December 10, 2008 TJRParticle Refrigerator1 The Particle Refrigerator Tom Roberts Muons, Inc. A promising approach to using frictional cooling for 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 TJRParticle Refrigerator2

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 been performed with 10 foils (25 nm each). December 10, 2008 TJRParticle Refrigerator3 Frictional Cooling Ionization Cooling

Simulation of a Thin Carbon Foil, Muons December 10, 2008 TJRParticle Refrigerator4 Useful Range < 2.2 keV Stops in Foil Operating Point 2.4 kV/foil G4beamline / historoot Compared to antiprotons, the useful range is smaller, and the operating point is closer to the upper edge of the useful range. Variance is large

Muon Refrigerator – Diagram December 10, 2008 TJRParticle Refrigerator5 Solenoid μ − In (3-7 MeV) μ − Out (6 keV) … Resistor Divider Gnd 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 20 cm 1,400 thin carbon foils (25 nm), separated by 0.5 cm and 2.4 kV MV Device is cylindrically symmetric (except divider); diagram is not to scale. Remember that 1/e transverse cooling occurs by losing and re-gaining the particle energy. That occurs every 2 or 3 foils in the frictional channel.

Refrigerator Output – KE Right after first foil December 10, 2008 TJRParticle Refrigerator6

Refrigerator Output – t Right after first foil December 10, 2008 TJRParticle Refrigerator7

Refrigerator T out vs Ke in Right after first foil December 10, 2008 TJRParticle Refrigerator8 Output in the Frictional Channel “Lost” muons at higher energy

Background: Muon Collider Fernow-Neuffer Plot December 10, 2008 TJRParticle Refrigerator9 R.B.Palmer, 3/6/2008.

Why a Muon Refrigerator is so Interesting! December 10, 2008 TJRParticle Refrigerator10 Refrigerator Transmission=12% Refrigerator Transmission=6% G4beamline simulations, ecalc9 emittances. (Same scale) Difference is just input beam emittance

Muon Losses Input Transverse Emittance Loss Mechanism 0.75 π mm-rad1.6 π mm-rad Decay while moving23%20% Escape out the end0% Scraping (radial)0% Stop in a foil23%9% Lose too little energy42%65% Survive in frictional channel12%6% December 10, 2008 TJRParticle Refrigerator11 Higher transverse emittance input beam was due to larger σ x’, σ y’. 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. December 10, 2008 TJRParticle Refrigerator12 Incoming (going right) Turn Around In the Frictional Channel (going left) Lost Outgoing (going left) One μ + Track

Those “Lost” muons Have Also Been Cooled December 10, 2008 TJRParticle Refrigerator13 “Lost” muons Transmission=65% This can surely be optimized to do better. (Same scale)

Comments on Space charge Be wary in applying the usual rules of thumb Low normalized emittance is achieved by low momentum, not small bunch size: σ x 25 mm σ y 25 mm σ z 673 mm 1.1 MeV/c (β=0.01) Clearly a careful computation including space charge is needed. December 10, 2008 TJRParticle Refrigerator14

An Inexpensive Experiment Using Alphas December 10, 2008 TJRParticle Refrigerator15 Resistor Divider -50 kV Supply +50 kV Supply Shows feasibility and measures transmission, not emittance or cooling Uses two 50 kV supplies to keep costs down. The source must be degraded to ~100 keV. Hopefully the source collimation will avoid the need for a solenoid (as shown). This is just a concept − lots of details need to be 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 same is true of most current cooling-channel designs. December 10, 2008 TJRParticle Refrigerator16

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 Refrigerator17