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 self-organization. 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 pressureand 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

B=2.5T; Ip=250kA; Pgyr=0.9MW

0 100 200 300 400 500 600 700 8000.0

0.5

1.0

1.5

2.0

ECR

Te

ne

Te,

ne.1

013

cm-3

t,ms-20 -10 0 10 20 30

0

500

1000

1500

2000

2500

3000#37337 540ms

560ms 570ms 590ms 610ms 700ms 800ms

Te,

eV

r, cm

-20 -10 0 10 20 301.5

2.0

2.5

3.0

3.5

4.0

#37337

540ms 560ms 570ms 590ms 610ms 700ms 800ms

ne1

013cm

-3

r, cm

-30 -20 -10 0 10 20 30

0,0

0,2

0,4

0,6

0,8

1,0 560ms 570ms 590ms 610ms 700ms 800ms

#37337

ne(

r) T

e(r)

/ne(

4cm

)Te(

4cm

)

r,cm

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

B=2.33T; Ip =180kA; off axis ECRH P=0.75MW; on axis P=055MW

0 200 400 600 800 10000

1

2

3

4

#40201

On-axis

Off-axis

r = 2.28cm

r = -14.75cm

T(t

),n

orm

aliz

ed t

o O

H

t, ms

0 5 10 15 20 25 30 350

1

2

3

4

5

#40201 561,696,705

705ms

696ms

561ms

OHne

r,cm

Density profiles are received from radio-interferometer together with reflectometer

-20 -10 0 10 200

1000

2000

3000

4000

t=730ms

t=705ms

t=696ms

t=561ms

OH

40201

Te

EC

E, k

eV

r

At the beginning of off axis ECRH central density increase is seen.

This result is supported by SXR diagnostic

540 550 560 570 5800.0

0.2

0.4

0.6

0.8

1.0

t2t

1

ECRH

39469

I SX

R(t

)

t,ms-20 -10 0 10 20

0.0

0.1

0.2

0.3

0.4

0.5

ECRH

39469

I SX

R(5

63m

s)-I

SX

R(5

46m

s)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)

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 ).

-20 -10 0 10 200.0

0.1

0.2

0.3

0.4

0.5

ECRH

39469I S

XR(5

63m

s)-I

SX

R(5

46m

s)

r-20 -10 0 10 20

0

200

400

600

800

1000

1200

t=546ms

t=563ms39469

Te

EC

E, k

eV

r

500 550 600 650 700 7500

1

2

3

4

5 (c)

OH

#40201

on-axis ECRH

off-axis ECRH

p(0

)/p

(=

0.5)

t (ms)

In spite of strong change of Te profile, the

pressure peakedness is permanent within the experimental accuracy

0 200 400 600 800 10000

1

2

3

4

#40201

On-axis

Off-axis

r = 2.28cm

r = -14.75cm

T(t

),n

orm

aliz

ed t

o O

H

t, ms

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 conservationThis 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

1.2 1.3 1.4 1.5 1.6 1.7 1.80.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

n e [1

019 m

-3]

Radius [m]

ECRH 5-10 ms after ECRH Ohmic

<(n

) e> [1

018 m

-2]

Abel recnstruction of

the interferometr results