt 2T
• Spiral with radius r p?/(0.3 Bsol) B??/B
• Particles with p? lt 0.3 BsolRsol/2 are trapped
• Focuses both and - particles

?-Factory Rf 200 MHz, 12 MV/m Capture in
string Of 30 bunches
µ-Collider Rf 200 MHz, Capture string of 10
bunches- Recombine after cooling
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Target to Cooling channel match

• Transverse match 20T to 2T solenoid
• R 25cm sx 0.1m ?x 0.1
• Longitudinal match
• rf 200 MHz (?1.5m) V gt10 MV/m
• Optimum cooling is P 200MeV/c, dP/P 10
• Want both signs (µ, µ-)
• Solution
• High-Frequency bunching and phase-energy Rotation
  (350 to 200 MHz rf)
• Capture into string of 12 bunches

500 MeV/c
0
-10m
10m
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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 ? 0.02 to 0.006m-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
• Cool before decay Ionization cooling

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Ionization 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?

13
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

14
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
• B within rf cavities ?

?? ? ??(? ??)
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Solenoidal focusing for coolingKim, Penn,
Sessler, Fernow, Palmer

• Lattices are sequences of solenoids and drifts
  (rf interlaced) (,-)
• FOFO, ASOL, RFOFO, SFOFO, DODO, SOSO
• Can have nearly constant focusing or focusing to
  small ?
• Large ?p/p acceptance possible
• Need gt 10 ?p/p
• Low ? can be much less than
• gt5? smaller
• Recent example ? 1cm (!!)
• At 200 MeV/c, Bmax25T
• Field flip not required

22
Cooling with ?? ? exchange and solenoids
Example rms Cooling equations with dispersion
and wedges (at ????) in x-plane
?? ? ??(? ??)
C. X. Wang and K. J. Kim, MuCOOL Note 240
(2002).
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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?-Factory Study 2A cooling channel

• Lattice is weak-focusing
• Bmax 2.5T, solenoidal ß? ? 0.8m
• ? ? from 0.018 to 0.0075m
• eeq ? 0.006m (LiH)
• Could be improved
• H2 Absorber (120A) or smaller ß?
• ? ?? 0.0055
• eeq ? 0.003m

Before
After LiH cooling
After H2 cooling
-0.4m
0.4m
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RFOFO Ring Cooler performance
Transverse before and after

• Cools longitudinally and transversely
• Can be adjusted for more transverse cooling

E-ct before and after
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Other cooling examples

• Ring Cooler (inject/extract)
• Kickers too strong?
• Instead wrap into spiral
• 4 turns
• Guggenheim
• 200MHz, 400 MHz, 800 MHz
• If not multiturn, circle is not needed
• Try other geometries
• Tapered ..
• Snake
• Wiggler ?

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Advanced Cooling conceptsMuons, Inc, Derbenev,
Balbekov

• Gas-filled rf cavities
• Helical Wiggler Cooler
• PIC-Parametric-resonance Ionization Cooling
• Use resonance beam dynamics to intensify focusing
• REMEX, low-energy emittance exchange
• Very low energy cooling

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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
• Can also use open cell cavities

Vacuum Pill-Box Cavities 800 MHz results
40MV/m?13MV/m
Muons, Inc. results 50 MV/m no change with B
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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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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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)
• At 15MV/m energy loss, need
• Spiral magnet appears advantageous

Typical case
32

• PIC-Parametric-resonance Ionization Cooling
• ( 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'

?
Then
First
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PIC/REMEX cooling (Derbenev)

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

Cools to e? 0.000002m ??
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Low-Energy coolingemittance exchange

• dPµ/ds varies as 1/ß3
• 200MeV/c ? 10MeV/c
• Cooling distance becomes very short
• 
  for H at Pµ10MeV/c
• Focusing can get quite strong
• Solenoid
• ß?0.006m at 50T, 50MeV/c
• But Beam is heated longitudinally
• (e6-D is constant)
• eN,eq 110-5 m at 50MeV/c
• Smaller momentum (10 MeV/c)
• for low-emittance collider

l
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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

ß? 0.026m (200 MeV/c, 1000 T/m) ß? 0.004m (40
MeV/c, 8000 T/m)
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?-?? Collider Cooling Scenarios Palmer et al.

• requires energy cooling and emittance exchange
  (and anti-exchange) to obtain small ?L, ex, ey
• Start with large beam from target, compress and
  cool, going to stronger focussing and bunching as
  the beam gets smaller
• ?p/p 10, ?? 0.1
• Bunching rf frequency increases
• In final cooling stages longitudinal emittance
  increases while transverse emittance decreases

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Baseline Cooling Scenario for Collider

• Steps 1,2 Bunching, phase rotation, cooling (?
  factory)
• ?? 10cm ? 6cm
• 3,4 6-D cooling with 200, 400 MHz Ring Coolers
• ?? 6cm ? 2.4cm? 1.0cm
• 5 compress to 1 bunch
• 6, 7 6-D 200, 400 MHz Coolers
• ?? 3cm? 1.0cm
• 8 800 MHz Ring Cooler
• ?? 1.0cm? 0.3cm
• 9 up to 50T coolers (H2, solenoids)
• ?? 0.4cm? 0.08cm
• Total length of system 0.8km

Guggenheim 6D cooler
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Simulated/extrapolated performance
39
Other applications- not just muons!

• . Stopping ? beam
• (for ?2e conversion experiment)
• C. Ankenbrandt et al., Muons, Inc.
• For BCNT neutron source
• Y. Mori - KURRI
• For beta-beam source
• C. Rubbia et al

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?2e experiment MECO
µ to e

• Mu-E COnversion Experiment
• ?- Z ? e- Z
• Stopped ?- beam
• Helical energy-loss cooling channel can greatly
  increase ?- intensity
• Muons, Inc./FNAL

41
FFAG-ERIT neutron source (Mori, KURRI)

• Ionization cooling of protons/ ions is
  unattractive because nuclear reaction rate ?
  energy-loss cooling rate
• But can work if the goal is beam storage to
  obtain nuclear reactions
• Absorber is beam target, add rf
• ERIT-P-storage ring to obtain neutron beam
  (Mori-Okabe, FFAG05)
• 10 MeV protons (ß v/c 0.145)
• 10Be target for neutrons
• 5µ Be absorber, wedge (possible)
• dEp36 keV/turn
• Ionization cooling effects increase beam lifetime
  to 1000 turns
• not actually cooling

42
ß-beam Scenario (Rubbia et al.)

• ß-beam another ?e source
• Produce accelerate, and store unstable nuclei for
  ?-decay
• Example 8B?8Be e? or 8Li?8Be e- ?
• Source production can use ionization cooling
• Produce Li and inject at 25 MeV
• nuclear interaction at gas jet target produces
  8Li or 8B
• 6Li 3He ? 8B p
• Multiturn storage with ionization cooling
  maximizes ion production
• 8Li or 8B is ion source for ß-beam accelerator
• C. Rubbia, A. Ferrari, Y. Kadi, V. Vlachoudis,
  Nucl. Inst. and Meth. A 568, 475 (2006).
• D. Neuffer, NIM A 583, p.109 (2008)

?e
43
ß-beams example 6Li 3He ? 8B n

• Beam 25MeV 6Li
• PLi 529.9 MeV/c B? 0.59 T-m v/c0.094
  Jz,0-1.6
• Absorber3He -gas jet ?
• Z2, A3, I31eV, z3, a6
• dE/ds 110.6 MeV/cm,
• If gx,y,z 0.13 (Sg 0.4), ß- 0.3m at
  absorber
• Must mix both x and y with z
• eN,eq 0.000046 m-rad,
• sx,rms 2 cm at ß- 1m
• sE,eq is 0.4 MeV
• Could use 3He as beam
• 6Li target ( foil or liquid)

44
Ionization Cooling Experimental RD Program

• MICE International Muon Ionization Cooling
  Experiment
• µ-beam at RAL ISIS
• Systems test of complete cooling system
• MuCOOL Program
• Rf, absorber, magnet RD-supports MICE
• MuCOOL test area (Fermilab)
• Muon Collider Task Force
• MUONS, Inc. (R. Johnson, et al.)
• High-pressure rf cavities
• Helical cooler, Parametric resonance cooler

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MICE beam line (ISIS, RAL)

• 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 2008-2010 time frame

MICE beam line and experimental area (RAL)
46
Muon Ionization Cooling Experiment (MICE)
MICE Measurement of Muon Cooling Emittance
Measurement _at_ 10-3 First Beam April 2008
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Summary

• Ionization Cooling can provide cooled muon beams
  for Neutrino Factory or Muon Collider
• Components are being built tested
• Collider cooling scenario development has had
  great progress but needs more..
• Longitudinal cooling by large factors
• Transverse cooling by very large factors
• Final beam compression with emittance exchange
• Other Ionization Cooling applications are
  appearing