Modelling of plasma edge turbulence with neutrals

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1 Modelling of plasma edge turbulence with neutrals Ben Dudson 1 1 York Plasma Institute, Department of Physics, University of York, Heslington, York YO1 5DD, UK 7 th IAEA TM on Plasma Instabilities 4-6 March 214 Frascati, Rome, Italy Ben Dudson, University of York 2D turbulence modelling (1 of 17)

2 Background: Transport in the tokamak edge Plasma edge region critical to reactor design Core performance Heat fluxes to divertor Particle fluxes to first wall Understanding of transport processes incomplete Leads to uncertainty in predictions for future devices *Figure: Ben Dudson, University of York 2D turbulence modelling (2 of 17)

3 Background: Transport in the tokamak edge Plasma turbulence simulations can make first-principles predictions* 2D (drift-plane) models such as ESEL and SOLT reproduce many features of experiment Currently missing potentially important physics, including neutral gas Here we present some ongoing work to include neutral gas physics, using BOUT++ *No fitted parameters *Figure: Ben Dudson, University of York 2D turbulence modelling (3 of 17)

4 Outline 2D electrostatic cold ion plasma model Evolution of plasma density, temperature, and vorticity Assumptions on parallel dynamics Key features of the resulting edge turbulence Neutral gas model Effect of fluctuations on neutral gas profiles Effect of neutral gas on edge turbulence Conclusions / Questions Ben Dudson, University of York 2D turbulence modelling (4 of 17)

5 2D electrostatic cold ion plasma model Plasma density n, electron pressure p e, and vorticity ω n t p e t ω t = (nv E B + nv mag ) + (D n n) + S n + Λ n ( ) 5 = p e V E B + p e 3 V mag 2 3 p e V E B + S p + Λ p + (D n T e n) + (χn T e ) = (ωv E B ) (nv mag ) + (µ i ω) + Λ ω with E B and magnetic drifts given by: V E B = b φ V mag = T e b B B Boussinesq approximation made, so vorticity is: ( n ) ω = B 2 φ n B 2 φ 1 Simakov,Catto Phys. Plasmas 1 (12) (23), Erratum: Phys. Plasmas 11 (5) 2326 (24) Ben Dudson, University of York 2D turbulence modelling (5 of 17)

6 2D electrostatic cold ion plasma model Plasma density n, electron pressure p e, and vorticity ω Boussinesq approximation A 2D model is constructed by approximating parallel dynamics 1 In the SOL: Sheath connected: Λ ω = 1 L n T e [ 1 In the core: Adiabatic electrons: 2 mi 4πm e exp (φ/t e ) Λ n = Λ ω = α DW T e 3/2 {φ Te log n} where T e is the flux-surface average of T e, and { } means the fluctuating part, with flux-surface average subtracted out. ] 1 L.Easy et al.. Phys. Plasmas 21, (214) 2 D.A.D Ippolito et al. PoP (212) Ben Dudson, University of York 2D turbulence modelling (6 of 17)

7 Simulation parameters Power through separatrix: 74 kw/m 2 Parallel connection length L = 1m (constant across SOL) A parameter α DW appears in parallel closure inside the separatrix This term approximates the electron response along closed field-lines, similar to Hasegawa-Wakatani Ben Dudson, University of York 2D turbulence modelling (7 of 17)

8 Structure of edge turbulence and shear layer Potential [Volts] Shear layer formed around separatrix Formation of isolated blobs in SOL a Ch. P. Ritz et al. Phys Fluids (1984) b H.Y.W.Tsui et al. Phys. Fluids B 5, 2491 (1993) c V.Antoni et al. PRL (1997) Radius from separatrix [mm] d G.S.Xu et al. Nucl. Fusion (29) e J.R.Myra et al. Nucl. Fusion (213) Ben Dudson, University of York 2D turbulence modelling (8 of 17)

9 Structure of edge turbulence and shear layer Potential [Volts] Shear layer formed around separatrix Formation of isolated blobs in SOL a Ch. P. Ritz et al. Phys Fluids (1984) b H.Y.W.Tsui et al. Phys. Fluids B 5, 2491 (1993) c V.Antoni et al. PRL (1997) Radius from separatrix [mm] d G.S.Xu et al. Nucl. Fusion (29) e J.R.Myra et al. Nucl. Fusion (213) Ben Dudson, University of York 2D turbulence modelling (8 of 17)

10 Structure of edge turbulence and shear layer Potential [Volts] Shear layer formed around separatrix Formation of isolated blobs in SOL a Ch. P. Ritz et al. Phys Fluids (1984) b H.Y.W.Tsui et al. Phys. Fluids B 5, 2491 (1993) c V.Antoni et al. PRL (1997) Radius from separatrix [mm] d G.S.Xu et al. Nucl. Fusion (29) e J.R.Myra et al. Nucl. Fusion (213) Ben Dudson, University of York 2D turbulence modelling (8 of 17)

11 Structure of edge turbulence and shear layer Potential [Volts] Shear layer formed around separatrix Formation of isolated blobs in SOL a Ch. P. Ritz et al. Phys Fluids (1984) b H.Y.W.Tsui et al. Phys. Fluids B 5, 2491 (1993) c V.Antoni et al. PRL (1997) Radius from separatrix [mm] d G.S.Xu et al. Nucl. Fusion (29) e J.R.Myra et al. Nucl. Fusion (213) Ben Dudson, University of York 2D turbulence modelling (8 of 17)

12 Structure of edge turbulence and shear layer Potential [Volts] Shear layer formed around separatrix Formation of isolated blobs in SOL a Ch. P. Ritz et al. Phys Fluids (1984) b H.Y.W.Tsui et al. Phys. Fluids B 5, 2491 (1993) c V.Antoni et al. PRL (1997) Radius from separatrix [mm] d G.S.Xu et al. Nucl. Fusion (29) e J.R.Myra et al. Nucl. Fusion (213) Ben Dudson, University of York 2D turbulence modelling (8 of 17)

13 Profiles and λ q Heat transport: Two-scale power flux, not necessarily connected with conduction/convection transition Insensitive to choice of core electron response α DW Near SOL λ q on similar scales as blob dynamics Heat flux [MW/m 2 ] Conduction Convection Total λ q =1.6 mm λ q =33.5 mm Radius from separatrix [mm] Heat flux [MW/m 2 ] Conduction Convection Total λ q =1.2 mm λ q =26.7 mm Radius from separatrix [mm] Heat flux [MW/m 2 ] Conduction Convection Total λ q =6.3 mm λ q =26.5 mm Radius from separatrix [mm] Ben Dudson, University of York 2D turbulence modelling (9 of 17)

14 Diffusive neutral gas fluid model Neutral gas density n n and pressure p n n n t p n t = (D n n) + S = (T n D n n) + (n n χ n T n ) Q Particle source/sink S from recombination and ionisation Neutral gas heating Q from charge exchange Corresponding terms added to plasma equations n t =... S p e =... 2 t 3 Q 2 3 R where R is the radiated power S = n 2 σ rc nn n σ iz Q = nn n σ cx 3 2 (T e T n ) R = (2.59T e 13.6) n 2 σ rc Recombination heats plasma above 5.25eV Ben Dudson, University of York 2D turbulence modelling (1 of 17)

15 Plasma-Neutral mean free paths 1 2 Charge exchange mean free path Gas diffusion rate D n = v th λ nn Mean free path λ nn combines charge-exchange and neutral-neutral collisions. Showing mean free paths for a 3K neutral gas atom Typical blob sizes 1 2cm Expect charge-exchange interactions, but ionisation only for largest and hottest blobs Electron density [m 3 ] Electron density [m 3 ] mm 1cm 1cm 1m Temperature [ev] Ionisation mean free path m 1cm 1cm 1mm 1m Temperature [ev] Ben Dudson, University of York 2D turbulence modelling (11 of 17)

16 Variation in neutral gas density At higher temperatures 2eV variation in neutral gas density due to interaction with fluctuations is observed Binormal [mm] Neutral gas density [m 3 ] Radius from separatrix [mm] 1e Neutral gas density (red dashed) and variation (black) % variation σ(n n )/ nn Radius from separatrix [mm] Neutral gas fluctuation levels around 4 5% for typical MAST edge parameters Approximation based on axisymmetric profiles reasonable 9 Average density n n [ 1 17 m 3 ] Ben Dudson, University of York 2D turbulence modelling (12 of 17)

17 Fluctuations modify neutral gas profiles Calculate average radial plasma profile Compare neutral gas profiles with and without fluctuations At separatrix T e 1 2eV, n e m 3 ) difference of 1 2%. Cross-sections are nonlinear in plasma parameters: σ ( n e, T e ) σ (n e, T e ) Neutral gas density [ARB] With fluctuations No fluctuations Difference is 17.6% Distance from separatrix [mm] Ben Dudson, University of York 2D turbulence modelling (13 of 17)

18 Fuelling by neutral gas How much difference does the particle source make? Replace fuelling from the core by ionisation of neutrals For now neglect momentum exchange: No friction or neutral wind Plasma particle source moves outwards, past the separatrix Electron temperature [ev] Electron density [1 19 m 3 ] Distance from separatrix [mm] 1% neutrals 75% neutrals 5% neutrals 25% neutrals % neutrals 1% neutrals 75% neutrals 5% neutrals 25% neutrals % neutrals Distance from separatrix [mm] Ben Dudson, University of York 2D turbulence modelling (14 of 17)

19 Fuelling by neutral gas How much difference does the particle source make? Replace fuelling from the core by ionisation of neutrals For now neglect momentum exchange: No friction or neutral wind Plasma particle source moves outwards, past the separatrix Makes little difference to near SOL power deposition Electron temperature [ev] Heat flux [MW/m 2 ] Distance from separatrix [mm] 1% neutrals 75% neutrals 5% neutrals 25% neutrals % neutrals 1% neutrals 75% neutrals 5% neutrals 25% neutrals % neutrals Radius [mm] Ben Dudson, University of York 2D turbulence modelling (14 of 17)

20 Ion-neutral friction Adding friction term: Charge exchange and recombination remove ion momentum (vorticity): ω ( t =... n ) B 2 φ } {{ } νω Flattens profiles inside and across separatrix Electron temperature [ev] Electron density [1 19 m 3 ] Distance from separatrix [mm] 1% neutrals 75% neutrals 5% neutrals 25% neutrals % neutrals 1% neutrals 75% neutrals 5% neutrals 25% neutrals % neutrals Distance from separatrix [mm] Ben Dudson, University of York 2D turbulence modelling (15 of 17)

21 Ion-neutral friction Adding friction term: Charge exchange and recombination remove ion momentum (vorticity): ω ( t =... n ) B 2 φ } {{ } νω Flattens profiles inside and across separatrix Results in a broadening of the SOL power deposition Electron temperature [ev] Heat flux [MW/m 2 ] Distance from separatrix [mm] 1% neutrals 75% neutrals 5% neutrals 25% neutrals % neutrals 1% neutrals 75% neutrals 5% neutrals 25% neutrals % neutrals Radius [mm] Ben Dudson, University of York 2D turbulence modelling (15 of 17)

22 Conclusions Fluctuations in the SOL lead to an increase in neutral gas density at the separatrix. In these simulations 15%. Fluctuations in neutral gas density 5%, so further approximation possible Neutral gas can have a significant impact on 2D edge turbulence simulations Fuelling (ionisation / recombination) due to neutrals: Has little effect on temperature profiles Flattens density profile in the near SOL, and steepens density profile in the far SOL Has little effect on near SOL heat flux Ion-neutral friction (mainly charge exchange): Reduces flow shear in the edge Flattens profiles across the separatrix Broadens SOL heat flux deposition Ben Dudson, University of York 2D turbulence modelling (16 of 17)

23 Interaction cross-sections Analytic forms used for ionisation, recombination, and charge exchange cross sections 1 Rate <σv > [m 3 s 1 ] Ionisation Recombination (n = 1 18 m 3 ) Recombination (n = 1 2 m 3 ) Recombination (n = 1 22 m 3 ) Charge exchange Electron temperature [ev] 1 Thanks to Eva Havlickova, CCFE Ben Dudson, University of York 2D turbulence modelling (17 of 17)