The g-2 Experimental Essentials
David Hertzog
University of Illinois  University of Washington
•
•
•
•
Beam / Ring
Magnetic Field
Detectors / Electronics / DAQ
A word on Systematics
e
Momentum
Spin
Hertzog / Experiment
DOE Intensity Frontier Review
The key ingredients to measure am to high precision
(1) Polarized muons
~97% polarized for forward decays
n
µ
(2) Precession proportional to (g-2)
 g  2  eB
a  spin  cyclotron  

2

 mc
(3) Pm magic momentum = 3.094 GeV/c
E field doesn’t affect muon spin when g = 29.3
e   
1   


  E 
a 
a m B   a m  2
mc 
g  1 


(4) Parity violation in the decay gives
average spin direction
m +  e + n e nm
p+
m+
The 900-m long decay beam: reduced flash; more store m/p
See also, M. Syphers
Flash compared to BNL
Parameter
FNAL/BNL
p / fill
0.25
p/p
0.4
p survive to ring
0.01
p at magic P
50
Net
0.05
Stored muons / POT
Parameter
BNL
FNAL
Gain FNAL/BNL
Benefits of a longer beamline




Reduced pion fraction that survive to ring
Permits “forward” decays (BNL was “off forward”)
Collects “all” forward muons
Eliminates “lost muon” systematic from muons born
at the end of the channel having a different phase
The anomaly is obtained from three wellmeasured quantities
a
p
T IME
The Storage Ring exists. It will be moved to FNAL
Talk by C. Polly
The Storage Ring components affect muon storage
Fast Kickers
Superconducting
inflector magnet
Electrostatic
Quadrupoles
e+ at 1 Detector
Muons enter the ring in short bunch and spread out in
predictable manner yielding key storage parameters:
6
“Early”
“Later”
g-2
g-2
9
12 ms
36
39
Distribution of equilibrium radii
42 ms
The present inflector magnet has closed ends which
scatter away ~half the incoming muon beam
As-used
Closed-ended
m
Prototype
Open-ended
Length = 1.7 m; Central field = 1.45 T
Open end prototype, built and tested
 x2 increase in stored muons
Improvements in the kicker are planned because
present one underkicks and pulse lasts too long.
149 ns cyclotron period
Kicker
waveform
This kick affects the storage efficiency
IDEAL kick  8%
REAL kick  <3 % ??
Stored Muons [arb scale]
300
Stored muons vs. kicker fraction
Room to
improve
250
200
150
80
85
90
95
100
105
[%]
KickerKick
Amplitude
110
We have developed a new simulation tool to guide our
improvements. It includes all major subsystems

Vacuum vessel

Inflector

Kickers

Quadrupoles

Collimators
Example: Collective beam motion for stored
muons is reproduced
The predicted horizontal and vertical betatron
oscillation frequencies match measured values
from E821 at the percent level.
We can simulate modified kicker pulse shapes
to predict storage improvements
% stored
10
Ideal Square Kick
8
6
4
2
Real LCR Kick
0
The p
(field)
Measurement
The ± 1 ppm uniformity in the average field is obtained
with special shimming tools.
The
dipole,
quadrupole
sextupole
are shimmed
independently
6 – 9 months required with cryogenics and ring on / off and in stable operating mode
Improvement of Field by Shimming
2000
1999
2001
shimming
shimming
At this level, one
hardly needs to know
the muon distribution
The magnetic field is measured and controlled using pulsed
NMR and the free-induction decay
Absolute Calibration Probe:
a Spherical Water Sample
Fixed Probes in the
walls of the vacuum tank
Trolley with matrix of 17 NMR Probes
Electronics,
Computer &
Communication
Position of
NMR Probes
The a
(precession)
and
EDM
Measurements
An “event” is an isolated positron above a threshold.
e+
NA2
N
A
<A>=0.4
digitized samples
An “event” is an isolated positron above a threshold.
e+
digitized samples
Traditional method of determining a is to plot
Number of events above threshold vs. Time
Geant
Event Method
NA2
N
Here, Asym is the average
asymmetry of events above
energy threshold cut
A
<A>=0.4
A complementary (integrating) method of determining
a is to plot Energy vs. Time
Geant
Event Method
Same this
GEANT
simulation
We will operate
mode
in parallel to above
Energy
Method
Parasitic Muon EDM Measurement using straw tube arrays
The EDM tips the precession plane,
producing an up-down oscillation
with time (out of phase with a)
Technique: Measure
up-going/
down-going
tracks vs. time, (modulo g-2):
BNL statistics limited




1 tracking station
Late turn-on time
Small acceptance
Ran 2 out of 3 years
FNAL: many stations, long runs,
expect ~10,000 x the events
See: B. Casey in “extra” materials
Detector systems



Calos: time and energy of decays
Hodoscopes: beam profiles, calo
seeds, muon loss monitor
In-vacuum Straws: stored muon profile
& independent EDM measurement
X
hodoscope
E821
e+
Hodoscope
New W/SciFi calorimeter development aimed at transverse
segmentation, high density and fast response
• Original prototype encouraging, results in
NIM
• New 25-channel array built and tested in
beam
• Magnetically immune SiPMs* used on 1
channel
– Excellent performance, comparable to PMTs
*a.k.a, Silicon Photomultipliers, “Geiger mode APDs, Multi-Pixel Photon Counter, …
W/SciFi Calorimeter Development
15 cm
Chris
Mandy
6 x 6 mm2 SiPM array
used on 1 channel
17 X0
12 cm
Brendan
MTest with many young physicists and students
Hertzog / Experiment
DOE Intensity Frontier Review
Early analysis shows promising
performance of large array
S of elements
1 RM = 1.7 cm
Hertzog / Experiment
s/E @ 2 GeV
8.5%
DOE Intensity Frontier Review
SiPM readout using Paul Rubinov’s
custom digitizer board prototypes
time
time
Simple, single pulse
Example with pileup
2 GeV
Pulse area
Energy resolution same as with PMTs
Hertzog / Experiment
DOE Intensity Frontier Review
Systematic error projections are in-line with statistical goal
For more details, Lee has
a few slides
Improvement vs time 
To here, requires “no”
improvements. To 0.07
requires some R&D
More details in
slides posted at the
end of this talk
Conclusions: The experimental method is mature
• New challenges:
–
–
–
–
Increased rate and total data volume
Systematic error demands on “stability”
The “ring” must be put back together
It must be shimmed to even higher uniformity
• R&D efforts
–
–
–
–
–
–
Calorimeters
SiPMs
NMR Probe placement
Kicker waveform
Inflector opening
In-vacuum straws
• Simulations efforts
– End-to-end beam transport
– Ring dynamics
– Calorimeter optimization
• Many young people are enjoying these development
opportunities and, like us, look forward to the experiment
Backup materials
Digitizers and DAQ: Basic Plan
• 500 MHz, 8 – 12 bit, continuous digitization on all
calorimeter channels
– For SiPMs, includes onboard voltage control
• 24 frontend computers each service one of the
detector stations
– High-level language control of event acceptance and formatting
• Built-in pileup control and diagnostic histograms
• We have considerable experience with these data
rates and volumes for similar precision experiments
(g-2, MuLan, MuCap, …)
Hertzog / Experiment
DOE Intensity Frontier Review
Error due to gain shifts in the calorimeters
• Systematic error on a previously ~ 0.13 ppm., goal
<0.03 ppm
– Gain was controlled to ~0.25%; shifts partially caused by ‘flash’
and / or PMT gating (or rate changes)
– Laser calibration system was not sufficiently pulse height stable,
so electron data early-to-late were used.
– If gain does not oscillate at g-2 frequency, it does not correlate
very much to a
– Presence of CBO leads to larger correlation to gain shift
• Solutions:
–
–
–
–
Reduce CBO
Lower average rates
Reduce flash
Better laser monitoring system (already demonstrated in MuLan
experiment at PSI)
Coherent betatron oscillations (CBO)
• Focusing and defocusing of stored muon beam can lead to a
systematic error in a.
n x  fc 1  n ,n y  fc n , n  0.135
– The horizontal aperture of the inflector is narrow, so the beam is focused in the
horizontal direction at the time of injection. The full-aperture ‘kick’ is not fully
efficient, so the average radius is off-center. As a result, the average radial
position of the beam, at a fixed location in the ring, oscillates:
fCBO  fc (1 c 1  n ) 2 f a
– The acceptance of electrons depends on radius, therefore an oscillation with
frequency near fCBO appears in the electron time spectrum. This leads to an error
when the spectrum is fit; the closer to 2fa, the larger the error.
• Potential improvements:
– Improve the efficiency of the full-aperture kick, so that beam does not
‘wobble
– RF to reduce CBO amplitude
– Add higher multipoles to wash out the CBO more rapidly
– Adjust the quadrupole E-field to keep fCBO as far away from 2fa as possible.
3 categories of pileup systematics
• Uncertainty in pileup fraction,
– ~ 8% for E821, 0.038 ppm error on a.
– Decreases with more statistics available to construct the pileup spectrum
• Uncertainty in the constructed pileup phase:
– 0.036 ppm
– Decreases with increased statistics
• ‘Unseen’ pileup: (from pulses too small to be seen)
– ~0.026 ppm
– Reduce backgrounds and use lower thresholds for pileup spectrum
reconstruction
• In general:
– A more highly segmented detector will reduce errors by about a factor of
2 – 3 , and with the same rate/burst we get a similar reduction in pileup.
– Increased number of beam pulses minimizes the instantaneous rate
– New digitizers will operate with lower threshold and longer sampling, which
greatly improves correction algorithm
What drives the detector choice?



Compact based on fixed space
Non-magnetic to avoid field
perturbations
Resolution is not critical for da
Useful for pileup & gain monitoring
 E821 “8%”; We propose 10% for
tungsten-based calorimeter


Pileup depends on signal speed and
shower separation
4/5 events separated was goal
 GEANT sim work in good shape

Many more details and studies
available. See also,
How was event rate obtained?
Proton complex
parameters and plans
Compared to achieved BNL stored
muon per proton rate and detailed
factors for beamline differences
Monte Carlo and
simple calculations
This is the key factor. We have calculated 11.5 so far, so we have
included a “100% contingency” in estimating the beam time request to
allow for something to go wrong.
MARS15 model of target, beamline simulation to capture / decay pions
Electrons from g-2 ring strike calo at
energy-dependent angle.
T/he energy vs. average striking angle
Positron entrance angle depends on energy: low-E showers
are “wider”
TOP DOWN VIEW
High
E
Low
m central radius
vacuum
E
Precision field improvements:
The New Muon (g-2) Collaboration, DOE – HEP – 5 February 2010
Calibration of the trolley probes:
0.09 → 0.06
• Issues:
– position of the probes inside the trolley
– uniformity of the field at the place where the
trolley probes are calibrated
– position of the plunging probe that transfers
the calibration
• Solutions
– better shimming of the field in the calibration
point.
– an indexing scheme needs to be developed
that will permit us to know more accurately
where the active part of the probes are inside
Interpolation with the fixed probes: 0.07 → 0.05
• Only 150 of the 370 fixed probes gave useful signals
because they were near pole boundaries
pole piece
pole piece
fixed probe
beam
vacuum chamber
• Need to move probes, or shim at pole boundaries, so
that we have more points constantly monitoring the field.
The New Muon (g-2) Collaboration, DOE – HEP – 5 February 2010