Analysis of radiation emitted by electrons and positrons through multiple volume reflection in a bent silicon crystal

Introduction
When a charged particle crosses a crystal with a small angle with respect to a
crystallographic axis (or plane), it suffers a series of correlated collisions (i.e. co-
herentinteractions)withtheneighbouringatomsinthesamerow(plane)[1]: this
isaresultoftheinfluenceofthecrystallatticeonthemotionofthechargedpar-
ticle[2]. Inthisconditionsachargedparticlemovesinthepotentialgeneratedby
severalaxesorplanes: apositiveparticlecanbecapturedinsidetheinteraxial(in-
terplanar) potential wells, while a negative particle oscillates around the atomic
planes (or axes). In other words the particle is channeled between or around the
planes(axes).
Ifthecrystalisbent,achanneledparticlefollowsthedirectionofthebentatomic
planes (or axes), thus bending from its initial direction by an angle equal to the
bendingangleofthecrystalitself[3]. Forthisreasonbentcrystalscanbeusedfor
extraction or collimation of particles from the circulating beam in an particle ac-
celerator. Overtheyears,bystudyingbentcrystals,othereffectswerediscovered
such as volume reflection (VR), consisting in the deflection of ’quasi-channeled’
particles in a direction opposite to that of crystal bending [4]. The VR angu-
lar deflection is fixed by the intrinsic crystal properties and is typically smaller
thanforchanneling. Nevertheless,thiseffectshowsalargerangularacceptance,
whichmakesitveryinterestingfromthepointofviewofthebeamextractionand
collimation. With the aim of increasing the VR angular deflection, two different
mechanismshavebeendevelopedinrecentyears: multivolumereflectioninase-
quenceofcrystals[5]andmultiplevolumereflectioninsideonecrystal(MVROC)
[6].
Inthisthesiswefocusourattentiononthelasteffect.
MVROCmayoccurundernearaxisalignmentwiththeparticlebeam: inthiscase
VR from several lying of planes sharing the same axis sum up leading to sig-
nificant deflection increase. In chapter 4 the procedure followed to evaluate the
meandeflectionangleandtheefficiencyforchargedparticlescrossingthecrystal
inMVROCgeometryispresented.
Introduction
The test described in this work have been performed in June 2010, on ex-
tractedH4-beamlineatCERN-SPS,byusingtwosecondarybeamsof120GeV/c
positronsandelectrons.
Itiswellknownthat,atthisenergy,electronsandpositronsaretheonlyparticles
forwhichradiationcontributessubstantiallytotheenergylossoftheparticledur-
ingitspassagethroughmatter[20]. Inamorphousmaterialthemechanismofra-
diationemissionisbremsstrahlung[7,8]. Ontheotherhand,whenachargedpar-
ticlesufferscorrelatedcollisionswithatomsduringitsmotioninasinglecrystal,
theprocessofradiationofaphotonconsiderablychangesincomparisonwithan
amorphousmedium,asaresultofthecoherentinteractionswiththemedia. The
energy radiated bye
+
/e
−
is more intense than standard bremsstrahlung. While
channeling[9]orVRradiations[10]havealreadybeenstudiedbefore,theradia-
tion due to MVROC, this phenomenon being discovered in 2007, is still investi-
gated. Inpreviewexperiment,thepositronradiationaccompanyingtheMVROC
was analyzed in the spectral regionE
γ
< 60 GeV [11]: the experimental results
have demonstrated that an increase in particle deflection by MVROC has natu-
rally lead to the same in radiation intensity. Our main purpose is to evaluate
the radiation spectra in the full range of energies up to 120 GeV, for both elec-
trons and positrons, in MVROC conditions. Finally, the experimental results on
MVROC radiation are presented in chapter 5, offering a first observation of the
hardregion(E
γ
> 60GeV)ofthespectra.
Chapter1
InfluenceofCrystalLatticeon
MotionofEnergeticCharged
Particles
This chapter is dedicated to an overview of the main concepts of coherent inter-
actionsforachargedparticlesmovinginacrystal[2].
In1912Stark[12]hadthefirstideathattheatomicorderincrystalmaybeim-
portantforthistypeofprocesses,buttheseoldideasofthedirectionaleffectsfor
achargedparticlemovinginacrystalweredormantuntiltheearly1960s, when
the channeling effect was discovered in computer simulations [13] and experi-
ments[14],whichobservedtoomuchlongrangesofionsincrystal.
The theoretical explanation of the channeling effects has been givenby Lind-
hard[1]: bychannelingismeantthataparticlepathnearthechannelcenteralong
amajoraxis(plane)inacrystalmayhaveacertainstability.
In the 1976 Tsyganov proposed to use slightly bent monocrystals to deflect
high-energyparticlebeams[3];hisideawasthatachanneledparticlewouldfol-
lowthedirectionofthebentatomicplanes(oraxes),thusdeviatingfromitsinitial
directionbyanangleequaltothebendingangleofthecrystal. In1979thepossi-
bility of steering beams of charged particles using bent crystal was first demon-
strated in an experiment on the deflection of 8.4 GeV protons beam extracted
fromthesynchrophasotronoftheLaboratoryofHighEnergies,JINR[16,17].
Inthefollowingyearsmanyothereffectswasdiscoveredstudyingbentcrys-
talssuchasvolume captureand volume reflection. Thefirstoneconsistsinthephe-
nomenonofcapturingachargedparticleintoachannelingmodeinthedepthof
abentsinglecrystalintheregionwheretheparticletrajectoriesaretangentialto
thecrystallographicplanes;itwasdiscoveredin1982usingabeamof1GeVpro-
4 InfluenceofCrystalLatticeonMotionofEnergeticChargedParticles
tons[35]. Thesecondoneconsistsinthedeflectionof’quasi-channeled’particles
( i.e. unchanneled particles that are moving in a trajectory nearly aligned to the
crystal planes) in a direction opposite to the crystal bending and hence opposite
totheoneofthechanneledparticlesdeflection; thiseffectcalled volume reflection
wasfoundincomputersimulationsin1987[4].
An other interesting effect was predicted in 2007, [6], called Multiple Volume
Reflections in One Crystal (MVROC). MVROC affects those particles entering a
bentcrystalwithasmallanglewithrespecttoacrystalaxisandconsistinasetof
volumereflectionsbydifferentplanescrossingtheaxis;thiseffectshouldincrease
thedeflectionofparticlesbyseveraltimes.
1.1 CoherentInteractionsinStraightCrystals
In this section the theoretical explanation of the channeling phenomenon given
by Lindhard is presented[1]. He has shown that when a charged particle has
a small incidence angle with respect to the crystallographic axis (or plane) the
successive collisions of the particle with the lattice atoms are correlated (i.e.
coherent scattering), and hence one has to consider the interaction of the charged
particlewiththeatomicstring(plane).
Anychargedparticletraversinganamorphousmedium(characterizedbyho-
mogeneity,isotropyandrandomness)oramisalignedcrystalmakesuncorrelated
collisionswithsingleatoms. Thesecollisionsmaybeofdifferentnature,depend-
ing on different impact parameters; the most common are angular scattering in
multiple collisions with atomic nuclei and energy loss in collisions with atomic
electrons. So in a random system the slowing-down process is independent of
directionandhencetheprobabilitydistributioninenergylossandscatteringan-
gledependsonlyonthemasspercm
2
penetrated,andithastobecomputedina
familiar way from single collisions. This is essentially a gas picture, and may be
called a random system, implying homogeneity, isotropy and random collisions.
However, it is important to realize that the approximation of a random system
isnotconfinedtorandomlydistributedatomsormolecules,butmaybealsoap-
pliedtomediawithlatticestructure.
An anisotropy due to lattice structure can thus result in some kind of corre-
lationsbetweencollisions(i.e.coherentinteractions). Asinglecrystalisatypical
example of a medium in which directional effect in stopping might appear, due
tobothinhomogeneity,anisotropyandlackofrandomness. Infact,acrystalisa
1.1CoherentInteractionsinStraightCrystals 5
regulararrangementofatomslocatedonalatticesothat,dependingonthepoint
ofviewoftheobservator,theatomsarearrangedinstringsorplane.
The directional effects for charged particles traversing crystal were found for
anumberofprocessesrequiringasmallimpactparameterinaparticle-atomcol-
lision (e.g., nuclear reactions, large-angle scattering and energy loss). We may
classifydirectionaleffectsforchargedparticlesmovingthroughsinglecrystalus-
ing two labels: ungoverned motion and governed motion. By ungoverned motion is
meant the approximation where the path of the particle may be assumed to be
essentially unaffected by the structure of the substance. Governed motion means
that a path deviates definitely from the one in a random system, because the
path is determined by the structure of the medium. Governed motion leads to
more fundamental changes in physical processes, whereas ungoverned motion
justshowfluctuationsinphysicaleffectsduetocorrelations.
Fortreatmentofpossiblegovernedmotionthescatteringangleoftheparticle
maybeassumedtobesmall,becausescatteringbylargeangleswouldimplythat
the original direction is completely lost, as well as correlations associated with
direction. The scattering of the particle is due to nuclear collisions, causing the
interaction with the charge distribution of an atom as a whole through nearly
elastic collision. Moreover, since collision requires that the particle comes close
to the atom, strong correlations between collisions occur if the particle moves at
asmallanglewitharowofatoms;ifitpassesclosetooneatominarow,itmust
alsopassesclosetotheneighbouringatomsinthesamerow. Thisleadsustothe
concept of string of atoms that is characterized merely by the constant distance
ofseparation, d,ofatomsplacedonastraightline;weassumethisastheperfect
string.
When the motion of a charged particle is aligned (or at a small angle) with a
string(orplane),acoherentscatteringwiththeatomsofthestring(orplane)can
occur. In the low-angle approximation we can replace the potentials of the single
atoms with an averaged continuous potential.The atomic string (plane) in the
continuumapproximationgentlysteersaparticleawayfromtheatoms,therfore
suppressingtheencounterswithsmallimpactparameterslistedabove.
TheChannelingPhenomenonareduetothefactthatthefieldsoftheatomic
axes and planes form the potential wells, where the particle may be trapped.
Channelingcouldbedevidedintwocase:
• Planarchannelingiftheparticleisboundwithatomicplanes;
• Axialchannelingiftheparticleisboundwithatomicstrings.