Ringberg Theory Meeting Impact of momentum correction on bootstrap current and ECCD in W7-X Yu. Turkin, C.D. Beidler, H. Maaßberg, N.B.Marushchenko Max-Planck-Institut fűr Plasmaphysik ,17491 Greifswald, Germany 2008, November 17

Outline Improved kinetic model (with momentum conservation and generalized formulation for trapped particle fraction ft ) is implemented in ray tracing and transport codes Results of predictive modeling of ECR heating of plasma in W7-X with focus on levels of bootstrap and driven currents are presented: Bootstrap current: DKES approach and Taguchi techniques (realization by C. Beider) Current drive models: high velocity limit (Lin-Liu, Taguchi-Fish) none- and relativistic Spitzer function, fraction of trap. particle: collisionless limit and generalized formulation. Bootstrap current for different magnetic configuration; density scan BC/ECCD for X2, O2 Motivation of this work is a necessity to know/control the toroidal currents in W7-X

Geometry of the ECRH system ECRH system: 10beams x 1MW , 30min

Geometry of the ECRH system ECRH system: 10beams x 1MW , 30min

Geometry of the ECRH beams 6 beams are shown, beam in red is the spare beam the other six beams are located in the next module; The beams propagate at angles optimized with respect to the absorption efficiency for O2 or X3-mode operations C1 reflecting stainless-steel liners V. Erckmann, P. Brand et al. Electron cyclotron heating for W7-X: physics and technology. Fusion Science and Technology, 52, 291(2007).

Transport Equations Ray tracing code TRAVIS calculates heating source Electric field Diffusion equation for current Boundary conditions:

Diffusion model Anomalous heat diffusivity at the edge only. D22 neoclassical heat diffusivity To avoid any confusion I would call this empirical diffusivity, because we don’t have any well established anomalous model.

Thermal transport matrix Neoclassical transport matrix D is the energy convolution of monoenergetic coefficients produced by DKES runs. Typical file of monoenergetic coefficients created by H.Maassberg contains ~3000 records D(r, Er/v, /v) Thermal D = Interpolation + Integrating with Maxwell distribution function, New! - this Database is used by C. Beidler for realization of Taguchi techniques Our working set for W7-X: Standard Configuration: <b>=0%, 2%, 4%; Low Mirror; High Mirror

Diffusion model with momentum correction Taguchi techniques realization by C. Beider, Compare with ‚old‘ model To avoid any confusion I would call this empirical diffusivity, because we don’t have any well established anomalous model.

Simulation procedure run till steady-state In simulation density is kept fixed. Density is rather flat: (W7-AS -> most shots have flat profiles) Temperatures, Fluxes, radial Electric field are calculated self-consistently Power deposition is updated periodically calling the ray tracing code TRAVIS with the new ne, Te semi-self-consistent coupling of codes run till steady-state

Dependencies on configuration Standard Configuration: <b>=0%; 2%; 4% Low Mirror High Mirror On-axis heating -> electron root Off-axis heating -> ion root only

Dependencies on configuration SC SC 4% Standard Configuration; Low Mirror; High Mirror HM LM Full line and symbol --- ‘Momentum corrected’ bootstrap current B/B00=1+b01cos(5) +b11cos(-5)… LM SC 4% HM

Dependencies on configuration SC SC 4% Standard Configuration; Low Mirror; High Mirror HM LM On-axis heating with electron root Off-axis heating with ion root only

ECCD: Dependencies on configuration Max. available ECCD at X2-mode ECCD in case of on-axis heating ECCD in case of off-axis heating <b>=2%;

configuration scan : interim summary We have done configuration scan for n=1020m-3 and X2-mode ECRH: Momentum correction for IBC : IBC Bootstrap current increases with mirror term decrease, but…. Enough ECCD to compensate bootstrap current Let’s move to high density: X2  O2 (2·1020m-3) density scan for <b>=2%

Density scan for 5MW ECRH With O2-mode we don’t have freedom of launching angles as for case of X2. That why we choose only 5MW (5 beams) Only beams produced counter current are used

BC : Density scan for 5MW ECRH X2 O2 Standard Configuration, <b>=2% Full line and symbol --- ‘Momentum corrected’ bootstrap current

ECCD: Density scan for 5MW ECRH X2 No significant difference between and high velocity limit (Lin-Liu, Taguchi-Fish) relativistic Spitzer function, ft in col.-less limit non-relativistic Spitzer function, ft in col.-less limit non-relativistic Spitzer function, ft is general (new!) ft n/v

BC and ECCD : density scan for 5MW ECRH X2 Our latest theoretical model for plasma currents: bootstrap current with momentum correction ECCD is calculated using relativistic Spitzer function with momentum conservation, ft in col.-less limit

Magnetic configuration control Before summary: why precise calculations of currents ? Magnetic configuration control W7-X magnetic configuration concept: Super conductive coils, no Ohmic transformer, low shear machine, flat iota, minimized bootstrap current Toroidal current changes rotational transform and magnetic configuration : low order rational values of iota can appear (islands inside) moves X-point -> potential danger for island divertor Fig. By A. Werner

Iota modification due to currents Before summary: why precise calculation of currents Ibc=+72kA Ieccd=-72kA So called current hole owing strong on-axis current drive Rotational transform calculation: -- current free part of the rotational transform see susceptance matrix S definition in P.I. Strand and W.A. Houlberg.. Physics of Plasmas. 8, 2782(2001).

More problems: time scales no transformer  skin-time ~ 1..2sec ~ a2 , L/R ~ 10..40sec ~ Rmajor  diagnostics : measurements of current (profile) ? …. However, control of current is other topic….

Summary & outlook Strategy is to have/create/apply the best tools available (H. Maassberg) Improved kinetic model (with momentum conservation and general ft ) is implemented in ray tracing and transport codes Perpendicular transport is not affected BC is noticeably affected  it is decreased we have benchmarked two modules written by H.M. and by C.B. For ECCD relativism is more important (at least for 2nd mode heating) ? relativistic Spitzer function for general ft is needed. Awaiting tasks: current evolution, design the current free scenarios: 10-30sec discharges, up to 30min discharges, avoid flat edge-iota, rationals, current hole NBCD Testing, benchmarking, extend DB of mag. configurations, …….

The END

Can we trust in our modeling? W-7x tau_E

Neoclassical predictions for LHD (Japan) Scan: n = (0.4 – 1) x 1020m-3 P = (1 – 4) MW B = 3T Configuration: lhd_boz10.r360q100b004a8020

Why do we use edge an ~ 1/n ? This choice consistent with W7-AS experience: some analysis of experiment gives D~ P0.85 / n LHD, W7-AS : no profile stiffness*: central part is not affected by the edge transport we choose 1/n ; edge 1-3m2/s For our calculations: 5 time increase of edge an leads only to 20% degradation of tE Transport is local in our modelling and does not necessarily influence the core transport. The profile stiffness was never seen in W7-AS However something must be added at the edge, because with only neoclassic losses the transport is stopped. In lack of knowledge we choose *IAEA Fusion Energy Conference 2002 *W7-AS: One step of the Wendelstein stellarator line, F. Wagner et al, PHYS. OF PLASMAS, 12, 072509 2005

4MW ECRH, density ne(0)=0.6 Dependencies of tE, Te(0),Ti(0), <b> on edge value of anomalous heat diffusivity 5 10 Te(0), keV Ti(0) c edge , m2/s 5 10 1 1.5 2 2.5 <b>, % c edge , m2/s 5 10 0.3 0.4 0.5 t E c edge , m2/s , s

Collection of Plasma Profiles

Geometry of the ECRH system ECRH system: 10beams x 1MW , 30min