Physics 590B – The Nuclear Option

• Introduction to Particle Detectors

• Introduction to Accelerators• Fission and Fusion

104/21/23 Physics 590B - Fall 2014

A Comment on Units…

• Particle Physicists are lazy:

• We will use energy and mass units interchangeably:– Also = 1 for simplicity…– To get back to mks units just sprinkle , c around until the

units work out– When I say “MeV” I mean 106, not 10-3 (meV)

04/21/23 Physics 590B - Fall 2014 2

2

19

(with c = 1)

1.602 10

E mc E m

eV J

Particle Detectors

04/21/23 Physics 590B - Fall 2014 3

Modern Particle Physics Experiments

Many common features in modern NP and HEP detectors – inner tracking, magnetic field, EM and hadronic calorimetry, outer muon chambers.

Want to determine particle track, charge, momentum, energy, type (id) ….

04/21/23 Physics 590B - Fall 2014 4

Central Magnetic Field

5

Interaction of Radiation with Matter (Low Energy Particle, Low Density Matter)

• Heavy Charged Particles (p, , etc)– When a charged particle passes through matter, it interacts

primarily with the atomic electrons in the material

– Conservation of energy and momentum for a heavy particle M incident on a light particle m gives:

• Elastic, head-on collision – this is the maximum energy loss

– Example: For a 5MeV particle, m ~ 4mn

• We immediately know several useful things:– A typical particle will undergo thousands of collisions before it

loses all its energy

M

mTT

4 Kinetic energy lost by M

keVm

mMeVT

n

e 6.24

45

04/21/23 Physics 590B - Fall 2014

6

Heavy Particles

• Useful Things (cont.)– The heavy particle is deflected by a negligible amount in a

collision

– The Coulomb force has an infinite range, so a particle interacts simultaneously with many electrons and effectively loses energy continuously along its path

• The energy required to ionize atoms is a few 10’s of eV, so many collisions will liberate atomic electrons– Known as “ rays”

– These rays will have their own collisions and lose energy in the material as well

04/21/23 Physics 590B - Fall 2014

7

Bethe-Block Equation

• The original calculation for energy loss of a charged particle is due to Hans Bethe (1930)– Bethe-Block Equation

• For a particle of charge ze, velocity v:

– The electron density is given by:

– I is the mean ionization energy for the material• In principle it is an average over all ionization and excitation

processes

• Approximately I/Z ~ 10 eV

2

2

22

2

2

2

2

0

2

1

2ln

4

4

I

cmzn

cm

e

dx

dE ee

e

A

ZNn A

e

eVIeVI AlAIR 163 86

04/21/23 Physics 590B - Fall 2014

8

Bethe-Block (II)

• Energy loss depends quadratically on v and z,but not on its mass M

• For low energies (<<1), the energy loss decreases as ~1/v2

• Reaches a minimum for E~3Mc2

– dE/dx ~ 2MeV g-1 cm2

• For ~1 the energy loss rises logarithmically – Referred to as “relativistic rise”

– Relativistic deformation of Coulomb field of incident particle increases effective impact parameter cutoff (semiclassical)

2

2

22

2

2

2

2

0

2

1

2ln

4

4

I

cmzn

cm

e

dx

dE ee

e

(note – divided by density)

04/21/23 Physics 590B - Fall 2014

9

Bethe-Block (III)

relativistic rise

1/v2 term

04/21/23 Physics 590B - Fall 2014

STAR TPC Particle ID by dE/dx

10

Energy Loss by Electrons and Positrons

• Electrons/Positrons travelling through matter also suffer collisions with atomic electrons– However, they will lost energy faster and scatter at larger angles

– Electrons can lose energy via bremmstrahlung

• Accelerated charge radiates energy

– Energy loss (also due to Bethe):

3

4)(2ln4

1374

12

)(ln

2

4

2

2

42

22

0

2

.

222

22

22

2

0

2

cm

cmT

cm

cmTZne

dx

dE

cmI

cmTTn

cm

e

dx

dE

e

e

e

ee

bremm

e

ee

ecollisions

T = kinetic energy of electron/positron

04/21/23 Physics 590B - Fall 2014

11

Collision vs. Bremm. Losses

• Which term dominates for electrons/positrons depends on the incident energy of the lepton

– Note that 1/ dE/dx isplotted

1600

)(2

2. Z

cm

cmT

dxdE

dxdE

e

e

collisions

bremm

04/21/23 Physics 590B - Fall 2014

12

Photons

• There are three relevant processes for the interaction of photons with matter:– Photoelectric Effect, Compton Scattering, Pair Production

• Photoelectric Effect– Absorption of a photon by an atomic e-

– Difficult to calculate but easily measured

– Most important at low E

• Compton Scattering– Scattering of a photon off an atomic e-

– Probability depends on scattering angle

04/21/23 Physics 590B - Fall 2014

13

Photons (cont.)

• Pair Production– Photon converts to an e+/e- pair– Presence of nucleus required for

momentum conservation• Recoil negligible

– Threshold at 2mec2

• Important at higher energies

• At a given energy, all three processes can contribute, but one process may dominate

• An interacting photon or electron rapidly leads to “shower” of electromagnetic particles in the material

22 cmTcmTE eeee

04/21/23 Physics 590B - Fall 2014

14

Attenuation Coefficients

• Consider an experiment where you have a beam of photons incident on a slab of material of thickness t

– Detected photons will have suffered essentially no interaction at all

• In contrast with protons of particles

– Define = probability per unit length to remove a photon from the beam (total linear attenuation coefficient)

t

photon beam

detector

teII

dxI

dI

0

= photoelectric effect = Compton scattering = pair production

04/21/23 Physics 590B - Fall 2014

15

Photon Attenuation

PE Effect Edges

Linear Attenuation Coefficient:04/21/23 Physics 590B - Fall 2014

16

Charged Particle Detectors

• Now that we know the processes by which radiation and matter interact, let’s look at how we can use this detect radiation

• Gas Filled Counters– Basic idea is simple – collect and count the ions/electrons formed

by the passage of radiation through a gas volume

– Ionization Chamber – basically a parallel plate capacitor

-4 ions/e 3x10 MeV 1

34~

eVI AIR

mVpf

ionCV 5.0~

10~

)/10602.1(103 194

(10pf ~ 10cm by 10cm by 1cm gap)

smoke detector

04/21/23 Physics 590B - Fall 2014

17

Ionization Chambers

• The ionization chamber gives you relatively small signals, need electronics to amplify the signal

• The size of the voltage/charge you collect is independent of the voltage you apply to the chamber– Just determines the drift speed of the ions/electrons

– To cross a 1cm gap takes about 0.01s – not a very fast detector!

• Ionization chambers are used as radiation monitors, where counting singles pulses is not important but you want a measure of the total radiation flux.

smVvd /1100@

04/21/23 Physics 590B - Fall 2014

18

Proportional Counters

• Designed to be able to count single pulses

• We want a faster drift time, so increase the voltage– This accelerates the ions/electrons

– Faster moving e- can have inelastic collisions to create more ionization

– This leads to an amplification of the original signal!

– Typically use a cylindrical geometry

)/ln( abr

VrE

b = cathode cylinder radiusa = anode wire radius

Very high E(r) near the anode wire, most of the amplification takes place here.

Size of the signal is still proportional to initial ionization. Drift times a few s. Physics 590B - Fall 201404/21/23

Collider Detector Schematic

04/21/23 19

ccc

e+

o

K+, +,p,…

lsp

Muon detectorsHadron calorimeter

Electromagnetic Calorimeter

Solenoid 1.4T 2.0T

SiliconDetector

Ko +-, …etc

Particle ID:Time of Flight

Jet

Tracking Chamber: Drift Chamber (COT) Fiber Tracker (SFT)

KeyCDF and D0CDF D0

Physics 590B - Fall 2014

20

Drift Chambers

• You can expand a proportional chamber into a multi-wire device (MWPC) or a Drift Chamber– Record the time of each pulse and use that information to better

localize the particle “hit”• Greatly increases the accuracy of the device (50-150 m)

External device gives a time reference.

Electric fields adjusted to be almost constant within a drift “cell”.

Timing of hit and known drift velocity used to produce accurate hit location.

04/21/23 Physics 590B - Fall 2014

Silicon Detectors (SS Drift Chamber)

• A silicon detector is essentially a reverse biased diode.

– Charge deposition by a charged particle creates a current

– Small feature size – excellent resolution• Even better if charge sharing is taken into account.

04/21/23 Physics 590B - Fall 2014 21

22

Scintillation Counters

• Basic idea is to convert the ionization to light, then collect the light– Has the advantage of a high efficiency even at low energies

• Organic Scintillators are typically a plastic doped with a fluorescing chemical. – Passage of ionizing radiation excites the molecules and sets them

into motion (vibration)– Excited state spacings are of order 1eV, vibrational spacings

around 1/10 eV– Excited states decay to the vibrational ground state quickly (~ps),

then later to the electronic ground state (~10ns)– As a result, the material is essentially transparent to its own

radiation!• Since most molecules are in the ground only one of many possible

transition photons is likely to be absorbed. • The doping elements shift the UV light to visible

04/21/23 Physics 590B - Fall 2014

23

Organic Scintillator

~1/10 eV

~eV

04/21/23 Physics 590B - Fall 2014

24

Photomultiplier Tube

• A PMT is a device thatcan detect a singlephoton, and amplify thesignal to usablelevels– Signal amplified at

dynodes (~100V potentialdifference)

– Typically a gain of 5-10 at each dynode, total gain ~107

• Scintillator/phototube combinations used extensively as single particle detectors (~ns transit times, ~10ps time resolution)

04/21/23 Physics 590B - Fall 2014

PID by Time-of-Flight

04/21/23 Physics 590B - Fall 2014 25

High resolution scintillation counterscan achieve a time resolution of 80-100ps.

“Walls” of scintillation counterscan be used in conjunction with a “start time” to determine particle IDby comparing momentum and TOF.

Si PMT’s (SiPM)

• Only potential replacement for a PMT

04/21/23 Physics 590B - Fall 2014 26

An array of parallel connected avalanche photodiodes (Geiger mode) with a quenching resistor.A single photon can trigger the avalanche breakdown with very high internal gain.

Individual microcell response independent of light intensity, device response is summed output of microcells. High QE, fast response, independent of magnetic field – but – gain is temp dependent!

Calorimeters (I)

• A calorimeter is a device that measures the energy of a particle.

• Incident particles interact and initiate a shower in the high-density calorimeter material– Electromagnetic Calorimeter: photons, e+/-

• Radiation Length: 6.37 g/cm2 for Pb (0.57 cm)

– Hadronic Calorimeter: hadrons (p,,K, etc.)• Hadronic Interaction Length: 119.6 g/cm2 for Pb (10.5 cm)

Simulated shower in a PbW crystal.

sampling detectors04/21/23 Physics 590B - Fall 2014 27

Both define 1/e distance

Calorimeters (II)

• Key Issues for Calorimetry– Energy Resolution

• Sampling or Homogeneous

• Readout Technology:– Scintillator (phototubes or avalanche

photodiodes)

– Wire Chambers (charged particles)

– Si (charged particles)

– Bolometric (phonons)

– Hadronic and Electromagnetic Sections

• Compensation (e/h = 1)

04/21/23 Physics 590B - Fall 2014 28

Cerenkov Counters (I)

• Cerenkov light is emitted when a particle travels faster than the speed of light in a medium– Similar to a sonic boom– Light emitted at a characteristic angle:

– Light depends on particle velocity• Different momentum for different masses

– Threshold Counter:• Just detect the light

– Ring Imaging Cerenkov (RICH):• Image the ring, measure the angle• Can be used to identify different particle types

nC

1cos

Cerenkov radiation from nuclear fission reactor core.

04/21/23 Physics 590B - Fall 2014 29

Cerenkov Counters (II)• Large, underground water

Cerenkov counters were instrumental in demonstrating solar neutrino oscillations.

• Cerenkov light is used to detect cosmic rays in air showers

Super Kamiokande04/21/23 Physics 590B - Fall 2014 30

Why Trigger?

• The purpose of a trigger system for an experiment is to select rare events and suppress background as efficiently as possible.– NOTE: This doesn’t mean a trigger only selects the physics we

want!

• A trigger system must match the physics event rate to the data acquisition rate.

04/21/23 Physics 590B - Fall 2014 31

Example: CDF/D0 Trigger In Run-II

• Beam crossing rate of 7.6MHz

• About 750k channels at ~4 bytes each– Total of ~3MB per event

• “Event” data rate ~20 TeraBytes/s

• Zero suppression of unoccupied channels approx a factor of 10– “Event” data rate still ~2 TeraBytes/s

• Trigger rejects 99.999% of crossings– Data rate to tape now ~20 MegaBytes/s

04/21/23 Physics 590B - Fall 2014 32

Efficiency and Deadtime

The goal of trigger and DAQ is to maximize the amount data sent to storage (for later analysis) for a desired process with minimal cost:

•Relevant efficiency is for events that will be useful for later analysis:

•For low rate process (e.g. e+e- to hadrons, Higgs production at Tevatron or LHC) try to accept all signal in trigger Maximize efficiency

•Deadtime is due to fluctuations when the rate into a stage of the trigger (or readout) approaches the rate it can handle (busy). Simple case of no buffering:

•Buffering incoming data reduces dead time, more buffering less dead time – If <Incoming Rate> > 1/<Execution Time>, dead no matter what!

•Minimizing dead-time helps all processes (and all budgets!)– 1% of machine time * 1 year = $$$$$04/21/23 Physics 590B - Fall 2014 33

operations * trigger * (1-deadtime)

trigger = Ngood(accepted)/Ngood(produced)

deadtime = (Input Rate) * (Execution Time)

Triggers and Deadtime

• Assume you get ne events per second (te=1/ne), and the time to record an event is tR

– The rate of recorded events is: nR= 1/(tR+te)

– The fraction of all events recorded is: f=nR/ne = (1+tR/te)-1

• You can’t change tR. What if you could select only the events you want to record?– Trigger processor decision time tp, triggered event rate nt

– nrej=Knt is rejected event rate (K is the rejection factor)

– The rate of recorded (triggered) events is now nt = 1/((tR+te) + K(tp+te))

04/21/23 Physics 590B - Fall 2014 34

1 11

(1 )

1(1 )

tP R e

pe

e

R

e

n Kf t t fG

tnt

Ktt

If tp<<te, tR>>te then G~K+1

Queuing Theory

• Consider a system with: – exponential arrival times with average rate

• Equal probability of event arrival per unit time

– exponential distribution of trigger service times with time constant (ratio )

• Usually isn’t exponential, but makes the math nice…

– A buffer depth N, where the system will produce dead time if the buffer becomes full

– The probability Pn that the buffer will have n events in time interval [t, t+dt] is given by:

04/21/23 Physics 590B - Fall 2014 35

dtPPPdP nnnn )( 11

Queuing Theory (cont.)

• Set the above equal to zero for a steady-state solution– Solve P0 , PN as a special case!

• Solve for the dead time as the probability (fraction of the time) that the buffer has N events

04/21/23 Physics 590B - Fall 2014 36

1 1 ( ) n n n ndP P P P dt

1

11

1

11

1

N

N N

N

P

PN

For =1, if N=1 then deadtime = 50%. If N=5, the deadtime is reduced to 16%.

BACKUP

04/21/23 Physics 590B - Fall 2014 37

38

Range Comparisonp, alpha lose energy

electrons scattered from beam

photons removed from beam

I/Io = 0.5

1 MeV alpha particles – 0.0003 cm in Al1 MeV electrons – 0.18 cm in Al1 MeV photons – 4.3 cm in Al

04/21/23 Physics 590B - Fall 2014

39

Neutrons (I)

• Neutrons have no charge, so no EM interaction

• Must have a strong interaction with nuclei in material

• Reactions like are possible

• For interactions with charged final states our previous discussion takes over:

– You can now either detect the or the photon shower

• For low (thermal) energies the primary process is neutron capture (n,)

• Neutrons will lose energy through (strong) elastic scattering in the material

nn,npn 2 ,, ,,

*LinB 710

04/21/23 Physics 590B - Fall 2014

40

Neutrons (II)

• For a neutron scattering off a nucleus A:

• For =180o (head-on collision):

– Heavy nuclei can slow neutrons down a lot

– For hydrogen this value is 0 – the neutron “knocks out” a proton

2

2

)1(

cos21

A

AA

E

E E = incident neutron energyE’ = final neutron energy

2

min1

1

A

A

E

E

04/21/23 Physics 590B - Fall 2014

41

Range

• In principle the range is given by:

– Doesn’t account for electron capture as the particle stops

– We can rewrite this in terms of a universal function

– So that for different particles incident at the same velocity:

0 1

T

dEdx

dEr OK since the path is

essentially straight

M

Eh

z

M

M

dEM

MEgzr

M

Egzvfz

dx

dE

22

22

)/(

1

)(

rM

Zr

M

Zp

p

p22

04/21/23 Physics 590B - Fall 2014

42

Range and Energy Loss

• Range and energy loss tabulated and available for a wide array of materials– The Particle Data Book

has a lot of good information

04/21/23 Physics 590B - Fall 2014

43

Geiger Counters

• If you increase the voltage further you will reach a point where amplification can take place anywhere in the cylinder– Large (1010) amplification,

but all incident radiation counts the same

– Ions striking the cathode could liberate electrons and start the process over again

– Typically mix in a hydrocarbon gas to quench the ions

– 90%Ar/ 10% Ethane mix 04/21/23 Physics 590B - Fall 2014

Efficiency and Deadtime II• Need to ensure full efficiency when detector channels are broken,

masking registers are used at the input from front-ends– For tracking mask on dead channels– For calorimeter mask off hot channels

• Need precise measurements of trigger and deadtime for cross-section measurements– Other cases (e.g. particle lifetime) need to evaluate other biases that trigger

may introduce (e.g. removing long lived decays)

• Measure deadtime by scaling rates of operational states of Trigger/DAQ system – Constant attention required during running to limit deadtime

• Need Mechanisms to evaluate the efficiency and biases– Redundant, independent paths– Lower bias triggers with accepted with a prescale– Zero bias - trigger on accelerator clock structure– Minimum bias – trigger on very low energy scattering

04/21/23 Physics 590B - Fall 2014 44

Minimizing Deadtime

• Introducing a trigger with decision time tp increases your ability to select the physics you want– Increasingly important for rare

events!• How do we minimize deadtime

even further? – Need to minimize the effect of the

trigger decision time tp

– This can be accomplished by “buffering” events in front of a set of trigger processors

• Works well for fixed target or asynchronous beam

– Alternatively, trigger deadtime can be eliminated by “pipelining” the trigger

• Works well for collider expts.

04/21/23 Physics 590B - Fall 2014 45

See Data Analysis Techniques for High Energy Physics by Fruhwirth, Regler, Bock, Grote and Notz.