GLAST Large Area Telescope: UPDATE Status of System-level Performance Simulations

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GLAST LAT Project
17 August, 2001
GLAST Large Area Telescope:
Gamma-ray Large
Area Space
Telescope
Status of System-level Performance
Simulations
UPDATE (to 26 July presentation)
S. Ritz
Goddard
LAT Instrument Scientist
ritz@milkyway.gsfc.nasa.gov
Representing the PDR/Baseline simulation group
For status see:
http://www-glast.slac.stanford.edu/software/PDR/
S. Ritz
0
GLAST LAT Project
17 August, 2001
System-level Performance Simulations
Outline
 Brief review of July 26 presentation, actions
 Work done since July
 background fluxes settled
 large generation runs
 trigger rate studies
 CAL bug fix, ACD segmentation final update
 tools for peeling off events, readback of events
 Status of actions
 The LIST (what’s left to do now that the tools are in place)
Result of much direct work by many people: Toby, Richard, Heather, Sasha,
Ian, Karl, Leon, Tracy, Eduardo, Arache, Regis, …
and based on the foundation provided by many others.
S. Ritz
1
GLAST LAT Project
17 August, 2001
Summary of Requirements
We use the simulation to evaluate the expected performance of the
instrument design:
• Effective Area as a function of energy
• FOV (Effective Area as a function of angle)
• Energy resolution
• PSF (68%, 95%) as a function of energy and angle. Make
parameterization for physics studies.
• Background rejection (and all of the above after background
rejection selections)
• Trigger rates and data volume after L1T and L3T
• Failure mode effects on performance
We use the beam tests and other measurements to verify the
simulation.
S. Ritz
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GLAST LAT Project
17 August, 2001
Work done for proposal
•
We did this work for the proposal:
Source
Chime
% rate
Avg L1T Rate
[Hz]
36
2019
g albedo
4
196
Electron
1
30
Albedo p
59
3224
TOTAL
•
5470
Why do it again for PDR/Baseline?
–
–
–
–
quantitative assessment of performance impact of incremental design changes
better modeling of backgrounds
check results and make improvements. move analysis forward.
side benefits: opportunity to use and improve tools. simulation and reconstruction
have undergone major architectural changes -- lost some functionality but gained
much more solid foundation. this is an opportunity to pull everything back together.
S. Ritz
3
GLAST LAT Project
PDR Simulation Work Requirements
17 August, 2001
(2/2001)
For PDR, we must present the basic performance parameters of the instrument
and show they meet the relevant LAT Performance Specifications.
The following elements must be in place to begin this evaluation process:
•updated, validated, and documented geometry to match the current design, along
with configuration control of the design parameters; review noise and threshold
parameters;
•updated source fluxes, incorporating the improved understanding;
•a documented release of the simulation and reconstruction in the new framework,
including the new event storage format;
•a version of the event display that is compatible with the new simulation,
reconstruction, and event storage format;
•machinery in place to generate the necessary statistics of signal and background
events. We specify a requirement of >10 million background events, with a goal of
100 million background events generated and analyzed. The machinery must
include a simple mechanism to identify each event uniquely, and the capability to
produce from an event list files with a subset of the full event sample;
•an updated version of merit, or an equivalent tool, to run in the new environment.
Ideally, this tool could run both on the stored events and on a new standard tuple.
Depending on the size of the full events, a standard tuple may be a practical
necessity.
•a basic analysis framework to operate on the new event stores.
S. Ritz
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GLAST LAT Project
17 August, 2001
CAL Geometry Update
Support frame
• new carbon cell design
implemented
• detailed description of top
and bottom supporting frames
CsI
cylindrical end supports
• detailed description of cell
closeout and electronics
compartment at the sides of
towers.
• all calorimeter dimensions
are up-to-date.
Work done by Sasha (CAL
group)
S. Ritz
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GLAST LAT Project
17 August, 2001
CAL Geometry Update (II)
41.5 mm
S. Ritz
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GLAST LAT Project
17 August, 2001
ACD and GRID Geometry Updates
•
•
•
•
ACD support structure
consists of an
approximated core
material and two face
sheets.
The gap between the tiles
and the towers reflects the
current design.
Thermal blanket is
modeled as it was for the
AO, using one average
density material.
Back-most side rows now
single-tiles NEW
Work done by Heather (ACD
group) with help from Eduardo
S. Ritz
• GRID flange between TKR and CAL (treated
as a separate volume) is undergoing
modification to reflect the current design.
• Also adding ACD base frame.
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GLAST LAT Project
17 August, 2001
TKR Geometry Update
closeouts
carbon-fiber walls + screws
MCM Boards
tray face, glue
Bias board, glue
New Features:
Dimensions correspond to latest design
Tungsten
Better treatment of top and bottom trays
More accurate composite materials
Silicon
MCM boards included
Better segmentation of tray faces
Bias board, tray face, glue
Work done by Leon (TKR group)
S. Ritz
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GLAST LAT Project
17 August, 2001
Level 1 Trigger
ACD LO
ACD (unused)
TKR
CAL-LO
CAL-HI
• TKR 3-in-a-row
• CAL-LO = any single log with recorded energy > 100 MeV
• CAL-HI = any tower with 3-layers-in-a-row each with >0 logs with
recorded energy > 1 GeV (NEW! see LAT-TD-00245-01, 16 July)
• L1 Trigger word:
___ ___ ___ ___ ___ <- (LSB)
• Will continue to study details of performance of new CAL-HI
proposal in this round of simulations.
• ACD throttle of L1T now included in tuple. NEW
S. Ritz
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GLAST LAT Project
17 August, 2001
Background Fluxes
• Implementation by source, comparisons and
justifications
• Sanity checking – EGRET A-Dome rates
• L1T rates
see
• LAT-TD-00250-01 Mizuno et al
• Note by Allan Tylka 12 May 2000, and presentations by Eric Grove
• AMS Alcaraz et al, Phys Lett B484(2000)p10 and Phys Lett B472(2000)p215
S. Ritz
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GLAST LAT Project
17 August, 2001
New Orbit-max Fluxes
(the new tools are great!!)
total
Integrates to ~10 kHz/m2
S. Ritz
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GLAST LAT Project
17 August, 2001
New Orbit-avg Fluxes
Integrates to ~4.2 kHz/m2
S. Ritz
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GLAST LAT Project
17 August, 2001
Sanity Check
• The measurements of the flux components may
have unsubtracted backgrounds – adding them up
could result in double-counting. Also, fluxes below
100 MeV are mostly blind guesses. Need a unitarity
check – look at EGRET A-dome rates.
• The proposed orbit-max flux amounts to ~10 kHz/m2
• Also sent fluxes to Eric Grove, Ormes and Kamae
for comments, and discussed fluxes with experts at
Goddard.
S. Ritz
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GLAST LAT Project
17 August, 2001
EGRET A-dome Rates (courtesy of Dave Bertsch)
SAA
A-dome has an
area of ~6 m2,
so orbit max
rate (outside
SAA and no
solar flares)
corresponds to
~16 kHz/m2
This
represents a
conservative
upper-limit for
us, since the
A-dome was
sensitive down
to 10’s of keV.
Note peak
rate is at
(24.7,260)
S. Ritz
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GLAST LAT Project
17 August, 2001
Orbit Max Rates – Preliminary!
all
chimemax
albedo_p_max
CR e- max
albedo e+e-
[inc albedo_g]
flux (kHz/m2)
9.9
4.2
2.6
0.043
2.2
L1T (Hz)
13,025
7,383
3,499
84
1,803
L1T frac
1
0.57
0.27
0.01
0.14
L1TV (Hz)
5,597
2890
1,729
38
739
L1TV frac
1
0.52
0.31
0.01
0.13
Notes:
• as we expected, the unthrottled L1T rate is now > 10 kHz
• with the ACD throttle on the TKR trigger, the total max rate is 6 kHz. If
the max A-dome rate is due entirely to particles that trigger us (it isn’t), naïve
scaling results in an orbit-max throttled rate of 9 kHz. Appears we have some
margin.
• we have a ceiling, finally.
S. Ritz
15
GLAST LAT Project
17 August, 2001
Data set generation planning
•
Main challenge is generating backgrounds ~ 50M events (~half-hour equiv.)
– Would take months to generate on a PC
– Use SLAC batch (Linux/Solaris) system, requires 2-3 days
• Linux build of pdrApp now running (7/24/01)
– Disk space (800 GB fileserver) is in place
– DataManager ready to generate and book-keep events
•
Since early June, we have been generating increasingly larger photon
and background data sets:
– iterate to find the bugs and missing pieces (inspect sets of events,
study distributions, effects of cuts, use tools, …)
– complete and exercise the infrastructure
– Generated 5M event data set ~1 week ago. Demonstrated. 50M
NEW
event run gearing up. Using avg flux. [one minor glitch last night]
– Exercised tuple preselections and chaining; subset selectivity
(remaining backgrounds at any stage of filtering); readback/reNEW
analysis/event display of event subsets last week. Need to finish
event history display.
S. Ritz
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GLAST LAT Project
17 August, 2001
Failure Modes Modeling
• Now part of our regular planning (see, e.g., May study on using
ACD as L1T throttle). Loss of functionality will be handled in the
simulation as an “after-burner” analysis on the large data set.
Tools to do this not yet tested. Difficult part is putting
awareness into the reconstruction (as we would if failure really
happens) – results for PDR will be rudimentary.
•ACD: loss of a single tile in three locations (front
corner, front middle, side).
•TKR: impact of loss of a layer on trigger
efficiency.
•TKR+CAL loss of a tower.
•Not possible to explore the infinite
combinatorics. Highest priority prior to PDR is to
do one tile and 1 TKR layer failure: L1T, L3T,
effective area impacts.
S. Ritz
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GLAST LAT Project
17 August, 2001
Actions from 26 July Presentation
• “Please make sure low energy positrons (100-300 MeV) are included in a
worst-case background analysis.” Done, extended below 100 MeV.
• “Please simulate the loss of ½ the light from 18 PMTs on one of the 12
electronics boards.” Withdrawn.
• “Please run the simulation with isotropic electrons of 10 GeV and show that
no more than 3 in 104 are accepted as gammas, along with the resulting
effective area.” On the list.
• “Will the trade study to identify potential ACD extension impact the grid
design, and will it be complete by September? If not, when? It may impact
S/C.” The essential gaps and geometries are now in the new simulation,
along with the potentially problematic fluxes. Already see not a likely
problem for on-board operations. Answer on ultimate ground-based
background rejection analysis will come with the full analysis automatically.
First hand-scan of residual events not worrisome, but new cuts are
necessary and must be carefully evaluated. The analysis is only part of the
issue. The issue should be systematically addressed by the IDT.
• Check that the physics of the simulation code to simulate low energy
proton interactions. On the list. If this is a problem, it will show up in the
analysis of the 50M event run shortly. Tools exist to evaluate.
S. Ritz
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GLAST LAT Project
17 August, 2001
Much Left To Do
• Re-do overall ground-based background rejection selections
validation. Deal with new fluxes. Recalculate Aeff and FOV.
• Specifically evaluate combined effect of ACD gap and low
energy particle fluxes.
• Demonstrate 10 GeV electron rejection.
• PSF evaluation vs. energy, angle, front/back.
• Energy resolution.
• Finish baselining L3 algorithms
Tools now ready.
Help is needed.
Join the fun.
S. Ritz
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GLAST LAT Project
17 August, 2001
Backups
S. Ritz
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GLAST LAT Project
17 August, 2001
L3 Filtering (orbit max case)
Open L1T rate: 13,025 Hz
Throttled L1T rate: 5,968 Hz
S. Ritz
albedo e+e-
electron
albdeo_g
albeo_p
chime
cut at 25 || CAL_Hi
ACD_DOCA
Not checked yet!
caveat: the current version of ROOT
interactive cuts is FLAKY! Beware.
21
GLAST LAT Project
17 August, 2001
L3 Filtering (Orbit Max Case)
DOCA cut, (#tracks>0||CAL>5 GeV
visible): 167 Hz
72 Hz at orbit max => ~30 Hz avg
#xtals
Track-CAL match
note!
>30 Hz even at orbit max due to <100 MeV e+e-.
Is that real? No matter, we can deal with it.
Cal_Fit_errNrm<15.
Not checked yet!
S. Ritz
22
GLAST LAT Project
17 August, 2001
L3 Filtering (Orbit Max Case)
Visible CAL energy
CAL Hi Rate: 40 Hz
“L3” inspection
of CAL_Hi not
implemented yet
Not checked yet!
Fraction of energy in front
3 CAL layers
Require fraction in 1st 3
CAL layers >10% OR
Cal_Energy > 10 GeV: 34
Hz at orbit max.
Just first looks
with new fluxes
and geometry.
Gamma
distributions on
the way.
S. Ritz
23
GLAST LAT Project
17 August, 2001
Results: status
• First peek at PSF looks ~not terrible (much to do!)
total
68%
100 MeV
normal inc.
3.44
1 GeV normal
incidence
0.59
total
95%
1.87
front
68%
front
95%
back
68%
2.3
4.45
5.8
0.47
1.62
0.84
back
95%
results are
pre-pre-prepreliminary!
2.08
Note: normal incidence
PSF is not particularly
relevant for physics –
just a well-defined
comparison point for
performance changes
and code checking.
“Normal” in Table
means 0-8 deg bin.
S. Ritz
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GLAST LAT Project
17 August, 2001
Aside: some definitions
Effective area
(total geometric acceptance) • (conversion probability) • (all detector and
reconstruction efficiencies). Real rate of detecting a signal is (flux) • Aeff
Point Spread Function (PSF)
Angular resolution of instrument, after all detector and reconstruction algorithm
effects. The 2-dimensional 68% containment is the equivalent of ~1.5 (1dimensional error) if purely Gaussian response. The non-Gaussian tail is
characterized by the 95% containment, which would be 1.6 times the 68%
containment for a perfect Gaussian response.
Histogram of Data
5
2000
lower
68%
95%
upper
y
1000
0
0
1
2
3
4
5
0
5
5
0
5
x
S. Ritz
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GLAST LAT Project
17 August, 2001
Experimental Technique
Instrument must measure the direction, energy, and arrival time of high energy
photons (from approximately 20 MeV to greater than 300 GeV):
Energy loss mechanisms:
- photon interactions with matter in GLAST
energy range dominated by pair conversion:
determine photon direction
clear signature for background rejection
- limitations on angular resolution (PSF)
low E: multiple scattering => many thin layers
high E: hit precision & lever arm
g Pair-Conversion Telescope
anticoincidence
shield
conversion foil
particle tracking
detectors
e+
S. Ritz
e–
calorimeter
(energy measurement)
• instrument must detect g-rays with
high efficiency and reject the much
higher flux (x ~104) of background
cosmic-rays, etc.;
• energy resolution requires calorimeter
of sufficient depth to measure buildup
of the EM shower. Segmentation useful.
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GLAST LAT Project
17 August, 2001
Primary Design Impacts of Science Requirements
g
Background rejection requirements
drive the ACD design (and influence
the calorimeter and tracker layouts).
Effective area and PSF
requirements drive the
converter thicknesses and
layout. PSF requirements
also drive the design of the
mechanical support.
Field of view sets the
aspect ratio (height/width)
e+
Energy range and energy
resolution requirements set
thickness of calorimeter
Electronics
On-board transient detection requirements,
and on-board background rejection to meet
telemetry requirements, drive the
electronics, processing, flight software, and
trigger design.
S. Ritz
e–
Time accuracy provided by electronics
and intrinsic resolution of the sensors.
Instrument life has an impact on detector technology
choices.
Derived requirements (source location
determination and point source sensitivity) drive the
overall system performance.
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GLAST LAT Project
17 August, 2001
Design and Simulations
gaps, dead areas included
Zoom in on a corner of
The GLAST baseline instrument design is
based on detailed Monte Carlo simulations. the instrument
scintillators
Two years of work was put into this before any
significant investment was made in
hardware development.
– Cosmic-ray rejection of >105:1 with
80% gamma ray efficiency.
– Solid predictions for effective area
and resolutions (computer models
now verified by beam tests). Current
reconstruction algorithms are
existence proofs -- many further
improvements are possible.
– Practical scheme for triggering.
– Design optimization.
front scintillators
module walls
First TKR module plane
The instrument naturally distinguishes
most cosmics from gammas, but the
details are essential. A full analysis is
important.
gamma ray
proton
Simulations and analyses are all OO (C++),
based on GISMO toolkit.
S. Ritz
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GLAST LAT Project
17 August, 2001
Simulations validated in detailed beam tests
Experimental setup in ESA for
tagged photons:
X Projected Angle
3-cm spacing, 4% foils, 100-200 MeV
Data
Containment Space Angle (deg)
Monte
Carlo
GLAST Data
68% Containment
95% Containment
10
(errors are 2)
1
Monte
Carlo
0.1
101
S. Ritz
102
103
Energy (MeV)
104
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GLAST LAT Project
17 August, 2001
Instrument Triggering and Onboard Data Flow
Level 1 Trigger
Hardware trigger based on special signals
from each tower; initiates readout
Function: • “did anything happen?”
• keep as simple as possible
x
x
x
Level 3
Processing
Level 2 Processing
• TKR 3 x•y pair
planes in a row**
workhorse g trigger
OR
• CAL:
LO – independent
check on TKR trigger.
HI – indicates high
energy event
ground
Upon a L1T, all towers are read out within 20ms
Instrument Total L1T Rate: <5 kHz>
rates are orbit averaged; peak L1T rate is
approximately 10 kHz. L1T rate estimate being revised.
**ACD may be used to throttle this rate, if req.
S. Ritz
Function: • reject background
efficiently & quickly with
loose cuts,
• reduce computing load
• remove any noise triggers
L3T: full instrument
Function: reduce data
to fit within downlink
• complete event
reconstruction
• tracker hits ~line up
x
x
x
• signal/bkgd tunable,
depending on analysis
cuts:
g:cosmic-rays ~ 1:~few
• track does not point to
hit ACD tile
L2 was motivated by earlier DAQ
design that had one processor per
tower. On-board filtering
hierarchy being redesigned.
Total L3T Rate: <30 Hz>
(average event
size: ~7 kbits)
On-board science analysis:
transient detection (AGN
flares, bursts)
Spacecraft
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GLAST LAT Project
17 August, 2001
LAT Instrument Basics
• 4x4 array of identical towers
Advantages of modular design.
• Precision Si-strip Tracker (TKR)
Detectors and converters arranged in 18
XY tracking planes. Measure the
photon direction.
• Hodoscopic CsI Calorimeter(CAL)
Segmented array of CsI(Tl) crystals.
Measure the photon energy.
• Segmented Anticoincidence Detector
(ACD First step in reducing the large
background of charged cosmic rays.
Segmentation removes self-veto effects
at high energy.
• Central Electronics System Includes
flexible, highly-efficient, multi-level
trigger.
Systems work together to identify and measure the flux of cosmic gamma
rays with energy 20 MeV - >300 GeV.
S. Ritz
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GLAST LAT Project
17 August, 2001
Background Rejection Overview
• First developer of background rejection analysis: Bill Atwood (lots of work
also by Jay, Toby, Heather, Cathie, Sawyer, Jose, Paul, Taro, SR, …
•Analysis done thus far for two main reasons:
(1) A reasonable way to quote our effective area.
(2) A proof of principle and a demonstration of the power of the instrument
design.
• Not the final background analysis! Other techniques are available to reduce the
backgrounds further with good efficiency (particularly using TKR pattern
recognition). The analysis for the AO response was done in triage mode, and
there is much to do now.
• Some science topics may require less stringent background rejection than
others. Issues of duration, visible energy range, etc.
Same points also hold for the event reconstruction we
have thus far.
S. Ritz
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GLAST LAT Project
17 August, 2001
Background Analysis
Ideally (and usually) cut variable distributions are examined several ways, first to check
the distribution is sensible and then for implementing the selections:
1) raw (after triggers, depending on tuple)
2) cumulative - the distribution of the next cut variable after all previous cuts. Note, this
order is arbitrary (mostly) and the distributions can be misleading, so….
3) “all but”: look at each variable distribution with every cut but this one applied.
4) niche areas: check for effects of each cut in different energy ranges and different angles
of incidence. (usually done with merit first)
5) interplay with track quality cuts: the effects of the track quality cuts and the
background rejection cuts are not orthogonal: track quality cuts usually help in background
rejection somewhat, and background cuts sometimes help clean up PSF. In one case, an
“all but” background distribution was empty! Optimize these together.
6) n-dimensionally (usually 2 at a time) : look for correlations and domains of wellclustered S/B for like variables.
Note that a neural net very well addresses (3), (5) and (6). These cuts
are not orthogonal, and there is a better space in which to make them.
S. Ritz
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GLAST LAT Project
17 August, 2001
Background Analysis (cont)
•
try to keep the cuts away from steep areas, or right next to
individual events (avoid fine-tuning).
• process is iterative:
With each variable, look at distributions for gammas and
background and choose a preliminary cut value.
Scan remaining background events and lost gamma events for
adjusting cut and to determine potentially new cut variables.
Check for cut redundancy and correlation. Check impact on
instrument performance. Merit is particularly useful here.
As a practical matter, some days are spent mostly improving the
rejection and other days are spent mostly improving the gamma
efficiency.
S. Ritz
34
GLAST LAT Project
17 August, 2001
AO Overview: Visible (CAL) Energy Distributions at Various Stages
Important: at
the time of the
large data set
generation for
the AO, the
albedo proton
flux was not
implemented.
It was
implemented
for the rate
studies, but the
energy
spectrum was
wrong. We
thought this
was pessimistic.
(38, actually, but who’s
counting?)
Although the cosmic ray
spectrum peaks around 4-20
GeV, the deposited energy is
typically much lower.
The region below 1 GeV is
the most difficult for
background rejection for
several reasons.
Note, after all selections, no background events remain with
visible energy greater than 200 MeV. This wasn’t easy.
S. Ritz
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GLAST LAT Project
17 August, 2001
Some references (beyond meeting presentations):
1) DoE proposal (1998)
2) Note of 9 August 1999 (describes cuts and problem areas
fairly well, needs distributions included)
3) AO response
however, better documentation is needed and will be done in this round
of studies.
STEPS
(note: description uses AO tuple variable names)
• The famous VETO_DOCA (only for CsI_Energy_Sum<20) - getting better,
but still somewhat broca. Needs improvement.
• “Hit pattern” - Surplus_Hit_Ratio, with an energy-dependent application.
Surplus_Hit_Ratio>2.25 || (CsI_Energy_Sum>1&&fst_X_Lyr>13) || CsI_Energy_Sum>5.
S. Ritz
36
GLAST LAT Project
17 August, 2001
Background Analysis Steps (II)
STEPS (continued)
• “CAL info” - CsI_Fit_errNrm, CsI_Xtal_Ratio -- keep events w/no
CAL info whenever possible.
CsI_Xtal_Ratio>0.25||CsI_No_Xtals<1
(CsI_Energy_Sum<1.&&CsI_Fit_errNrm<10.)||CsI_Fit_errNrm<4.||CsI_No_Xtals<1
• “Track quality” (most recent selections developed by Jose)
• “S/C induced event cuts” - designed to remove cosmics whose primary
interaction is in the S/C. This is our single largest residual background!
No_Vetos_Hit<1.5 || (CsI_Energy_Sum>1. && No_Vetos_Hit<2.5) || CsI_Energy_Sum>50.
CsI_eLayer8/CsI_Energy_Sum<0.08 || CsI_eLayer1/CsI_Energy_Sum>0.25 ||
CsI_Energy_Sum>0.35||CsI_No_Xtals<1
CsI_moment1<15. || CsI_moment1<80.&&CsI_Energy_Sum>0.35||CsI_Energy_Sum>1.||
CsI_No_Xtals<1
Surprisingly
efficient
even at high energy
CsI_Z>-30.||CsI_No_Xtals<1
Only needed in BACK
CsI_No_Xtals_Trunc<20.||CsI_Energy_Sum>75.||fst_X_Lyr<12
Quality_Parm>10 (composite track quality parameter, cut effective against low-energy stubs
from splash-up)
S. Ritz
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GLAST LAT Project
17 August, 2001
Background Analysis To Do
Next steps:
•Use better background flux model. Low energy p and e albedo must be dealt with.
Demonstrate high-energy electron rejection.
•Improve low energy Aeff, work on inefficiencies (Surplus_Hit_Ratio,
CsI_Fit_errNrm)
• VETO_DOCA: needs work. Mainly a tracking issue. Seed tracks with hit tiles,
track quality selections for loop.
• Document, put correct implementation into merit.
• Simplify analysis (make prettier, simpler). Bring in neural net. More sophisticated
tracking (downward “ ”) & CAL pattern recognition. (post-PDR)
V
•Further improvements in rejection (at time of AO, integrated residual background
rate was ~ 6% of extragalactic diffuse rate). Also, study background rate
differentially (by visible energy bin). More work on upward-going energy events.
• Evaluate impact of limited set of instrument failure modes (see end of talk)
S. Ritz
38
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