History of PARASOL! T. Takizuka! Graduate School of Engineering, Osaka University!! PARASOL was developed at Japan Atomic Energy Agency!
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1 History of PARASOL! T. Takizuka!!! Graduate School of Engineering, Osaka University!! PARASOL was developed at Japan Atomic Energy Agency! OSAKA UNIVERSITY! 20th NEXT Meeting, Kyoto Terrsa, Kyoto, Jan 2015!
2 Edge Plasma Research for Fusion Hot plasma in the core region is transported across magnetic field lines to the peripheral region (closed field), and brought out to the scrape-off-layer region.! Since SOL/divertor plasmas attach walls directly, plasma particles and heat escape to the walls mainly along magnetic field lines (open field).! Utilizing this nature, we expect divertor functions! for the heat removal, ash exhaust, impurity! shielding (retention) in fusion reactors,! such as ITER and DEMO.!
3 Importance of Edge Plasma Simulation To understand the complex system of plasma edge in! fusion devices, numerical simulations are indispensable.!! various non-dimensional parameters ρ*, β, ν* + l A&M-mfp, L rad (T e )! complex geometries of magnetic configuration and wall! Multi-element Integrated Simulation for SOL-divertor plasmas! SOLPS, EDGE2D/NIMBUS, UEDGE, SONIC, EMC3/EIRENE etc! Integrated SOL-divertor! code developed in JAEA! fluid model! Monte Carlo! model! H. Kawashima, K. Shimizu, T. Takizuka, et al., Plasma Fusion Res. 1 (2006) 031. H. Kawashima, K. Shimizu, T. Takizuka, Plasma Phys. Control. Fusion 49 (2007) S77.
4 Particle Modeling! Various physics models ( e.g., boundary condition at the divertor! plate V // = C s, parallel heat conduction q // = κ // // T etc. ) are! employed in the fluid modeling for SOL-divertor plasmas.! Kinetic approach is necessary to validate such physics models.! One of the most powerful kinetic models is particle simulation! R. Cohen, X.Q. Xu, Contrib. Plasma Phys. 48 (2008) 212. C.K. Birdsall, IEEE Trans. Plasma Sci. 19 (1991) 65. J.P. Verboncoeur, Plasma Phys. Control. Fusion 47 (2005) A231. PARASOL code has been developed for studying! the physics of SOL and divertor plasmas.! ( PARticle Advanced simulation for SOL and divertor plasmas )! T. Takizuka et al., proc. 8th IAEA Conf., Brussels 1980, Vol. 1 (1981) p.679. R. Chodura, Phys. Fluids 25 (1982) T. Takizuka et al., J. Nucl. Mater (1984) 104. T. Takizuka, M. Hosokawa, Contrib. Plasma Phys. 40 (2000) 471. T. Takizuka, Plasma Sci. Technol. 13 (2011) 316.
5 Toroidal Quadrupole! open system => large end loss : improvement by r.f.?! T. Takizuka et al.,. Plasma Phys. 17 (1975) 887. PIC simulation (N i0 = N e0 = 2500, m i /m e = 25)! Collisions are essential for the end loss! τ = τ ic ln (R m ) + 2R m τ it! Collision model using modified Langevin s equation, dv/dt = Σ [ ν (v V) + A ]! Small angle scattring, Conservation of momentum and energy in the system! T. Takizuka, Master thesis, 1972 (Kyoto University).
6 Binary collision model ( Takizuka-Abe model )! (1) In a time interval,! a particle in a cell! suffers binary colli-! sions with an ion! and an electron! which are chosen! randomly in the! same cell.! Random selection of collision pairs!! At first; random rearrangement of! addresses in every cell! at every time step.!! Next ;! e i (2) Change in the! relative velocity! results from a! coulomb interaction.!! Total momentum! and total energy! are conserved! < Θ intrinsically.! 2 > ~ ν d Δt Landau collision integral like-particles ion-electron T. Takizuka, H. Abe, J. Comput. Phys. 25 (1977) 205.
7 Importance of collisions Importance of collisions! v // diffusion to high energy f e x divertor plate Importance of collisions! pitch-angle! scattering! V! neo-classical! diffusion! mirror! end loss! V //!
8 Poloidal Divertor in a Tokamak! T. Takizuka et al., Plasma Phys. Control. Nucl. Fusion Res (proc. 8th Int. Conf., Brussels) Vol. 1 (IAEA, Vienna, 1981) 679. Particles are lost from the core! to the SOL region by the! anomalous diffusion:! <δ 2 > = D Δt! Pre-sheath and sheath are! formed in the SOL.! Collision is absent in this work.!
9 Particle Simulation of Divertor Plasma! Combination of PIC Code and Binary Colision Model! T. Takizuka et al., J. Nucl. Mater. 128&129 (1984) 104. Reference: 1D collisionless PIC! R. Chodura, Phys. Fluids 25 (1982) 1628.
10 History of the PARASOL code! Prehistory (1975~1985)! Binary collision model! PIC code of 2D poloidal divertor! PIC+BiC code of 1D divertor! A period of rest (1985~1995)! Single CPU with ~ 10 MFLOPS! FACOM , M200, M380! N i ~ 2500, K t ~ 10 4! NEXT (Numerical EXperiment of Tokamak) project (1995~)! Integrated modeling project (2000~)! 1D PARASOL! 1D-dynamic PARASOL! 2D-slab PARASOL! 2D-separatrix PARASOL! 2D-toroidal PARASOL! Massively parallel computer! Intel Paragon XP/S (75 MFLOPS)! 64 PEs N i ~ 10 5, K t ~ 10 5! SGI Origin 3800 (1 GFLOPS/PE)! Altix 3700Bx2 (6 GFLOPS/PE)! 128 PEs N i ~ 10 6, K t ~ 10 6! HELIOS (2013 by Azuma)!
11 PARASOL! Charged Particles! Magnetic Field! (given)! Electrostatic! Field! Poisson s! Equation! PIC! method! Binary collision! model! Hot Source, NBI Source! Anomalous Diffusion! Equations of Motion! Density! RF Heating! Coulomb Collision! MC! Neutral Particles! Straight Motion! Elastic Collision! Plasma-Wall Interaction! A&M! MC! Recycling, Radiation Cooling, Charge Exchange etc.! T. Takizuka, M. Hosokawa, K. Shimizu, Trans. Fusion Technol. 39 (2001) 111. T. Takizuka, Plasma Interaction in Controlled Fusion Devices: 3rd ITER International Summer School, AIP Conference Proceedings 1237 (2010) 138. T. Takizuka, Plasma Sci. Technol. 13 (2011) 316.
12 System size! Fusion plasma L/λ D > 10 4 / PARASOL plasma L/λ D < 10 3! System size L, Mesh size Δ ~ λ D! Particle number N (L/λ D ) 1,2,3 dimension! Characteristic time for equilibrium L/C s Time steps K t (m i /m e ) 1/2 (L/ λ D ) Computation time t c (m i /m e ) 1/2 (L/ λ D ) 2,3,4 PARASOL simulations are available to study open-field plasmas with smaller values of! L/λ D ~ , because characteristics are almost unchanged by changing L/λ D value! except the sheath region.! 1 eφ / T e x/ L L / λd0 = 200 L / λd0 = λ D 20 λ D 0.5 φs 0.50 By introducing the binary collision model, we can flexibly perform! PARASOL simulations at any arbitrary collisionality L // / l mfp Adopt collision cut-off technique near the wall to keep collisionless sheath
13 Full particle model of PARASOL simulates! correctly the edge plasma! m i dv i /dt = e (E + v i B), dr i /dt = v i Ion polarization drift is essential!! polar V! x ~ (Ω i B)-1 de x /dt ~ (Ω i B) -1 v x E x / x ( v x Θ v // )! φ ρ i /L = 0.01 g-c full instability no m.p.s. magnetic pre-sheath x! PARASOL 2D-slab code!
14 n / n (0) V / ΘC s /2 PARASOL Simulation for Physics Modeling! V ExB Θ V // Verification of the Bohm criterion! 1D PARASOL simulation! Oblique B (Θ = B x /B << 1), E y B z drift! V ExB hot source V x 0 x / L 1/ m i V x 2 Θ 2 T eff//! V x = ΘV // + V ExB! T eff// = T e// + γ a T i//! γ a! γ a adiavatic index! γ a 3! 0 1 T i// / T 2 e// 2D PARASOL simulation! 1D : T. Takizuka, M. Hosokawa, Contrib. Plasma Phys. 40 (2000) D : T. Takizuka, M. Hosokawa, K. Shimizu, J. Nucl. Mater (2003) V/ΘC s V x ΘV // -1/2 x / L V ExB 0 1/2 m i V x0 V x * Θ 2 T eff! V x0 = ΘV // + V ExB! V x * = V x0 + nʹ T e// /n B! T eff = T eff// + (V //ʹ /ΘΩ) T eff!
15 Supersonic flow in the cold divertor! Supersonic M plate > 1 for C (R Γ /R p ) (T plate /T throat ) 1/2 < 1! R Γ : particle flux amplification, R p : momentum flux loss, T plate /T throat : cooling ratio! 0.4! w/o cooling! 100! T / T e0! T e! T i! 10! M plate! V // / v e0! 0! 0.05! hot source! supersonic! w/o cooling! radiation! cooling! 0! 0! 0.5! x / L! M! 1! 0.1! 0.01! 0.1! 1! 10! T. Takizuka, M. Hosokawa, K. Shimizu, J. Nucl. Mater (2001) 753. C! M throat! PARASOL simulation results agree very well with analytical formula
![01 to large ~1 [3].! 1.0! T e /T e0! 0.4! 0.2! 0.0! 0.0 x / L 0.5 f rad! l mfp /L! f rad! l mfp /L! 0.1! 10 2! 10-2! 0.5! 10 3! 10-1! 0.5! α e! 0.0! 0.0! 0.2! 0.4! 0.6! f rad! PARASOL simulation shows that!](/docs-images/85/92082149/images/16-2.jpg "α e value is changed by situations;! α e increases with f rad [1,2].! [1] A. Froese, T. Takizuka, M. Yagi, Plasma Fusion Res. 5 (2010) S1017. [2] A. Froese, T. Takizuka, M. Yagi, Plasma Fusion Res. 5 (2010) 26.")
16 Kinetic effect on the parallel heat transport in SOL! Collisional l mfp << L! q e// = q SH = - κ e// dt e /ds! Collisionless l mfp >> L! q e// = α e q FS = α e nt e v eth! Harmonic average model! q eff -1 = q SH -1 + (α e q FS ) -1! T e source region intermediate region q radiation region divertor plate Various values of flux-limiting! factor α e have been reported! from small ~0.01 to large ~1 [3].! 1.0! T e /T e0! 0.4! 0.2! 0.0! 0.0 x / L 0.5 f rad! l mfp /L! f rad! l mfp /L! 0.1! 10 2! 10-2! 0.5! 10 3! 10-1! 0.5! α e! 0.0! 0.0! 0.2! 0.4! 0.6! f rad! PARASOL simulation shows that! α e value is changed by situations;! α e increases with f rad [1,2].! [1] A. Froese, T. Takizuka, M. Yagi, Plasma Fusion Res. 5 (2010) S1017. [2] A. Froese, T. Takizuka, M. Yagi, Plasma Fusion Res. 5 (2010) 26. [3] W. Fundamenski, Plasma Phys. Control. Fusion 47 (2005) R163.
17 Bohm criterion for two-ion-species plasmas! v // (a.u.)! 1! 0! species 1! species 2! m 2 /m 1 = 4! theoretical! curves! 1! 0.5! electron! x / L! L // / l mfp = 0.1! L // / l mfp = 2! L // / l mfp = 50! 0.5! v 2 //! v 2 //! v 2 //! v 1 //! v 1 //! v 1 //! PARASOL! result! v 1 // = v 2 //! S. Azuma, A. Fukuyama, T. Takizuka, Contrib. Plasma Phys. 52 (2012) 512.
18 ELM Heat Propagation in 1D SOL-Divertor Plasmas! Enhanced heat and particle fluxes to divertor plates due to ELMs in H-mode are crucial issues (erosion and lifetime of the plates)! D α div (a.u.) 1 JT-60U 0 10 time (s) 10.1 pressure 0 Core ELM Pedestal SOL particle heat r sep n(0)! ELM source! steady-state source! time! Propagation time of ELM heat flux, a key factor to influence! the plates, is studied using 1D-dynamic PARASOL!
19 Time evolution of the ELM heat flux to a divertor plate! Fast-time-scale behaviors! (electron response) are! affected by collisions.! Slow-time-scale behaviors! are affected by recycling.! T. Takizuka, M. Hosokawa, Contrib. Plasma Phys. 46 (2006) 698. T. Takizuka, N. Oyama, M. Hosokawa, Contrib. Plasma Phys. 48 (2008) 207.
20 SOL Flow Pattern in Tokamaks SOL flow important for the particle control in fusion reactors.! The flow works to expel He ashes and to retain impurities! in the divertor region, if it is directed towards the plate.! B t! I p! In tokamak experiments, however,! the flow direction is sometimes! opposite; from the plate side to the! SOL middle side in the outer SOL.! This backward flow is seen when the single null point is located in the ion B drift direction.! ITER! N. Asakura, ITPA SOL and Divertor Topical Group, J. Nucl. Mater (2007) 41. Physics mechanisms of the backward flow have not fully been known,! though many simulation studies have been carried out with the fluid model.! Kinetic simulations are considered to bring a breakthrough on this subject.! Effects of drifts, banana particles, self-consistent electric fields including! sheath etc. important for SOL flow formation are all taken into account.!
21 Full particle simulation with 2D-toroidal PARASOL code! θ! θ Z! z / θ = 0! Stationary profiles of! n e and T e! b W! z = b w φ φ = 0! z = 0 0! R! r Hot source z = -- b W w! r = r 0 - a w R 0 - a W! R 0! r = r 0 Rr = 0 r+ 0 + aa W! w A w = r 0 /a w! N i0 = 10 6, M R x M Z = 320 x 512, m i /m e = 400, ρ i /a 0.02, D 10-5 ac s,! l mpf /L // 1, Θ = 0.2 (q is not constant for the change of A = R 0 /a)!
22 SOL Flow (V // ) Pattern ( red : co-flow to I p, blue : counter-flow )! Upper-null point! Lower-null point! T. Takizuka, K. Shimizu, N. Hayashi, M. Hosokawa, M. Yagi, Nucl. Fusion 49 (2009) Additive or Subtractive! between original SOL flow! and orbit-induced flow! On this physics finding from PARASOL simulation,! a new model of ion-orbit-induced flow was developed.! T. Takizuka, K. Hoshino, K. Shimizu, M. Yagi, Contrib. Plasma Phys. 50 (2010) 267.!
23 Formation of Electric Field in a Tokamak Plasma Electric field (or ExB drift flow shear) important for confinement performance.! In open-field SOL/divertor plasmas, electrons flow out faster to the wall,! and plasma potential becomes positive against the wall.! How is the potential profile in closed-field core plasmas? Even in a straight tokamak, potential profile is varied by the FLR effect.! n profile unchanged! convex φ profile for small ρ*! Hollow φ profile for large ρ*!
24 In toroidal plasmas, hollow φ profiles are easily formed.! ρ* dependence for A = 1000! A dependence for small ρ*! 3.0 ρ*= ρ*= eφ / T e! eφ / T e A = 1000! Dependence on ρ*! banana! eφ / T e! eφ / T e ρ*/θ A! 2.0 A = 1000 A = 14 A = 5.5 eφ / T e! eφ / T e A = 5.5 Θ = ρ*= eφ / T e! eφ / T e A = 5.5 ρ*= ρ*= Θ= 0.2 T. Takizuka, M. Hosokawa, Two-dimensional Full Particle Simulation of the Formation of Electrostatic Field in a Tokamak Plasma, 11th IAEA TM on H-mode Physics and Transport Barriers, Tsukuba, T. Takizuka, Plasma Sci. Technol. 13 (2011) 316.
25 (a.u.) (x E b ) n e T 0.2 i 0.5 T e 0.1 φ profiles are varied! by the beam injection! 0.0 (x V b ) R 0.0 (x E b ) 0.4 Φ (A = 1000) 0.5 V // (A = 1000) 0.2 Φ (A = 5) 0.0 (x V b ) 0.0 V // (A = 5) CO injection R CTR injection V // (A = 5) 0.0 (x E b ) CO injection R Φ (A = 1000) CTR injection V // (A = 1000) Φ (A = 5) R T. Takizuka, M. Honda, Modeling of Rotation, 1st ITPA Transport & Confinement TG meeting, Milano, T. Takizuka, Plasma Sci. Technol. 13 (2011) R
26 Presentations at NEXT meetings 2nd (1997) Divertor Simulation Modeling! 4 th (1999) Damping Model for Divertor Particle Simulation! 5 th (2000) Progress of Divertor Simulation in NEXT Project! 6 th (2001) Divertor Simulation Physics Study and Prediction 7 th (2002) Development of Divertor Simulation Code PARASOL by M. Hosokawa! Two Dimensional Structure of Divertor Plasma 2D PARASOL Simulation 8 th (2003) Recent Results of PARASOL Simulations! 10 th (2005) ELM Simulation with PARASOL! 11 th (2006) Structure and Dynamics of Divertor Plasmas! 12 th (2007) Present Status of PARASOL Simulation!! 19 th (2013) Bohm criterion for two-ion-species plasmas in a wide range of! of mass ratio and collisionality by S. Azuma! 20 th (2015) History of PARASOL!
27 References [1] T. Takizuka, H. Abe, J. Comput. Phys. 25 (1977) 205. [2] T. Takizuka et al., Plasma Phys. Control. Nucl. Fusion Res (proc. 8th Int. Conf., Brussels) Vol. 1 (IAEA, Vienna, 1981) 679. [3] T. Takizuka, K. Tani, M. Azumi, K. Shimizu, J. Nucl. Mater. 128&129 (1984) 104. [4] T. Takizuka, K. Tani, M. Azumi, Particle Simulation of Divertor Plasma, proc. US-Japan Workshop on Advanced Plasma Modeling (Nagoya, 1985) IPPJ-818 (IPP, Nagoya University, 1987). [5] T. Takizuka, M. Hosokawa, Contrib. Plasma Phys. 40 (2000) 471. [6] T. Takizuka, M. Hosokawa, K. Shimizu, Trans. Fusion Technol. 39 (2001) 111. [7] T. Takizuka, M. Hosokawa, K. Shimizu, J. Nucl. Mater (2001) 753. [8] T. Takizuka, M. Hosokawa, K. Shimizu, J. Nucl. Mater (2003) [9] T. Takizuka, M. Hosokawa, Contrib. Plasma Phys. 46 (2006) 698. [10] H. Kawashima, K. Shimizu, T. Takizuka, et al., Plasma Fusion Res. 1 (2006) 031. [11] H. Kawashima, K. Shimizu, T. Takizuka, Plasma Phys. Control. Fusion 49 (2007) S77. [12] T. Takizuka, M. Hosokawa, Trans. Fusion Sci. Technol. 51, 271 (2007). [13] T. Takizuka, N. Oyama, M. Hosokawa, Contrib. Plasma Phys. 48 (2008) 207. [14] T. Takizuka, K. Shimizu, N. Hayashi, M. Hosokawa, M. Yagi, Nucl. Fusion 49 (2009) [15] T. Takizuka, Plasma Interaction in Controlled Fusion Devices: 3rd ITER International Summer School, AIP Conference Proceedings 1237 (2010) 138. [16] T. Takizuka, K. Hoshino, K. Shimizu, M. Yagi, Contrib. Plasma Phys. 50 (2010) 267. [17] A. Froese, T. Takizuka, M. Yagi, Plasma Fusion Res. 5 (2010) S1017. [18] A. Froese, T. Takizuka, M. Yagi, Plasma Fusion Res. 5 (2010) 26. [19] A. Froese, T. Takizuka, M. Yagi, Contrib. Plasma Phys. 50 (2010) 273. [20] T. Takizuka, Plasma Sci. Technol. 13 (2011) 316. [21] S. Azuma, A. Fukuyama, T. Takizuka, Contrib. Plasma Phys. 52 (2012) 512. [22] A. Froese, T. Takizuka, M. Yagi, Contrib. Plasma Phys. 52 (2012) 534.
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