SawtoothSawtooth pacing with mode conversion pacing with mode conversion current drive on current drive on AlcatorAlcator CC--ModMod

A. A. ParisotParisot, , S.J. Wukitch, P. , P. BonoliBonoli, M. Greenwald, A. , M. Greenwald, A. Hubbard, Y. Lin, R. Parker, M. Porkolab, A.K. Ram, J.C. Hubbard, Y. Lin, R. Parker, M. Porkolab, A.K. Ram, J.C.

Wright Wright MIT Plasma Science and Fusion Center, Cambridge MA USA

34th EPS conference on Plasma Physics

July 2-6 2007, Warsaw, Poland

B02

Outline

Sawtooth period changes with MCCD:

1.1. Sawtooth period evolution with mode conversion around Sawtooth period evolution with mode conversion around q=1 surface.q=1 surface.

2.2. Evaluation of the MCCD currents with full wave TORIC Evaluation of the MCCD currents with full wave TORIC modelingmodeling

3.3. Analysis of the sawtooth period evolution in heating Analysis of the sawtooth period evolution in heating phasing : localized heating and current drive effectsphasing : localized heating and current drive effects

ICRF mode conversion

In multi ion species plasma, the fast wave dispersion relation indicates possible mode conversionmode conversion at the ion-ion hybrid layer S = n||

2.

Mode conversion current drive

Mode converted waves damp primarily on electrons.

Strong localized electron Strong localized electron heating is obtained (MCEH)heating is obtained (MCEH)

MCEH demonstrated in reactor MCEH demonstrated in reactor relevant plasmas.relevant plasmas.

ICRF mode conversion could therefore find applications for localized current drive in future tokamak reactors.

The technique scales favorably to reactor plasmas, without density limits.

The wave physics is complicated

MCCD has not been extensively studied in experiments.

Applications of MCCD for sawtooth control are being investigated in Alcator C-Mod experiments.

Control of long (monster) sawteeth in presence of fast ions is a critical issue for ITER and future tokamak reactors:

Crashes will be associated with larger rearrangements of the plasma core (inversion radii > 0.5) than for usual sawteeth, and may• Provide seed islands for NTMs• Induce transcients heat and particle influx on PFCs

In C-Mod high performance discharge, large crash trips ICRF heating system, effectively limiting the increase in stored energy.

Experiments on sawtooth Experiments on sawtooth control with MCCDcontrol with MCCD

Sawtooth control with localized MCCD near the q = 1 surface has Sawtooth control with localized MCCD near the q = 1 surface has been demonstrated in Alcator Cbeen demonstrated in Alcator C--Mod experiments. Mod experiments.

The mode conversion layer was swept through the q = 1 surface The mode conversion layer was swept through the q = 1 surface in co, counterin co, counter--CD and heating phasing. CD and heating phasing.

The sawtooth period was varied from 3 to 12 ms.The sawtooth period was varied from 3 to 12 ms.

The sawtooth period evolution is consistent with localized The sawtooth period evolution is consistent with localized current drive near the q = 1 surface. current drive near the q = 1 surface.

A. Parisot et al., PPCF, A. Parisot et al., PPCF, 49 (2007) 219-235

ICRF system on Alcator C-Mod

MC layer swept through q=1 surface

Significant sawtooth period changes were observed

As MC layer swept As MC layer swept outwards through outwards through inversion radius, inversion radius, sawtooth period varied sawtooth period varied from 3 to 12 msfrom 3 to 12 ms

Sawtooth reheat rate / Inversion radius

The mode conversion layer location is deduced from concentration estimates and the magnetic field evolution.

Sawtooth reheat rate suggests heating profiles are similar. The antenna phasing is the only parameter varied.

The sawtooth period evolution is consistent with localized current drive near the mode conversion layer.

Full wave modeling and Full wave modeling and MCCD calculationsMCCD calculations

The EhstThe Ehst--Karney parametrization overestimates the MCCD Karney parametrization overestimates the MCCD efficiency, but captures parametric dependencies well. efficiency, but captures parametric dependencies well.

Net currents can be driven by the mode converted Ion Cyclotron Net currents can be driven by the mode converted Ion Cyclotron Waves, with limited efficiency.Waves, with limited efficiency.

Strong upStrong up--down asymmetries in the mode conversion process down asymmetries in the mode conversion process are predicted by in full wave TORIC simulations. are predicted by in full wave TORIC simulations.

The MCCD currents are calculated with the quasilinear diffusion The MCCD currents are calculated with the quasilinear diffusion operator build from full wave electric field solution in TORIC. operator build from full wave electric field solution in TORIC.

Poloidal field effects and MC to IBW vs ICW

Mode converted waves excited at the MC layer can be studied with a 1st order FLR dispersion relation in a slab geometry.

Two MC regimes are found:Two MC regimes are found: Where θ is the angle between k and Bp in the poloidal cross section

FW Ion Bernstein Wave (IBW)Bp cos θ ≈ BR small

FW Ion Cyclotron Wave (ICW)Bp cos θ ≈ BR large

Poloidal field effects can be included and result in a k|| upshift/downshift:

The TORIC code solves MaxwellThe TORIC code solves Maxwell’’s s equations in 2D geometryequations in 2D geometry

Finite Larmor radius for theconductivity tensor σM. Brambilla, Plasma. Phys. Cont. Fusion 41, 1 (1999)

Full wave simulations with TORIC

TORIC predicts mode conversion from FW to:IBW close to the midplaneICW away from it, with up-down asymmetry

In CIn C--Mod, MC to ICW usually dominates.Mod, MC to ICW usually dominates.

Zeff

Driven current profiles predicted by TORIC

The width of the predicted driven current profiles is consistentThe width of the predicted driven current profiles is consistent with the with the sawtooth period evolution, sawtooth period evolution, given the relative position of the mode given the relative position of the mode conversion layer and inversion radius.conversion layer and inversion radius.

TORIC predicts coTORIC predicts co--current drive with heating (symmetric) phasingcurrent drive with heating (symmetric) phasing

Up-down asymmetry in the ICW deposition

Asymmetry in driven current profiles can be related to an up-down asymmetry in power deposition.

For mode converted waves,

This explains the profiles in counter current drive phasing

Sawtooth period modeling and Sawtooth period modeling and upup--down asymmetriesdown asymmetries

The sawtooth period evolution observed in heating phasing is The sawtooth period evolution observed in heating phasing is consistent with driven currents predicted by TORIC. consistent with driven currents predicted by TORIC.

TORIC predicts net MCCD currents are driven in heating phasing,TORIC predicts net MCCD currents are driven in heating phasing,as a results of the upas a results of the up--down asymmetry in the power deposition. down asymmetry in the power deposition.

This can explain the similarily between the observed evolution This can explain the similarily between the observed evolution in in heating and coheating and co--current drive phasing. current drive phasing.

Electron temperature measurements with ECE and simulations Electron temperature measurements with ECE and simulations with the Porcelli model suggest that localized electron heating with the Porcelli model suggest that localized electron heating effects are not dominant in these MCCD experiments. effects are not dominant in these MCCD experiments.

Simulations with Porcelli model

The Porcelli model predicts the sawtooth period evolution given The Porcelli model predicts the sawtooth period evolution given heating and driven current profiles. heating and driven current profiles.

F. Porcelli, Plasma Phys. Cont. Fusion 38 (1996) 2163-2186

Given a set of plasma profiles, as evolved by a transport code, the model predicts if a sawtooth crash will occur.

The trigger conditions are based on the linear stability of m = 1 internal kink modes. The modes are usually marginally stable in ideal MHD (when fast particle effects can be ignored). Stability depends on local conditions in a narrow layer around the q =1 surface.

The growth rate γ is calculated using a two fluids model, taking in account the plasma resistivity and kinetic ion response. A crash is predicted if γ is large enough to overcome stabilization by drift wave and diamagnetic effects. This is essentially a condition on the local magnetic shear.

Comparison heating – CD with simplified model

A simplified MATLAB code in a cylinder can illustrate the heating and driven current profile effects for parameters close to experimental values.

For efficiencies J/P as in TORIC, current drive effects dominateFor efficiencies J/P as in TORIC, current drive effects dominate

TRANSP analysis with the Porcelli trigger conditions indicate thTRANSP analysis with the Porcelli trigger conditions indicate that at currents currents in heating phasing are needed to account for the sawtooth periodin heating phasing are needed to account for the sawtooth period changes changes

G. Bateman et al., Phys. Plasmas, 13 (2006) 072505

Conclusions and future work

Sawtooth control with mode conversion current drive has been demonstrated in Alcator C-Mod experiments.

The Ehst-Karney parametrization overestimates the MCCD currents. More accurate calculations is based on building a quasilinear diffusion operator from the electric field solution in TORIC.

The similarity between the sawtooth period evolution in co-CD and heating phasing can be explained by asymmetries in the mode conversion process, resulting in net current drive for heating phasing.

Future work will focus on shortening the sawtooth period in presence of fast ions heated by ICRF minority heating.

Acknowledgements

The authors gratefully thank R. Bilato and M. Brambilla (Max Planck Institute for Plasma physics, Garching, Germany) for providing access to the QLDCE module in TORIC ; J. Decker and Y. Peysson for helping set up the coupling between TORIC.

Work supported by USDOE Coop. Agreements DE-FC02-99ER54512 and DE-FG02-91ER54109. This research utilized the MIT Plasma Science and Fusion Center Theory Group parallel computational cluster.

Contact : wukitch@psfc.mit.edu