Transcript Coalescing Ring

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 Physics
1. Muon Decays in Rings
Decay length
p  m c
Ldk   c
2 p
C  2 R 
eBf
p  eB
p  eBfR
where f is the fill factor
So the number of turns to decay is given by
Ldk ce Bf
ndk 

 297Bf (Tesla)
C
2 m c
First-Order Ring Physics
2. Space Charge
 
Numbers: Compare
3 ro
N
2  n B 2
  /  p at the same energy
ro / rop 
mp
m
9
 np /  n  40
N / N p 
1
20
p
Bp / B 
3

( ) p /( )   (
2
2
m
mp
)2 
1
80
    p
B  2

C
for Gaussian bunch
First-Order Ring Physics
3. Slippage
f
p

f
p
Here,
1

2
0
where
and it’s easier to use
2R p
C  2R  2
t p
Nc, number of turns to coalesce=
L0  t2 p L 0  t2eBf
nc 

2 R p
2p
nc m L0 t2

ndk   p
L0
2R

1
2

1
t2
R 1 p
 2
R t p
Where Lo=half-length
of bunch train
Assuming momentum
spread is constant
p  eB
p  eBRf
Schematic of the LINAC and
Coalescing Ring
Coalescing Ring
vernier LINAC
LINAC
Muon Coalescing Ring
The following parameters are assumed for the Coalescing Ring:
Injection
extraction
Injection beam : 1.3GHz bunch structure
# of bunches/train = 17
Ring Radius = 52.33m; Revolution period= 1.09s
Energy of the muon = 20 GeV (gamma = 189.4)
gamma_t of the ring = 4
Radius=52.3m
Constraints:
Muon mean-life = 2.2us (rest frame)
Muon mean-life in lab = 418us
for 20 GeV beam
Time (90% survival) = 43.8us
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
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 4654 s
• Scenario3: vernier linac and rf cavities in
the ring  takes about 38 s
1st Scenario
Muon Bunch train from the LINAC
Muon Bunch train in the coalescing bucket
T=0 sec
dE~ 20 MeV
Muon Bunch train in the coalescing bucket
T= 31.6 sec
Muon Bunch train in the coalescing bucket
T= 54 sec
dE~ 200 MeV
Bunch Length~ 1.5ns
2nd Scenario
• A vernier-linac to give a tilt in the
Longitudinal Phase-space
Bunch train before
the special
purpose pre-linac
Muon Bunches
after pre-linac
•And next inject the beam into the Coalescing Ring
Muon Bunch train in the Coalescing Ring
T=0 sec
Muon Bunch train in the Coalescing Ring
T=46 sec
dE~ 100 MeV
Bunch Length~ 4ns
Muon Bunch train in the Coalescing Ring
T=71 sec
dE~ 60 MeV
Bunch Length~ 3ns
3rd Scenario
Muon Bunch train in the Coalescing Ring
T=0 sec
Muon Bunch train in the Coalescing Ring
T=38 sec
dE~ 200 MeV
Bunch 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.