Introduction of radiation damage calculation in PHITS for high-energy region Yosuke Iwamoto Nuclear Science and Engineering Center Japan Atomic Energy Agency Outline • Introduction • Displacement per atom (DPA) calculation method • Comparison between PHITS and other codes • RaDIATE examples with PHITS • Summary 1
Scale of irradiation effect Primary Change of Knock-on material Atom Vacancy properties Size (m) e.g. Thermal conductivity, Diffusion and Size (m) electrical resistivity interstitial growth process atom Atomic collisions Nuclear reactions 10 -20 10 -15 10 -10 10 -5 10 0 10 5 10 10 Time (sec) To evaluate radiation damage, a fundamental parameter DPA that characterizes lattice displacement events is required. 2
� � Micr crosco scopic c effect cts s on material DPA: average number of displaced atoms per atom of a material s disp : displacement cross-section DPA= ! 𝜏 #$%& 𝐹 𝜚 𝐹 𝑒𝐹 f : irradiation fluence (particles/cm 2 ) Frenkel pair Self interstitial atom Related to the number of Frenkel pairs N F : DPA=∑ N i N i vacancy N i = number of particles F a scale of radiation damage intensity. DPA is used as a damage-based exposure unit and used to compare radiation damage by different radiation sources. MC codes (PHITS, MARS, FLUKA, MCNP…) calculate DPA values: 1. Using database of s disp → limitation for kind of incident particles and materials. 2. Calculating s disp for all particles with physics models event by event This presentation shows radiation damage calculation with physics models in PHITS 3
Physical Processes Vacuum Material Collision included in PHITS Transport Collision T. Sato et al., JNST 50 (2013) 913. • Magnetic Field • Gravity External Field • Super mirror (reflection) and Optical devices • Mechanical devices, T0 chopper Transport between • dE/dx : SPAR, ATIMA code Ionization process collisions Continuous-slowing-down for charge particle Approximation (CSDA) • δ-ray generation • Microdosimetric function • Track-structure simulation Nuclear Data based (JENDL-4.0 etc.) Low-energy Neutrons Event Generator Mode Collision Photons, Electrons Electromagnetic cascade with EGS5 with High-energy nucleons Intra-Nuclear Cascade nucleus Evaporation Heavy Ions Quantum Molecular Dynamics 4
Map of Models in PHITS Proton, Pion e - / e + Neutron Nucleus Muon Photon (other hadrons) 1 TeV 1 TeV/u 1 TeV Intra-nuclear cascade (JAM) Quantum Virtual + Evaporation (GEM) Low ← Energy → High Photo- Molecular Photo- 3.0 GeV Nuclear Dynamics Nuclear JAM/ Intra-nuclear cascade (INCL4.6) (JQMD) d JAM/ EPDL97 JQMD + + QMD EGS5 or + t + Evaporation (GEM) Evaporation EGS5 GEM GEM 3 He (GEM) 20 MeV + 200 MeV a JENDL 10 MeV/u + Nuclear 1 MeV NRF Ionization Data Library ATIMA 1 keV 1 keV 1 keV (JENDL-4.0) JENDL4 based all secondary particles are specified Event generator mode 0.1 meV Next slide: DPA calculation method 5
DPA ca calcu culation method in PHITS (1)Energy transfer (2)Cascade damage with Coulomb scat. approximation Interstitial atom vacancy projectile target PKA secondary Nuclear reaction target PKA s = ò d ( t ) 0 . 8 t s h max Coul T dt disp dam × dt 2 T t d d Coulomb scattering Number of displacement atoms Y. Iwamoto et al., NIMB 274 (2012) 57. 6
(1)Energy transfer with Coulomb scattering M. Nastasi et al., “Ion-Solid Interaction: Fundamentals and Applications “ Charged particle E p :kinetic energy , (Z 1 , M 1 ) leads to the deflection of the particles target PKA T: transferred energy , (Z 2 , M 2 ) Coulomb scat. cross section: one parameter p 2 1 / 2 a f ( t ) Screening functions: [ ] s = d ( t ) TF dt - 1 / q - - = l + l 1 / 2 1 / 2 m 1 m q f ( t ) t 1 ( 2 t ) coul 3 / 2 2 t Thomas-Fermi l =1.309, m =1/3, q =2/3 dimensionless collision parameter: q T º e = e 2 2 sin 2 t ( ) T 2 max T : Transferred energy to target atom T max :maximum transferred energy 4 M M E = 1 2 p + 2 ( M M ) 1 2 e :dimensionless energy Large t large T in close collisions Ea TF M = 2 Small t small T in distance collisions + 2 Z Z e ( M M ) 1 2 1 2 Next slide: cascade damage approximation 7
(2) Cascade damage approximation s = ò d ( t ) 0 . 8 t s h max Coul T dt disp dam × dt 2 T t d d 1 Defect production efficiency = x e e = e T ( ) T ( ) T ( ) dam + × e 1 k g ( ) cas Damage energy: transferred to lattice atoms reduced by the losses for electronic stopping atoms in the displacement cascade number of displaced atoms using phenomenological approach: N NRT NRT(Norgett, Robinson, Torrens: 1975) •0.8: displacement efficiency derived from MD simulation of Robinson, Torrens 1972 •T d : threshold displacement energy. Bonds should be broken to displace an atom. e.g. set to 40 eV in Ti but varies 15 – 90 eV in other atom 8
Efficiency of the defect production in material N - - = + ´ 0 . 437 3 h = 0 . 7066 T 2 . 28 10 T for Cu D dam dam N M.J. Caturla et al., J. Nucl. Mater. 296 (2001) 90. NRT N D : number of stable displacements at the end of collision cascade MD Account for atom recombination N NRT : number of defects calculated by NRT model in elastic cascading 1x10 5 s disp with h reproduces experimental data PHITS-NRT in the high-energy region up to GeV for Cu. Displacement cross sections (b) PHITS-BCA,MD Iwamoto Jung Y. Iwamoto et al., JNM 458 (2015) 369. 1x10 4 Greene P. Jung, JNM 117 (1983) 70. G.A. Greene et al., Proc. of AccApp’03 (2004) 881. Note: there are new efficiencies proposed Cu by Stoller and Nordlund. 1x10 3 PHITS will include them soon. 10 0 10 1 10 2 10 3 In this presentation, NRT-DPAs are reported. Incident proton energy (MeV) 9
Comparison between PHITS and SRIM codes 100keV/u Ti+Ti 2MeV p+Ti SRIM can simulate Ed=40eV the transport of ions Ed=40eV in matter without nuclear reaction. http://www.srim.org/ 2MeV p+C 100keV/u C+C Good agreement. Ed=31eV Ed=31eV 10
Comparison between PHITS and SRIM codes DPA x 10 -24 / source DPA x 10 -24 / source ü PHITS results are in good agreement ü differences between two results: with SRIM results. Secondary particles created from sequential nuclear reactions 11
Comparison between PHITS, SRIM and MARS codes Courtesy of Nikolai MOKHOV and Francesco CERUTTI MARS result: Courtesy of Nikolai Mokhov Good agreement. 12
RaDIATE example with PHITS Proton gaussian beam Energy: 0.18, 0.8, 3, 30, 120, 400GeV 180MeV 400 GeV (PHITS is not available at 7 TeV.) proton 𝜏 + = 𝜏 - = 0.43𝑑𝑛 120 GeV z 30 GeV 90 cm long, R=1.3 cm C-target, density=1.84g/cm 3 0.8,3GeV Tally region: 90 cm long, r=0.2cm DPA depth distribution in C-target 180 MeV: Bragg peak of protons contributes DPA. 0.8-30 GeV: Damage may occur at surface. 120GeV, 400 GeV: DPA increases with depth. Other outputs (energy deposition, gas production) will be reported by Nikolai. 13
Summary The displacement calculation method in PHITS is available for all incident particles, wide energy range (eV-TeV), and all materials. Agreements between PHITS and other codes are good. In the high energy region (> ~20 MeV) for proton and neutron, DPA created by secondaries increase due to nuclear reactions. Future works New defect production efficiency (Nordlund) will be implemented. (just implemented!) Benchmark experiments will be performed at RCNP (100-400MeV) and J-PARC (400MeV-30GeV, see Meigo-san’s talk). This work has been supported by JSPS KAKENHI Grant Number 16H04638. 14
Experimental displacement cross section Displacement cross section could be experimentally validated in Irradiation on metal at cryogenic temperature. Recombination of Frenkel pairs by thermal motion is well suppressed. Experimental displacement cross section Damage rate D r = 1 Δ ρ metal : Electrical resistivity change(Ωm) s metal exp r f Φ: Beam fluence(1/m 2 ) FP ρ FP : Frenkel-pair resistivity (Ωm) J. Nucl. Mater. 49 (1973/74) 161. Resistivity increase is the sum of resistivity per Frenkel pair 15
Development of cryogen-free cooling system at FFAG/KURRI GM cryocooler (RDK- 205E, Sumitomo inc.) Cold head Sample was cooled by conduction coolant via Al and oxygen-free high-conductivity 125 MeV, 1 nA copper (OFHC). proton Target assembly 16
Experimental results of copper Electrical resistance Displacement cross section (b) increase 1.53 µ W Expt. 125 MeV, 1 nA Calc. Expt. Cu 24 hours irradiation Fluence:1.45 × 10 18 (1/m 2 ) Systematic experimental data Proton energy (MeV) Electrical resistivity changes of copper Displacement cross section of copper 17
Evaluation of radiation damage The average number of Displaced atoms Per Atom of a material (DPA) is used in 0.7dpa Stress (MPa) 3.6dpa evaluation of reactor and accelerator as a damage-based exposure unit. Unirradiation DPA = ò s f ( E ) ( E ) dE Damage depending on disp. DPA and temperature Displacement cross section Fluence Strain (%) Irradiation effect on AlMg3 for 600 MeV proton irradiation Contribution of proton is higher than that of neutron. DPA All p n DPA for target at J-PARC ADS Target Test Facility (TEF-T) using Monte Carlo particle transport code PHITS 18 Y. Iwamoto, et al., J. Nucl. Sci. Technol 51 (2014) 98-107.
① JENDL-4.0 を用いた PHITS と NJOY2012 の損傷エネルギー断面積の比較 47 Ti 19/11
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