121 2 3 4 5 6 7 8 9 10 11

D1 D2 D3 D4 D5D6

61 2 3 4 5

Decouplers

Long 9" lines

Line stretchers

Stubs

Antennas

To transmitters

"Cubes"

Quarter-wave transformers

Test cell boundary

Vacuum bdy

NSTX HIGH HARMONIC FAST WAVE CALCULATIONSFOR DEVELOPMENT OF CD OPERATIONS

HHFW Characteristics in NSTX

• f = 30 MHz

• fci = 3.3 MHz (at center for D+ ions, B0 = 0.45 T)

• ci ≈ 10 (at center) to 20 (at outer edge)

• High density (≥ 1019 m-3) and low B give high dielectric constant = 50 – 100

HHFW Characteristics in NSTX

• f = 30 MHz

• fci = 3.3 MHz (at center for D+ ions, B0 = 0.45 T)

• ci ≈ 10 (at center) to 20 (at outer edge)

• High density (≥ 1019 m-3) and low B give high dielectric constant = 50 – 100

NSTX antennas installed in the vacuum vessel Boron Nitride limiters surround each antenna

HHFW SYSTEM OVERVIEW

12 current straps6 resonant loops6 stub decouplers6 quarter wave transformersStraps 1-7, 2-8 ,... connected

in resonant loops

Substantial inter-strap coupling (k21 ≈ 0.1 in vacuum) compensated for by decouplers

Electrical length of each loop is 2

Currents in straps at each end are out of phase (π phasing)

P. M. Ryan, D. W. Swain, M. D. Carter, E. F. Jaeger, R. A. Rasmussen, J. B. Wilgen, ORNLJ. R. Wilson, J. C. Hosea, B. P. Leblanc, C. K. Phillips, A. L. Rosenberg, PPPL

T. K. Mau, UC-San Diego, P. T. Bonoli, MIT, R. W. Harvey, CompX, and the NSTX Team

HHFW SYSTEMCIRCUIT FOR 6 TRANSMITTERS, 12-ELEMENT ANTENNA ARRAY

ABSTRACT

Improvements in the vacuum feedthroughs permitted higher power HHFW current drive experiments to be performed on NSTX in 2003. Up to 4.3 MW was applied to He plasmas, raising the peak central electron temperature up to 2.3 keV. Normalized current drive efficiency estimates ( ~ 0.035x1019 AW-

1m-2) were similar to those previously obtained for D plasmas at lower power (2.1 MW) and Te0 (1.4 keV) for similar conditions (kz = 7.6 m-1, <ne> ~ 1x1019 m-

3, Ip = 0.5 MA). Studies are being performed with the full-wave code AORSA to determine the optimum launched wave spectrum which will both heat the electrons effectively and drive current efficiently with the present system. These calculations will be compared to results from both ray-tracing codes and other full-wave codes. The RANT3D code will be used to calculate the plasma loading for these phasing scenarios so that power tuning/matching requirements can be anticipated.

ABSTRACT

Improvements in the vacuum feedthroughs permitted higher power HHFW current drive experiments to be performed on NSTX in 2003. Up to 4.3 MW was applied to He plasmas, raising the peak central electron temperature up to 2.3 keV. Normalized current drive efficiency estimates ( ~ 0.035x1019 AW-

1m-2) were similar to those previously obtained for D plasmas at lower power (2.1 MW) and Te0 (1.4 keV) for similar conditions (kz = 7.6 m-1, <ne> ~ 1x1019 m-

3, Ip = 0.5 MA). Studies are being performed with the full-wave code AORSA to determine the optimum launched wave spectrum which will both heat the electrons effectively and drive current efficiently with the present system. These calculations will be compared to results from both ray-tracing codes and other full-wave codes. The RANT3D code will be used to calculate the plasma loading for these phasing scenarios so that power tuning/matching requirements can be anticipated.

Cut through antenna midplanes, viewed from above

Ip

Bt

158 cm radius

19 cm radius

12

3

4

5

6

7

8

9

10

1112

88°

HHFW SYSTEM

• 6 MW Power (six 1 MW transmitters).• 12-Element Antenna Array.• Each transmitter drives one half-wave

resonant loop.• Shunt decouplers compensate for

inductive coupling between straps, effectively isolating transmitters from one another.

• Digital feedback control of phase shift between array elements.

HHFW SYSTEM

• 6 MW Power (six 1 MW transmitters).• 12-Element Antenna Array.• Each transmitter drives one half-wave

resonant loop.• Shunt decouplers compensate for

inductive coupling between straps, effectively isolating transmitters from one another.

• Digital feedback control of phase shift between array elements.

= array phase shift

HHFW PHASED-ARRAY OPERATION

REAL TIME FEEDBACK CONTROL OF ARRAY PHASE HAS BEEN IMPLEMENTED

• Inter-source phase control– Set electronically via a computerized waveform generator– Feedback control of source phases to fix the phases of antenna

currents

• Can set for any inter-source phasing, and can vary with time during a shot

– Pre-programmed phase(t)– Operated with constant , and changed by 45° during a shot

(e.g, 90° to 45°)– Phase errors generally < 10º.

REAL TIME FEEDBACK CONTROL OF ARRAY PHASE HAS BEEN IMPLEMENTED

• Inter-source phase control– Set electronically via a computerized waveform generator– Feedback control of source phases to fix the phases of antenna

currents

• Can set for any inter-source phasing, and can vary with time during a shot

– Pre-programmed phase(t)– Operated with constant , and changed by 45° during a shot

(e.g, 90° to 45°)– Phase errors generally < 10º.

Counter-CD Co-CD

Calculated Spectra From RANT3D

HHFW WAVE SPECTRA

• Fixed 180º phase shift between strap pairs 1-7, 2-8, … prevents spectral peak from being smoothly varied with .

– Full 12-element array operation at = ±30º, ±90º gives single-peaked wave spectra.

– At other relative phases, the system operates as two 6-element arrays, leading to double-peaked wave spectra.

• Plasma response asymmetries are smaller at smaller wave numbers.

• Plasma loading is smaller at smaller wave numbers. B (near antennas)

Pitch angle of the magnetic field at the antennas can be as large as 45º

• Asymmetries between co-CD and counter-CD directions are more pronounced at higher wavenumbers.

• Asymmetric plasma response means even symmetric phasings can give rise to directional wave spectra.

LOADING WITH PHASING IS 2X THE LOADING WITH

Measured load resistance Rload* for co-, counter-, and phasing agrees with calculations

12x12 impedance matrix from RANT3D (Im part, diag. term suppressed) shows asymmetry

Strap # Strap #

Asymmetry in plasma response causes observed loading imbalance between co-CD and counter-CD phasing

ASYMMETRIC PLASMA RESPONSE

Asymmetric response to symmetric array excitationcaused by large pitch angle of magnetic field

kz power spectrum from GLOSI/RANT3D calculations

•TORIC (Bonoli and Brambilla)

– Full-wave ICRF field solver strictly valid in the ion FLR limit of (ki)2 << 1

– Run Order Reduction Algorithm (ORA) to obtain correct electric field polarization for the HHFW

– Poloidal field neglected with ORA in TORIC - (B = 0).

•AORSA (Jaeger)– Power deposition profiles from TORIC agree with profiles from the AORSA

code, which has no limitations on kI and includes poloidal field effects.

Calculated electron power absorption profiles are coupled to Ehst-Karney adjoint solution for current drive efficiency to obtain current density profiles.

TORIC sees significant reduction in JFW due to absorption by trapped electrons.

Power deposition profiles

SUMMARY OF CURRENT DRIVE CALCULATIONS FOR 7 m-1

Co-CD Cntr-CD Total I ICD/P FW

(kA) (kA) (kA) (A/W) (A•m-2/W)0D 110 70 180 0.056 0.034TORIC 96 50 146 0.046 0.028CURRAY 162 79 241 0.075 0.046

SUMMARY OF CURRENT DRIVE CALCULATIONS FOR 7 m-1

Co-CD Cntr-CD Total I ICD/P FW

(kA) (kA) (kA) (A/W) (A•m-2/W)0D 110 70 180 0.056 0.034TORIC 96 50 146 0.046 0.028CURRAY 162 79 241 0.075 0.046

Driven Current Density Profiles

TORIC and AORSA give similar power absorption profiles.

•CURRAY (Mau)– Ray-tracing code uses 11-110 rays to represent launched spectrum.– Power distribution : P() ~ cos2(koL)– Dispersion relation is hot electron and cold ion.– Damping is linear on Maxwellian species and includes hot plasma effects to

all orders in ki, using k determined locally via an order reduction scheme.

• Power absorption and current density profiles from CURRAY are peaked on axis for both co- and counter-CD cases

• Nearly all power (96-100%) is absorbed on the electrons.

HHFW CURRENT DRIVE MODELING

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0

ne

(x10

-19

m-3

)

1.61.41.21.00.80.60.40.2

Radius (m)

Plasma Density for co-, counter-CD Phasing(107899, 107907)

co-CD (t = 393 ms) co-CD (t = 510 ms) counter-CD (t = 393 ms) counter-CD (t = 510 ms)

HHFW CURRENT DRIVE - EFFECT ON LOOP VOLTAGE107899: Co-CD, PHHFW = 2.1MW, solid lines 108907: Counter-CD, PHHFW = 1.2 MW, dotted lines

Co-CD and counter-CD experiments were run with array phasings of = (k|| ~ 7.6 m-

1)

Measurement of the current density profile awaits the installation of the MSE diagnostic (2003). In the meantime, ICD can be estimated from the difference in loop voltage between co/cntr-CD phasings for similar plasma conditions.

Assumptions:• Steady-state conditions (t > L/R)• Plasma ohmic resistance (RP) and pressure

profiles (IBS) are independent of array phasing.• Driven current is proportional to the RF power

(Ico/Pco = Icntr/Pcntr) and inversely proportional to the density.

Then the relation IP = (V-0.5*IP*dLi/dt)/RP + IBS + ICD (where the loop voltage is both driving the ohmic current and changing the magnetic stored energy) can be used to estimate the driven current.

ICD ~ 180 kA (110 kA co, 70 kA counter)

ICD/PRF = 0.05 A/W

FW = ICD<ne>R/PRF = 0.034 x 1019 A • m-2/W

Measurement of the current density profile awaits the installation of the MSE diagnostic (2003). In the meantime, ICD can be estimated from the difference in loop voltage between co/cntr-CD phasings for similar plasma conditions.

Assumptions:• Steady-state conditions (t > L/R)• Plasma ohmic resistance (RP) and pressure

profiles (IBS) are independent of array phasing.• Driven current is proportional to the RF power

(Ico/Pco = Icntr/Pcntr) and inversely proportional to the density.

Then the relation IP = (V-0.5*IP*dLi/dt)/RP + IBS + ICD (where the loop voltage is both driving the ohmic current and changing the magnetic stored energy) can be used to estimate the driven current.

ICD ~ 180 kA (110 kA co, 70 kA counter)

ICD/PRF = 0.05 A/W

FW = ICD<ne>R/PRF = 0.034 x 1019 A • m-2/W

The RF power levels and gas feed were adjusted to similar electron temperature and density profiles for co- and

counter-CD phasings.

The changing internal inductance needs to be taken into account when comparing the loop voltage difference.

0.22 V

0.22 V

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.01.61.41.21.00.80.60.40.2

Radius (m)

Electron Temperature for co-, counter-CD Phasing(107899, 107907)

co-CD (t = 393 ms) co-CD (t = 510 ms) counter-CD (t = 393 ms) counter-CD (t = 510 ms)

THE VOLTAGE DIFFERENCE BETWEEN CO-CD AND COUNTER-CD PHASINGS IS INDICATIVE OF HHFW DRIVEN CURRENT, BUT THE CURRENT DENSITY PROFILE MEASUREMENTS FROM THE MSE DIAGNOSTIC ARE NEEDED TO BE CERTAIN.

THE VOLTAGE DIFFERENCE BETWEEN CO-CD AND COUNTER-CD PHASINGS IS INDICATIVE OF HHFW DRIVEN CURRENT, BUT THE CURRENT DENSITY PROFILE MEASUREMENTS FROM THE MSE DIAGNOSTIC ARE NEEDED TO BE CERTAIN.

RF ON (counter-CD)RF ON (co-CD)

neL

Te(0)

Co-CD Counter-CD

VLOOP, Internal Inductance2.0

1.5

1.0

0.5

0.0

Internal Inductance (normalized)

0.50.40.30.20.10.0

time (s)

110145 (co-CD) 110152 (cntr-CD)

1.6x1013

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0

ne

(cm

-3)

140120100806040

Radius (cm)

110145 at 0.31 s (co-CD) 110145 at 0.39 s (co-CD) 110152 at 0.31 s (cntr-CD) 110152 at 0.39 s (cntr-CD)

2.5

2.0

1.5

1.0

0.5

0.0140120100806040

110145 at 0.31 s (co-CD) 110145 at 0.39 s (co-CD) 110152 at 0.31 s (cntr-CD) 110152 at 0.39 s (cntr-CD)

1.2

1.0

0.8

0.6

0.4

0.2

0.0

Loop Voltage (V)

0.50.40.30.20.10.0

time (s)

Measured 110145 (co-CD) Measured 110152 (cntr-CD) Corrected 110145 (co-CD) Corrected 110152 (cntr-CD)

• He operation• = ± /2 (k|| = ±7.6 m-1)• Ip = 500 kA, B0 = 0.45 T

0.27 V

• I = 208 kA (123 kA co, 85 kA cntr)• ICD/PRF = 0.03 A/W• FW = 0.03 x 1019 A•m-2/W

AORSA predicts 183 to 256 kA with 4.3 MWfor the co-CD case

Te profiles at 0.31 and 0.39 s ne profiles at 0.31 and 0.39 s

Normalized Internal Inductance

Loop Voltage

2.5

2.0

1.5

1.0

0.5

0.0

<ne

> (x10

19 m

-3), T

e

(0) (keV)

0.60.50.40.30.20.10.0

time (s)

RF On

Te(0)

<ne>

Co-CD (solid)Cntr-CD (dotted)

Te(0) and line-average ne

DEUTERIUM OPERATION (2002) HELIUM OPERATION (2003)Repair and modification of the vacuum feedthroughs permitted power to be increased to 4.3 MW for the 2003 current drive experiments in He. Current drive efficiencies, based on decrease in loop voltage, are similar to those obtained at lower power in D plasmas in 2002.

3.0x106

2.5

2.0

1.5

1.0

0.5

0.0

Driven Current Density (A/m

2)

1.00.80.60.40.20.0

Ψ1/

=1 19 -3ne e m =1 19 -3ne e m =1 19 -3ne e m

3.0x106

2.5

2.0

1.5

1.0

0.5

0.0

Driven Current Density (A/m

2)

1.00.80.60.40.20.0

Ψ1/

=1 19 -3ne e m = 19 -3ne e m =3 19 -3ne e m =4 19 -3ne e m

2.0x106

1.5

1.0

0.5

0.0

Driven Current Density (A/m

2)

1.00.80.60.40.20.0

Ψ1/

=1Te keV =Te keV =3Te keV

2.0x106

1.5

1.0

0.5

0.0

Driven Current Density (A/m

2)

1.00.80.60.40.20.0

Ψ1/

=1Te keV =Te keV =3Te keV =4Te keV

Driven current profiles as a function of density for Te(0) = 2 keV

kz = 7.6 m-1 kz = 3 m-1

kz = 7.6 m-1 kz = 3 m-1

Driven current profiles as a function of electron temperature for ne(0) = 2e19 m-3

0.14

0.12

0.10

0.08

0.06

0.04

0.02

0.00

Current driven per power absorbed (A/W)

4.03.53.02.52.01.51.0

Central density ne(0) (x1019

m-3

)

Dotted -100 x 100 modesSolid - 136 x 136 modes

kz = 3 m-1

kz = 7.6 m-1

0.14

0.12

0.10

0.08

0.06

0.04

0.02

0.00

Current driven per power absorbed (A/W)

4.03.53.02.52.01.51.0

Central Temperature Te(0) (keV)

Dotted -100 x 100 modesSolid - 136 x 136 modes

kz = 7.6 m-1

kz = 3 m-1

Density scan at constant temperature(Te(0) = 2 keV)

Temperature scan at constant density(ne(0) = 2e19 m-3)

Ref

lect

ion

Co

effi

cien

t

Match for -90º

Ref

lect

ion

Co

effi

cien

t

Match for -45º

Ref

lect

ion

Co

effi

cien

t

Match for -30º

Ref

lect

ion

Co

effi

cien

t

Match for -60º

Full-wave calculations (AORSA) predict higher current drive efficiencies efficiencies for kz = 3 m-1 ( = -30º) for central electron temperatures as low as 1 keV.

Full-wave calculations (AORSA) predict higher current drive efficiencies efficiencies for kz = 3 m-1 ( = -30º) for central electron temperatures as low as 1 keV.

• For Te(0) < 1 keV, the electron heating efficiency is higher for larger kz.

• Heat at high kz and switch to low kz during the pulse for more efficient CD.

• Need to maintain a match (reflection coefficient < 0.3) during phase shifting.

• The plasma impedance code GLOSI and the antenna analysis code RANT3D were used to calculate the loading as a function of phase shift for a typical plasma case.

• Average loading seen by each of the six transmitters is 13.5 at -90º, 15.9 at -60º, and 14.7 at -30º.

• Loading should be high enough to couple full power to the plasma without exceeding antenna voltage limits.

• For Te(0) < 1 keV, the electron heating efficiency is higher for larger kz.

• Heat at high kz and switch to low kz during the pulse for more efficient CD.

• Need to maintain a match (reflection coefficient < 0.3) during phase shifting.

• The plasma impedance code GLOSI and the antenna analysis code RANT3D were used to calculate the loading as a function of phase shift for a typical plasma case.

• Average loading seen by each of the six transmitters is 13.5 at -90º, 15.9 at -60º, and 14.7 at -30º.

• Loading should be high enough to couple full power to the plasma without exceeding antenna voltage limits.

CALCULATIONS FOR OPERATIONAL DEVELOPMENT OF CD SCENARIOS

EXAMPLES OF DYNAMIC PHASE SHIFT FOR VARIOUS MATCH CONDITIONS

• Difficult to maintain < 0.3 as array phase shift is changed from -90º to -30º.

• Feedback control on antenna voltage rather than transmitter power will be implemented during the next run period.

• May be used in conjunction with plasma position control feedback to maintain match.

• Difficult to maintain < 0.3 as array phase shift is changed from -90º to -30º.

• Feedback control on antenna voltage rather than transmitter power will be implemented during the next run period.

• May be used in conjunction with plasma position control feedback to maintain match.

DYNAMIC PHASE SHIFTING DURING PULSE

EXP PTS

EXP PTS