1 ST workshop 2005 Numerical modeling and experimental study of ICR heating in the spherical tokamak Globus-M O.N.Shcherbinin, F.V.Chernyshev, V.V.Dyachenko,

1

ST workshop 2005

Numerical modeling and experimental study of ICR heating in the spherical

tokamak Globus-M

O.N.Shcherbinin, F.V.Chernyshev, V.V.Dyachenko, V.K.Gusev, Yu.V.Petrov, N.V.Sakharov

A.F.Ioffe Physico-Technical Institute, St.Petersburg, Russia

2

Outline

1. Specific features of ICRH experiments on spherical tokamaks.

2. Model for numerical simulation.

3. Effect of light ion content in plasma on RF heating efficiency (simulation and experiment).

4. Effect of the second hydrogen harmonic position on ion heating.

3

Specific features of ICR heating at small plasma aspect ratio

• Due to strong variation of toroidal magnetic field along major radius, several ion cyclotron harmonics exist simultaneously in plasma cross- section.

• For typical conditions of spherical tokamaks (low Bt and high ne) it is necessary to use low frequency RF power (5-10 МHZ). So the wavelength is much larger than plasma dimensions and width of resonance and cut-off zones.

• Tokamak Globus-M operates with high hydrogen concentration (10-50)% in deuterium plasma.

• The shadow of the limiter in Globus-M is too shallow to place there a multi-element antenna to excite a well shaped wave spectra .

4

Cyclotron Harmonics in Globus-M

Magnetic fields in equatorial plane of Globus-M

-20 0 20x, cm

-40

-20

0

20

40

y, c

m

-20 -10 0 10 20r, cm

0

0.4

0.8

1.2

B,

T

1

3 4

B cD

B cD /2 ,B cH

B cD /3

B cH /2

cD cD,

cH

cD

Cyclotron harmonic positions in Globus-M cross-section

for 7.5 MHz at B0=0.4 T

5

Dispersion Curves for 7.5 MHz

Blue lines – FMS waves, red lines – Bernstein waves

Broken lines – imaginary part of refractive indices

-20 -10 0 10 20r, cm

0

1000

2000

3000

Re(

NX),

Im(N

X)

50% H+50% D

-20 -10 0 10 20r, cm

10% H +90% D

C D C DC DC Dii

ii

Model accepted for numerical simulation

Plasma is confined between two cylindrical surfaces.

All plasma parameters change in radial direction only. They follow the

behavior of plasma parameters in the equatorial plane of the real

Globus-M tokamak.

Cyclotron absorption, magnetic pumping and Landau damping are included in the code. The effects related to poloidal inhomogeneity

are absent in the calculations.

Spectra of excited waves are calculated using 3-D antenna model.

7

RF Energy Absorption Profiles

absorption by electrons (TTMP and Landau damping)absorption by protons and by deuterons (cyclotron absorption and

Bernstein wave absorption)

-20 -10 0 10 20

dP

/dr,

rel

.un

. C H=2%

-20 -10 0 10 20

dP

/dr,

rel

.un

. C H=30%

-20 -10 0 10 20

C H=10%

-20 -10 0 10 20

C H=20%

-20 -10 0 10 20

C H=50%

0 10 20 30 40 50C H , %

0

20

40

60

80

100

En

erg

y fr

acti

on

, %

pro tons

deu te rons

electrons

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Spectrum excited by a single-loop antenna

-200 -100 0 100N z

Pra

d, a

rb.u

n

The peaks correspond to resonator modes excited in

the chamber (calculated in the cylindrical geometry).

The broken line shows the idealized spectrum if all

excited waves are completely absorbed in the plasma

without any reflection from

inner plasma layers.

9

Spectra excited by various antennas

-200 -100 0 100N z

Pra

d,

arb.

un

-200 -100 0 100N z

Spectrum of single-loop antenna

Spectrum of a set of 4 one-loop antennas

(in 0π0π mode).

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RF Energy Absorption Profilesin case of 4 antennas

absorption by electrons (TTMP and Landau damping)absorption by protons and by deuterons (cyclotron absorption and

Bernstein wave absorption)

-20 -10 0 10 20

-20 -10 0 10 20

-20 -10 0 10 20

0 10 20 30 40 50 CH, %

0

20

40

60

80

100

En

erg

y fr

acti

on

, %

-20 -10 0 10 20

dP

/dr,

rel

.un

.

-20 -10 0 10 20

dP

/dr,

rel

.un

.

C H=50%C H=30%electrons

pro tons

C H=20%C H=10%C H=2%

deute rons

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Comparison of absorption profiles for different antennas - 1

-20 -10 0 10 20

-20 -10 0 10 20r, cm

-20 -10 0 10 20r, cm

dP/d

r, r

el.u

n.

-20 -10 0 10 20

dP/d

r, r

el.u

n.

C H=20%

C H=10%

A single-loop antenna A set of 4 antennas

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Comparison of absorption profiles for different antennas - 2

-20 -10 0 10 20r, cm

-20 -10 0 10 20

C H=50%

C H=30%

-20 -10 0 10 20

dP

/dr,

re

l.un.

-20 -10 0 10 20r, cm

dP

/dr,

re

l.un.

A single-loop antenna A set of 4 antennas

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Energy Spectra of Ionswith/without RF pulse

IP = 185 kA

ne(0)=3.1019 m-3

Pinp= 120 kW

f = 7.5 MHz

0 1 2 3 4 5107

108

109

1010

1011

nH/(n

H+n

D) = 20%

ICRHaccelerated

particles

Thermalizedparticles

H D TD

OH 183 eV ICRH 322 eV

cx /

E0.5 (

eV

3/2c

m2 s

ter

s)-1

E (keV)

#11360-11363, t =165 ms

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Evolution of Ion Temperaturewith/without RF pulse

IP=185 kA

ne(0)=3.1019 m-3

Pinp= 120 kW

f = 7.5 MHz

130 140 150 160 170 180100

200

300

400 OH #11360,11361 ICRH #11362,11363

NPA ACORD-12Ioffe Institute

Globus-M2004.12.27 (#11360 - 11363)

TD (

eV

)

t (ms)

RF

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Ion heating in dependence on H-concentration

Bt/Bt0=1

In OH-regime TD=TH=180-200 eV

0 20 40 60 80

C H , %

0

100

200

300

400

500

TD

,TH,

eV

- T H

- T D

The 2nd H-harmonic is absent in the plasma

volume.

B0 = 0.4 T, ne(0) ≈ 3.1019 m-3, IP = 195 – 230 kA, f

= 7.5 MHz, Pinp = 120 kW.

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RF energy absorption profiles for CH=20% calculated for equatorial Globus-M parameters:

Bo = 0.4 T, Ip= 200 kA, Ne(0)= 51013cm-3.

absorption by electrons (TTMP and Landau damping)absorption by protons and by deuterons (cyclotron absorption and

Bernstein wave absorption)

-20 -10 0 10 20r, cm

dP

/dr,

rel

.un

.

f=7.5M H z

-20 -10 0 10 20r, cm

f=8.5M H z

-20 -10 0 10 20r, cm

f=9.1M H Z

C H

C H

— H — D— e

Ion Temperature Behaviorin dependence on Bt

Bt0=0.4 T

Ip= 190-210 kA

CH=15%, 30%

f = 7.5 MHz

Pinp= 120 kW

In OH regime

TD=180-200 eV

0.8 0.9 1Bt/Bt0

100

150

200

250

300

350

TD

, eV

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TH/TD ratio in dependence on Bt

0.75 0.8 0.85 0.9 0.95 1Bt / Bt0

1

1.1

1.2

1.3

1.4

TH

/TD

Bt0=0.4 T

Ip= 190-210 kA

CH=15%

f = 7.5 MHzPinp= 120 kW

In OH regimeTD=180-200 eV

a=23 cmr – position of 2nd H-

harmonic in cross-section at given Bt/Bto

26 cm21 cmr=17,5 cm 23

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Ion heating in dependence on H-concentration with/without

the 2nd H-harmonic

Bt/Bt0=1 Bt=0.8Bt0

In OH-regime TD=TH=180-200 eV

0 20 40 60 80

C H , %

0

100

200

300

400

500

TD

,TH,

eV

- T H

- T D

0 20 40 60 80

C H , %

0

100

200

300

400

500

TD

,TH, e

V - T H

- T D

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Conclusions The ICRF heating experiments were carried out on the

Globus-M spherical tokamak where conditions for several cyclotron harmonics were fulfilled simultaneously.

The experiments with hydrogen-deuterium plasma have shown that the ion heating efficiency does not practically depend of concentration of light ion component but increases slightly with rise of CH from 10% to 70% .

It is shown that presence of 2nd H-harmonic in front of the antenna diminishes efficiency of on-axis ion heating.

Experimental results are in agreement with numerical modeling by 1-D wave code.

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Globus-M RF antennaOutside arrangement

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RF antenna set-upand voltage distribution in the antenna resonator

-2 0 0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0 2 2 0x , c m

-4 0

-2 0

0

2 0

4 0

y, c

m

0 4 0 8 0 1 2 0 1 6 0x 1 , c m

0

2

4

6

U, k

V

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Globus-M characteristics

Parameter Designed Achieved

Toroidal magneticfield 0.62 T 0.55 TPlasma current 0.5 MA 0.36 MAMajor radius 0.36 m 0.36 mMinor radius 0.24 m 0.24 mAspect ratio 1.5 1.5Vertical elongation2.2 2.0Triangularity 0.3 0.45Average density 11020 m-3 0.71020 m-

3

Pulse duration 0.2 s 0.085 sSafety factor, edge4.5 2Toroidal beta 25% ~10% OH

ICRF power 1.0 MW 0.5 MW Frequency 8 -30 MHz 7–30 MHZ Duration 30 mc 30 mc

NBI power 1.0 MW 0.7 Mw Energy 30 keV 30 keV Duration 30 mc 30 mc

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Dispersion Curves for 9.1 MHz

-20 -10 0 10 20

0

1000

2000

3000

10% H +90% D

-20 -10 0 10 20

0

1000

2000

3000

50% H +50% D

C D C D C H

C D

i i5 0 % H

C H

C D

C DC Di i

1 0 % H

25

Magnetic Field DistributionIn equatorial plane of the Globus-M chamber

R0 = 36 cm, a0 = 23 cm

B0 = 0.4 T, Ip= 250 kA, f=9 MHz

blue line – toroidal vacuum field

green line – poloidal field

violet line – paramagnetic field

red line – full magnetic field

dashed red line – full magnetic

field without paramagnetic

component