Jorgenson D.W. Econometrics (MIT, 2000)(ISBN 0262100940)(493s)_GL
J.R. Wilson, R.E. Bell, S. Bernabei, T. Biewer, J. C. Hosea, B. LeBlanc, M. Ono, C. K. Phillips...
-
Upload
emmeline-tucker -
Category
Documents
-
view
219 -
download
3
Transcript of J.R. Wilson, R.E. Bell, S. Bernabei, T. Biewer, J. C. Hosea, B. LeBlanc, M. Ono, C. K. Phillips...
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