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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
2 R. Prater, Radio Frequency Power in Plasmas, April 27-29, 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
3 R. Prater, Radio Frequency Power in Plasmas, April 27-29, 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
4 R. Prater, Radio Frequency Power in Plasmas, April 27-29, 2015
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
€
⊥
5 R. Prater, Radio Frequency Power in Plasmas, April 27-29, 2015
• 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
€
⊥
6 R. Prater, Radio Frequency Power in Plasmas, April 27-29, 2015
• 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
⊥
7 R. Prater, Radio Frequency Power in Plasmas, April 27-29, 2015
It is the high frequency that shifts the interaction off-axis
27D28 D
28D29D
29D30D
30D31D
31D32D
32D33D
33D34D
34D35D
35D
36D
36D
37D
37D
38D
38D
39D
39D
40D
40D
41D
41D
42D
42D
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:
8 R. Prater, Radio Frequency Power in Plasmas, April 27-29, 2015
• 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
9 R. Prater, Radio Frequency Power in Plasmas, April 27-29, 2015
• 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
10 R. Prater, Radio Frequency Power in Plasmas, April 27-29, 2015
122976 is characterized by negative central shear to ρ=0.6, requiring current to peak near there
122976.03021
11 R. Prater, Radio Frequency Power in Plasmas, April 27-29, 2015
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
48D
48D
49D
49D
50D
50D
50D
51D
51D
51D
52D
52D
53D
53D
54D
54D
48
12 R. Prater, Radio Frequency Power in Plasmas, April 27-29, 2015
• 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
13 R. Prater, Radio Frequency Power in Plasmas, April 27-29, 2015
• 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
14 R. Prater, Radio Frequency Power in Plasmas, April 27-29, 2015
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
15 R. Prater, Radio Frequency Power in Plasmas, April 27-29, 2015
(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
16 R. Prater, Radio Frequency Power in Plasmas, April 27-29, 2015
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
17 R. Prater, Radio Frequency Power in Plasmas, April 27-29, 2015
• 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
18 R. Prater, Radio Frequency Power in Plasmas, April 27-29, 2015
• 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
19 R. Prater, Radio Frequency Power in Plasmas, April 27-29, 2015
• 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
20 R. Prater, Radio Frequency Power in Plasmas, April 27-29, 2015
• 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
21 R. Prater, Radio Frequency Power in Plasmas, April 27-29, 2015
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
22 R. Prater, Radio Frequency Power in Plasmas, April 27-29, 2015
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
23 R. Prater, Radio Frequency Power in Plasmas, April 27-29, 2015
• 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
24 R. Prater, Radio Frequency Power in Plasmas, April 27-29, 2015
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
25 R. Prater, Radio Frequency Power in Plasmas, April 27-29, 2015
• 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
26 R. Prater, Radio Frequency Power in Plasmas, April 27-29, 2015
• 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
27 R. Prater, Radio Frequency Power in Plasmas, April 27-29, 2015
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
28 R. Prater, Radio Frequency Power in Plasmas, April 27-29, 2015
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)
29 R. Prater, Radio Frequency Power in Plasmas, April 27-29, 2015
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
30 R. Prater, Radio Frequency Power in Plasmas, April 27-29, 2015
• 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