Initial results from mode conversion Initial results from mode conversion current drive experiments current drive experiments

on Alcator Con Alcator C--ModMod

A. Parisot, S.J. Wukitch, P. Bonoli, A. Hubbard, Y. Lin,A. Parisot, S.J. Wukitch, P. Bonoli, A. Hubbard, Y. Lin,R. Parker, M. Porkolab, A.K. Ram, J.C. Wright R. Parker, M. Porkolab, A.K. Ram, J.C. Wright

MIT Plasma Science and Fusion Center, Cambridge MA USA

47th Annual Meeting of the APS Division of Plasma Physics,

Oct 24-28 2005, Denver, Colorado

KP1. 00031

Outline

This poster reports experimental and numerical studies of mode This poster reports experimental and numerical studies of mode conversion current drive (MCCD) on the Alcator Cconversion current drive (MCCD) on the Alcator C--Mod Mod tokamak. tokamak.

Results from initial MCCD experiments:

1.1. Sawtooth period evolution with MC deposition around Sawtooth period evolution with MC deposition around q=1 surface.q=1 surface.

2.2. Preliminary loop voltage experiments Preliminary loop voltage experiments

Mode conversion physics and TORIC simulations

3.3. Full wave TORIC simulations and predictions for MCCDFull wave TORIC simulations and predictions for MCCD

4.4. Current drive efficiency for mode converted ion Current drive efficiency for mode converted ion cyclotron wavescyclotron waves

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.

Localized electron suggests possible current drive

Mode converted waves damp primarily on electrons localized electron localized electron heatingheating close to the mode conversion layer.

This interaction with electrons suggests possible current drive if the directionnality of the wavesdirectionnality of the waves can be controlled.

Due to poloidal field effectspoloidal field effects (see part 3.), the initial k|| spectrum imparted by the fast wave antenna is lost as the parallel wavenumber upshifts and downshifts.

1.1. Can we drive currents from mode converted waves ? Can we drive currents from mode converted waves ? 2.2. What can we learn about mode conversion physics from current What can we learn about mode conversion physics from current

drive studies ?drive studies ?

Experiments have been performed on the Alcator CExperiments have been performed on the Alcator C--Mod tokamak to Mod tokamak to measure currents or currentmeasure currents or current--related effects in the mode conversion related effects in the mode conversion regimeregime.

Full wave TORIC simulations are used to make numerical predictioFull wave TORIC simulations are used to make numerical predictions of ns of current drive, including Fokkercurrent drive, including Fokker--Planck treatment of trapping and Planck treatment of trapping and quasilinear effects. quasilinear effects.

1. Sawtooth period changes1. Sawtooth period changesLocalized current close to the q=1 surface changes

the sawtooth period by affecting the shear dq/dr and therefore the stability of m=1 kink modes.

Initial MCCD experiments in 2003 showed large difference in sawtooth period between co and counter current drive phasing for deposition just inside the inversion radius.

Co-CDCounter-CD

In the 2005 campaign, a scan of the mode conversion layer locatiIn the 2005 campaign, a scan of the mode conversion layer location on through the q=1 surface was performed in co, counter and heatingthrough the q=1 surface was performed in co, counter and heatingphasing. phasing.

The observed evolution of the sawtooth period is consistent withThe observed evolution of the sawtooth period is consistent withlocalized current drive from mode converted waves.localized current drive from mode converted waves.

MC layer swept through q=1 surface

Sawtooth period changes

Evolution of the Evolution of the sawtooth period as sawtooth period as mode conversion mode conversion layer swept through layer swept through q=1 surface q=1 surface consistent with local consistent with local changes in the shear.changes in the shear.

Consistent with estimated MC layer position relative to inversion radius

3He ion cyclotron layer goes inside inversion radius at 0.65s rules out ICCD effect

Sawtooth reheat rate

Sawtooth reheat rate after Sawtooth reheat rate after crash indicates similar crash indicates similar deposition profiles in deposition profiles in co/counter and heating co/counter and heating phasingsphasings

Consistent with MC layer crossing inversion radius surface around ~ 0.7 - 0.8 s

No 3He minority heating contribution in the sawtooth reheat rate. 3He cyclotron layer moves inwards during field ramp-down, • inside q=1 after 0.65 s • reaches magnetic axis at 1.25 sSuggests absence of energetic ion population.

Ohmic Ohmic + RF

2. Loop voltage measurements2. Loop voltage measurementsIf sufficiently large net currents can be driven using mode converted waves,

changes in the loop voltage between co and counter-CD phasings would yield a direct measurement of the current drive efficiency.

Initial experiments were inconclusive. Changes in loop voltage Initial experiments were inconclusive. Changes in loop voltage consistent with current drive could not be obtained.consistent with current drive could not be obtained.

Using TORIC modeling, optimized scenarios for net current drive have been determined. In the best achievable conditions on C-Mod, the simulations predict 100 kA could be driven.

High ne x Zeff values on C-Mod make obtaining large efficiencies difficult.

Sawtooth oscillations are present in nearly all plasmas in C-Mod and complicate the loop voltage analysis.

Modeled discharge :• BT=5.4 T • Ip=0.8 MA,• ne0 = 1.4 x 1020 m-3,• Te0 = 5 keV • USN (high L-H thres.)• 65% D, 15% 3He, 5% H• J-port @ 50 MHz (MCCD)• D and E-port @80 MHz (Heating)

TORIC simulations predict 100 TORIC simulations predict 100 kA could driven in CkA could driven in C--ModMod

Target scenario from TORIC

Scenario/target for loop voltage measurements

Te is the electron temperaturePRF MC power to electronsne electron densityZeff effective charge

where

For a given MCCD scenario, current drive efficiency is largely determined by normalization factor:

Maximize the ratio above. Examples of achieved parameters:

5 keV

ne0 ~ 1.6 x 1020 m-3

low for C-Mod, but leads to Zeff ~ 4

Zeff < 2 achieved after boronization

Initial experiments are inconclusive

In such plasma conditions, we did not observe changes in loop In such plasma conditions, we did not observe changes in loop voltage consistent with current drive.voltage consistent with current drive.

The loop voltage in co-CD should be lower than in counter-CD.

Sawtooth oscillations complicate the analysis

Sawteeth oscillations have different period and amplitude betweeSawteeth oscillations have different period and amplitude between co n co and counterand counter--CD. The loop voltage evolution may be determined by CD. The loop voltage evolution may be determined by MHD physics in addition to resistive current diffusion.MHD physics in addition to resistive current diffusion.

Discussion and plans

Achieving proper conditions for loop voltage measurements of MCCAchieving proper conditions for loop voltage measurements of MCCD D on Alcator Con Alcator C--Mod is difficult. Mod is difficult.

C-Mod operates at high densities. Product ne0 x Zeff ~ constant (except for boronization) and higher than in other machines.

Combining parameters achieved in different discharges could lead to larger efficiencies than presently obtained by factor 2-3, but room for improvement is limited.

Nearly all plasmas in C-Mod are sawtoothing. This complicates the loop voltage approach.

ne Zeff ~ constant (except after boronization)

3. MCCD physics and TORIC modeling3. MCCD physics and TORIC modelingDue to poloidal field effects, the fast wave can be mode converted to Ion

Cyclotron Waves (ICW) instead of Ion Bernstein Waves (IBW) at the ion-ion hybrid layer.

The full wave code TORIC predicts net currents can be driven by The full wave code TORIC predicts net currents can be driven by mode converted Ion Cyclotron Waves. mode converted Ion Cyclotron Waves.

Strong up-down asymmetries in the ICW deposition result in net currents due to the upshift/downshift of k|| in toroidal geometry.

In constrast, currents driven by IBW are small and ambipolar.

Comparing TORIC predictions and results from MCCD experiments coComparing TORIC predictions and results from MCCD experiments could uld be a further test of the model. MCCD involves different aspects be a further test of the model. MCCD involves different aspects of mode of mode conversion physics than adressed in previous comparisons.conversion physics than adressed in previous comparisons.

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 Berstein 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 Maxwell’s The TORIC code solves Maxwell’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.

Good agreement between TORIC and experiments

TORIC predictions have been compared with experimental results on the Alcator C-Mod tokamak.

The agreement between TORIC and experimental results gives good The agreement between TORIC and experimental results gives good confidence in the model used and the code.confidence in the model used and the code.

Power deposition profilesPower deposition profilesPhase contrast imagingPhase contrast imaging

Y. Lin et al., PPCF 47 (2005) 1207-1228

Net currents results from up-down asymmetry

Due to upshift in kDue to upshift in k|||| from poloidal field effects, upfrom poloidal field effects, up--down asymmetries down asymmetries can result in net current drive.can result in net current drive.

For mode converted waves, k⊥ is large, thus:

Above the midplane, m < 0 k|| < 0Below the midplane, m > 0 k|| > 0

i.e. MC waves induce co or i.e. MC waves induce co or counter current drive depending counter current drive depending on where they damp relative to on where they damp relative to the midplane. the midplane.

TORIC predicts net current drive from ICW

Current drive with IBW is ambipolar

ICW can drive net currentsICW can drive net currents

weak upweak up--down down asymmetryasymmetry

leads to ambipolar leads to ambipolar currentscurrents

strong upstrong up--down down asymmetryasymmetry

leads to net currentleads to net current

Motivation for studying MCCD by ICW

The efficiency and driven current profile for MCCD involves diffThe efficiency and driven current profile for MCCD involves different erent aspects of mode conversion physics compared to deposition aspects of mode conversion physics compared to deposition profiles or PCI measurements.profiles or PCI measurements.

Power deposition profiles resolve flux surface dependence

PCI line-integrated along vertical chordsresolve major radius dependence

Driven currents reflect upreflect up--down asymmetriesdown asymmetries+ local current drive efficiency+ local current drive efficiency

⇒⇒ Comparison between MCCD predictions and experiments could Comparison between MCCD predictions and experiments could be a further test for TORIC model and our physical understandingbe a further test for TORIC model and our physical understanding

...local current drive efficiency must be treated carefully:...local current drive efficiency must be treated carefully:• It also determines the current profiles in addition to wave physics• Small efficiencies will make current measurements difficult

4. Current drive efficiency for ICW4. Current drive efficiency for ICWLocal current drive efficiency determines the driven current profiles in addition to

wave physics.

Magnetic trapping strongly reduces the current drive efficiency Magnetic trapping strongly reduces the current drive efficiency for offfor off--axis mode conversion scenarios.axis mode conversion scenarios.

TORIC presently uses the Ehst-Karney parametrization to calculate driven current profiles. Magnetic trapping effects are included.

Initial calculations show differences between the Ehst-Karney parametrization and the Fokker-Planck results.

To have a better treatment of magnetic trapping and of the polarTo have a better treatment of magnetic trapping and of the polarization of ization of mode converted waves, TORIC has been coupled with the Fokkermode converted waves, TORIC has been coupled with the Fokker--Planck Planck code RELAX for current drive calculations. code RELAX for current drive calculations.

MCCD efficiency (Ehst-Karney)

Ion Cyclotron Waves damps on electrons with ω/k|| vthe ≤1

Efficiency in TORIC is evaluated with Ehst-Karney parametrization Ehst and Karney, Nucl Fusion 31 (1991)

Current drive at vCurrent drive at vphph ~ v~ vthethe is least is least efficientefficient

Magnetic trapping further Magnetic trapping further decreases the efficiencydecreases the efficiency

Efficiency for off-axis current drive is strongly reduced by magnetic trapping

Current drive from ICW is evaluated using the Ehst-Karney parametrization for the fast wave (AW damping), as the two wavescannot be distinguished in TORIC.

To check whether this approach is appropriate, the current driveTo check whether this approach is appropriate, the current driveefficiency from ICW can now be computed through Fokkerefficiency from ICW can now be computed through Fokker--Planck Planck simulations.simulations.

⇒ In latest implementation of TORIC, a quasilinear diffusion operator for electrons is calculated from the TORIC fields.

Bilato et al., Nucl. Fusion, 42 (2002) 1085-1093

Quasilinear FP calculations of the efficiency

⇒ The diffusion operator is imported in the Fokker-Planck solver RELAX, which solves the bounce-averaged FP equation on circular flux surfaces.

Westerhof et al., Rijnhuizen Report 92-211 (1992)

Coupling with other FP codes (CQL3D, DKE) is also considered.

Initial FP calculations

Preliminary results from FokkerPreliminary results from Fokker--Planck simulations show differences Planck simulations show differences with Ehstwith Ehst--Karney predictions for MCCD by ICW.Karney predictions for MCCD by ICW.

• RELAX in good agreement with the Ehst-Karney predictions for a FWCD test case.

• Possible reasons for difference: wave polarization, treatement of magnetic trapping (trapped/passing boundary) in RELAX, etc...

Summary

Measured evolution of the sawtooth period in CMeasured evolution of the sawtooth period in C--Mod as mode Mod as mode conversion layer is swept through q=1 surface gives strong conversion layer is swept through q=1 surface gives strong experimental indication of localized MCCD.experimental indication of localized MCCD.• Experiments compared evolution in co, counter and heating phasing in

D(3He) plasmas.

Initial experiments attempting to measure net currents from modeInitial experiments attempting to measure net currents from modeconverted waves through loop voltage differences were converted waves through loop voltage differences were inconclusive.inconclusive.• Large current drive efficiencies are difficult to obtain on C-Mod• Sawtooth oscillations complicate the loop voltage analysis

Full wave simulations with TORIC predict net current drive from Full wave simulations with TORIC predict net current drive from mode converted Ion Cyclotron Waves on Alcator Cmode converted Ion Cyclotron Waves on Alcator C--Mod.Mod.• Strong up-down asymmetries in ICW deposition leads to net current drive• Fokker-Planck calculations of the current drive efficiency for ICW are being

implemented using the fields calculated by TORIC.

Future work

In order to test the consistency between TORIC simulations and In order to test the consistency between TORIC simulations and experimental changes in the sawtooth period, the data will be anexperimental changes in the sawtooth period, the data will be analyzed alyzed using the Porcelli model.using the Porcelli model.

The Porcelli model for the sawtooth period will be implemented in TRANSP and the evolution of the sawtooth period will be simulated using the deposition and driven current profiles predicted by TORIC.

Account for the effect of electron heating close to the q=1 surface Is the current profile shape predicted by TORIC consistent with

sawtooth period changes (including heating phase for which TORICpredicts net current drive) ?

Use model to estimate the current drive efficiency ?Small current densities are sufficient to affect the sawtooth period.

Can we distinguish between IBW and ICW current drive ?Evaluate other possible mechanims for sawtooth period changes, like

fast particles or ICCD.

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

Acknowledgements

The authors gratefully thank R. Bilato, M. Brambilla and A. Peeters (Max Planck Institute for Plasma physics, Garching, Germany) for providing access to the QLDCE module in TORIC and the Fokker-Planck code RELAX.

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 : parisot@mit.edu