development of helicon current drive in the diii-d tokamak · 2015-05-19 · 9 r. prater, radio...

1 R. Prater, Radio Frequency Power in Plasmas, April 27-29, 2015

Development of Helicon Current Drive

in the DIII-D Tokamak

R. Prater, C. Moeller, R. Pinsker, O. Meneghini General Atomics M. Porkolab, MIT E.F. Jaeger, XCEL Engineering, Inc. C. Lau, Oak Ridge National Laboratory V. Vdovin, Kurchatov Institute Presented at the IAEA Technical Committee Meeting on Steady-State Operation of Magnetic Fusion Devices May 26-29, 2015

Tue Mar 31 11:22:07 2015


•  Ph.D. from Moscow Institute of Physics and Technology in 1964

•  Worked at Kurchatov Institute since 1964 •  Carried out seminal work,

theory and experiment, on ICRF with 2 ion species

•  Developed STELION and STELEC full wave codes

•  INTOR, ITER expert groups and ITPAs; STAC

•  Grand prize from MAIK publisher for 2013 paper on CD by Helicons and LHCD

Victor Vdovin, 1937 - 2015


•  Helicons are fast waves at a high harmonic (>20) of the ion cyclotron frequency but below the LH frequency (also called ‘whistlers’)

•  The high frequency does two important things: •  Improves the damping, so high performance plasma conditions

can provide full damping on the first pass •  Gives the wave the whistler-like quality of primarily following field

lines, with also a small radial component, so the waves spiral around and toward the magnetic axis

•  The spiral trajectory plus strong damping imply off-axis CD

•  Not a new idea: suggested by Mau (Aries RS, 1997) and Koch (DEMO, 2011)

Helicons are calculated to be effective at driving off-axis current in high beta tokamaks


G(ω)

0 0.2 0.4 0.6 0.8 1.0 f (GHz)

k⊥

kAlfvenk (1/m)⊥

0

500

1000

1500

30

20

10

0

40

n =0.5x10 /m20 3

n =0.5x10 /m20 3

e

e

B = 1.6 Tn = 4.6v /v = 2.0||

||

tefci

•  High frequency (~30 fci) increases the factor G(ω) by a factor ~20

•  The factor k also increases with frequency, improving the damping

High frequency improves damping of the fast wave

€

Im(k⊥) =π4

βe ξe e−ξ e

2k⊥G (ω), ξe ≡

v||vte

Chiu, Chan, Harvey, Porkolab, NF 1989

€

⊥


•  High density doesn’t much affect the factor G(ω)

•  But density does increase k

approximately linearly, improving absorption

•  Increasing density also increases the βe factor

High density improves damping of the fast wave

€

Im(k⊥) =π4

βe ξe e−ξ e

2k⊥G (ω), ξe ≡

v||vte

Chiu, Chan, Harvey, Porkolab, NF 1989

G(ω)

0 0.2 0.4 0.6 0.8 1.0 f (GHz)

k⊥

kAlfvenk (1/m)⊥

0

500

1000

1500

30

20

10

0

40

n =1.0x10 /m20 3n =0.5x10 /m20 3

n =0.5x10 /m20 3

ee

e

n =1.0x10 /m20 3e

B = 1.6 Tn = 4.6v /v = 2.0||

||

te

€

⊥


•  Smaller radial wave velocity v is beneficial because it keeps the wave trajectory at larger minor radius for a longer time

Increasing density also slows down the radial velocity of the helicon

0 0.2 0.4 0.6 0.8 1.0 f (GHz)

0

0.5

1.0

1.5v (10 m/s)7⊥

n =0.5x10 /m20 3e

n =1.0x10 /m20 3e

•  At the low density edge, the radial velocity is large, giving the beneficial effect of transmitting the power through the SOL rapidly

⊥


It is the high frequency that shifts the interaction off-axis

27D28 D

28D29D

29D30D

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31D32D

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33D34D

34D35D

35D

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43D

43D

44D 45D

46D

47D 48D

49D

50D

51D

52D

53D

54D 55D

60 MHz 500 MHz

•  The ray trajectory is spiral rather than straight through the center

•  n|| behavior is MUCH more regular, ~1/R

•  The ray is fully damped, so minimal interaction with boundary

4D4D

5D

5D

6D6D

420

-2-4-6 0

3

6

0 0.5 1.0 1.5 2.0 0 0.5 1.0 1.5 2.0 poloidal arc length (m) poloidal arc length (m)

~1/R

n n|| ||

For 500 MHz case:


•  Many discharges in DIII-D

have βe > 0.02 at the mid-radius region

High βe is needed for strong absorption

n20(a/2)=0.5, Bt=1.6 T, f=500 MHz Chiu, Chan, Harvey, Porkolab, NF 1989

•  Minimum βe for sufficiently strong absorption is around 0.015

0.5 1.0 1.5 2.0 2.5 B (T)

0.0

0.01

0.02

0.03

0.04β (a/2)e

DIII-D shots 120000-153000


•  Target discharge has Ip and Bt ramps to generate a current profile that supports stable operation βN=3.8, H98Y2=1.5 –  shortly after ramps end, a 2/1

tearing mode destroys the confinement

•  Purpose of helicon CD is to demonstrate a method to help sustain the current profile obtained via the ramps, in a steady-state compatible way => use this equilibrium as a

viable starting point

Target DIII-D equilibrium is a high performance discharge that requires current drive for sustainment

122976

2/1 mode starts

Ip ramp ends


122976 is characterized by negative central shear to ρ=0.6, requiring current to peak near there

122976.03021


GENRAY calculations show effective current drive near the mid-radius

n||(a) = 3.0±0.30, f=500 MHz ne(0) = 10.3, Te(0) = 3.4, Ti(0) = 7.2, Zeff ~ 2.2 βe(ρ=0.5) = 3.2%

ICD = 60.3 kA/MW η = nIR/P = 0.62x1019 A/W/m2

ζ = 33 n20 I R / P TkeV = 0.64

j/P (A/cm /MW)

0

5

10

15

0 0.2 0.4 0.6 0.8 1.0 rho

Helicon60.3 kA/MW

2

€

37D

37D

38D

38D

39D

39D

40D

40D

41D

41D

42D

42D

43D

43D

44D

44D

45D

45D

46D

46D

47D

47D

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49D

50D

50D

50D

51D

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51D

52D

52D

53D

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54D

54D

48


•  Poloidal angle of 45 deg is good choice for location of antenna on the outboard midplane –  also avoids midplane heating systems and diagnostics

•  Little benefit seen from inboard side launch, from separate study

Systematic variation of antenna location and n|| shows best values to use in modeling

Driven current (kA/MW) ρ of current drive peakDriven current (kA/MW) rho of peak of CD

O. Meneghini, OMFIT


•  CQL3D uses completely

different models than GENRAY for absorption and current drive –  inputs to CQL3D are the

wave trajectory and electric field polarization from GENRAY

•  Agreement between CQL3D and GENRAY is very good –  differences are

independent of power, implying not quasilinear effects

Absorption and current drive models in GENRAY validated by CQL3D Fokker-Planck code


CQL3D shows that the effect of waves is a parallel flux in a small region of v|| and low v_perp

•  Only electrons with v|| near 2vth and small v_perp are directly affected by the wave fields

•  No direct interaction with trapped electrons

u /vnorm

u

/

vnor

mpe

rp

||

u /vnorm||

u

/

vnor

mpe

rp

-4 -2 0 2 4 v / v|| th

-4 -2 0 2 4 v / v|| th

4

2

0

v

/

vpe

rpth

4

2

0

v

/

vpe

rpth

RF Flux (1 MW) f (1 MW)

Log(Total Flux) (1 MW) f (10 MW)

e

e


(a) Magnitude E+ (b) Electron absorption

DIII-D #122976.02900: 400x400 modes, f = 500 MHz, B0 = 1.38 T, δ0 = 1.0e-05, ν/Ω=0, nφ = 60, n|| = 3.18, (Edison: 5 hrs on 4096 proc) lmax = 50, Pe = 1 MW, damp = 500.0

AORSA full wave code shows electric field pattern similar to that of ray tracing


Power absorbed Driven current 01

j (A/m2/MW)

q (W/m3/MW)

Electrons Pe = 1.0 MW

Ions

ICD= 75 kA

AORSA full wave code shows slightly larger current drive than ray tracing, but at slightly smaller minor radius

Note: no absorption by fast ions


•  At maximum tilt, the DIII-D beam drives NBCD that peaks around ρ=0.45

•  Total driven current for left source is 26 kA/MW for signs of Ip and Bt that maximize NBCD

Off-axis NBCD drives about half the helicon current in the same discharge

Off-Axis Neutral Beam Will Provide a Broader Range of Profile Control, Enabling a Range of Physics Studies

• Design will provide flexible aiming up to 15° from horizontal

On-Axis (5 MW) Off-Axis (5 MW)

Energy Density (MW/m3)

Torque Density (N-m/m3)

Current Density (MA/m2)

1.5

1.0

0.5

0.02.0

1.0

0.5

0.0

1.5

-0.550

40

20

10

20

00 1.00.80.60.40.2

Normalized Radius

M.R. Wade/Budget Planning Meeting/March 2010 062-10/MW/jyNATIONAL FUSION FACILITYDIII–D

NUBEAM

26 kA/MW


•  Density reduced 25% to avoid excessive refraction of EC waves

•  The ECCD is 19 kA/MW, or 15 kA/MW when scaled to original density

ECCD drives one quarter the helicon current in the same discharge

19 kA/MW


•  When ne and Te are scaled downward, the driven current scales with fixed dimensionless efficiency

•  The minor radius of the CD

decreases slowly with βe, but when βe becomes less than 1.5% the minor radius falls rapidly

Scans of density and temperature show off-axis current drive with constant dimensionless efficiency

€

ζ = 33n20 ICD R / TkeV PCD


•  Over the range 2.8 < n||< 4.2 the driven current hardly changes

•  Results differ from LHCD experiments, which show a strong increase by decreasing launched n||

•  This result can be understood from the detailed ray data

Driven current is quite insensitive to launched n||

n|| (a) CD (kA/MW) rho2.8 63.1 0.543.0 60.0 0.543.2 59.0 0.543.4 59.8 0.543.6 60.8 0.543.8 61.5 0.544.0 61.2 0.554.2 59.8 0.58


Insensitivity to launched n|| can be understood by considering the behavior of v||/vte

• Propagation is a spiral with slowly decreasing radius • As wave propagates, v||/vte decreases, and when

v||/vte gets to ~2 the wave is absorbed => CD tends to be at fixed ρ and magnitude


Strong damping increases CD efficiency, partly by avoiding the reduction due to trapping

LETTERS

is the zero order (Maxwellian) electron distribution, 2 isthe distance along the magnetic field line and L = I d£is the length of the field line. For passing particles,these integrals are performed over one poloidal circuit.

The only approximation employed in the numericalsolution of Eq. (1) is the replacement of the electron-ion collision operator by the Lorentz collision operator.Other than this, the only approximations are those usedin formulating Eq. (1), namely, linearizing the colli-sion operator and working in the banana limit. Asimple model field with circular flux surfaces is used;however, the results are not restricted to large aspectratios.

These calculations are done for several choices ofion charge (Z), inverse aspect ratio, poloidal locationwhere the wave heating occurs (0), a range of phasevelocities (w = co/k||Ve), and both Landau damping(LD) and Alfve"n wave (AW) types of resonance. On agiven poloidal flux surface \f/, the RF driven currentdensity, is expressed [1, 4] as

= (j,rB)/(B2) =V

where V = dV/di/' is the derivative of the toroidalvolume, pRF is the RF heating power density, and ()denotes the flux surface average [5]. In our normaliza-tion, the current drive efficiency is related to a dimen-sionless function fj as

V =38.4 x IP18 Te

m A a.

where m A is the Coulomb logarithm, r^ is the localelectron density, and the units are SI and keV. Bycomparing the numerically determined fj with our ana-lytic expression it proves possible to select constants inthe fj expression so as to fit closely the numericalvalues over the range studied. The final results arefunctions fj (Z, e, 6, w) of four variables, for bothwave types.

In addition to Giruzzi's work [3] there have beenother studies relevant to our problem. The first calcu-lation of trapping effects on current drive by LD, inRef. [6], yielded fj values in only rough agreementwith our numerical results for w > 1.4. Subsequentnumerical LD calculations agree closely with ourresults for w > 1.4: Taguchi's results [7] are within3 % of ours and the CQL values in Ref. [8] arewithin 6%. The alternative semi-analytic calculationin Ref. [8] is less accurate (e.g. 28% too small at

e = 0.25 and w = 3.5, compared to the numericalresults). The main defect of these previous calculationsis that they are useless for w ^ 1, since no explicit 6dependence appears. We find (see Fig. l(a)) a steepreduction in fj at w < 1 as 0 decreases from ir to 0.

i i i i i i i10

50

30 —

UJcr5 3ooLUN_ l<

trO |

0.5

XS

>

-

- /

/

i

V .

37T

/

//

o-a-

i i i i 111

(b) AW,Z= 1

\.

7 / 0r /

7 7

/ / ,/ 1 I/I 1 1 1

1 1 1

r

i i i

if —

-

-

-i i i i i

5 —

O.I 0.3 10

FIG. 1. Current drive efficiency versus parallel phase velocityfor Z = 1 and (a) Landau damping and (b) Alfvin wave damping.The dashed curve is for e = 0; dotted is for e = 0.03 and 0 = ic;no chain-dashed is for e = 0.25; and the solid curves are fore = 0.10, with wave damping at four different poloidal angles.The curves are analytical formula and the points are numericallyderived. (Points at e = 0.25 from Ref. [8].)

1934 NUCLEAR FUSION, Vol.31, No.10 (1991)

€

ξee−ξ e

2

€

ξe ≡ v|| /vte

Ehst-Karney, Nuclear Fusion

Max 0.43 at 0.73

0.037 at 2.0

€

ξe

€

ε = 0.1

Landau damping factor

Strong damping


•  V. Chan and A. Garofalo have been working on obtaining a true steady-state using realistic sources and GLF23 transport •  use their equilibrium and profiles

•  Economical source of off-axis current drive is needed •  Neutral beams ruled out for many technical reasons •  LHCD drives current only in plasma edge, but not at r=0.6 •  ECCD works, but power requirement is high

•  Helicons offer opportunity for improved current drive efficiency

FNSF-AT needs off-axis CD to achieve steady-state

Helicons may reduce the tension between high density for improving the divertor and low density for improving current drive efficiency


n||(antenna) = -2.2, f=1.2 GHz n20(0) = 2.8, Te(0) = 21.5, Ti(0)=21.6, Zeff ~ 1.8 βe(ρ=0.5) = 1.8%

GENRAY shows helicon rays propagate spirally in FNSF and drive off-axis current efficiently

ICD = 38.8 kA/MW η = nIR/P = 2.3x1019 A/W/m2

ζ = 33 n20 I R / P TkeV = 0.35

39 kA/MW

21D21D

22D22D

23D

23D

24D

24D

25D

25D26D

26D27D

27D

28D

28D

29D

29D

30D

30D

31D

31D

32D

32D

33D

33D

34D

34D

35D

35D


•  CD is independent of n|| for same reason as in DIII-D: n|| changes as ray propagates until v||/vte = 2

FNSF calculations also exhibit weak dependence on the launched n||

n|| (ant) CD (kA/MW) Rho of peak j1.8 36.1 0.622.0 38.1 0.602.2 38.4 0.622.4 36.5 0.662.6 33.8 0.68


•  The comb-line is a transmission line fed only at one end, followed by a sequence of radiating elements coupled inductively

•  The comb-line works best for weak to moderate coupling per

antenna element along the antenna –  moderately large gap is desirable –  launches narrow spectrum => avoid low n|| with accessibility

problems

•  Wave amplitude decays radially exponentially near antenna, with radial scale length of order the parallel wavelength/2π –  for DIII-D, the falloff distance for Poynting flux is 1.8 cm –  Antenna is designed to couple 90% of power over a length of 2 m

with 5 cm gap between the Faraday screen and the propagating layer (~2x1018/m3)

Launching the helicon benefits from use of a comb-line traveling wave antenna


Prototype Comb-line Traveling Wave Antenna under construction for installation in DIII-D in November 2015

• Depth of slots in Faraday screen affects element-to-element coupling • 20 cm total height includes two parallel but coupled comb-lines

• 10-50 radiators • Feedthroughs only at ends • Radiators connected inductively and capacitively • 4 or more straps per wavelength and long length gives narrow n_parallel spectrum

Radiating element

Feed

Ground plane Two elements,

of 12 for proto-type antenna, 40 for 1 MW antenna • Tilted so FS is parallel to magnetic field


Transmission line nature of comb-line provides flexibility in operating point

vφ =1LC

Z = LC,

• By increasing LC the phase velocity can be reduced • Actual antenna is dispersive, so group velocity can be reduced in order to strengthen coupling

B/B , large v B/B , lower v 0 0 g g

• Adjustment of the slot depth between Faraday screen elements makes significant improvement in ability to couple through a gap • The 10 MHz bandwidth of the klystron makes possible operational changes in n of ±0.6

(Highly idealized)

||

1 m 1 m

Power remaining: 50% 27% 510

500

490

480

470

460

450

440

4300 1 2 3 4 5 6

n_parallel

Large groupvelocity

Smaller groupvelocity

frequency(MHz)


Power source: a 1.2 MW 476 MHz klystron from the SLAC B-factory

PEP- II Linac Accelerator Systems Department

• 

B-Factory RF Klystrons (1.2 MW) under construction

C. Pearson


•  Helicons offer significant improvement in off-axis current drive efficiency over ECCD and NBCD, both for DIII-D and FNSF

•  The physics is well understood from modeling calculations

•  Comb-line antennas are an effective technology for launching helicons (fast waves) and a prototype antenna is scheduled for installation in DIII-D in November

•  DIII-D is an excellent facility for testing this physics due to high

βe, CD measurement capability, and antenna expertise

Summary

development of helicon current drive in the diii-d tokamak · 2015-05-19 · 9 r. prater, radio...

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