Molecular Dynamics Simulations of the Interactions Between Tungsten Dust and Beryllium Plasma-Facing Material

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1 Plasma Science and Technology, Vol.17, No.12, Dec Molecular Dynamics Simulations of the Interactions Between Tungsten Dust and Beryllium Plasma-Facing Material NIU Guojian ( ) 1,2,LIXiaochun( ) 1, XU Qian ( ) 1, YANG Zhongshi ( ) 1, LUO Guangnan ( ) 1 1 Institute of Plasma Physics, Chinese Academy of Sciences, Hefei , China 2 University of Science and Technology of China, Hefei , China Abstract In the present research, molecular dynamics simulation is applied to study the interactions between tungsten dusts and a beryllium plasma-facing material surface. Calculation results show that it is quite difficult for nanometer-size dust particles to damage the plasma-facing material surface, which is different from the micrometer-size ones. The reason may be the size difference between dust and crystal grains. The depth of dust penetration into plasma-facing materials is closely related to the incident velocity, and the impacting angle also plays an important role. Dust and material surface damage is also investigated. Results show that both incident velocity and angle can significantly influence the damage. Keywords: molecular dynamics, tokamaks, dust, plasma-facing materials PACS: Vy, Fa, y, Yy, Hf DOI: / /17/12/16 (Some figures may appear in colour only in the online journal) 1 Introduction Over the past few years significant progress has been achieved towards the understanding of dust behaviors in fusion devices through experiments, modeling and model validation [1 3]. Many plasma processes, such as brittle destruction [4], volume polymerization [5],cracking development [6],arcing [7], flaking of blisters [8] and surface melting [9] etc., contribute to the production of dust particles. Off-normal plasma events such as edge localized mode (ELM) [10,11] also play a significant role in dust generation. Dust particles increase the operation difficulties of plasma sustainment since dust is a source of impurities and facilitates radiation power [12]. Moreover, dust can penetrate deeply into core plasma and contaminate the plasma. The contamination can increase the amount of impurity concentration in plasma or even lead to disruption [13,14]. Because of the large surface area, re-deposited dust particles can also increase fusion fuel [15]. As a result dust generation and its transport have been attracting great interest. Because the dust-pfm (Plasma-Facing Materials) interaction is closely associated with the service life of PFM and impurity generations, it is also a crucial issue in fusion science. Low velocity dust particles can deposit on the PFM surface and form dust film on it. R. J. Hong et al. [16] and G. J. Niu [17] et al. studied the interaction process between tungsten dust and tungsten plasma-facing materials. Smirnov et al. reported that tungsten dust with high velocity can damage the beryllium first wall with the aid of the finite element method [18]. Although several studies have been performed for the dust-pfm interactions, it remains a major unsolved problem. The rest of this paper is organized as follows. In section 2, we briefly outline the molecular dynamics (MD) simulation methods. We investigate the effect of tungsten dust impacting into beryllium plasma-facing material in section 3. Finally, we summarize our results and provide concluding remarks in section 4. 2 Methods 2.1 Molecular dynamics and simulation geometry The interaction between dust particles and plasmafacing materials is simulated by classical molecular dynamics simulation employing many-body interatomic potentials implemented in the LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) code. The simulation system is made up of a dust particle and a PFM surface. The dust material is tungsten (W) while the material of PFM is beryllium (Be). The dust particle s radius is about 12 Å containing 456 atoms/dust and their shape is spherical. The di- supported by the National Magnetic Confinement Fusion Science Program of China (Nos. 2013GB105001, 2013GB105002, and 2015GB109001), National Natural Science Foundation of China (Nos , and ), as well as Technological Development Grant of Hefei Science Center of CAS (No. 2014TDG-HSC003) 1072

2 NIU Guojian et al.: Molecular Dynamics Simulations of the Interactions Between W Dust and Be PFM mension of the PFM surface is Å 3 in the x-, y-andz-directions, which has been tested as enough for simulation. The z-direction is the [0001] direction of the Be lattice. The x- andy-directions are perpendicular to the z-direction. The thickness of PFM is 200 Å. The structure of W material is body-center cubic (BCC) and the lattice constant a=3.165 Å, meanwhile Be is a hexagonal close-packed (HCP) lattice with a=2.32 Åandc=1.558 a. The dropping point of the dust is randomly selected to avoid its influence. The time step is automatically adapted in the MD simulation to keep the moving distance of each atom less than 1 Å in one step, with the minimum time step set as s. The purpose of doing this is to avoid unphysical strange calculation results due to the overlong moving distance of atoms in one simulation step. The temperature of the system is 300 K while the temperature of the dust particles is ignored. Periodical conditions are applied in the directions perpendicular to the incident direction. Although the magnetic field direction is almost parallel to the PFM surface, dust particles do not impact the PFM surface at a big incident angle, according to the simulation results of DTOKS in MAST [19]. In the present study two typical incident angles are selected, i.e. 0 o and 45 o, to investigate the influence of the incident angle. A thermal bath is set around the PFM. A six-angstrom-thick atom layer at the edge and bottom of the PFM is kept at a constant temperature of 300 K, while in other parts, the NVE ensemble is applied, i.e., the atoms number (N) and total energy (E) are constant. Several parallel simulations have been performed to ensure the correctness of the results. 2.2 Molecular dynamics potential The forces between atoms are described by the bonding-order potential (BOP) [20]. The total energy of this potential is Vij R and V ij A spectively. form: U BOP = i>j [ f (r ij ) V R ij b ij + b ji 2 ] Vij A, (1) are the repulsive and attractive terms, re- These are pair potentials of a Morse-like Vij R = D [ 0 S 1 exp β ] 2S (r r 0 ), (2) Vij A = SD [ 0 S 1 exp β ] 2/S (r r 0 ), (3) The function f is 1 r (R D) f (r)= sin(π (r R) /2D) R r D. 0 r (R + D) (4) R and D are potential parameters to determine the cutoff distance of the interaction. The parameter b ij is the bond order term, which includes three-body interactions and angularity: where and b ij =(1+ξ ij ) 1/2, (5) ξ ij = f ik (r ik ) g ik (θ ijk )e 2μ ijk(r ij r ik ), (6) k i,j [ ] g (θ) =γ 1+ c2 d 2 c 2 d 2 +(h +cosθ) 2, (7) where c, d, h are potential parameters and θ is the angle between two bindings. Binding-order potential is too soft for high pressure cases, so the ZBL (Ziegler-Biersack-Littmark) pairpotential U ZBL is applied to improve the compressibility. The details of the ZBL potential are discussed in Ref. [21]. So the actual potential used in the present research is a combination of ZBL and BOP with the form of U actual =(1 h (r)) U ZBL + h (r) U BOP. (8) The function h(r) is 1 h (r) =. (9) 1+e AF(r rc) The value of parameters D 0, r 0, β, S, γ, c, d, h, D, R, μ, A F and r C were given in Ref. [19]. 3 Results and discussions 3.1 Dust velocity Dust velocity is a key parameter for dust-pfm interactions. In the present research, the velocity of dust is estimated according to the model in Ref. [18]. The relation between dust radius R d and velocity v is ( ) Rd0 v = v 0 + A ln. (10) R d where D 0 and r 0 are the bond energy and the length of the dimer molecule, respectively, S and β are potential parameters and r is the distance between two atoms. Here A = ζ f H vap m 1/2 i, (11) ζ h m d T 1/2 1073

3 Plasma Science and Technology, Vol.17, No.12, Dec where R d and v are the dust particle s radius and speed, and R d0 and v 0 are the initial radius and speed, respectively. n and T are the plasma density and temperature, H vap is the heat of vaporization per atom of dust material, m i isthemassofaplasmaion,m d is the mass of a dust material atom, and ζ h and ζ f are numerical factors accounting for geometry in plasma heat and momentum flux to the dust particle, respectively. For a Be dust in deuterium plasma, using n =10 13 cm 3, T =10 ev, H vap =7 ev, m i = g, m d = g, ζ f 10, and ζ h 20, we have A(W)=82 m/s. Note that the value of the heat of evaporation H vap used here takes into account the sublimation of W at high temperatures. The value of A(C) is 1000 m/s according to Ref. [18]. It means that the velocity of W dust particles is much less than that of carbon dusts, which is consistent with previous research results. If the initial radius R d0 is 1 μm, the final radius R d = 10 nm and initial velocity v 0 = 0, the final velocity of W dust v 200 m/s. Considering the different initial radii and velocity of the dust particles and the complicated forces acting on the dust particles, the velocity of the dust particles may be much greater than 200 m/s. So we reasonably assume the velocity to be in the range of m/s for W dust particles. On the other hand, experimental results show that dust particles can obtain higher velocities of the order of km/s, so in the present research, dust with 1000 m/s speed is also taken into account. 3.2 Interactions of W dust and Be surface Three velocities are considered, viz. v = 100 m/s, 500 m/s and 1000 m/s. Considering the different velocity directions of dust particles, two impacting angles are examined, θ =0 o and θ =45 o. So six simulation cases have been implemented in the present study. The final states of these simulations are shown in Fig. 1, (a) to (f) for the cases of v =100 m/s and θ =0 o, v =100 m/s and θ =45 o, v =500 m/s and θ=0 o, v =500 m/s and θ=45 o, v=1000 m/s and θ=0 o, v =1000 m/s and θ=45 o,respectively. When the incident velocity is 100 m/s, dust particles land on the PFM surface with little damage to it, as shown in Fig. 1(a). The dust particles only affect a shallow surface layer of Be PFM. By comparing Fig. 1(a) and (b), the profile of the final state of the dust/pfm interaction is not affected by the impacting angle when the incident velocity is 100 m/s. When the incident velocity reaches 500 m/s, the dust particles affect deeper than the 100 m/s dusts. Several W atoms escape from the dust particle and penetrate into the deeper part of the Be surface; the depth is about several atom layers, as shown in Fig. 1(c). The effect of the oblique incident is not significant when v = 500 m/s, as compared with Fig. 1(d). When the incident velocity v = 1000 m/s, dust particles can cause more significant damage on the Be surface. The dust can affect a deeper location in the Be PFM surface, as shown in Fig. 1(e). Meanwhile, the effect of the incident angle becomes obvious. The structure with direction along the dust velocity is damaged more seriously, as shown in Fig. 1(f). (a) Velocity and angle incident into sheath are v = 100 m/s, θ =0 o (b) Velocity and angle incident into sheath are v = 100 m/s, θ =45 o (c) Velocity and angle incident into sheath are v = 500 m/s, θ =0 o (d) Velocity and angle incident into sheath are v = 500 m/s, θ =45 o (e) Velocity and angle incident into sheath are v = 1000 m/s, θ =0 o (f) Velocity and angle incident into sheath are v = 1000 m/s, θ =45 o Fig.1 Tungsten dust impacting into the beryllium surface. 455 atoms in one dust particle 1074

4 NIU Guojian et al.: Molecular Dynamics Simulations of the Interactions Between W Dust and Be PFM In macroscopic terms, the compressive stresses on the PFM surface σ s can be estimated by [22] σ s ρ s C s V, where V is the normal dust impact speed, ρ s and C s are mass density and sound speed of the PFM surface, respectively. If the compressive stresses σ s are greater than the ultimate strength G of the plasma-facing material, the surface will be damaged. The ultimate strength, sound speed and mass density of Be materials are G(Be)=1.31 GPa, C s (Be)=12870 m/s and ρ s (Be)= 1.82 g/cm 3, respectively. According to these data, the threshold velocity for W dust damaging the Be surface is approximately equal to 55 m/s. That is, if the normal component velocity is greater than 55 m/s, dust particles can damage the PFM surface. R. D. Smirnov also indicated in Ref. [18] that micrometer-size W dust particles with 1000 m/s speed can seriously damage the Be surface and cause sputter atoms. However, in the present molecular dynamics simulations, the damage caused by W dust particles is much less serious than the results in Ref. [18] and no sputter atoms are found. The reason may be the size difference between dust particles and crystal grains. The existence of crystal grains makes materials more fragile and easier to damage. The size of crystal grains is of the order of micrometers, so the dust particles with micrometer-radius can generate significant damage on it. For dust particles with a nanometer radius, however, the Be material is almost a perfect lattice because of the great size differences. A molecular dynamics simulation indicates that W dust particles cannot produce a significant crater unless the dust speed is higher than 3 km/s. This means that it is difficult for nanometer size dust particles to damage the PFM surface. In order to study the penetration depth of dust into the PFM surface, we defined the maximum depth z max of dust particles. The depth z max is defined as the location of the deepest dust atom along the normal direction of the material surface. The maximum dust depth as a function of incident velocity and angle is shown in Fig. 2. The absolute value of maximum depth increases with the growth of incident velocities. When the incident velocity is 100 m/s, the maximum depth is about 7 Å. When the incident velocity increases to 500 m/s, the maximum depth is about 10 Å. When the incident velocity is up to 1000 m/s, the depth is about 20 Å. The maximum depth is also related to the incident angle. If the incident angle is 45 degrees, the maximum depth z max is about 5 Å, 10 Åand 14 Åwhen the velocity is 100 m/s, 500 m/s and 1000 m/s, respectively. The reason is that the perpendicular velocity decreases with the growth of the incident angle: perpendicular velocity v = v cosθ, whereθ is the incident angle. The interaction of dust-pfm can damage both dust particle and plasma-facing material. The damage on dust and PFM is described by the number of displaced atoms. The displaced atoms refer to an atom which is knocked out of its lattice. The number of displaced atoms in dust particles as a function of dust velocity and incident angle is shown in Fig. 3. It is apparent that the increase of incident velocities facilitates the damage of dust particles. The number of displaced atoms is 5.44, 45.0 and 136 when the incident velocity is 100 m/s, 500 m/s and 1000 m/s, respectively, under normal impact conditions. The reason for the facilitating effect of dust velocity is obvious. With the increase of incident velocity, the collision between dust and PFM becomes more serious, and it is easier for the atoms to obtain enough energy to escape from the original location. As the impacting velocity increases, the interactions between dust and PFM become more violent and it is easier for the atoms to obtain enough energy to escape from the lattice. On the other hand, the impact angle θ also plays an important role in dust damage. The number of displaced atoms reaches 9, 80 and 231 in the cases of v=100 m/s, 500 m/s and 1000 m/s under the condition of θ=45 o, respectively. Although the impact angle θ decreases the normal incident velocity v, it offers a tangential velocity v which is perpendicular to the normal direction of the PFM surface. Such tangential velocity facilitates the damage of dust particles. One reason is that the tangential friction force of PFM makes more atoms escape from the dust particles. The other reason is that the slippage of dust particles offers escaping space for dust atoms. Fig.2 Maximum depth of dust in the PFM surface as a function of dust velocity and incident angle Fig.3 Number of atoms knocked out of the lattice in dust particles as a function of dust velocity and incident angle 1075

5 Plasma Science and Technology, Vol.17, No.12, Dec The dust-pfm interactions can also damage the PFM surface. The number of displaced atoms in PFM as a function of dust velocity and incident angle is shown in Fig. 4. The number of displaced atoms is 5900, 6250 and 6393 when the incident velocity is 100 m/s, 500 m/s and 1000 m/s under normal impact condition, respectively. This is because when the incident velocity increases, the collided PFM atom can get more energy in the collision process. The higher kinetic energy of collided atoms enhances the probability for PFM atoms to escape from the lattice. The impacting angle stimulates the damage of PFM. The number of displaced atoms reaches respectively 6442, 6635 and 6937 in the cases of v=100 m/s, 500 m/s and 1000 m/s under the condition of θ=45 o. The possible reason for the promoting effect of the incident angle is similar to the effect of the incident angle on dust particles. The tangential velocity v of dust particles offers a friction force on PFM atoms. This force knocks PFM atoms more easily out of the PFM surface because the surface escaping energy is less than the displacement threshold energy in the material. Furthermore, the oblique impacting offers escaping space for displaced atoms, as shown in Fig. 5. For the normal impacting case, the PFM atoms under the landing point of dust particles restrict the movement space of displaced atoms. That is, if one dust atom escapes from its lattice, it must penetrate into the deeper part of the PFM surface which costs the kinetic energy of escaping atoms. But for the oblique impact cases, displaced atoms do not need to penetrate, they can stay on the PFM surface far away from the dust. Since the dust particle can slip on the PFM surface, the location at which the dust finally stops is not necessarily the hitting point of the dust as it lands on the PFM surface. Fig.4 Number of atoms knocked out of the lattice in plasma-facing materials as a function of dust velocity and incident angle Fig.5 Explanation of the promoting effect of oblique impacting on dust and PFM damage The promotion scale η which is defined as the ratio of the displaced atoms number under oblique impacting to that under normal impacting for the same incident velocity η (45 o )= N (v, θ =45o ) N (v, θ =0 o ). Thevaluesofη for different velocities are listed in Table 1. It can be seen that the η value is quite similar for different impacting energies. The value of η for dust particles is around 1.7, meanwhile η 1.07 for PFM. Such a consistency in the data implies that the value of η is almost independent of incident velocity but related to the impacting angle and the materials of dust and PFM. Detailed studies of the dependence on the impacting angle will be performed in the future. Table 1. Ratios of the number of displaced atoms of oblique impact to normal impact Dust Promotion scale Promotion velocities of dust scale of PFM 100 m/s m/s m/s Conclusions In the present research, the interaction between tungsten dust and beryllium plasma-facing material is investigated by the molecular dynamics simulation method. The incident velocity is estimated with the help of the method in Ref. [18]. The impacting velocity of W dust particles is selected from 100 m/s to 1000 m/s, together with two typical incident angles, viz. 0 o and 45 o. The simulation results show that the dust particles with a speed of 100 m/s and 500 m/s stick on the Be surface and cannot cause serious damage. Meanwhile the incident angle does not significantly affect the dust/pfm interaction. The dust particles with 1000 m/s velocity can cause more serious damage on the Be surface compared to the dusts with m/s velocities, and the influence of the incident angle becomes remarkable. However, the damage caused by nanometer-size dust particles is much less serious than that caused by micrometer-size particles. This may be caused by the size effect of crystal grains. The existence of crystal grains make materials easier to damage. The size of crystal grains is of the order of micrometers, so the dust particles with a micrometer-radius can generate significant damage. But the nanometer-size particles face an almost perfect lattice because their size is much smaller than crystal grains. The size differences may be the main reason for the difficulties of damaging the PFM surface by dust. The penetration depth of dust particles in the PFM surface is also investigated in the present simulation. The depth is closely related to the incident velocity of dust particles. The incident angle of dust also plays a 1076

6 NIU Guojian et al.: Molecular Dynamics Simulations of the Interactions Between W Dust and Be PFM significant role in the dust depth. With the growth of the incident angle, the depth of dust particles in the PFM surface is reduced. This is because the increase of the incident angle decreases the normal impacting velocity which plays a crucial role in the dust depth in the PFM surface. The damage on dust and the PFM surface caused by dust/pfm interactions is also investigated. The number of displaced atoms is used to measure the damage. The results show that the damage on dust and the PFM surface is directly related to the incident velocities. The increase of velocity facilitates the damage. Oblique impacting promotes the damage on both dust and the PFM surface. The promotion scale which is the ratio of a displaced atom number under oblique incident to that under normal impacting, however, is independent of the incident velocity. Acknowledgment The authors gratefully acknowledge the operation team of HIRFL for their help. The authors would also like to thank Yukihiro Tomita and Gakushi Kawamura for providing helpful discussions and advices. References 1 Krasheninnikov S I, Smirnov R D, Rudakov D L. 2011, Plasma Phys. Control. Fusion, 53: Sharpe J P, Petti D A, Bartels H W. 2002, Fusion Eng. Des., 63-64: Girard J P, Garin P, Taylor N, et al. 2007, Fusion Eng. Des., 82: Pestchanyi S, Wurz H. 2001, Phys. Scr., T91: 84 5 Hong S, Berndt J, Winter J. 2003, Plasma Sources Sci. Technol., 12: 46 6 Makhlaj V A, Garkusha I E, Aksenov N N, et al. 2013, J. Nucl. Mater., 438: S233 7 Balden M, Endstrasser N, Humrickhouse P W, et al. 2014, Nucl. Fusion, 54: Nishijima D, Iwakiri H, Amano K, et al. 2005, Nucl. Fusion, 45: Lipschultz B, Coenen J W, Barnard H S, et al. 2012, Nucl. Fusion, 52: Bary B D, West W P, Rudakov D. 2009, J. Nucl. Mater., : Wurz H, Pestchanyi S, Bazylev B, et al. 2001, J. Nucl. Mater., 290: Winter J, Gebauer G. 1999, J. Nucl. Mater., 266: Tuccillo A A, Alekseyev A, Angelini B, et al. 2009, Nucl. Fusion, 49: Rudakov D L, Litnovsky A, West W P, et al. 2009, Nucl. Fusion, 49: Ivanova D, Rubel M, Philipps V, et al. 2011, Phys. Scr., T145: Hong R J, Yang Z S, Niu G J, et al. 2013, Plasma Sci. Technol., 15: Niu G J, Li X C, Ding R, et al. 2014, Plasma Sci. Technol., 16: Smirnov R D, Krasheninnikov S I, Pigarov A Y, et al. 2009, J. Nucl. Mater., : Martin D, Bacharis M, Coppins M, et al. 2008, Eur. Phys. Lett., 83: Bjorkas C, Henriksson K O E, Probst M, et al. 2010, J. Phys. Condens. Matter., 22: Ziegler J F, Biersack J P, Littmark U. 1985, The Stopping and Range of Ions in Matter. Pergamon Press, New York 22 Zukas J A. 1990, High Velocity Impact Dynamics. Wiley, New York (Manuscript received 9 December 2014) (Manuscript accepted 17 April 2015) address of corresponding author LUO Guangnan: gnluo@ipp.ac.cn 1077