december 10, 2008 tjrparticle refrigerator1 the particle refrigerator tom roberts muons, inc. a...

December 10, 2008 TJR Particle Refrigerator 1

The Particle Refrigerator

Tom Roberts

Muons, Inc.

A promising approach to using frictional coolingfor reducing the emittance of muon beams.

Introduction

• Frictional cooling has long been known to be capable of producing very low emittance beams

• The problem is that frictional cooling only works for very low energy particles, and its input acceptance is quite small in energy:– Antiprotons: KE < 50 keV– Muons: KE < 10 keV

Key Idea: Make the particles climb a few Mega-Volt potential, stop,

and turn around into the frictional cooling channel. This increases the acceptance from a few keV to a few MeV.

• So the particles enter the device backwards; they come back out with the equilibrium kinetic energy of the frictional cooling channel regardless of their initial energy.

• Particles with different initial energies turn around at different places.• The total potential determines the momentum (energy) acceptance.December 10, 2008 TJR Particle Refrigerator 2

Frictional Cooling

• Operates at β ~ 0.01 in a region where the energy loss increases with β, so the channel has an equilibrium β.

• In this regime, gas will break down – use many very thin carbon foils.• Hopefully the solid foils will trap enough of the ionization electrons in

the material to prevent a shower and subsequent breakdown.

Experiments on frictional cooling of muons have beenperformed with 10 foils (25 nm each).


FrictionalCooling

IonizationCooling

Simulation of a Thin Carbon Foil, Muons


Useful Range

< 2.2 keVStopsin Foil

OperatingPoint

2.4 kV/foil

G4beamline / historoot

Compared to antiprotons, the useful range is smaller, and theoperating point is closer to the upper edge of the useful range.

Variance is large

Muon Refrigerator – Diagram


Solenoid

μ− In(3-7 MeV)

μ− Out(6 keV)

…Resistor DividerGnd

HV Insulation First foil is at -2 MV, so outgoing μ− exit with 2 MeV kinetic energy.

Solenoid maintains transverse focusing.

μ− climb the potential, turn around, and come back out via the frictional channel.

10 m

20cm

1,400 thin carbon foils (25 nm), separated by 0.5 cm and 2.4 kV.

-5.5 MV

Device is cylindrically symmetric (except divider); diagram is not to scale.

Remember that 1/e transverse cooling occurs by losing andre-gaining the particle energy. That occurs every 2 or 3 foilsin the frictional channel.

Refrigerator Output – KERight after first foil


Refrigerator Output – tRight after first foil


Refrigerator Tout vs Kein

Right after first foil


Output in the Frictional Channel

“Lost” muonsat higher energy

Background: Muon ColliderFernow-Neuffer Plot


R.B.Palmer, 3/6/2008.

Why a Muon Refrigeratoris so Interesting!


RefrigeratorTransmission=12%

RefrigeratorTransmission=6%

G4beamline simulations,ecalc9 emittances.(Same scale)

Difference is just input beam emittance

Muon Losses

Input Transverse Emittance

Loss Mechanism 0.75 π mm-rad 1.6 π mm-rad

Decay while moving 23% 20%

Escape out the end 0% 0%

Scraping (radial) 0% 0%

Stop in a foil 23% 9%

Lose too little energy 42% 65%

Survive in frictional channel 12% 6%


Higher transverse emittance input beam was due to larger σx’, σy’. Larger-angle particles have larger β at turn-around, and can already be out of the frictional regime at the first foil.

Challenge: can we use all those higher-energy muons?

Dominant Loss Mechanism

• The dominant loss mechanism is particles losing too little energy in a foil and leaving the frictional-cooling channel.

• This happens much more frequently for muons than for antiprotons.• Many are lost right at turn-around.


Incoming(going right)

Turn Around

In the FrictionalChannel

(going left)

Lost

Outgoing(going left)

One μ+

Track

Those “Lost” muons Have Also Been Cooled


“Lost” muonsTransmission=65%

This can surely be optimized to

do better.(Same scale)

Comments onSpace charge

• Be wary in applying the usual rules of thumb

• Low normalized emittance is achieved by low momentum, not small bunch size:

σx 25 mmσy 25 mmσz 673 mm<pz> 1.1 MeV/c (β=0.01)

• Clearly a careful computation including space charge is needed.


An Inexpensive ExperimentUsing Alphas


Resistor Divider

-50 kVSupply

+50 kVSupply

• Shows feasibility andmeasures transmission,not emittance or cooling

• Uses two 50 kV suppliesto keep costs down.

• The source must bedegraded to ~100 keV.

• Hopefully the sourcecollimation will avoid theneed for a solenoid (asshown).

This is just a concept −lots of details need tobe worked out.

This is a simple, tabletop experiment that should fit within an SBIR budget.

100 nm Carbon

Foils

Collimated Alpha

Source(degrader?)

Detector

Vacuum Chamber

Typical Alpha Track

LOTS more work to do!

• Investigate space charge effects• Investigate electron cloud effects

– Will electrons multiply in the foils and spark?

• Investigate foil properties, handling, etc.• Engineer the high voltage• Will foils degrade or be destroyed over time?• Design the input/output of the refrigerator (kicker, bend?)• Design the following acceleration stages

There are many unanswered questions, but the sameis true of most current cooling-channel designs.


Conclusions

• This is an interesting device that holds promise to significantly improve the design of a muon collider.

• Much work still needs to be done to validate that.


december 10, 2008 tjrparticle refrigerator1 the particle refrigerator tom roberts muons, inc. a...

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