NIKHEF ��������

Physical foundations of theCompton Beam Loss

Monitor

J�J�M� Steijger

Nationaal Instituut voor Kernfysica en Hoge�Energiefysica �NIKHEF��P�O� Box ����� NL��� DB Amsterdam� The Netherlands�

October ��� ����

Abstract

This report describes the physical foundations of the Compton BeamLoss Monitor �cblm�� The processes taking place in a collimator� thesource of the photon beam� and the Compton absorber �where the photonsare converted to an electron current� are studied using a Monte Carlo sim�ulation� Finally an estimate is made of the signal which can be achievedin a practical example�

�

Contents

� Introduction �

� Description �

� The collimator �

��� Energy deposit � � � � � � � � � � � � � � � � � � � � � � � � � � � � ���� Photon yield � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� Compton�absorber ��

� Application ��

�

� Introduction

The protection of the new generation of linear accelerators against unforeseenbeamlosses in the equipment making up these machines starts with the earlydetection of any displacements of the beam� The energy stored in the beameg� in tesla the charge in a single bunch is � nC and the beam energy is��� GeV representing an energy of ���� J in each pulse� is large and unlikethe beam in storage rings new bunches are being produced almost continuouslyin tesla at a rate of ��� MHz during an accelerator pulse of �� �s �ve ofthese pulses are present each second ����� The protection devices must thereforebe very sensitive to protect the machine reliably and to ensure the survival ofthe exposed compoents� The energy contained in the beam is in the order often MW therefore the system must be sensitive to a loss of ���� of the beamor less� It must also be fast to reduce the number of bunches produced to a safenumber or stop the injection altogether�

In this report we describe the physical underpinning of one example of sucha system� The Compton Beam Loss Monitor cblm� ��� consists of three parts�A collimator converts high energy electrons into photons� These photons areconverted in a so�called Compton�absorber into lower energy electrons� Theseelectrons are stopped in the �nal component the electron�absorber� The sig�nal which is measured is the current between the Compton�absorber and theelectron�absorber� Section � describes this device in more detail� The nextsections are devoted to the interactions which take place in the consecutiveparts� Section � �nally gives an estimate of the size of the signal which can beobtained in an elaborated example�

� Description

The Compton Beam Loss Monitor cblm� discussed in this section is a simpli��cation of a device which could be used for the protection of an accelerator� Thepurpose of this simpli�ed apparatus is to bring to light the physical foundationsand the caveats which must be observed when designing a usable device�

Figure � shows the schematic diagram of a cblm� The three main compo�nents of the monitor are the collector of the beam electrons which are about tobe lost a converter to produce a measurable signal and the measuring electrode�

The purpose of the device is to measure the �rst stages of the beam�lossprocess when only a tiny fraction of the beam current is involved� Instead ofdetecting the small change in the beam�current the cblm aims to measure thesmall current of electrons which are being lost� To this end a relatively tothe size of the local apertures of the machine� small constriction is deliberatelyintroduced to scrape the deviant electrons from the beam but large enoughcompared to the size of the beam� not to obstruct the passage of the main cur�rent� The electromagnetic shower which develops in a thick collimator convertsa single electron at beam energy into many photons and electron�positron pairs�These are of a much lower energy and therefore easier to detect� In addition the

�

energy they carry is spread out in space which reduces the local intensity of theheatload on the components downstream of the collimator�

The photons and charged particles thus produced can be detected in manyways� In the cblm the photons are converted to electrons in the Compton�absorber� This consists of a thick plate of aluminium where the photons arescattered on the atomic electrons� Some electrons will be knocked out of theiratomic orbits and have enough energy to escape the aluminium� These electronsare stopped in the last element of the cblm� The signal is the current whichthese electrons carry between the Compton�absorber and the �nal element ofthe cblm� The resulting cblm has no parts which are sensitive to radiationdamage and is able to stand a considerable amount of heat�

� The collimator

When a beam particle hits the collimator it initiates an electromagnetic cascadein which the single particle is multiplied to a shower of photons and electron�positron pairs� This multiplication is advantageous for it simpli�es the detectionof the beam particle� On the other hand it also increases the rate at which energyis deposited in the material� Approximate formulae exist for the developmentof these showers �� �� but these are valid only when the shower remains com�pletely contained inside the material� This is not the case for the collimator inwhich a beam particle is typically entering very close to the surface of the bore�The e�ect of the presence of this interface is studied with a Monte Carlo ���simulation� An electron with energy E� entering a cylindrical copper collimatorwith outer radius Rout cm a bore with radius Rin cm and a length of t radiationlengths is simulated�

��� Energy deposit

The �rst quantity studied is the heat generated in the collimator� The energydeposited in a copper collimator is compared in �gure � with the energy lost ina full cylinder of the same dimensions� The Monte Carlo results for this caseare close to the approximate formula ���

dE

dt� E�b

bt�a�� exp�bt�

�a�� ��

where the energies are in GeV and the thickness t in radiation lengths� Theconstant a is found from the peak position and is found to be ������ Theconstant b is taken to be ��� ��� and E� is the energy of the beam particle��� GeV in these simulations� In the collimator part of the shower is lost inits bore� The Monte Carlo shows the de�cit of energy�loss at intermediatedistances � � t � ��� and the small excess at greater thickness which iscaused by charged particles and photons from that part of the shower which isnot contained and re�enter the body of the collimator at some distance� Thise�ect is shown clearly in �gure �� The energy lost in the collimator is shown

�

absorberElectronCollimator

absorberCompton

Figure �� Schematic diagram of a Compton beam loss monitor� From left toright� the collimator which converts high energy electrons in photons� The pho�tons are converted in a so�called Compton�absorber to lower energy electronswhich in turn are stopped in the electron�absorber� The current which is mea�sured between the Compton�absorber and the electron�absorber is proportional tothe beam current lost in the collimator�

thickness [rad lengths]

∆E [G

eV m

m-1

]

Collimator, d = 1 mmCollimator, d = 0.1 mmCylinder

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 5 10 15 20 25 30

Figure �� Energy lost in the shower of a single beam electron �E� � ��� GeV��The full symbols are the results of the calculation on the full cylinder� The fullline is the result of an approximate formula� The open symbols are the resultfor a collimator� when the particle enters �� and � mm away from the insidesurface� respectively�

�

there in two slices at t � �� X and t � �� X where X is one radiation length�At the shorter distance only the core of the shower shows while at the largerdepth the interior wall of the collimator also is heated considerably�

For the design of the collimator the density of the heat generated is the moreinteresting quantity� The lateral distribution of the shower can be approximatedby the sum of two exponentials ���� The intensity of the narrow core decreaseswith the distance over which the shower develops while the broader halo be�comes relatively more intense with distance� The density of energy�loss see�gure �� peaks therefore at a shorter distance compared to the total energy�losscf� �gure ��� The maximum energy�loss in one mm� is about �� MeV perelectron which is equivalent to �� J g�� if one bunch charge� � nC� hits thecollimator Cu � � ��� g cm���� The speci�c heat of copper Cp ��� can beapproximated by

Cp � ��� ��� ������ � ����T � ������ � ����T �� ��

where T is the temperature in �C and Cp is in J g�� K��� Figure � showsthe heat needed to raise one gramme of copper from room temperature to T�C� Using these data it is found that the �� J g�� deposited in the peak of theshower caused by one bunch causes a temperature rise to about ��� �C�

��� Photon yield

Inside the shower many photons and charged particles are produced� Brems�strahlung and pair creation are the main interactions which create photons whena high energy electron traverses material and produce electron�positron pairsfrom these photons� In the context of the cblm we are interested in the �uxof photons which are able to escape the collimator either through the bore orthe back face� Figure � shows this number as a function of the thickness ofthe collimator� The curve for the full cylinder is similar to the curve for theenergy loss shown in �gure � but has its maximumat a slightly larger thicknessand a more pronounced tail towards greater depth in the collimator� When theshower develops close to the inside wall part of it will escape through the boreof the collimator� That part does not contribute to the production of furthergenerations of particles but also is not attenuated in the material� The �gureshows that at larger thickness the last e�ect is dominant and an increasedphoton production compared to the case of the full cylinder results� When thebeam electron enters the collimator very close to the inside wall the decreasedparticle production prevails and the yield becomes less� Similarly the photonspectrum shows also that for those situations where more of the shower escapedthrough the bore of the collimator the spectrum is harder for the collimatorcompared to the case of the full cylinder see �gure ��

The photons are produced in a cone with a double exponentially distributedapex angle� This distribution re�ects the double exponential lateral distributionin the shower region ���� Figure shows the rms�value of this distributionshowing as expected a wider distribution when the shower is more developed

�

x (t = 10X) [cm]

y [c

m]

t = 10X

-5

-2.5

0

2.5

5

-10 -5 0 5 10

x (t = 20X) [cm]

y [c

m]

t = 20X

-5

-2.5

0

2.5

5

-10 -5 0 5 10

Figure �� Pro le in a plane perpendicular to the beam�direction� of the heatdeveloped in the collimator� The central circle is the bore� The beam particlehits the collimator at �x�y� � ������� The two slices are at � and radiationlength �left and right hand panel�� respectively� At greater depths that part ofthe shower which escapes in the bore may re�enter�

depth [ rad.lengths]

∆Em

ax [M

eV m

m-3

]

0

10

20

30

40

50

60

70

80

90

0 5 10 15 20 25 30

Figure �� Energy lost in a mm� of the copper collimator in the core of the showerof a single beam electron �E� � ��� GeV��

T [°C]

∆Q [J

g-1

]

0

50

100

150

200

250

300

350

400

450

500

0 200 400 600 800 1000

Figure �� The heat �Q needed to raise � gramme of copper from room�temperature to a nal temperature of T �C�

thickness [rad lengths]

phot

ons

per

lost

bea

m e

lect

ron Collimator, d = 1 mm

Collimator, d = 0.1 mmCylinder

0

2000

4000

6000

8000

10000

12000

14000

0 5 10 15 20 25 30

Figure �� The number of photons escaping the collimator as a function of itsthickness t in radiation lengths� The full symbols are the results of the calculationon the full cylinder� The open symbols are the result for a collimator� when theparticle enters �� and � mm away from the inside surface� respectively�

�

Eγ [MeV]

phot

ons

per

elec

tron

lost

t = 10Xt = 24X

10-1

1

10

10 2

10 3

10 4

10-1

1 10 102

103

Eγ [MeV]

R t=10X, d=1 mmt=10X, d=0.1 mmt=24X, d=1 mmt=24X, d=0.1 mm

0

1

2

3

4

5

10-1

1 10 102

Figure �� Left hand panel� the spectrum of photons escaping from a full cylindercaused by the hit of a single beam electron �E� � ��� GeV�� Right� The ratioR of the spectra from a collimator and the full cylinder� R has been adjustedto take out the di�erence in total intensity� The spectrum is harder when theelectron hits closer to the surface of the bore� or the collimator is thicker� i�e�when more of the shower is allowed to escape through the bore�

thickness [rad. lengths]

apex

pho

ton

cone

[mra

d]

0

20

40

60

80

100

120

140

160

180

200

0 5 10 15 20 25 30

Figure � The divergence of the photon beam as function of collimator thickness�The electron energy is � GeV� the collimator is made from copper�

��

i�e� a thicker collimator� The angle grows approximately linear with thicknessfor thin collimators until it levels at some maximumvalue which for the energyE� � ��� GeV� and collimator material considered Cu� is about � � mrad�This maximumis reached for a collimator with a thickness of about �� radiationlengths�

� Compton�absorber

The collimator has converted a single straying electron in a shower of about��� photons and similar numbers of charged particles mostly electrons andpositrons� Since pair creation is the most probable interaction in the showerthe numbers of electrons and positrons are nearly in balance� There is a smallexcess of electrons caused by the Compton scattering of the photons on atomicelectrons in the collimator� In some of these interactions electrons will be ejectedfrom the material� These electrons account for most of the excess� The �ux ofphotons and charged particles can be detected by a variety of means e�g� ion�ization chambers semiconductor detectors scintillators or �Cerenkov detectors�The ideal detector for the beamloss monitor is simple robust and radiation hard�The cblm attempts to measure the current carried by the electrons knocked outby Compton scattering� In principle this can be done at the collimator itselfsee above�� However the collimator must be electrically insulated in that caseintroducing problems with the rf�impedance of the accelerator and with thecooling which is necessary because of the dissipation in the collimator see sec�tion ����� The cblm uses a second much lighter absorber to convert the photon�ux in electrons which are stopped in a further block of material� This sectionlooks at the interactions which take place in the second absorber�

The Compton cross�section is given by ���

�C � ��r�e

�� � �

��

��� � ��

� � ���

�

�log� � ���

��

�

��log� � ��� �

� � ��

� � ����

��

��

where � is the photon energy E�mec�

and re is the classical electron radius� Thekinetic energy T of the scattered electron is distributed according to ���

d�

dT�

�r�emec���

�� �

s�

���� s���

s

�� s

�s �

�

�

��� ��

with s � TE�� The maximum energy which can be transferred to the electronis

Tmax � E�

���

� � ��

�� ��

Figure � shows the Compton cross�section and the energy spectrum of the scat�tered electrons� The maximum cross�section of about ���� barn per electroncreates about ��� electron per photon in a centimetre aluminium�

��

Compton scattering creates electrons some of which have enough energy toescape the aluminium absorber and can be stopped in the next part causing auseful signal� The range of the Compton electrons can be approximated by

R � aT b� ��

where R is the range and T the kinetic energy of the electrons� These equa�tions show that the Compton cross�section �C is large for low photon energieswhere the range of the Compton electrons is small� Moreover for low pho�ton energies the transmission of the aluminium absorber is small� The yield ofphoto�electrons created by the photo�electric e�ect is neglected in the followingbecause in that case either the cross�section is negligible or the range of thephoto�electrons is too small to allow them to escape the absorber�

The probablity that a Compton electron is created at a depth x in the ab�sorber is proportional to the photon �ux present at depth x and the probabilitythat the electron can escape the absorber�

P E�� x� � T E� � x��T�Tx dx� ��

PE� � x� is this probability TE� � x� the transmission of photons with energyE� through a layer of thickness x of the absorber and �T�Tx the probabilitythat the Compton scattering process results in an electron with energy greaterthan Tx the energy needed to escape the absorber of thickness t from a depthx

Tx �

�t� x

a

���b

� �

The factor �T�Tx in equation � can be calculated by integrating equation �

�T�Tx �

Z Tmax

Tx

�r�emec���

�� �

s�

���� s���

s

�� s

�s �

�

�

��dT� ��

In �gure �� the results of a Monte Carlo calculation and this analysis are com�pared� The curves are similar indicating that the important dependences aretaken into account� The energy lost by the photons during the passage throughthe absorber is neglected in this analysis� The e�ect of this would be that in theintermediate energy range some strength is lost because the photons have lostenergy and the Compton electrons therefore have a smaller range and cannotescape� In the high energy region some extra strength will appear because thesmaller photon energy has a greater Compton cross�section�

In summary� in the Compton absorber photons in the energy range from afew MeV to a few hundred MeV contribute most to the generation of currentbetween the Compton absorber and the electron absorber backing it� Thisis the result of the balance between the falling Compton cross�section andthe requirement that the Compton electrons have enough energy to escape theabsorber� The Compton absorber has to have a thickness of a few centimetresfor optimum results�

��

Eγ [MeV]

σ Com

pton

[bar

ns]

10-3

10-2

10-1

1

10-3

10-2

10-1

1 10 102

103

Ee [MeV]σ C

ompt

on [b

arns

]

Eγ = 10 MeVEγ = 5 MeVEγ = 1 MeV

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10

Figure �� Left� the Compton cross�section per electron as a function of thephoton energy� Right� the energy spectrum of the scattered electron�

Eγ [MeV]

elec

tron

yie

ld [%

]

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

10-1

1 10 102

103

Eγ [MeV]

elec

tron

yie

ld [%

]

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

10-1

1 10 102

103

Figure ��� Left� the yield of Compton electrons escaping an absorber of thicknesst per incident photon of energy E� calculated as described in the text� Right� thesame quantity calculated by a Monte�Carlo method �geant�� Absorber thicknesst � ��� ��� � � � � cm�

��

� Application

In this last section a possible application in tesla ��� is considered� The beamparameters for this machine are E� � ��� GeV charge in a single bunch is� nC� The sections in the accelerator are �� m long which is the distance weassume between the collimator and the Compton absorber see �gure ���� Thecollimator is taken to be �� cm long and made of copper� The Compton absorberhas an annular shape with internal radius of � cm and external radius of �� cmis made of aluminium and has a thickness of � cm� Beam particles are lostin the collimator creating a beam of photons� A small part of this beam isintercepted by the Compton absorber �� m away and is converted to electrons�In spite of the unfavourable geometry � a distance of two metres between thecollimator and the Compton absorber would increase its acceptance by a factorten � one beam particle in the collimator is converted to two in the Comptonabsorber� The charge pulse is converted to a voltage pulse on the capacitanceof the electron absorber� Assuming a threshold of �� mV the system should besensitive to the loss of about � � ���� of the bunch charge equivalent to ��� mJof beam energy� for each ��� pF of this capacitance� This factor falls shortof the factor ���� which was set as a goal in the introduction� The di�erencecan be achieved by reducing the repetition rate of the accelerator or the bunchcharge during the tuning of the machine�

��

References

��� R� Brinkmann G� Materlik J� Rossbach and A� Wagner Ed��� ConceptualDesign of a � GeV e�e� Linear Collider with Integrated X�ray LaserFacility� DESY������ �����

��� D�E� Broom et al� Review of particle physics� European Physical JournalC���� �����

��� G�A� Akopdjanov et al� Determination of photon coordinates in a hodoscopecherenkov spectrometer� Nucl� Instruments and Methods ����������� �����

��� P�J�T� Bruinsma et al� A machine protection system based on the detectionof beam induced radiation� http���www�nikhef�nl�pub�projects�tesla�����

��� R� Brun et al� Cern program library long writeup w����� �����

��� W�R� Leo� Techniques for nuclear and particle physics experiments� SpringerVerlag Berlin �� ��

��� Y�S� Touloukian and E�H� Buyco� Speci�c heat metallic elements and alloys�In Thermophysical properties of matter volume �� IFI�Plenum �����

��

50 m

10 cm

5 cm 7 cm

15 cm

collimator

Compton absorber

Figure ��� Schematic drawing �not to scale� of the cblm for tesla� Thesedimensions are used for the Monte Carlo calculations presented in this section�

��