# Presentation: 824594

## Low-Energy Ionization “Cooling”

**David Neuffer**
- Fermilab

## Outline

**Low-energy cooling-protons**
**ions and “beta-beams”**
**Low-energy cooling – muons**
**emittance exchange**

## μ Cooling Regimes

**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)

## Cooling/Heating equations

**Cooling equations are same as used for muons**
**mass = a m****p****, charge = z e **
**Some formulae may be inaccurate for small ****β****=v/c**
**Add heating through nuclear interactions**
**Ionization/recombination should be included**
**For small ****β****, longitudinal dE/dx heating is large**
**At ****β**** =0.1, g****L**** = -1.64, ∑****g**** = 0.36 **
**Coupling only with x cannot obtain damping in both x and z**

**0.0**

**1.0**

**3.0**

**5.0**

****

## Low-energy “cooling” of ions

**Ionization cooling of protons/ ions has been unattractive because nuclear reaction rate is competitive with energy-loss cooling rate**
**And other cooling methods are available**
**But can have some value if the goal is beam storage to obtain nuclear reactions**
**Absorber is also nuclear interaction medium**
**Y. Mori – neutron beam source **
**NIM paper**
**C. Rubbia, Ferrari, Kadi, Vlachoudis – source of ions for ****β****-beams**

## Miscellaneous Cooling equations 

- For small β:

**Better for larger mass?**

## Example 

**ERIT-P-storage ring to obtain directed neutron beam  ****(Mori-Okabe, FFAG05)**
**10 MeV protons**
**9****Be target for neutrons**
**σ**** ≈ 0.5 barns **
**β**** = v/c =0.145**
**Large ****δ****E heating**
**Baseline Absorber**
**5****μ Be absorber**
**δ****E****p****=~36 keV/turn**
**Design Intensity**
**1000Hz, 6.5×10****10****p/cycle**
**100W primary beam**
**< 1.5 kW on foil **
**0.4 kW at n****turns**** =1000**

## ERIT results 

**With only production reaction, lifetime is 30000 turns **
**With baseline parameters, cannot cool both x and E**
**Optimal x-E exchange increases storage time from 1000 to 3000 turns (3850 turns = 1ms) **
**With x-y-E coupling, could cool 3-D with g****i****= 0.12**
**Cooling time  would be ~5000 turns**
**With ****β********=0.2m, ********δ****E****rms**** = 0.4MeV, ************,N ****= 0.0004m ****(x****rms****=2.3cm)**
**x****rms****= 7.3cm at ****β********=2m ****(would need r =20cm  arc apertures)**
**	****	**(but 1ms refill time would make this unnecessary)

## ERIT-recent results

**Lattice changed from spiral to radial sector**
**spiral sector had too small vertical aperture**
**With cooling effects, beam has ~1000 turn lifetime in ICOOL simulation **
**	****	****(Mori and Okabe FFAG06)**

## Emittance exchange parameters

**with g****L,0**** = -1.63, ****η**** = 0.5m, **
**need G = 3.5****m****-1**** to get g****L****=0.12**
**(L****W**** =0.3m)**
**For 3-D cooling, need to mix with both x and y**
**Solenoid cooling rings **
**Also “Moebius” lattice ****(R. Talman)**
**Single turn includes x-y exchange transport**
**solenoid(s) or skew quads**
**in zero dispersion region for simplicity**
**Solenoid: BL =  ****π**** B****ρ**** **
**For 10 MeV p : BL = 1.44T-m**
**Complete period is 2 turns**

## “Wedge” for thin foil

**Obtain variable thickness by bent foil**** ****(Mori et al.)**
**Choose x****0****=0.15m, L****W****=0.3, ****δ****o****=5μ**
**then a=0.15, ****δ****R****=2.5**
**for g****L,0**** = -1.63, η = 0.5m**
**Barely Compatible with ****β********* = 0.2m**
**Beam energy loss not too large?**
**<1kW Power on foil**

- a=0.15

- Beam

## Other heating terms:

**Mixing of transverse heating with longitudinal could be larger effect:  ****(Wang & Kim)**

- At ERIT parameters: βx= 1.0m, βz= 16m, η=0.6m, Be absorber,
- dδ2/ds= 0.00032, dθ2/ds= 0.0133  only 5%, 1.5% changes ...
- At βx= 0.2m, ~25% change  ...

## β-beam Scenario

**Neutrino Source **
**Decay Ring**

**     ****Ion production: **Target  -  Ion (8B or 8Li ?) Conversion Ring

**Ion Driver **
- 25MeV Li ?

**Decay ring**
- B = 400 Tm B = 5 T          C = 3300 m     Lss = 1100 m
- 8B:    = 80
- 8Li:   = 50

**Acceleration to medium energy ** RCS

**8z**
**GeV/c**

**Acceleration to final energy**
- Fermilab Main Injector

**Experiment**

**Ion acceleration **Linac

**Beam preparation **ECR pulsed

**Ion production**

**Acceleration**

**Neutrino source**

## Conventional Beta beam ion source

- ν-sources

- v*-sources

**Want: **
**lifetime  ~1s **
**large ****ν****-energy**
**ν**** and ****ν***** **
**easily extracted atoms **
** ****Number of possible ions is limited (****v ****sources easier)**
**Noble gases easier to extract**
** ****6****He****2**** “easiest” ****E****ν********* =1.94MeV**
**18****Ne****10**** for ****ν****       ****E****ν**** =1.52MeV**
**(****8****B, ****8****Li) have ****E ****ν ****,****ν ********* =~7MeV**
**Want 10****20**** ****ν**** and ****ν***** / year... **

## β-beam Scenario (Rubbia et al.)

**Produce Li and inject at 25 MeV**
**Charge exchange injection **
**nuclear interaction at gas jet target produces ****8****Li or ****8****B**
**Multiturn with cooling maximizes ion production**
**8****Li or ****8****B is caught on stopper(W)**
**heated to reemit as gas**
**8****Li or ****8****B gas is ion source for ****β****-beam accelerate**
**Accelerate to B****ρ**** = 400 T-m**
**Fermilab main injector**
**Stack in storage ring for:**
** ****8****B********8****Be + e****+****+****ν**** or ****8****Li********8****Be + e****-****+ ****ν***** ****neutrino source**

## Cooling for β-beams (Rubbia et al.-NuFACT06)

**β****-beam requires ions with appropriate nuclear decay**
**8****B********8****Be + e****+**** + ****ν**
**8****Li********8****Be + e****-**** + ****ν*******
**Ions are produced by nuclear interactions**
**6****Li**** + ****3****He ******** ****8****B**** ****+ n**
**7****Li**** + ****2****H**** **** ******** ****8****Li**** + ****1****H**
**Secondary ions must be collected and reaccelerated**
**Either heavy or light ion could be beam or target**
**Ref. 1 prefers heavy ion beam – ions are produced more forward (“reverse kinematics”)**
**He or ****2****H beam on Li has other advantages ....**
**Parameters can be chosen such that target “cools” beam**
**(losses and heating from nuclear interactions, however...) **

## β-beams example: 6Li + 3He   8B + n 

**Beam: ****25MeV ****6****Li****+++**** **
**P****Li**** =529.9 MeV/c  B****ρ**** = 0.59 T-m****; v/c=0.09415**
**Absorber:****3****He  **
**Z=2, A=3, I=31eV, z=3, a=6**
**dE/ds= 1180 MeV/gm/cm****2****, L****R****= 70.9 gm/cm****2**
-  (ρHe-3= 0.09375 gm/cm3)Liquid, (ρHe-3= 0.134∙10-3P gm/cm3/atm in gas)
** ****If g****x**** = 0.123  (****Σ****g**** ****= 0.37),  ****β****┴**** ****=0.3m at absorber**
**ε****N,eq****=**** ~  0.000046 m-rad**
**σ****x,rms****= 1.2 cm at ****β****┴**** ****=0.3m, **
**σ****x,rms****= 3.14 cm at ****β****┴**** ****=2.0m**
**σ****E,eq**** is ~ 0.4 MeV**
**ln[ ]=5.68**

## Cooling time/power: 6Li + 3He   8B + n 

- Nuclear cross section for **beam loss is 1 barn (10****-24 ****cm****2****)** or more
- σ = 10-24cm2,corresponds to ~5gm/cm2 of 3He
- ~10 3-D cooling e-foldings ...
- Cross-section for 8B production is ~10 mbarn
- At best, 10-2  of  6Li  is converted
- Goal is **10****13****/s**** ****of ****8****B** production
- then at least 1015 Li6/s needed
- Space charge **limit is ~10****12**** ****6****Li/ring**
- Cycle time is <10-3 s
- If C=10m,  τ =355 ns, 2820 turns/ms
- 5/2820=1.773*10-3**  **gm/cm2 (0.019 cm @ liquid density ...)
- 2.1 MeV/turn energy loss and regain required ...(0.7MV rf)
**0.944 MW** cooling rf power...

## Complementary case- 7Li + 2H   8Li +1H

- Nuclear cross section for **beam loss is 1 barn (10****-24 ****cm****2****)** or more
- σ = 10-24cm2,corresponds to ~3.3gm/cm2 of 2H
- ~9 3-D cooling e-foldings ...
- Cross-section for 8Li production is ~100 mbarn
- 10-1  of  7Li  is converted ?? **10 × better than ****8****B neutrinos**
- Goal is **10****13****/s**** ****of ****8****Li** production
- then at least 1014 Li7/s needed
- Space charge **limit is ~10****12**** ****7****Li/ring**
- Cycle time can be up to 10-2 s, but use 10-3s
- If C=10m,  τ =355 ns, 2820 turns
- 3.3/2820=1.2*10-3**  **gm/cm2 (0.007 cm @ liquid  D density ...)
- 1.3 MeV/turn energy loss and regain required ...(0.43MV rf)
**0.06 MW** cooling rf power...

## Space charge – Direct/inverse ?

**At N = 10****12****, B****F**** =0.2, ****β****=****0.094****, z=3, a=6,**** ****ε****N,rms****= 0.000046:**
**	****δν**** ****≈**** 0.2**** **
** ****tolerable ??**
**Space charge sets limit on number of particles in beam and on transverse emittance **
**Effect is reduced for “direct kinematics”**
** ****(D/He beam, Li target)**

**Is “direct” source better than “inverse” source?**
**6****Li****3**** beam + ****3****He****2**** target**
**or**
**3****He****2**** beam + ****6****Li****3**** target**
**Beam energy, power on target less (1/2to 1/3)**
**Li foil or gas-jet target?**
**Gas-jet nozzle for wedge effect**
**> 0.1MW power on target**

## Rubbia et al. not completely wrong

**...****But contains mistakes**
**Longitudinal emittance growth  2****× ****larger  **
**(than NuFACT06 presentation) **
**synchrotron oscillations reduce energy spread growth rate but not emittance growth rate**
**Emittance exchange needs x-y coupling and balancing of cooling rates to get 3-D cooling**
**More complicated lattice**
**3-D cooling needed to get enough ions**
**Increases equilibrium emittance, beam size**
**increase needed for space charge, however**
**Ion production to storage ring efficiency is not 100%  ...**

## μ Low-Energy “cooling”- emittance exchange

**dP****μ****/ds**** ****varies as ~1/β****3**
- “Cooling” distance becomes very short:
**                                  ****for liquid H at ****	****	****              ****P****μ****=****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**

**P****μ**

**L****cool**

**200**
**MeV/c**

**10**

**0.1 cm**

**100 cm**

##  ICOOL Simulation results

**Low-Energy muons in H****2**** absorber**
**50 MeV/c (4 cm **** H****2****)**
**30 MeV/c (0.7cm ****H****2****)**
**15 MeV/c (0.8****mm H****2 ****or 80****μ ****Be or... ****)**
**Could use gas absorbers/jets ?**
**Results follow rms eqns**
**less multiple scattering ...**
**Typical section:**
**reduces P by 1/3P**
**δ****p increases by factor of 2**
**ε****x****, ****ε****y**** reduced by 1/√2**

## ICOOL Multiple Scattering effects

**New Model 6 (Fano model) much less rms scattering than Model 4(Moliere/Bethe)**
**At 200 MeV/c ****μ**** on H****2****,  M4 scattering  ~10% > rms eq.**
**M6 scattering (****θ****2****)**** is ~30% less than rms eq.**
**Low energy scattering less at low momentum**
**At 15 MeV/c,  M4 scattering  ~40% < than rms eq.**
**M6 scattering (****θ****2****)**** is ~60% less than rms eq.**
**Which is more accurate? rms eq., model 4 or 6 or ??**

## Comments

**Can fit into end-stage cooling (with similar effects?)**
**Can use gas jet absorbers to avoid having windows **
**P****jet **** ****> 1 atm possible**
**Need “rf” to reduce dp/p (longer bunches for multistep )**
**1mm bunch can grow to 1m bunch length**
**Voltage is relatively small**
**L****μ**** = 660βγ**
**Reacceleration **
**of ~1m bunches**

- Approximate effect
- Of low-E emittance exchange

## Summary

**Low energy ionization cooling has possible important applications**
**Protons for neutron generation (Mori et al.)**
**β****-beam source production (Rubbia et al.)**
**Cooling of ****μ’s to minimum transverse emittance**
**REMEX that might work ...**
**“****Cooling” is predominantly emittance exchange**
**X-y-z exchange needed for “real” cooling**

## ILC Status

## X-sections, kinematics