Impact of neutral atoms on plasma turbulence in the tokamak edge - PowerPoint PPT Presentation

Impact of neutral atoms on plasma turbulence in the tokamak edge region C. Wersal P . Ricci, F .D. Halpern, R. Jorge, J. Morales, P . Paruta, F . Riva Theory of Fusion Plasmas Joint Varenna-Lausanne International Workshop 29.08. - 02.09. 2016

Introduction Model Two-point model Fueling Conclusions Physics at the periphery of a fusion plasma ◮ Toroidal limiter Limiter Core Edge SOL Christoph Wersal - SPC Neutrals in the turbulent tokamak edge 2 / 37

Introduction Model Two-point model Fueling Conclusions Physics at the periphery of a fusion plasma ◮ Toroidal limiter ◮ Radial transport due to turbulence Plasma Christoph Wersal - SPC Neutrals in the turbulent tokamak edge 2 / 37

Introduction Model Two-point model Fueling Conclusions Physics at the periphery of a fusion plasma ◮ Toroidal limiter ◮ Radial transport due to turbulence ◮ Parallel flow in the SOL to the limiter Plasma Christoph Wersal - SPC Neutrals in the turbulent tokamak edge 2 / 37

Introduction Model Two-point model Fueling Conclusions Physics at the periphery of a fusion plasma ◮ Toroidal limiter ◮ Radial transport due to turbulence ◮ Parallel flow in the SOL to the limiter ◮ Recombination on the limiter Plasma Neutrals Christoph Wersal - SPC Neutrals in the turbulent tokamak edge 2 / 37

Introduction Model Two-point model Fueling Conclusions Physics at the periphery of a fusion plasma ◮ Toroidal limiter ◮ Radial transport due to turbulence ◮ Parallel flow in the SOL to the limiter ◮ Recombination on Ionization the limiter ◮ Ionization of neutrals ◮ Density source ◮ Energy sink Plasma Neutrals Christoph Wersal - SPC Neutrals in the turbulent tokamak edge 2 / 37

Introduction Model Two-point model Fueling Conclusions Physics at the periphery of a fusion plasma ◮ Toroidal limiter ◮ Radial transport due to turbulence ◮ Parallel flow in the SOL to the limiter ◮ Recombination on Ionization the limiter ◮ Ionization of neutrals ◮ Density source ◮ Energy sink Plasma Neutrals Christoph Wersal - SPC Neutrals in the turbulent tokamak edge 2 / 37

Introduction Model Two-point model Fueling Conclusions Physics at the periphery of a fusion plasma ◮ Toroidal limiter ◮ Radial transport due to turbulence ◮ Parallel flow in the SOL to the limiter ◮ Recombination on Ionization the limiter ◮ Ionization of neutrals ◮ Density source ◮ Energy sink Plasma ◮ Recycling Neutrals Christoph Wersal - SPC Neutrals in the turbulent tokamak edge 2 / 37

Introduction Model Two-point model Fueling Conclusions Movie Christoph Wersal - SPC Neutrals in the turbulent tokamak edge 3 / 37

Introduction Model Two-point model Fueling Conclusions The tokamak scrape-off layer (SOL) ◮ Heat exhaust ◮ Confinement ◮ Impurities ◮ Fusion ash removal ◮ Fueling the plasma (recycling) Christoph Wersal - SPC Neutrals in the turbulent tokamak edge 4 / 37

Introduction Model Two-point model Fueling Conclusions 1. Modeling the periphery 2. A refined two-point model with neutrals 3. Gas puff fueling simulations Christoph Wersal - SPC Neutrals in the turbulent tokamak edge 5 / 37

Introduction Model Two-point model Fueling Conclusions Modeling the periphery Christoph Wersal - SPC Neutrals in the turbulent tokamak edge 6 / 37

Introduction Model Two-point model Fueling Conclusions Modeling the periphery ◮ High plasma collisionality, local Maxwellian Christoph Wersal - SPC Neutrals in the turbulent tokamak edge 6 / 37

Introduction Model Two-point model Fueling Conclusions Modeling the periphery ◮ High plasma collisionality, local Maxwellian ◮ d / dt ≪ ω ci , k 2 ⊥ ≫ k 2 � Christoph Wersal - SPC Neutrals in the turbulent tokamak edge 6 / 37

Introduction Model Two-point model Fueling Conclusions Modeling the periphery ◮ High plasma collisionality, local Maxwellian ◮ d / dt ≪ ω ci , k 2 ⊥ ≫ k 2 � ◮ Drift-reduced Braginskii equations n , Ω , v � e , v � , i , T e , T i Christoph Wersal - SPC Neutrals in the turbulent tokamak edge 6 / 37

Introduction Model Two-point model Fueling Conclusions Modeling the periphery ◮ High plasma collisionality, local Maxwellian ◮ d / dt ≪ ω ci , k 2 ⊥ ≫ k 2 � ◮ Drift-reduced Braginskii equations n , Ω , v � e , v � , i , T e , T i ◮ Flux-driven, no separation between equilibrium and fluctuations Christoph Wersal - SPC Neutrals in the turbulent tokamak edge 6 / 37

Introduction Model Two-point model Fueling Conclusions Modeling the periphery ◮ High plasma collisionality, local Maxwellian ◮ d / dt ≪ ω ci , k 2 ⊥ ≫ k 2 � ◮ Drift-reduced Braginskii equations n , Ω , v � e , v � , i , T e , T i ◮ Flux-driven, no separation between equilibrium and fluctuations ◮ Kinetic neutral equation Christoph Wersal - SPC Neutrals in the turbulent tokamak edge 6 / 37

Introduction Model Two-point model Fueling Conclusions Modeling the periphery ◮ High plasma collisionality, local Maxwellian ◮ d / dt ≪ ω ci , k 2 ⊥ ≫ k 2 � ◮ Drift-reduced Braginskii equations n , Ω , v � e , v � , i , T e , T i ◮ Flux-driven, no separation between equilibrium and fluctuations ◮ Kinetic neutral equation ◮ Interplay between plasma outflow from the core, turbulent transport, sheath losses, and recycling Christoph Wersal - SPC Neutrals in the turbulent tokamak edge 6 / 37

Introduction Model Two-point model Fueling Conclusions Fluid plasma model and interaction with neutrals ∂ n [ φ , n ]+ 2 ∂ t = − ρ − 1 B [ C ( p e ) − nC ( φ )] − ∇ � ( nv � e )+ D n ( n )+ S n + n n ν iz − n ν rec (1) ⋆ ω + B 2 ∂ ˜ ω n ∇ � j � + 2 B ω ) − n n ∂ t = − ρ − 1 [ φ , ˜ ω ] − v � i ∇ � ˜ n C ( p )+ D ˜ ω ( ˜ n ν cx ˜ ω (2) ⋆ ∂ v � e � j � � [ φ , v � e ] − v � e ∇ � v � e + m i n + ∇ � φ − 1 + D v � e ( v � e )+ n n = − ρ − 1 ν n ∇ � p e − 0 . 71 ∇ � T e n ( ν en + 2 ν iz )( v � n − v � e ) ⋆ ∂ t m e (3) ∂ v � i [ φ , v � i ] − v � i ∇ � v � i − 1 n ∇ � p + D v � i ( v � i )+ n n = − ρ − 1 n ( ν iz + ν cx )( v � n − v � i ) (4) ⋆ ∂ t � 1 � 0 . 71 � � ∂ T e [ φ , T e ] − v � e ∇ � T e + 4 T e n C ( p e )+ 5 + 2 T e = − ρ − 1 2 C ( T e ) − C ( φ ) ∇ � j � − ∇ � v � e (5) ⋆ ∂ t 3 B 3 n Te ( T e )+ S Te + n n n ν iz ( − 2 3 E iz − T e + m e v � e ( v � e − 4 3 v � n ))+ n n m e 2 + D Te ( T e )+ D � n ν en 3 v � e ( v � n − v � e )) m i m i � 1 � ∇ � n � � ∂ T i [ φ , T i ] − v � i ∇ � T i + 4 T i n C ( p e ) − τ 5 + 2 T i = − ρ − 1 2 C ( T i ) − C ( φ ) ( v � i − v � e ) − ∇ � v � e (6) ⋆ ∂ t 3 B 3 n Ti ( T i )+ S Ti + n n n ( ν iz + ν cx )( T n − T i + 1 + D Ti ( T i )+ D � 3 ( v � n − v � i ) 2 ) ∇ 2 ω = ω + τ ∇ 2 ⊥ φ = ω , ρ ⋆ = ρ s / R , ∇ � f = b 0 · ∇ f , ˜ ⊥ T i , p = n ( T e + τ T i ) + boundary conditions + kinetic neutral equation Christoph Wersal - SPC Neutrals in the turbulent tokamak edge 7 / 37

Introduction Model Two-point model Fueling Conclusions The density equation ∂ n ⋆ [ φ , n ]+ 2 ∂ t = − ρ − 1 B [ C ( p e ) − nC ( φ )] − ∇ � ( nv � e ) (7) + S n + n n ν iz − n ν rec + D ⊥ n ( n ) ◮ ExB drift ◮ Curvature terms ◮ Parallel advection ◮ Plasma source from core ◮ Interaction with neutrals ◮ Perpendicular diffusion Christoph Wersal - SPC Neutrals in the turbulent tokamak edge 8 / 37

Introduction Model Two-point model Fueling Conclusions The density equation ∂ n ⋆ [ φ , n ]+ 2 ∂ t = − ρ − 1 B [ C ( p e ) − nC ( φ )] − ∇ � ( nv � e ) (7) + S n + n n ν iz − n ν rec + D ⊥ n ( n ) ◮ ExB drift ◮ Curvature terms ◮ Parallel advection ◮ Plasma source from core ◮ Interaction with neutrals ◮ Perpendicular diffusion Christoph Wersal - SPC Neutrals in the turbulent tokamak edge 8 / 37

Introduction Model Two-point model Fueling Conclusions The density equation ∂ n ⋆ [ φ , n ]+ 2 ∂ t = − ρ − 1 B [ C ( p e ) − nC ( φ )] − ∇ � ( nv � e ) (7) + S n + n n ν iz − n ν rec + D ⊥ n ( n ) ◮ ExB drift ◮ Curvature terms ◮ Parallel advection ◮ Plasma source from core ◮ Interaction with neutrals ◮ Perpendicular diffusion Christoph Wersal - SPC Neutrals in the turbulent tokamak edge 8 / 37

Introduction Model Two-point model Fueling Conclusions The density equation ∂ n ⋆ [ φ , n ]+ 2 ∂ t = − ρ − 1 B [ C ( p e ) − nC ( φ )] − ∇ � ( nv � e ) (7) + S n + n n ν iz − n ν rec + D ⊥ n ( n ) ◮ ExB drift ◮ Curvature terms ◮ Parallel advection ◮ Plasma source from core ◮ Interaction with neutrals ◮ Perpendicular diffusion Christoph Wersal - SPC Neutrals in the turbulent tokamak edge 8 / 37

Introduction Model Two-point model Fueling Conclusions The density equation ∂ n ⋆ [ φ , n ]+ 2 ∂ t = − ρ − 1 B [ C ( p e ) − nC ( φ )] − ∇ � ( nv � e ) (7) + S n + n n ν iz − n ν rec + D ⊥ n ( n ) ◮ ExB drift ◮ Curvature terms ◮ Parallel advection ◮ Plasma source from core ◮ Interaction with neutrals ◮ Perpendicular diffusion Christoph Wersal - SPC Neutrals in the turbulent tokamak edge 8 / 37