Ionization Cooling for a ν-Factory or Collider

David Neuffer

Fermilab

7/15/06

2

Outline Cooling Requirements

ν-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/fernow/www/icool/readme.html T. Roberts, G4BeamLine (Muons, Inc.) http://www.muonsinc.com/

ColliderOverview

5

Collider ParametersParameter 4TeV(2000) 4TeV low emittance Collision Energy(2E) 4000 4000 GeV Energy per beam(E) 2000 2000 GeV Luminosity(L=f0nsnbN2/42) 1035 1035 cm-2s-1 Source Parameters 3.8 MW 1.0 MW p-beam Proton energy(Ep) 16 8 GeV Protons/pulse(Np) 42.51013 221013 Pulse rate(f0) 15 20 Hz acceptance(/p) 0.2 0.05 -survival (N/Nsource) 0.25 0.2 Collider Parameters Mean radius(R) 1200 1000 m /bunch(N±) 1.251012 21011 Number of bunches(nB) 4 2 Storage turns(2ns) 1500 2000 Norm. emittance(N) 0.610-2 2.510-4 cm-rad Geom.. emittance(t =N/) 310-7 1.310-8 cm-rad Interaction focus o 0.3 0.1 cm IR Beam size =(o)½ 3.1 0.36 m E/E at collisions 0.12 0.2%

6

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 20—50 GeV)

- Storage ring Store ’s until decay (~300 B turns)

e + e* decays

produce neutrino beams directed toward:

Long base line neutrino detector (2000—8000 km away …)

1020 to 1021(e, *) /SS/year

7

Producing and Capturing Collaboration baseline:

10GeV p-beam on Target (Hg-jet) immersed in 201.75 T solenoid, taking ~300 MeV/c

μ-Collider:Rf: ~200 MHz,Capture string of ~20 bunches-Recombine aftercooling

ν-Factory:Rf: ~200 MHz,12 MV/mCapture in stringOf ~50 bunches

8

Cooling Requirements Beam from target has

,rms 2×10-2 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 0.8×10-2m-rad; ║,rms 0.06 m-rad/bunch

Collider Goal is maximal cooling of maximum number of both

+ AND -; high luminosity needed. Cooling by > ~100 in each of x, y, z is required ,rms 0.5 to 0.025×10-4m-rad; ║,rms 0.04 m-rad

9

Cooling Summary

10

Transverse cooling: Particle loses momentum

P( and ) in material

Particle regains P (only) in RF

Multiple Scattering in material increases rms emittance:

Muon Cooling-general principle

P

s

ds

dP1

P

s

ds

dP1PP xx

zL)cp(

E

22

x

R2

2s2

x

2

N,

11

Ionization Cooling Principle

p

s

ds

dp1pp xx

Loss of transverse momentum in absorber:

p

s

ds

dp1N,N,

2

2

2 3 2

2

1

1

2

N

N

ms

s

N r

R

d

ds

dP

P d

d

d s

dE

E ds

E

m c L E

s

Heating bymultiple scattering

Absorber Accelerator

Momentum loss is opposite to motion, p, p x , p y , E decrease

Momentum gain is purely longitudinal

Large emittance

Small emittance

12

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?

ds

d

2ds

dE

E

1

ds

d2

rms

N2N

2 2 2

2 2 2

rms s

R

d z E

ds c p L

13

Transverse cooling limits Transverse Cooling –

equilibrium emittance

2

, 22 s

N eq dE

R ds

E

m c L

equilibrium scattering angle

2

2 22 s

dE

R ds

E

m c L

Material Properties for Ionization Cooling

Material Symbol Z, A Density dE/ds (min.) LR LR dE/ds σθ∙βγ½ gxN/ gm/cm3 MeV/cm Cm MeV mm-mrad/cm Hydrogen H2 1, 1 0.071 0.292 865 252.6 0.061 37 Lithium Li 3, 7 0.534 0.848 155 130.8 0.084 71 Lith. H LiH 3+, 7+ 0.9 1.34 102 137 0.0824 68 Beryllium Be 4, 9 1.848 2.98 35.3 105.2 0.094 88 Carbon C 6, 12 2.265 4.032 18.8 75.8 0.110 122 Aluminum Al 13, 27 2.70 4.37 8.9 38.9 0.154 238 Copper Cu 29,63.5 8.96 12.90 1.43 18.45 0.224 503 Tungsten W 74, 184 19.3 22.1 0.35 7.73 0.346 1200

Want materials with small multiple scattering (large LR),but relatively large dE/ds, density ()

Want small at absorbers => strong focusing - equilibrium emittances (/) smallest for low-Z materials

14

Ionization Cooling problems Must focus to very small β

β : 1m → ~1mm

Intrinsic scattering of beam is large θrms > ~0.1 radians

Intrinsic momentum spread is large σP/P > ~0.03

Cooling must occur within muon lifetime = 2.2γ s or L = 660 βγ m pathlength

Does not (directly) cool longitudinally

15

Longitudinal “Cooling”

Energy cooling occurs if the derivative :

(dE/ds)/E= gL(dp/ds)/p > 0

gL(E) is negative for E < ~ 0.2 GeV

and only weakly positive for

E > ~ 0.2 GeV

Ionization cooling does not

effectively cool longitudinally

2

2

2 2 2e

β

γL 2 2m c β γ 2

I(Z)

(1- )2g = - + 2

γ ln -β

Energy straggling increases energy spread

22

2rms 2 2e e e 2

d ΔE= 4π r m c n γ 1-

ds

2 2 22 2 e

A e e 2 2

2m c γ βdE Z 1 δ= 4πN ρr m c ln -1-

ds A β I(Z) 2β

16

“Emittance exchange” enables longitudinal cooling:

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

00

1 /dE dEds ds

L

dp dsdE gdsE E cp p

-12

L 2 2T

1 (ka) a dpΔg = =

γ 1+ (ka) p da

(if due to path length)

17

Partition Numbers, δE-δt cooling

00,LL gg

g

P (MeV/c)

gL

0

-1

With emittance exchange the longitudinal partition number gL changes:

0x 1g

But the transverse cooling partition number decreases:

The sum of the cooling partition numbers(at P = P ) remains constant:

0,LLyxg g2ggg)P(

Σg > 0

2

2

2 2 2e

β

γ2g

2m c β γ 2I(Z)

(1- )Σ = 2β + 2

ln -β

18

Cooling + Energy straggling ...

pRFcτ 3 2

s

αλ1β =

β γ eV cosφ 2π mc

Energy spread E cooling equation:

2

1ncmr4E

g2

ds

d 22

e

22ee

2E2

dsdE

L2E

2rmsμ cτL L

Lμ

d ΔEdp βdε g= - ε +

ds p ds 2 ds

Longitudinal Emittance Cooling equation:

Longitudinal Cooling requires:Positive gL (η, “wedge”), Strong bunching (βcτ small)

Large Vrf, small λrf

MeVμ μ MeVmrf

mμ 0

Δp (m βγ) 105.66V » >> = = 0.16

L L βγ 660Energy loss/recovery

Before decay requires:

2βp e 2

2L μ

σ 1-m= ×

p 2g m log[]-β

Equilibrium σp:

19

μ Cooling Regimes

Efficient cooling requires:

Frictional Cooling (<1MeV/c) Σg=~3

Ionization Cooling (~0.3GeV/c) Σg=~2

Radiative Cooling (>1TeV/c) Σg=~4

Low-εt cooling Σg=~2β2

(longitudinal heating)

~ 0

dEdx

E

2 2 22 2

2 2

214 ln 1

( ) 2e

A e e

m cdE ZN r m c

ds A I Z

20

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 -

rB2

Br

2

,equil.

2Bρβ =

B

Strong focussing possible: β = 0.13m for B=10T, p = 200 MeV/c

β = 0.0027m for B=50T, p = 20 MeV/c

But: Solenoid introduces angular motion L damped by cooling + field flips No chromatic correction (yet) B within rf cavities ?

( )

21

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 r=0

22

More complete coupled cooling equations:

( ) / 2s x y

( ) / 2a x y

θD, θW are dispersion, wedge angles

Scattering terms

Wang and Kim, (MuCOOL 240) have developed coupledcooling equations including dispersion, wedges, solenoids,and symmetric focussing (βx = βy = βT)

2 26 D x y xy zL

23

Cooling with exchange and solenoids (Wang and Kim)

dsd

x21

LdsdP

21

dsd

xdsdP

xx

2rms

2rms HL

PPg

ds

d

2rms

dP dPy dθds ds1

y Lds 2

dε= - ε +β + β θ L

ds P P

dsd

21

dsd

z21

zdsdP

Lz

2rms

z

22rms

Pg

ds

d

ds

dH)(

PL

P)1(

ds

dL 2rms

LyxLdsdP

21ds

dP

2g

Example: rms Cooling equations with dispersion and wedges (at ==) in x-plane:

The additional correlation and heating terms are “small” in “well-designed” systems.

2

xx

ηH =

β

L

B eBθ = =

2Bρ 2P

24

Study 2 Cooling Channel (for MICE)

Cell contains Rf for acceleration/bunching H2 absorbers

Solenoidal magnets

sFOFO 2.75m cells

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

Simulation Results

25

Study2 cooling channel Focusing function at absorbers: 0.5m→0.2m

Total length of channel 100+m Cools to ~0.002m

26

Study 2A cooling channel Lattice is weak-focusing

Bmax = 2.5T, solenoidal

β ≅ 0.8m

Cools transversely from ~0.018 to ~0.007m

in ~70mBefore After cooling

-0.4m +0.4m

27

RFOFO ring cooler performance Example cools longitudinally

more than transversely Can be adjusted for more

transverse cooling

E-ct before and after

Transverse before and after

28

RF Problem: cavity gradient in magnetic field is limited?

Vacuum Cavities800 MHz results: 40MV/m→13MV/m

Muons, Inc. results: 50+ MV/m no change with B

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

10% of liquid H2

29

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, k=2π/λ, solenoid field B0, transverse field b(a)

2 21 ( ) 1 ( )( ) ( )

ka kap a B b a

k ka

-12

L 2 2T

1 (ka) a dpΔg = =

γ 1+ (ka) p da

30

Comments on Helical Wiggler parameters

1/T2 ≅ 0.67 for equal cooling at ∑g=2

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…)

P 200 MeV/c (0.67T-m)

λ 1.0m

a 0.16m

=ka= P/Pz 1

B 5.5T (Bρ/B=0.12m)

b(a) 1.28T (Bρ/b=0.52m)

b'(a) -0.46T/m

D(a)- dispersion 0.29m

Δg =1/T2 0.9

Typical case

31

Helical Wiggler 3-D Cooling (Pµ=250MeV/c)

Cooling factor

~ 50,000 ×

Yonehara, et al.

32

Helical wiggler R&D Need Magnet design

Solenoid, dipole + quad

Displaced solenoid coils can provide needed field

Matching in/out

33

+- Collider Cooling Scenarios +- Collider

requires energy cooling and emittance exchange (and anti-exchange) to obtain small L, εx, εy 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 …

34

Updated Scenario (Palmer-5-1-06)

PIC?

Low EmttanceMuon Collider

REMEX?

“Guggenheim” 6D cooler

800 MHz 6D cooler

35

Palmer scenario to do: Matching from section to section Buncher/Wiggler – 3D dynamics Reoptimization

Phase rotation buncher is ν-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?

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 xx’=const 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’

37

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 < ~ β

No “realistic” simulations

38

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

Example: Solenoids + quads + dipoles+rf 2m cells β = 1.4cm, ηx= 0.0m

Problems: Large σp/p (~3%)

Large σθ (>0.1)

Short absorber – 1cm Be = 3MeV

Solution approach: Use simulations to

tune this as a resonant beam line

39

Cooling scenario (~Muons, Inc.)

40

Low-Energy “Cooling”=REMEX 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/β2

βt scales as β

– Solenoid βt p/B

εN,rms Pμ2 ???

Decrease εN,transverse while εlong increases

“wedgeless” emittance exchange

εN,rms × 1/30, εlong ×300 ???

g

P (MeV/c)

gL

0

-1

2

2 3 2

1

2N s

NR

d EdE

ds E ds m c L E

2

, 22 s

N eq dEt R ds

E

g m c L

41

Low-Energy “cooling”-emittance exchange

dPμ/ds varies as ~1/β3

“Cooling” distance becomes very short:

for H at Pμ=10MeV/c

Focusing can get quite strong: Solenoid:

β=0.002m at 30T, 10MeV/c

εN,eq= 1.5×10-4 cm at 10MeV/c

Small enough for “low-emittance” collider

116dP

cmP ds

22

0.3

PB

B B

Pµ

Lcool

200MeV/c

10

0.1 cm

2

, 22 s

N eq dEt R ds

E

g m c L

100 cm

11

cool

dPL

P ds

42

Emittance exchange: solenoid focusing Solenoid focusing(30T)

0.002m

Momentum (30→10 MeV/c) L ≈ 5cm R < 1cm Liquid Hydrogen (or gas)

2

, 22 s

N eq dEt R ds

E

g m c L

Pµ

Lcool

200MeV/c

10

0.1cm

Use gas H2 if cooling length too short

11

cool

dPL

P dsεN,eq= 1.5×10-4 cm at 10MeV/c

-Will need rf to change p to z

43

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 ...

-Cooling Li lens parameters B(T) B (T/m) radius(cm) Length(m) I (MA) (=0.7r)

10 1000 1 1 0.50 0.25ms

15 3000 0.5 1 0.375 64s 20 8000 0.25 1 0.25 16s

0.3

PB

B B

β =0.026m (200 MeV/c, 1000 T/m)β =0.004m (40 MeV/c, 8000 T/m)

44

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

45

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)

46

MTA experimental program Rf: 805, 201 MHz, gas-filled

201MHz just reached 16 MV/m 805 MHz 3T, gas-cavity test

H2 absorbers

47

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)

T Target Sheffield

A Pion Capture ISIS

B Decay Solenoid EID

C Muon Transport Channel

Liverpool?

D Diffuser Oxford

48

Incoming muon beam

Diffusers 1&2

Beam PIDTOF 0

CherenkovTOF 1

Trackers 1 & 2 measurement of emittance in and out

Liquid Hydrogen absorbers 1,2,3

Downstreamparticle ID:

TOF 2 Cherenkov

Calorimeter

RF cavities 1 RF cavities 2

Spectrometer solenoid 1

Matching coils 1&2

Focus coils 1 Spectrometer solenoid 2

Coupling Coils 1&2

Focus coils 2 Focus coils 3Matching coils 1&2

10% cooling of 200 MeV muons requires ~ 20 MV of RF single particle measurements =>out/ in ) = 10-3

49

MICE Experiment

50

Last Slide

51

Postdoc availability – Front end Optimization