1 a.i.ryazanov, e.v.semenov and a.ferrari dpa calculations in irradiated graphite collimator...
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A.I.Ryazanov, E.V.Semenov and A.Ferrari
DPA calculations in irradiated graphite DPA calculations in irradiated graphite collimator materials under 7collimator materials under 7 TeV and 450 TeV and 450
GeV proton beamsGeV proton beams
06.03.2015, CERN, Geneva, Switzerland
National Research Centre” Kurchatov Institute”European Organization for Nuclear Research
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Energy flux of secondary protons formed in graphite at different distances along the beam of 7 TeV protons
06.03.2015, CERN, Geneva, Switzerland
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Energy flux of secondary electrons formed in graphite at different distances along the beam of 7 TeV protons
06.03.2015, CERN, Geneva, Switzerland
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Energy flux of secondary charged pi-mesons formed in graphite at different distances along the beam of 7 TeV protons
06.03.2015, CERN, Geneva, Switzerland
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Cumulative energy flux of secondary neutrons formed in graphite at different distances along the beam 7 TeV protons
06.03.2015, CERN, Geneva, Switzerland
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Displacement cross-section
06.03.2015, CERN, Geneva, Switzerland
( , )( ) ( )i
di
d T EE T dT
dT
( , )id T E
dT
- Differential cross-section of secondary particles (neutrons and others) with kinetic energy E to interact with target graphite atom, that will have energy T.
ν (T) is the cascade function (number of collisions created by primary knock-on atom with energy T),i is the index of summation over various nuclear reaction channels.
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C a s c a d e f u n c t i o n
( )2 d
TT
E K i n c h i n и P e a s e
( )( ) 0 . 8
2D a m
d
E TT
E N R T
M o n a t o m i cm a t e r i a l s
D i a t o m i c a n dp o l y a t o m i c m a t e r i a l s
N u m e r i c a l c a l c u l a t i o n s
06.03.2015, CERN, Geneva, Switzerland
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Cascade function
06.03.2015, CERN, Geneva, Switzerland
ˆ( )( ) 0.8
2 d
T TT
E
1/6 3/4ˆ( )
1 (3.4008 0.40244 )i i i
TT T
k
2( )T
ii T i T
A T a
A A Z Z e
2 1/30
2/3 2 /3 1/ 2
(9 /128)
( )i T
aa
Z Z
0a
iA TA
iZ TZ
dE
are atomic numbers of incident and target atoms, respectively,
and
- Bohr radius,
and
- displacement energy,
are atomic masses of incident and target atoms, respectively,
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The crystal structure of graphite showing the ABAB stacking sequence of graphene planes in
which the carbon atoms have three fold coordination.
06.03.2015, CERN, Geneva, Switzerland
The value of Ed lies between 24 and 60 eV. (Ed =25eV)
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1010
Differential cross-section of electrons and charged pions
06.03.2015, CERN, Geneva, Switzerland
12 2 2 2 2
202 4 4 2
( , ) 4 11
137p T R mT
p m m m
d E E a Z E EZE E E
dE m c E E E E
/p c 2
02R
eE
a
2
2
2 ( 2 )p p pm
T
E E m cE
M c
McKinley and Feshbach formula for low-Z materials
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Displacement cross-section of secondary neutrons formed in graphite under 7 TeV proton beam irradiation
06.03.2015, CERN, Geneva, Switzerland
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Displacement generation rate of point defect production
06.03.2015, CERN, Geneva, Switzerland
Gd =max
( ) ( )d
Tp
d
E
nE E dE
np is the total number of protons in a bunch(1.1*1011),
τ is the time gap between bunches (26 ns),
Ф(Е) is the energy spectrum of secondary particles having energy E and interacting with graphite atoms,
σd (E) is the cross section of defect formation with the secondary particle energy E.
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Displacement rate of DPA produced by secondary protons at different distances along the beam of 7 TeV protons per each bunch
06.03.2015, CERN, Geneva, Switzerland
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Displacement rate of DPA produced by secondary pions at different distances along the beam of 7 TeV protons per each bunch
06.03.2015, CERN, Geneva, Switzerland
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Displacement rate of DPA produced by secondary neutrons under 7 TeV proton beam irradiation per each bunch
06.03.2015, CERN, Geneva, Switzerland
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The spectrum of pions (π-) produced in graphite at different distances along the beam of 450 GeV protons (FLUKA)
06.03.2015, CERN, Geneva, Switzerland
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Displacement cross sections for secondary pions with energies up to 450 GeV in graphite
06.03.2015, CERN, Geneva, Switzerland
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Cross section of defect formation for secondaryπ–mesons in graphite near 450 GeV proton beam
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Generation rate of primary radiation point defects (DPA) in graphite versus energy of pions at different distances along the beam of
450 GeV protons per each bunch
06.03.2015, CERN, Geneva, Switzerland
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The spectrum of secondary relativistic electrons produced in graphite at different distances along the beam of 450 GeV protons (FLUKA)
06.03.2015, CERN, Geneva, Switzerland
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Displacement cross sections for secondary electrons with energies up to 450 GeV in graphite
06.03.2015, CERN, Geneva, Switzerland
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Generation rate of primary radiation point defects (DPA) in graphite versus energy of secondary electrons at different distances along the
beam of 450 GeV protons per each bunch
06.03.2015, CERN, Geneva, Switzerland
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Energy spectra of secondary neutrons formed as a resultof interaction of 450 GeV proton beam with graphite
along beam axis
06.03.2015, CERN, Geneva, Switzerland
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Generation rate of point defect formation (DPA) under irradiation by secondary neutrons along axis of 450 GeV
proton beam
06.03.2015, CERN, Geneva, Switzerland
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ConclusionConclusion
06.03.2015, CERN, Geneva, Switzerland
Maximum of displacement rates for 7 TeV protons correspond to the following secondary particles:
•Protons – 0.012 dpa/s per proton bunch•Pions – 0.11 dpa/s per proton bunch•Neutrons – 0.018 dpa/s per proton bunch
Maximum of displacement rates for 450 GeV protons correspond to the following secondary particles:
•Electrons – 4e-3 dpa/s per proton bunch•Pions – 4.3e-3 dpa/s per proton bunch•Neutrons – 4e-3 dpa/s per proton bunch
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