J.R. Wilson, R.E. Bell, S. Bernabei, T. Biewer, J. C. Hosea, B. LeBlanc, M. Ono, C. K. Phillips

Princeton Plasma Physics Laboratory

P. Ryan, D.W Swain

Oak Ridge National Laboratory

45th Annual Meeting of Division of Plasma PhysicsAmerican Physical Society

October 27 – 31, 2003Albuquerque, New Mexico

Investigation of the Possible Role of Parametric Decay during HHFW Heating on NSTX

Supported by

Columbia UComp-X

General AtomicsINEL

Johns Hopkins ULANLLLNL

LodestarMIT

Nova PhotonicsNYU

ORNLPPPL

PSISNL

UC DavisUC Irvine

UCLAUCSD

U MarylandU New Mexico

U RochesterU Washington

U WisconsinCulham Sci Ctr

Hiroshima UHIST

Kyushu Tokai UNiigata U

Tsukuba UU Tokyo

JAERIIoffe Inst

TRINITIKBSI

KAISTENEA, Frascati

CEA, CadaracheIPP, Jülich

IPP, GarchingU Quebec

High Harmonic Fast Wave Heating has been successful on NSTX

• Efficient heating of electrons– Electron temperatures of 2-4 keV obtained

• Unidirectional currents have been driven

– Up to 120 kA of Co current

– Efficiencies comparable to those obtained on D-

IIID seen (Ryan:LP1.019)

Unexpected Behavior has been Observed

• Attempts to measure power deposition profile by

power modulation have proven unsuccessful

(Swain:LP1.017)

• Current drive efficiencies have sometimes been

low(Ryan:LP1.019)

• Edge rotation and impurity heating has been

observed (Biewer:LP1.024)

Er from He II and C III (cold)Ohmic v. RF heated

The Er at the edge most region of the plasma (R>146 cm) is more negative during RF heated plasmas than during Ohmic.

For R<146 cm the Er is similar (for the region measured)

Implies that RF leads to ion loss at the edge of the plasma.

Er~-5 kV/m

RF on

Ohmic

More power leads to more heating

From NSTX Shot 110133 to 110145 the applied RF power was increased. Empirically, Ti increases as PRF

0.47.

Negative poloidal velocity is upwards on the outboard midplane.Negative toroidal velocity is opposite to the direction of Ip.

Various non RF Specific Effects may be Responsible

• Stiff transport profiles could explain lack of central Te

modulation

• MHD has been observed to affect current drive

efficiency

• Edge effects may be instrumental complications due

to enhanced neutral densities

A Possible Specific RF Effect is Parametric Decay

• Observed in many rf heating experiments (CMOD, ASDEX, DIIID, JET)

• Not usually sufficiently strong to play a major role in energy balance:

Exception: Lower Hybrid current drive where it is responsible for density limit

Characteristics of Parametric Decay

• Review of Parametric Decay for the edge plasma in the ICRF Regime has been given by Porkolab Eng. Fusion and Design 12 (1990) pg. 93

• Three wave coupling process with selection rules:0 = 1 + 2 k0 = k1 + k2

These correspond to energy and momentum conservation

Since the “pump” fast wave has a long perpendicular wavelength and the “daughter” waves are expected to have short wavelengths the latter condition can be taken as:

k1 = -k2

Parametric Decay Theory• Dispersion Relation:

• Where

€

ε(ω,k) =1+ χj

j

∑ (ω,k)

€

χj

=1/k 2λDj

2 1+ ζ0 j

ΓlZ ζ

lj( )l

∑ ⎛

⎝ ⎜

⎞

⎠ ⎟

€

Γl

= Il

bj( )e

−bj

€

ε 1,k

1( )ε ω2,k

2( ) = −1

8μ

e− μ

i

2

χe

ω1,k

1( ) − χe

ω2,k

2( )( ) χi

ω1,k

1( ) − χi

ω2,k

2( )( )[ ]

€

ζlj

= ω − lΩj( ) /k

||v

tj

€

bj= k

⊥

2 rcj

2

€

rcj

2 = vtj

2 /2Ωj

2

€

λDj

2 = vtj

2 /2ωpj

2

The Parametric Coupling Constant is given by:

€

μσ=

eZσ

mσ

r E

0⊥•

r k ⊥

ω0

2 − Ωσ

2 +E

0||k

||

ω0

2

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

2

+

r E

0⊥×

r k ⊥( ) • ˆ z

2

Ωσ

2

ω0

2 − Ωσ

2( )

2

ω0

2

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥

1/ 2

The first term is due to the polarization drift, the second the parallel drift and the third the E x B drift

We will now assume that we will have decay into an ion Bernstein wave and either another ion Bernstein wave, an ion quasi-mode or an electron quasi-mode

For HHFW, i and the polarization term will dominate.E0 is in the poloidal direction and this allows the IBW wave to propagate poloidally and stay in resonance with the pump

Combining the expression for the dispersion relation and the coupling, keeping only the polarization term and assuming the side band is a resonant IBW yields the following expression:

€

γ0

+ γ2( )

∂ε

∂ω2R

= Im1

4

eZi

mi

Eyk

y( )2

ω0

2 − Ωi

2( )

2

χe

ω1( ) − χ

eω

2( )( ) χi

ω1( ) − χ

iω

2( )( )

ε ω1,k

1( )

⎛

⎝

⎜ ⎜

⎞

⎠

⎟ ⎟

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥

Where γ is the normalized growth rate of the instability and γ2 the normalized damping of the IBW.

The electron coupling term has been dropped since e << 1

We now look for values of the right hand side >1.

1

2

3

0 5 10 15 20

13

14

0 5 10 15 20

1

2

3

13

Fre

quen

cy (

i)

Wavenumber (kperprci)

14

5 10 15

1

2

Dispersion relation for IBW and quasi-mode

Frequency matching condition selects kperp

200

To make the Growth rate large you could have ε0 or χi(1) largeOno Phys Fluids 23 (1980) p. 1675

ε= 0 corresponds to a resonant lower frequency wave e.g. another Bernstein wave. However, it is very difficult to get both frequency and wave-number matching simultaneously for two resonant waves

χi() will be large when = i

This is the ion quasi-mode, quasi because ε ≠ 0

The quasi-mode has no kperp dependence so simultaneous matching of frequency and wave number is easily achieved

For χi large we are left with only the electron susceptibilitiesFor 1 = i the electron susceptibility terms can be simplified to:

€

χe

ω1( ) − χ

eω

2( ) =1− k

⊥

2 rce

2( )

k||v

te

i πω1+ ω

0−ω

1( )Zω

1−ω

0

k||v

te

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥

The first term dominates and to have growth we only requirethat

€

1− k⊥

2rce

2 > 0

This is easily satisfied

Numerically calculating the normalized growth rate for i yields

Nor

mal

ized

gro

wth

rat

e

i

0

0.1

0.2

-0.10.7 0.8 0.9 1.0 1.1

Te , Ti = 50 eVne = 2 x 1018

B = 2.3 kG

Growth rate maximizes for k|| = i/0.7vte

Growth rate is found to decrease with increasing edge temperature and increase with increasing edge density

Where does the coupled power go?

Both the ion Bernstein wave and the ion quasi-mode should deposit their energy into the majority ions

The quasi-mode does not propagate and deposits its energy locally but because of its low frequency it can not contain much energy

The Bernstein wave will propagate until it reaches the next cyclotron harmonic - for NSTX this is within about 10 cm of the edge

So all the parametrically coupled power should damp within 10 cm of the edge

Dispersion relation for daughter Bernstein wave

r(m)

r(m)

r(cm)

Power absorption for edge launched fast wave and IBW

Fast wave

IBW wave

Fra

ctio

n of

laun

ched

pow

er

abso

rbed

Parametric decay is expected to occur in NSTX HHFW experiments

• Decay into ion Bernstein wave and ion quasi-mode is

preferred

• Decay takes place at the plasma edge

• Decay waves will heat ions in outer 10 cm of plasma

• Threshold power level increases with increasing edge

temperature and decreases with increasing edge

density

• May explain edge heating and electric field change

seen on edge rotation diagnostic