Density profile changes are the
result of the profile consistency
effect.
K.Razumova
The very important feature of tokamak
plasma behavior is its abilities for selforganization. About 20 years ago it was
shown that plasma aspire to form the
pressure profile corresponding to the best
confinement for given conditions and then
try to keep it, when we put any external
forces.
Self-consistent profiles in
OH and L modes realise for
the relative plasma
pressure
and radius, normalized on
any rational magnetic
surface
a= (q=5 in a given case)
Results for different tokamaks: T-10, T-11,
TFR, TM-3, PLT, ASDEX, PDX.
Yu.V.Esipchuk, K.A.Pazumova, Plasma Phys. and Contr. Fusion,
V.28 (1986) p. 1273
ON AXIS ECRH
3000
B=2.5T; Ip=250kA; Pgyr=0.9MW
2500
2000
13
Te, eV
-3
2.0
Te, ne.10 cm
540ms
560ms
570ms
590ms
610ms
700ms
800ms
#37337
ne
1.5
1500
1000
1.0
Te
500
0.5
ECR
0
0.0
0
100
200
300
400
500
600
700
-20
800
-10
t,ms
3.0
13
ne10 cm
-3
3.5
2.5
2.0
1.5
0
r, cm
10
20
30
1,0
ne(r) Te(r)/ne(4cm)Te(4cm)
540ms
560ms
570ms
590ms
610ms
700ms
800ms
#37337
-10
10
20
30
r, cm
4.0
-20
0
560ms
570ms
590ms
610ms
700ms
800ms
#37337
0,8
0,6
0,4
0,2
0,0
-30
-20
-10
0
r,cm
10
20
30
In spite of substantial changes in Te and ne profiles
during on-axis ECRH and gas puffing, the
normalized pressure profile remains to be the
same.
We can conclude that “pump-out” under on-axis
ECRH is the result of the pressure conservation
effect.
OFF AXIS + on AXIS ECRH
4
T(t),normalized to OH
#40201
r = 2.28cm
3
Te ECE, keV
B=2.33T; Ip =180kA; off axis ECRH
P=0.75MW; on axis P=055MW
4000
t=730ms
40201
t=705ms
3000
2000
t=696ms
1000
2
OH
r = -14.75cm
t=561ms
1
0
On-axis
-20
-10
0
r
10
20
Off-axis
0
0
200
400
600
800
1000
At the beginning of off
axis ECRH central
density increase is seen.
t, ms
5
#40201 561,696,705
561ms
4
696ms
705ms
ne
3
OH
2
1
0
0
5
10
15
20
r,cm
25
30
35
Density profiles are
received from radiointerferometer together
with reflectometer
This result is supported by SXR diagnostic
ISXR(563ms)-ISXR(546ms)
0.5
1.0
39469
ISXR(t)
0.8
0.6
0.4
39469
0.4
0.3
0.2
0.1
0.2
ECRH
0.0
540
t1
550
t,ms
560
t2
570
0.0
580
-20
-10
ECRH
0
10
20
r
Off axis ECRH. Change of line averaged SXR intensity
profile at moment t2 in relation to that at moment t1
before heating (ISXR(t2,r)-ISXR(t1,r)). (no Abel inversion)
39469
1200
0.4
39469
t=563ms
1000
Te ECE, keV
ISXR(563ms)-ISXR(546ms)
0.5
0.3
0.2
0.1
800
t=546ms
600
400
200
0
0.0
-20
-10
ECRH
0
10
20
-20
-10
r
r
0
10
20
We can interpret this data in such a way:
ISXR  Zeff n2 (Te). Just in the heating region the main
term is (Te). But decrease of ne leads to a strong
decrease of ISXR in more central regions. As the central Te
does not changed during this time we can conclude that
the central ISXR increase must be due to the central
density increase (Zeff n2 ).
#40201
(c)
4
#40201
p(0)/p(r=0.5)
4
3
2
on-axis ECRH
1
T(t),normalized to OH
5
2
r = -14.75cm
1
On-axis
Off-axis
0
0
0
500
r = 2.28cm
3
OH
550
600
650
200
400
600
800
t, ms
off-axis ECRH
700
750
t (ms)
In spite of strong change of Te profile, the
pressure peakedness is permanent within the
experimental accuracy
1000
Conclusion
Plasma property to keep its pressure profile
lead to density decrease in the heating
region.
So n(r):
1) flatten under on axis heating, that we call
the “Pump Out”;
2) has steep gradient in the central zone
under the off axis heating.
1.
As it was demonstrated theoretically [9-11], the
self-consistent profiles are in agreement with the
principle of minimum free energy in the plasma.
The plasma tries to establish profiles of its parameters, in
accordance to the minimum energy principle, which is
connected with plasma instabilities (best confinement).
The external influences like boundary conditions, heating
power deposition profile, and so on, do not permit to
stabilize the instabilities completely. The OH process has
the least constraints, so it leads to the best confinement,
albeit that Ohm’s law is also a limitation of plasma
freedom.
The shape of the plasma profiles is governed by the
pressure profile p(r)=ne(r) T(r), but not by the electron
temperature Te(r), or the density profiles ne(r) separately.
We can conclude that the density pump-out is the result
of p(r)/p(0) conservation, or (which is the same) p/p
conservation
This process may take place very rapidly, because it is a
loss of equilibrium.
In ITB regions, the higher p is permitted since the
instabilities that normally restore the pressure profile are
suppressed.
.
All experimental results may be explained as follows:
Rational magnetic surfaces are the cells with a high
transport, which is determined by the before
mentioned instabilities. When these cells touch
each other, the high transport takes place in a wider
region. This decreases the local value of the
pressure gradient p. When the self-consistent
pressure profile is distorted by auxiliary heating,
pellets or other means, the distances between cells
are increased (or decreased); this changes the
transport and keeps the relative pressure profile
p(r) practically constant.
If we limit the maximum number mMax near the
rational surfaces with low m and n values, a gap with
no rational surfaces will be seen, and so the ITBs could
be preferably formed there.
Decreasing dq/dr, we make better confinement in this
ITB region. Wider the zone dq/dr=0, wider the
enhanced confinement zone.
What does happen, when we try to increase the
pressure gradient p somewhere in a plasma? The
density of rational magnetic surfaces increases in this
region, therefore the transport coefficients increase
also.
Confinement will depend not only on the density of
rational surfaces, but on the dimension of cells.
Of course this explanation needs further experimental
checks. Rational surfaces have a number of
peculiarities, like Geodesic Acoustic Modes (GAM),
supra-thermal electron generation, and so on.
One must take into account that ITER will
have self-consistent profile
1.4
18
-2
<(n)e> [10 m ]
1.2
1.0
0.8
0.6
0.4
0.2
0.0
3.0
19
-3
ne [10 m ]
2.5
2.0
1.5
1.0
0.5
0.0
1.2
1.3
ECRH
5-10 ms after ECRH
Ohmic
1.4 1.5 1.6 1.7 1.8
Radius [m]
Abel recnstruction of
the interferometr results