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DIII-D, #89943, t=1.7 sec. 1. The first critical gradient. - PowerPoint PPT Presentation
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critical gradients(II)i second (II)
e
i-ITB
valuesused in
ourcriterion
zp - deviation
z0 - distance between
critical gradients
valuesused in
JETcriterion
zp
z0
First (I) and
electrons
ions
hea
t fl
uxe
s i,
e (a
.u.)
-aT'/T
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A=5, =1, =0, T-10A=3, =1.6, =0.3, JETA=1.4, =1.75, =0.325, MAST
T-10
JET
MAST
Tc=
-RT
c'/T
c
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5 Critical gradients,normalised to minor radius
MAST, A=1.5
JET, A=3
T-10, A=5
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aT
c'/T
c
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14First critical gradient
DIII-D, #89943, t=1.7 sec
-R/L
Te=
-RT
c'/T
c
r/a
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qexp
DIII-D #89943t=1.7 s
qcalc
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DIII-D, #89943, t=1.7 sec
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Shear
Z0i
1. The first critical gradient
We find the first critical gradient by the canonical profiles theory. The canonical profile for the function = 1/q (denoted below as с) can be found by the solution of the Euler equation for the free plasma energy functional [1]
2G c2/ + (/2) / ((1/ V) (VGc)) = Cc/V.(1)
Here: index S means the plasma boundary,
iс = 1/V /(G Vс) is the dimensionless current density,
V is the plasma volume, V= V/,
G = R2<(grad )2/r2> is the metric coefficient.
The solution of Eq. (1) and the constants С and are determined by the following four boundary conditions:
c(0) = 0 ~ 1, c(0) = 0, c(max) = S,
X [ic/(2G c)]S = G(a)1/2 S /0 (2)
The first dimensionless critical gradients for the temperature and density are following:
Tc = R/LTc -RTc/Tc = - 2/3 R ic/ic,
nc -Rnc/n = - 1/3 R ic/ic. (3)