Energy Distribution ofEnergy Distribution ofCosmic Ray MuonsCosmic Ray Muons

Paul HinrichsPaul HinrichsWith David LeeWith David Lee

Advised by Phil DuderoAdvised by Phil Dudero

The ExperimentThe Experiment

Cosmic rays are particles impingent on Cosmic rays are particles impingent on Earth from outer spaceEarth from outer space– Appear at Earth’s surface mainly as muonsAppear at Earth’s surface mainly as muons

Goal of the experiment: measure the Goal of the experiment: measure the energy distribution of cosmic ray muons at energy distribution of cosmic ray muons at Earth’s surfaceEarth’s surface

References describe the muon energy References describe the muon energy spectrum as “almost flat below 1 GeV”spectrum as “almost flat below 1 GeV”

The ExperimentThe Experiment

Three scintillation Three scintillation detectors: photomultiplier detectors: photomultiplier tube with plastic paddletube with plastic paddleAbsorber material slows Absorber material slows or stops incoming muons; or stops incoming muons; here, lead (here, lead (=11.4 g/cm³)=11.4 g/cm³)Electronics to process Electronics to process and read out PMT signaland read out PMT signalMeasure energy by Measure energy by varying the absorber varying the absorber thickness and examining thickness and examining the ratio of count ratesthe ratio of count rates

PMT A

PMT B

PMT C

Discriminator

Coincidence Logic UnitC

ou

nte

rs (

6)

NIM-TTL Adapter

PCI Timer/Counter

Computer

The ApparatusThe Apparatus

The ApparatusThe Apparatus

The DiscriminatorThe Discriminator

PMT outputs a raw negative pulse, about PMT outputs a raw negative pulse, about 100mV high and lasting about 10ns100mV high and lasting about 10ns

Discriminator cleans this raw signal up: Discriminator cleans this raw signal up: whenever the PMT output goes below a whenever the PMT output goes below a threshold voltagethreshold voltage, the discriminator , the discriminator outputs a NIM logic pulse of fixed lengthoutputs a NIM logic pulse of fixed length

Set threshold voltage to change sensitivitySet threshold voltage to change sensitivity

The DiscriminatorThe Discriminator

Coincidence UnitCoincidence Unit

Four-way coincidence Four-way coincidence unit: 4 selectable unit: 4 selectable input channelsinput channelsButtons on the front Buttons on the front allow independent allow independent selection of each selection of each channelchannelThe coincidence unit The coincidence unit pulses if all selected pulses if all selected channels pulse channels pulse simultaneouslysimultaneously

Other LogicOther Logic

Counters display number of counts since Counters display number of counts since they were last resetthey were last reset

NIM-TTL adapter converts NIM pulses NIM-TTL adapter converts NIM pulses (negative true, about -1V) to standard TTL (negative true, about -1V) to standard TTL logic (positive true, +5V)logic (positive true, +5V)

Adapter is needed to interface with Adapter is needed to interface with computer, which only accepts TTL signalscomputer, which only accepts TTL signals

Computer Data CollectionComputer Data Collection

The computer collects data with a NI 6602 The computer collects data with a NI 6602 PCI counter and timer cardPCI counter and timer card– 3 input channels3 input channels

The counting program, written by Kurt The counting program, written by Kurt Wick and modified by us, counts for Wick and modified by us, counts for N N periods of length periods of length TTAllows us to record and later analyze data Allows us to record and later analyze data over time: we have counts for each minute over time: we have counts for each minute of data collection, not just totalsof data collection, not just totals

CalibrationCalibration

PMTs first require calibrationPMTs first require calibrationMore than one variable:More than one variable:– PMT drive voltage determines sensitivity, PMT drive voltage determines sensitivity,

pulse height, noisepulse height, noise– Discriminator threshold can cut out some Discriminator threshold can cut out some

noise, though not allnoise, though not all

Usually, discriminator threshold is set low, Usually, discriminator threshold is set low, and the coincidence unit discards and the coincidence unit discards uninteresting eventsuninteresting events

Calibration ProcedureCalibration Procedure

Align all three paddles directly on top of Align all three paddles directly on top of each othereach otherSet the coincidence unit to output Set the coincidence unit to output coincidences on:coincidences on:– AC, the top and bottom panelsAC, the top and bottom panels– ABC, all three panelsABC, all three panels

Adjust the supply voltage and threshold Adjust the supply voltage and threshold voltage for B until the ratio ABC:AC is ~1voltage for B until the ratio ABC:AC is ~1Permute A, B, C and repeat for A and CPermute A, B, C and repeat for A and C

Muon AbsorptionMuon Absorption

Need to know what particle energies are Need to know what particle energies are stopped by a given amount of leadstopped by a given amount of lead

In this energy range, almost all energy In this energy range, almost all energy loss is due to ionizationloss is due to ionization

Use the Bethe-Bloch equation to predict Use the Bethe-Bloch equation to predict energy loss of incoming muons, as a energy loss of incoming muons, as a function of their current energy:function of their current energy:

Z

EC

cM

QE

I

Qcm

A

ZK

dx

dE e )(

2

)(2ln

1422

2max2

2max

222

21

2

Muon AbsorptionMuon Absorption

Use MATLAB to evaluate and plot Use MATLAB to evaluate and plot –dE/dx–dE/dx::Muon Energy Loss in Lead

0

5

10

15

20

25

30

35

40

45

50

0 200 400 600 800 1000 1200 1400 1600 1800 2000

E (MeV)

-dE

/dx

(x i

n c

m)

Muon AbsorptionMuon Absorption

Knowing Knowing –dE/dx–dE/dx, we can calculate the range , we can calculate the range R R of a muon with energy of a muon with energy E’E’::

Choosing Choosing EEcutcut sufficiently small (0.15 MeV here) sufficiently small (0.15 MeV here) means we can neglect it, and consider only the means we can neglect it, and consider only the integral contributionintegral contributionIntegrate numerically with MATLAB to find the Integrate numerically with MATLAB to find the range of a muon with given energyrange of a muon with given energy

Can also solve numerically for Can also solve numerically for EEminmin given given RRmaxmax

E

EdE

dE

dxERR

cut

)( cut

Muon AbsorptionMuon Absorption

Muon Range in Lead

0

20

40

60

80

100

120

140

160

180

0 200 400 600 800 1000 1200 1400 1600 1800 2000

E (MeV)

Max

imu

m R

ang

e (c

m)

Experimental ErrorsExperimental Errors

Error in numerical computations is Error in numerical computations is negligiblenegligible

Bethe-Bloch equation, using the continuous Bethe-Bloch equation, using the continuous stopping approximation, is only about 1–2% stopping approximation, is only about 1–2% accurate in predicting muon rangeaccurate in predicting muon range

Path length differences are only 0.1–0.2%, Path length differences are only 0.1–0.2%, given the dimensions of our apparatusgiven the dimensions of our apparatus

Statistical error, proportional to Statistical error, proportional to NN

Practical ConsiderationsPractical Considerations

Maximum range:Maximum range:– About 130 cm available for leadAbout 130 cm available for lead– Theoretical maximum absorption ~1.7 GeVTheoretical maximum absorption ~1.7 GeV

Point GranularityPoint Granularity– Each lead brick is 5 cm thickEach lead brick is 5 cm thick

StatisticsStatistics– Low count rate: about 300 triple coincidences Low count rate: about 300 triple coincidences

in 24 hours with in 24 hours with no no bricksbricks

Preliminary ResultsPreliminary Results

Data from a typical run:Data from a typical run:Counts over 24 hours, 24 Layers of Bricks (120 cm Pb)

0

1

2

3

4

5

6

7

8

9

0 120 240 360 480 600 720 840 960 1080 1200 1320 1440

Minute, from 11:50AM, April 12 to 11:50AM, April 13

Ch

ann

el C

ou

nts

AB AC ABC

Totals:

A – 1275

B – 232

C – 110

Per Minute:

A – 0.885

B – 0.161

C – 0.076

Preliminary ResultsPreliminary Results

Detector geometry means total flux Detector geometry means total flux through ABC, assuming no absorption, through ABC, assuming no absorption, has the form has the form ABC, ExpectedABC, Expected = K = K ABAB

Use data collected with no absorber to Use data collected with no absorber to determine K experimentallydetermine K experimentally

We can then examine the ratio We can then examine the ratio ABC, MeasuredABC, Measured / / ABC, ExpectedABC, Expected to determine how to determine how

much flux is being stoppedmuch flux is being stopped

Preliminary ResultsPreliminary ResultsMuon Flux vs Maximum Energy Attenuated

0

0.2

0.4

0.6

0.8

1

1.2

0 200 400 600 800 1000 1200 1400 1600 1800

Maximum Energy Attenuated (MeV)

Mu

on

Flu

x R

atio

Preliminary ResultsPreliminary ResultsObserved Particle Energy Distribution

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 200 400 600 800 1000 1200 1400 1600 1800

Particle Energy, MeV

Pro

bab

ility

of

Ob

serv

atio

n

PDF CDF

Future WorkFuture Work

Take more dataTake more data

Try to calculate K analytically and Try to calculate K analytically and compare with the measured valuecompare with the measured value– Difference between expected and observed Difference between expected and observed

values give the efficiency of the detectorvalues give the efficiency of the detector

Refine computation of distribution functionRefine computation of distribution function

ReferencesReferences

Particle Data Group, Particle Data Group, Review of Particle Physics Review of Particle Physics (2006)(2006)..

Leo, William R., Leo, William R., Techniques for Nuclear and Techniques for Nuclear and Particle Physics ExperimentsParticle Physics Experiments,, Springer-Verlag, Springer-Verlag, Berlin, 1994.Berlin, 1994.

Groom, D.E., Striganov, N.V., and Mokhov, S.I.; Groom, D.E., Striganov, N.V., and Mokhov, S.I.; Muon Stopping Power and Range Tables Muon Stopping Power and Range Tables 10 MeV10 MeV––100 TeV, 100 TeV, Atomic Data and Nuclear Atomic Data and Nuclear Data Tables Data Tables 7878, 183, 183––356 (2001).356 (2001).

Questions?Questions?

Acknowledgements:Acknowledgements:– Phil, for general advicePhil, for general advice– Kurt Wick, for helping us set up the apparatusKurt Wick, for helping us set up the apparatus– Professor Michael DuVernois, for providing Professor Michael DuVernois, for providing

supplemental equipment, along with expertisesupplemental equipment, along with expertise– Michael Hamman and Timothy Weaver, who Michael Hamman and Timothy Weaver, who

worked on this project during MXP last yearworked on this project during MXP last year– Peter Karn and Dave Kearsley, for general Peter Karn and Dave Kearsley, for general

help and emotional supporthelp and emotional support