Muon Coalescing 101
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Transcript of Muon Coalescing 101
Muon Coalescing 101
Chuck Ankenbrandt
Chandra Bhat
Milorad Popovic
Fermilab
NFMCC Meeting @ IIT March 14, 2006
Context for this talk • Suppose that some day:• A proton driver based on an 8-GeV linac exists;• High-int. muon beams are available with low emittances in all three planes;• The proton driver linac can be used to accelerate both protons and muons.
• Achieving low emittances requires parametric resonance ionization cooling. However, Slava Derbenev has found that PIC doesn’t work well for very intense bunches because of space-charge tune shifts. That led Rolland Johnson and Slava to develop scenarios that produce a large number of less intense bunches.
• In one specific scenario, each of ten equally spaced proton bunches produces a train of sixteen equally spaced muon bunches. That works as is for a neutrino factory; however, to achieve high luminosity in a collider, it is highly desirable to combine the bunches.
• That in turn led them to ask the question addressed in this talk: How can muon bunches be combined to enhance the luminosity of a muon collider?
General combining considerations
• Combining ought to be done after accelerating to high energy, where space charge is not a problem and adiabatic damping of beam sizes provides room to operate. At high energy, momentum-dependent path lengths work better than velocity differences for combining bunches.
• There are two bunch-combining techniques presently used operationally for protons at Fermilab: slip-stacking and coalescing. The specific implementations used for protons are much too slow for muons. The approach described here is a fast form of coalescing. Fast coalescing ignores slow niceties, so reducing the dilution of longitudinal emittance is a major consideration.
First-Order Ring Physics1. Muon Decays in Rings
cLdk eBp eBfRp
eBf
pRC
22
)(2972
TeslaBfmc
Bfce
C
Ln dkdk
Decay length
So the number of turns to decay is given by
mcp where f is the fill factor
First-Order Ring Physics2. Space Charge
22
3
B
Nr
n
o
for Gaussian bunch
p
Numbers: Compare p /
9/
m
mrr popo
40/ nnp
20
1/ pNN
3/
p
p BB CB
2
80
1)()/()( 222
pp m
m
at the same energy
First-Order Ring Physics3. Slippage
p
p
f
f
where
and it’s easier to use
p
eBfL
p
p
R
Ln ttc
22
20
20
22
11
t
012
Here,
p
p
R
R
t
2
1
p
pRRC
t
2
22
Nc, number of turns to coalesce=R
L
20
p
Lm
n
n t
dk
c
20
eBp
eBRfp
Where Lo=half-length of bunch train
Assuming momentumspread is constant
Schematic of the LINAC and Coalescing Ring
Coalescing Ring
20 GeV Muon
LINAC
Bunch train
with 1.3GHz structure
Bunch LE~ 0.03 eVs
dE~ 20 MeV
vernier LINAC
Muon Coalescing RingThe following parameters are assumed for the Coalescing Ring:
Injection beam : 1.3GHz bunch structure # of bunches/train = 17 Ring Radius = 52.33m; Revolution period= 1.09s Energy of the muon = 20 GeV (gamma = 189.4) gamma_t of the ring = 4
If we assume Ring-Radius/rho (i.e., fill factor) = 2, then B-Field = 2.54T (This field seems to be reasonable) h for the coalescing cavity = 42, 84 Number of trains/injection = less than 37 (assuming ~100ns for injection/extraction) RF voltage for the coalescing cavity = 1.9 MV (h=42) = 0.38 MV (h=84) fsy ~ 5.75E3Hz Tsy/4 = 43.5us Number of turns in the ring ~40
Constraints:Muon mean-life = 2.2us (rest frame)Muon mean-life in lab = 418us for 20 GeV beamTime (90% survival) = 43.8us
Radius=52.3m
Injection extraction
Initial Simulation Results
• Three scenarios in a 20 GeV ring for up to 37 groups of 17 bunches of 1.3GHz
• Scenario1: rf cavities in the ring takes 54 s
• Scenario2: vernier linac takes about 46-54 s
• Scenario3: vernier linac and rf cavities in the ring takes about 38 s
1st ScenarioMuon Bunch train from the LINAC
Muon Bunch train in the coalescing bucketT=0 sec
dE~ 20 MeV
Muon Bunch train in the coalescing bucketT= 31.6 sec
Muon Bunch train in the coalescing bucketT= 54 sec
dE~ 200 MeVBunch Length~ 1.5ns
2nd Scenario• A vernier-linac to give a tilt in the
Longitudinal Phase-space
Muon Bunches after pre-linac
•And next inject the beam into the Coalescing Ring
Bunch train before the special
purpose pre-linac
Muon Bunch train in the Coalescing RingT=0 sec
Muon Bunch train in the Coalescing RingT=46 sec
dE~ 100 MeVBunch Length~ 4ns
Muon Bunch train in the Coalescing RingT=71 sec
dE~ 60 MeVBunch Length~ 3ns
Muon Bunch train in the Coalescing RingT=0 sec
3rd Scenario
Muon Bunch train in the Coalescing RingT=38 sec
dE~ 200 MeVBunch Length~ 1.5ns
Summary and conclusions
• Fast coalescing requires:• Short muon bunch trains (less than half the
distance between proton bunches)• A large momentum ‘ramp’ across each train• Small transition gamma (weak focusing lattices?)• Large radial acceptance in the ring• The energy ramp can be generated with a vernier linac
and/or with rf cavities in the ring.• Coalescing leads to multiple constraints (on ring
circumferences, bunch spacings, rf frequencies, etc.)• Longitudinal emittance dilution is a concern.• Of course, global optimization is required.
Mindset and motivation• We are much more likely to get a proton driver if it can be designed
and sited in such a way that it provides a versatile multistage upgrade path to transform existing facilities into sources of megawatt-class proton beams (as well as being an ILC testbed).
• We are much more likely to get a proton driver, a stopping muon program, a neutrino factory, and a muon collider if we can maintain synergy among all of them. In particular, the path to a neutrino factory should not diverge from the path to a muon collider.
• Even though a neutrino factory might be implemented with only modest muon cooling, early achievement of extreme muon cooling would have several important advantages:
• Muons could be accelerated in the proton driver linac;• The rest of the neutrino factory (except cooling) would be
easier to implement;• The path from the neutrino factory to the muon collider
would be much easier.