the toroidal helicon experiment at ipr -...

THE TOROIDAL HELICON THE TOROIDAL HELICON EXPERIMENT AT IPREXPERIMENT AT IPR

Supervisor

Prof. Dhiraj BoraD.D.G, ITER

Institute for Plasma Research Gandhinagar, Gujarat (India)

Acknowledgement

Dr. S.K.P.TripathiUCLA

Manash Kumar Paul

MOTIVATIONMOTIVATION

• To explore toroidal counterparts of conventional Helicon modes

• Advanced applications of Helicon waves in toroidal plasma experiments

Ø In terms of an RF source to ionize neutrals, sustain plasma and drive toroidal plasma current

HELICON WAVE DISPERSION HELICON WAVE DISPERSION Helicon waves are derived from Maxwell’s equations (with EMHD assumptions)

20

00

00 ,,,

B

BEenj

enBj

EjBtB

Eo

×−=

×==×∇

∂−∂

=×∇ µ

For a perturbation exp i(m?+kz-? t),0

0

0

0 )(en

jikBen

BjEBi =

××∇=×∇=ω

Where n0 and B0 are equilibrium density and external magnetic field

( ) ( ) ( ) 0BJJ0BBeni 0 ∇•−∇•=ω

Cylindrical Helicon plasma Toroidal Helicon plasma*

BB

kBen

BB

α

ωµαψ

ψ

=×∇=>

==

×∇=

0

00

×∇=

+

=

ψ

θ

BB

RrB

B Tcos

10

−

+=

1cos2cos2

010

001cos

12

li

liR

r

θθ

θαψ

where

So,

where

( )θcos|| rRkl +=and

Here,

* S. K. P. Tripathi and D. Bora, Phys. Plasmas 8(3), 697 (2001)

DIFFERENCE DIFFERENCE -- LINEAR AND TOROIDALLINEAR AND TOROIDAL

Ø B-Profiles of m = +1

Ø Infinitely conducting wall

=> Br=0 (at boundary)

Wave magnetic field componentsin Cylinder

Wave magnetic field componentsin Torus

Mode Coupling Possible !!

EXPERIMENTAL SETEXPERIMENTAL SET--UPUP

System LayoutSystem Layout

Gas Argon Base Pressure 10–5 mbarFill Pressure (2-5)x10–3mbar

Major radius 30cmMinor radius 10.5cmMagnetic field 1 kG (max.)

Pulse duration 50msLauncher Right Helical Input Power 2 kW (max.)Impedance L-type and Pi-type

Matching Networks

Op. Frequency (7-9), (30-33) MHz

Plasma density 1018 m-3

Electron Temp. 10eV

IpDual Rogowskicoil

Br,?,fCentre-tapped B-dot probes (with bifilar windings )

Vf, ne, Te, EEDF

RF compensated Langmuir probe

Plasma Parameters

Diagnostics

LOW FREQUENCY CURRENT DRIVELOW FREQUENCY CURRENT DRIVE

• Helicon wave excited at (7-9)MHz*

• Same source initiate breakdown and sustain the plasma• Drive IP = 1 kA with PRF = 1kW*

• Dominated by resonant Wave-Particle interactions (~750A with 1kW)

• Helicity supported - nonresonant processes also indicated (~230A with 1kW)

• Quality of current drive**, for LHCD, in present conditions, 200A with 1kW.

Nonresonant part need amplification

* S.K.P. Tripathi and D.Bora, Nucl. Fusion, 42, L15 (2002)

** D.A.Ehst and C.F.F.Karney, Nucl. Fusion, 31, 1933 (1991)

Helicon CD, as good as LHCD !!!

NONRESONANT CURRENT DRIVENONRESONANT CURRENT DRIVE

• Operating frequency increased to increase the phase velocity

• Nonresonant (ponderomotive forces*) contribution amplified

* Petri?z´ilka V. and Tataronis J.A., Plasma Phys. Control. Fusion, 36, 1027 (1994)

• Magnetic field (BT) increased

• Appropriate diagnostics designed and developed

MODE IDENTIFICATIONMODE IDENTIFICATION

• Wave magnetic field components measured at

ne = 2x1012cm-3, Prf = 1.3kW, BT = 0.8 kGauss, p = (2-3)x10-3mbar

• m=+1 mode excited at 32 MHz

• Density jumps*

• Dispersion reln (fit) for helicon wave

κω

∝e

Tn

B

* Manash Kr. Paul and D.Bora, Phys. Plasmas, 12, 062510 (2005)

EEDF measured at (1016 - 1018) m- 3

CURRENT DRIVECURRENT DRIVE

• Early decay of Ip*

1

2

* Manash Kr. Paul and D.Bora, Phys. Plasmas 14 082507 2007

BT > 0.5kGauss support Helicon

mode

CURRENT DRIVE CONTD.CURRENT DRIVE CONTD.

For BT = 0.4 kGauss0.6 kGauss0.9 kGauss

Pressure = 2x10- 3mbar

Prf = (0.6- 1.5)kW

Jump in density and plasma current after 0.75kW during low BT expts.

ESTIMATION OF CURRENT DRIVEESTIMATION OF CURRENT DRIVE

( ) eJeJqon

mePBeJEenqqojon ∇•+•∇+×−=2

η

Jh = (0.325-1.740)A cm-2

for ne = (1010-1012)cm-3, => Ip = (25-140)A

• Measured av. Ip = (30-150) ±10% A

• Estimated plasma resistivity ? = 8 Om*

Almost exact reversal of Ip !!

JC = 10-3 times Jhfor ne = 1012 cm- 3

* John Dawson and Carl Oberman, Phys. Fluids, 5, 517 (1962)

CONCLUSION & FUTURE WORKCONCLUSION & FUTURE WORK

• Approximately 80% of the total plasma current is driven by the nonresonant interactions

• CD efficiency, estimated from the ratio of PRF and ne?Jh , is 6x1016 A W-1 m-2

• These waves could be considered for starting up and then sustaining an efficient toroidal discharge.

• Our experimental studies have established the current driving and discharge sustaining capabilities of Helicon waves.

• Study of poloidal mode coupling

• Study of stability of toroidal helicon plasma in our device

THANK YOUTHANK YOU

EEDFEEDF• Electron energy distribution (EEDFEEDF) measured using RFCLP to verify the

absence of energetic electrons in present parameter regime.

• A valid application of the Druyvesteyn formula requires collisionless electron motion near the probe.

For the probe to be non-intrusive effectively,

?d(0.1mm) < r(0.5mm) < ?mfp(10mm)

• Electron energy distribution measured at (1016 - 1018)m- 3, reveal absence of anysuper-thermal species for current drive by resonant process.

• EEDF at higher power shows rise in temperature of bulk electrons.

)(8

2/3

2

2

bpb

e VVFmAe

dVId

−=

PARAMETRIC STUDY OF CDPARAMETRIC STUDY OF CD

• Peak value of Ip is chosen from a profile, for comparison • In the high pressure regime, low Ip obtained, at

constant Prf (~1kW)• Higher electron-neutral collisions may be responsible

ANALYSIS OF NONRESONANT CURRENT ANALYSIS OF NONRESONANT CURRENT DRIVEDRIVE

Plasma Resistivity EstimationPlasma Resistivity EstimationPlasma resistivity ? is calculated for high frequency waves in the ion rest frame*, in the limits ((?? / / ?? pp) << 1) << 1.

( )( ) ( )

−= 1ln

6216Re 42

62

321

ezvm

mvZe

p

th

th ωπωη

Here ? , Z, e, ? p, m, vth represent operational frequency, charge state, electronic charge, plasma frequency, electronic mass and electron thermal velocity respectively.

The value of plasma resistivity obtained in present parameter regime is ˜ 8 Om.

Plasma impedance plays an important role in deciding the magnitude of contribution of wave helicity in the plasma current driven at present operational regime.

*John Dawson and Carl Oberman, Phys. Fluids, 5, 517 (1962)

ANALYSIS OF NONRESONANT CURRENT ANALYSIS OF NONRESONANT CURRENT DRIVE: CONTD.DRIVE: CONTD.

Helicity Current DriveHelicity Current Drive

( )( )( )( ) ( )rBBBrB

BBBeJhJenrrrr

rrr

×∇−×∇=

×∇−=×=

θθ

φηµ0

( ) ( )[ ]

∂

∂+

∂

∂−−

++

∂

∂+

∂

∂

+=

θ

φθφθθθθ

φ

φθ

θφθ

B

r

B

r

BrBrBB

rR

BBBrB

rBrR

cossincoscos

1

Contribution by the helicity of helicon waves in plasma current drive can be expressed as hall (JXB) term in the momentum equation

• Wave magnetic field components, axial, radial and azimuthal variations of the same have been measured by B-dot probes on the plasma axis and these values are used for above estimation.

• Numerically estimated value of Jh vary betn.

(0.325-1.740)A cm-2 for ne = (1010-1012)cm-3, which is (25-140)A (peak).

• Experimentally measured av. plasma current Ip vary betn. (30-150) ±10% Amp.


Current from convective termCurrent from convective term

( )( )φφ

θφ

θφθφ

φη

∂

∂

++

∂

∂+

∂

∂=∇•=

J

rR

JJ

r

J

r

JrJeJeJcJem

eoncos

32 rrr

The convective term present in the momentum equation is derived from the formula given below. Current components, derived in toroidal coordinates are substituted in the equation given below.

Wave magnetic field values being very small in comparison to the ambient magnetic field, nonlinear effects in present investigation are negligibly small.

Magnitude of JC turns out to be 10-2 times helicity term at 1011cm- 3 .

Jc further diminishes to 10-3 times Jh at 1012cm- 3 plasma density.

DIFFUSION/PRESSURE GRADIENT CURRENT

For steady state plasma, net contribution from pressure gradient term is

θBrp

Rr

difJ ∂∂

≈

2

1

Almost exact reversal of Ip also shows negligible impacton plasma current due to pressure anisotropy


(approx. for bootstrap mech.*)

*M.Kikuchi and M.Azumi, Plasma Phys. Contr. Fusion, 37, 1215 (1995)

ANTENNA DESIGNANTENNA DESIGN

• Helicon waves form cavity modes in a bounded system

• Wavevectors no longer continuous but eigenvalues determined by boundary conditions (Br = 0 (r = a))

• Length chosen according to toroidal mode number and phase velocity

• Radius optimized according to capacitive effects, dispersive parameter (a , for radial eigen modes) and gain factor (a/ak||)

Right Helical AntennaLength = 11 cm, Radius = 6cm

DISCHARGE MODE TRANSITIONSDISCHARGE MODE TRANSITIONS

•• Capacitive modeCapacitive mode(0.2(0.2-- 0.3)kW & (0.10.3)kW & (0.1-- 0.25)kGauss0.25)kGauss

. . •• Potential diff. sustained discharge • Power transfer E (sheath) to plasma • Power distributed at antenna edges

•• Inductive modeInductive mode(0.3(0.3-- 0.5)kW & (0.3 0.5)kW & (0.3 -- 0.4)kGauss0.4)kGauss

•• E sustained discharge • Concentric to the antenna.

•• Helicon modeHelicon mode(0.6(0.6-- 0.9)kW & (0.50.9)kW & (0.5--0.6)kGauss0.6)kGauss

•• Wave sustained discharge • Uniform distribution of power in

antenna diameter give rise to higher density at centre during Helicon discharge

Ø Effect of an oscillating Vp on LP present a great difficulty in interpretation of probe data when the RF excursions bring the electron current out of the exponential region.

Ø Passive technique chosen for simplicity and better performance at almost all frequencyØ Harmonics considered in the plasma potential are

where ß is fraction of 1st harmonic present in Vp.

Ø Only first harmonic is considered for low ß at higher harmonics

Ø Capacitance of the cylindrical guard ring -- r = 1 cm, l = 10 mm, C = 300 pF for 30MHz.

Ø Also, , where Vo is potential between probe tip and LC-sections andVp is plasma potential. Usually, ? 2CL>>1, so that V0>Vp.

In order to achieve compensation within 1% of Vp, we take ? 2CL~100.

Ø Since j ? L << 100 to make the sheath drop equal to 1% of the probe potential, harmonic rejection (HR) components are calculated for 2nd term=3rd term=30.

Vp = Vp sin ? t + ßVp sin 2 ? t,

LjCj

LCLj

LCLj

CjZ

TT

ωω

ωω

ωω

ω

+=

−+

−+=

1

111

222

2

112

1

CLCL

VV

p2

20

1 ωω

−−=

DIAGNOSTICS: RFCLP CONTD.DIAGNOSTICS: RFCLP CONTD.

REQUIREMENTS FOR EEDFREQUIREMENTS FOR EEDFØ A valid application of the Druyvesteyn formula requires collisionless electron motion

near the probe. ⇒ Debye length (?d) << electron mean free path (?e).

and the probe radius << ?e (non-intrusive)In the present case, ?d( 0.1mm) < probe radius (0.5mm)<< ?e(10mm)

Ø Sheath radius = 0.1mm and probe radius = 0.5mm. So, the ratio is 0.2, which is small enough to neglect the sheath effect in our case.

Ø The effect on the Langmuir probes due to BT is negligible since the probe dimensions are much smaller than the Larmour radius (RL= 0.1mm) of the collected plasma species.

Ø Electrons with Larmour radius smaller than the dimensions of the probe can either becollected through cross-field diffusion or from flux tubes intersecting the probe. The electron saturation current is reduced by a factor (s)

+⊥= a

eTiT

DD

eis πλ 2

121

||16

For electrons, radial diffusion is strongly inhibited whereas for ions, the ion diffusion is not severely limited. So, the usual standard expressions for the electron and ion probe currents will be used with appropriate corrections for the effective probe area.

TEMPORAL VARIATIONTEMPORAL VARIATION

ØØ Spatial evolution of floating potential is Spatial evolution of floating potential is essential to understand the discharge essential to understand the discharge equilibrium of a pulsed RF breakdown. equilibrium of a pulsed RF breakdown.

ØØ The closed contours obtained from the The closed contours obtained from the spatial profiles of floating potential provide spatial profiles of floating potential provide information about the discharge equilibrium. information about the discharge equilibrium.

ØØ Closed curves obtained, reveal that a steady Closed curves obtained, reveal that a steady state discharge is obtained between state discharge is obtained between (15(15-- 35)ms.35)ms. the steady state discharge the steady state discharge obtained in our experiment.obtained in our experiment.

ØØ Higher Plasma density in the central region.Higher Plasma density in the central region.

ØØ The density jump at the beginning indicates The density jump at the beginning indicates the initial transient phase of RF breakdown.the initial transient phase of RF breakdown.

ØØ Higher electron temperature with minute Higher electron temperature with minute variation is expected during steady state variation is expected during steady state high power Helicon discharge.high power Helicon discharge.


Efficiency of Helicon wave current drive Efficiency of Helicon wave current drive

211618

106ln

104.38 −−×=

Λ

×== mAmpW

nT

Jn

P

e

e

he

rfCD η

ηη

Current drive efficiency* for the present case, is calculated from the plasma parameters and the value of plasma impedance, given by

Here ln? , ne, Te represent coulomb logarithm, local electron density in SI units and electron temperature in keV respectively.

Efficiency can also be estimated from the ratio of ne?Jh and Prf, written in terms of toroidal wave damping factor (?) as

?CD = ?/vf e?=> higher wave damping for efficient current drive

*D.A.Ehst and C.F.F.Karney, Nucl. Fusion, 31, 1933 (1991)

the toroidal helicon experiment at ipr -...

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