1 A.I.Ryazanov, E.V.Semenov and A.Ferrari DPA calculations in irradiated graphite collimator materials under 7 TeV and 450 GeV proton beams 06.03.2015,

11

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

22

Energy flux of secondary protons formed in graphite at different distances along the beam of 7 TeV protons


33

Energy flux of secondary electrons formed in graphite at different distances along the beam of 7 TeV protons


44

Energy flux of secondary charged pi-mesons formed in graphite at different distances along the beam of 7 TeV protons


55

Cumulative energy flux of secondary neutrons formed in graphite at different distances along the beam 7 TeV protons


66

Displacement cross-section


( , )( ) ( )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.

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


88

Cascade function


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,

The crystal structure of graphite showing the ABAB stacking sequence of graphene planes in

which the carbon atoms have three fold coordination.


The value of Ed lies between 24 and 60 eV. (Ed =25eV)

1010

Differential cross-section of electrons and charged pions


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

1111

Displacement cross-section of secondary neutrons formed in graphite under 7 TeV proton beam irradiation


1212

Displacement generation rate of point defect production


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.

1313

Displacement rate of DPA produced by secondary protons at different distances along the beam of 7 TeV protons per each bunch


1414

Displacement rate of DPA produced by secondary pions at different distances along the beam of 7 TeV protons per each bunch


1515

Displacement rate of DPA produced by secondary neutrons under 7 TeV proton beam irradiation per each bunch


1616

The spectrum of pions (π-) produced in graphite at different distances along the beam of 450 GeV protons (FLUKA)


1717

Displacement cross sections for secondary pions with energies up to 450 GeV in graphite


Cross section of defect formation for secondaryπ–mesons in graphite near 450 GeV proton beam

1919

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


2020

The spectrum of secondary relativistic electrons produced in graphite at different distances along the beam of 450 GeV protons (FLUKA)


2121

Displacement cross sections for secondary electrons with energies up to 450 GeV in graphite


2222

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


2323

Energy spectra of secondary neutrons formed as a resultof interaction of 450 GeV proton beam with graphite

along beam axis


2424

Generation rate of point defect formation (DPA) under irradiation by secondary neutrons along axis of 450 GeV

proton beam


2525

ConclusionConclusion


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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Thank you very much for your Thank you very much for your attention!attention!

Documents

1 A.I.Ryazanov, E.V.Semenov and A.Ferrari DPA calculations in irradiated graphite collimator materials under 7 TeV and 450 GeV proton beams 06.03.2015,