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CHATTOPADHYAY et al.: ANALYSIS OF DISRUPTIVE INSTABILITIES IN ADITYA TOKAMAK DISCHARGES 827

Many groups around the world have revisited these

phenomena and newer ideas are emerging.

Considering this point of view we report here the

plasma disruptions in the medium size, low β

tokamak, Aditya

18

. We have analysed a number ofdisruptive shots in ohmically heated plasma with the

plasma current, I p, in the range 73 kA≤ I p≤82kA and

safety factor q(a) range 3≤q(a)≤3.3.

2 Experimental Details

The basic parameters of Aditya tokamak 18 are:

major radius R0=75 cm, minor radius a=25 cm,

toroidal magnetic field BT ≈0.75 T, central temperature

T 0≈400 eV, plasma current I P lies between 65 and 85

kA and discharge duration up to 100 ms. The two

main diagnostics used in the analysis are soft X-ray

diagnostic system with an array of 12 surface barrierdetectors (ORTEC, active area 50 sq mm, thickness

100 micro metre) placed inside an imaging camera18

and a garland of 36 Mirnov coils19. SXR tomography

was done with the help of analytical method 20,

assuming rigid rotation21-23 of the mode.

3 Disruption

The plasma pulse shown in Fig. 1 is a typical

example of how internal and major disruption occur

in Aditya tokamak operated in the previously

mentioned current range. This corresponds to a

plasma current, I P≈75 KA [Fig. 1(a)] which disrupts

at 96.4 ms. The SXR emission [Fig. 1(b)] goes below

zero at 79.9 ms, far behind the total current disruption

time which indicates a rapid temperature drop at thistime. Growing amplitude in poloidal magnetic field

derivative (Mirnov oscillation) [Fig.1(c)], spikes in

Hα line emission [Fig. 1(d)] and negative loop voltage

[Fig. 1(e)] seem to be strongly correlated with the

cessation of soft X-ray emission.

3.1 Internal disruption

The presence of sawtooth event [Fig. 1(b)] was

observed in Aditya tokamak for the first time in

December, 1995, when the device was operated with

high plasma current. Since then these have been

observed in many experimental situations and under

different machine conditions24. The period and

amplitude of the sawteeth [Fig. 1(a)] are seen to

change slightly with time with an average frequency

of 0.98 kHz, and no transients were observed in loop

voltage [Fig. 1(e)]. Figure 1(f) is the evolution of hard

X-ray which indicates the good confinement and low

density of runaway electrons. Fig. 2 shows the

expanded version of SXR signals at tangent chord

radius at r =1.56 cm [Fig. 2(b)] and r =6.24 cm

[Fig. 2(a)]. An inverted sawtooth [Fig. 2(a)] is

Fig. 1 — Time history of plasma current (a), soft X-ray signal of the central chord (b), Mirnov oscillation (c), H α spectra (d), loop voltage

(e) and time evolution of hard X-ray (f) in a typical Aditya discharge



INDIAN J PURE & APPL PHYS, VOL 44, NOVEMBER 2006828

observed for each sawtooth crash [Fig. 2(b)]. Figure

2(c) shows the signal as observed in Mirnov coil at

that particular time interval, showing fast increase in

amplitude associated with sawooth crashes. These

phenomena are associated with the energy transport

from inner to the outer region of the q=1 magnetic

surface. Loop voltage signal [Fig. 2(d)] has nonegative value in sawteeth region which negates any

minor disruption in this region. Not only that when

minor disruptions occur, which deteriorate the

confinement and increase the plasma Z eff value, the

crashes no longer reached a rapid and/or sharp decay

as shown in Fig. 2(a and b). In this situation, it has

been reported that decay time almost increases 3 fold

and m/n=1/1 oscillations are predominant during this

period 25. The average time for sawtooth crashes

measured in several discharges lies in the interval 40

μs ≤τc≤90 μs. Fig. 3(a) shows the expanded view of

the traces found from different detectors in the samedischarge. The oscillations are not pure sinusoidal

which indicate the mixture of modes. The horizontal

scale is time in millisecond whereas the vertical label

refers to the tangent chord radius, r, in centimeters

(0<r <7cm). There is obviously a node near 6 cm

because after that a phase reversal in SXR radial

mode structure occurs [Fig. 3(a)]. This radius is

related to the location of the q=1 surface and is called

inversion radius, r inv. Figure 3(b) shows the relative

sawtooth amplitude, Δ Ã/ A, of the sawtooth oscillation

Fig. 3 — Line integrated SXR emissivity at different radial

positions versus time is shown in (a). (b) shows the the relative

amplitude, Δ Ã/ A of sawteeth oscillation versus tangent chordradius , r with inversion radius at 6 cm

of different chords. The sawtooth amplitude becomes

zero at r =6 cm which is identified as r inv because

outside of this radius sawtooth is inverted. Calculating

from the empirical law26 r inv = 0.5a/√q(a) , we get theinversion radius as 6.3 cm for q(a)=3.3 and a=23 cm,

Fig. 2 — SXR signals of the detectors at tangent chord radius(a) r =6.24 cm and (b) r =1.56 cm. Mirnov oscillations and loopvoltage are shown in Fig (c) and Fig (d) respectively

(a)

(b)




which is in good agreement with experimentally

found r inv, taking into account the accuracy of such

measurement.

The most interesting phenomenon is the presence

of two modes during the internal disruptions; one at4.88 kHz for m=1 mode and another at 9.76 kHz.

Mode with frequency 9.76 kHz is observed in the

disruption region, which is identified as m=2 mode.

Figure 4 is the Fourier analysis of the signal in a

sawtooth which shows the existence of two modes,

one at 4.88 kHz and another at 9.76 kHz. Fourier

analysis of other soft X-ray signals, performed on the

whole or part of the sawtooth like relaxation also

yielded these two modes besides the other modes of

low intensities. The two prominent frequencies of the

precursor mode to sawtooth crashes might be the

harmonics of the m=1 mode. This only proves that the precursor mode is not 100% sinusoidal which is not

uncommon in a toroidal system. This m/n=2/1 mode

on the q=1 surface, therefore, easily couples to the

m/n=2/1 mode on the q=2 surface at the time of

disruption. It is not unusual because EQUIPE TFR 17

has also observed such two modes. They have

explained this as the growth of a new mode, with an

m=1 structure and the frequency of m=2 mode

localized in the vicinity of q=1 surface at the time of

the growth of the normal m=2 mode at q=2 surface.

Full explanation with strong experimental support of

this phenomenon is not possible at this stage.

Sequence of tomographic images depicting the time

evolution of the SXR emissivity contours are as

shown in Figs 5 and 6. Figure 5 is the contour plots of

SXR emissivity before sawtooth crash and Fig. 6 is

those for sawtooth crash. No prominent shift of the

central region is observed in internal disruption as

shown in Fig. 5. Some distortion in the structure may

be due to the presence of other higher m modes

besides the prominent m=1 mode and/or small

artifacts. A prominent m=1 mode rotation occurred atinternal disruption radius as shown in Fig. 6. Pushing

of the central region towards m=1 inversion region is

also obvious and indicates Kadomtsev like disruption.

Rotation of the perturbation is not sinusoidal, as the

motion of the peak of the emissivity is not uniform

from one frame to another. The cause of the island

rotation might be due to ω∗ diamagnetic effect (the so

called drift tearing mode27) or to radial electric field,

E r , giving rise to Er B drift, where B is the toroidal

magnetic field. Figure 7 shows a few 3D emissivity

plots at sawtooth crash region. The rotation of mode

and corresponding flat region of emissivity are verydistinct.

3.2 Major disruption.

The major disruptions, of ohmically heated plasma,

in Aditya tokamak in the range are observed by

noticeable precursor oscillations, sudden

disappearance of SXR signals much before the total

current disruption, burst of Mirnov oscillations and

negative spikes in the loop voltage. The duration of

major disruption event changes from shot to shot and

lies in the range 3.3-19.2 ms. Cessation of SXR

emission before the total current disruption also variesfrom shot to shot and the time lies in the range 1.9-

18.5 ms. This phenomenon indicates that due to

disruptive activity temperature drops abruptly below

100eV in the core to stop SXR emission. Fourieranalysis of the the MHD signals shows m/n=2/1 was

always the dominant and responsible mode for major

disruption in all the shots. Such long duration major

disruptive event is not uncommon and has already

been observed by Vannucci et al. in TEXT-U

tokamak 28. Figure 8 shows that the disruption starts

around the time 77.2 ms with current fall of ∼35%

[Fig. 8(a)] and stopping of sawtooth oscillation[Fig. 8(b)]. After a short while SXR emission stopstotally at 77.9 ms [Fig. 8(b)] followed by a lot of

phenomena like a small spike in current [Fig. 8(a)],

burst in Mirnov oscillation [Fig. 8(c)], spikes in H α

emission [(Fig. 8d)] and negative loop voltage

[Fig. 8(e)]. After that a lot of negative loop voltages

are seen at 79.4, 80.8, 92.9 and 94.4 ms in the loop

voltage with continuous current decay until current

ends at 96.4 ms. A burst in Mirnov oscillation, spikes

in H α spectrum and voltage surge in the loop voltage

Fig. 4 — Frequency spectra of the soft x-ray signal (a). The lower

trace (b) is the original SXR signal. 128 points (27) of the data are

considered. The sampling time is 8 μs




Fig. 5 — Contour plots of soft X-ray emissivity before the sawtooth crash, showing not so prominent mode rotation and shifting ofcentral region towards sawtooth inversion radius

just before the total current disruption (Fig. 8) are the

common physical phenomena in tokamak plasma

disruption. Analysis of Mirnov coil oscillations at the

time of disruptive events shows the dominant m/n=2/1

mode oscillation19. Figure 9 shows that the frequency

of soft X-ray and Mirnov oscillation match well at the

time of disruptive events indicating the presence of

m/n=2/1 frequency in SXR signal. The presence ofnegative spikes in the loop voltage and the burst in

Mirnov oscillation prior to the disruptions rule out the

interaction between the plasma column and the wall

(limiter) of the vessel as the possible cause of

disruption. In these discharges position feedback

control was not operative. In the event of plasma

column disruption, due to contact with the limiter,

there would be no negative spikes in the loop voltage

or burst in Mirnov oscillations. The radiative power

stayed well below the input power (figure not shown)

which indicates that the discharge is far away from

the density limit. Hence, the contraction of the current

channel and consequently plasma detachment as a

result of edge cooling is not the main disruption

triggering mechanism in this case. Z eff values and the

H α spectra also indicate that impurities and/or

transportation of H atoms are not the main factor for

disruption. Judging all aspects, it seems that coupling between the m/n=2/1 and m/n=1/1 modes could be the

realistic mechanism for the cause of disruption. The

presence of m/n=2/1 mode at the time of sawtooth

oscillation favours the coupling of m/n=1/1 mode at

q=1 surface with m/n=2/1 mode at q=2 surface very

easily. Calculation regarding the q=2 resonant

magnetic surface localization and the width of the

corresponding island from the empirical relation

given by K Toi et al.29 and F Salzedas et al.30 showed

that there may be less chances of islands interacting




Fig. 6 — Contour plots of soft X-ray emissivity at sawtooth crash, showing prominent m=1 mode rotation and

shifting of central region towards sawtooth inversion radius

with the limiter because q=2 surface is well inside the plasma.

4 Discussion and Conclusion

The experimental sawteeth periods were found to

vary between 980 to 1050 μs and were compared with

the scaling laws. Reasonable agreement was found

using the expression of EQUIPE TFR 26, which gives

the value of 1135 μs. The internal disruption

(sawtooth relaxation) mentioned presently, is a very

interesting phenomenon. The dominant frequencies at

the time of internal disruption could be the harmonicsof the same mode which is very common in toroidal

system. The presence of such harmonics makes the

SXR signals non-sinusoidal and can couple in

resonance with the mode oscillations in higher

q-surfaces to accelerate the major disruption. The

observation of the internal disruption with growing

m/n=1/1 oscillation and the tomographic images

indicate that the sawtooth instabilities seem to be due

to the total reconnection model by Kadomtsev, but the

crash time according to Kadomtsev model does not




Fig. 7 — 3D plots of soft X-ray emissivity at internal disruptive region (as shown in Fig. 6), showing clearly the mode rotation and flatemissivity region

Fig. 8 — Expanded time history of plasma current (a), SXR emission (b), Mirnov oscillation (c), H α spectra (d) and loop voltage (e) atdisruptive period. Disruption starts at 77.2 ms and ends with total current loss at 96.4 ms. Complete cessation of SXR emission occurs at

77.9 ms

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