I

Characteristics of DisruptiVe Plasma

Current Decay in the HT-2 TOkamak

Mitsushi Abe, Kazuhiro Takeuchi and Michio Otsuka E14ergy Research Laboratory. Hitachi Ltd..

Hitachi 319-12.

(Received June 8, 1992/revised manuscript received November 16, 1992)

AbSt ract

Motions of plasma current channel and time evolutions of eddy current distribution on the

vacuum vessel during disruptive plasma current decay were studied experimentally in the

Hitachi tokamak HT-2. The plasmas are vertically elongated and circularly shaped plasmas.

A disruptive plasma current decay has three phases. During the first phase, a large

displacement of the plasma position without plasma current decay is observed. Rapid plasma

current decay is observed during the second phase and the decay rate is roughly constant with

time. The eddy current distribution is like that due to the shell effect whichcreates a poloidal

field to reduce the plasma displacement. During the third phase, the plasma current decays

exponentially. The second phase is Qbserved in slightly elongated and high plasma current

(> 20kA) circularly shaped plasmas. The plasma current decay rates in the second phase

depend on the plasma cross sectional shape, but they do not in the third phase. The magnetic

axis moves from the plasma area to the vacuum vessel wall between the second and third

phases.

KeywordS: plasma disruption, magnetic analysis, tokamak, electromagnetic force, equilibrium magnetic

field,

I

1. INTRODUCTION Disruption is one of the key problems in

tokamak device design as it causes thermal and

mechanical trouble. The former is due to rapid

dissipation of the plasma thermal energy. The

latter is due to the eddy currents and electro-

magnetic force caused by disruptive plasma current

(Ip) decay. From the viewpoint of mechanical

design, understanding the characteristics of disrup-

tive lp decay and predicting electromagnetic force

on the vacuum vessel wall during disruption are important [1] .

Disruptive lp decay rates and plasma-coil

interactions in post disruptive plasma have been

experimentally examined in some tokamaks[2-4] ,

however, plasma current channel motion during

dusruptive lp decay was not clarified. Experi-

ments on disruptions in large tokamaks have also

been carried out. The lp decay rates in large

tokamaks were reported [5-9] and it was shown

that the poloidal current on the vacuum vessel can

not be ignored during vertical displacement events

(VDE'S) and the force due to poloidal current and

toroidal field should be take into account for the

tokamak device design [10-1l] . However, a gener-

al understanding of the disruptive lp decay phase

352

I

~~f d*~t;~~~,-~~'fl~~~

has not been gained yet. The motion of the plasma

current channel and the configuration of the magnetic field during disruptive lp decay should be

examined experimentally.

The Hitachi tokamak HT-2 has magnetic probes, both inside (plasma side) and outside of the

vacuum vessel wall[12] . , This placement allows

measurement of the eddy current on the vessel wall,

determination of the plasma current channel

locations and magnetic field configuration even

during disruptive lp decay [12-14] . The magnetic

analysis code SHP[14] models the plasma current

distribution using a few filamental loop currents

and has already been applied to the HT-2 experi-

ments to study the plasma motion during disrup-tions [12] . The results showed that the poloidal

field due to the shell effect of toroidal eddy currents

plays an important role in plasma motion at an early

phase of lp decay. However, in the last phase, the

plasma motion can not be explained by the poloidal

field distribution. In order to solve this discrepan-

cy, the field input type equilibrium code FITEQ[13] ,

which is an MHD equilibrium code like that presented in ref. [15] , was modified to analyze

plasmas during disruptive lp decay.

In this paper, we discuss the characteristics of

disruptive lp decay in the HT-2 tokamak. The

phases of lp decay are identified from the lp

waveform during disruption. Then, the magnetic

configuration during disruptive lp decay is discus-

sed, considering the reasons for changes of the eddy

current distribution and the lp decay waveform.

Following this, the decay time of lp during plasma

disruptions is exam,ined.

Characteristics of Disruptive Plasma Current Decay in the HT-2 Tokamak ~~~S, ~tF~l4~2

intended to produce an equilibrium poloidal field.

The B coils are designed for a reverse flux swing of

the iron core, but they are also used for the

equilibrium poloidal field. In the latter case, some

of the HY coils are also used for the reverse swing.

The vacuum vessel is made of 9mm th.ick stainless

steel. The magnetic penetration time is 1.3ms for

the vertical field and 1.5ms for the horizontal field.

The vacuum vessel loop resistance 9v is 14m9.

The decay time of the net toroidal current on the

vacuum vessel is roughly 0.05ms. The poloidal

angle 6 is measured in the counterclockwise

direction.

The HT-2 has 36 magnetic probes, 15 flux loops

and two Rogowski coils to measure the poloidal

Table I Parameters of HT-2 Tokamak

Parameter Symbol Value Unit

Plasma current Electron density (tine averaged)

Plasma major radius Plasma mimr radius Elongation P p+V2 Toroidal fietd

Vacuum vesset ,oop resistance tron core flux swing

Safety tactor at surface

Discttarge duraton

IP

n. Rp

ap x

A BT

~v

qs

0-55 1 -3xl Otg

0.39-0.44 0.08-0, 1 2

0.9- I .45

0,8-1 . 1

1 .O

14 O,oe2 3,0

70

A m4 m m

T m~ Wb

ms

2. EXPERIMENTAL SETUP AND MAGNETIC MEASUREMENT

2. 1. Experimental device and cause of disrup-

tion

The experiments are carried out in a small

tokamak, the Hitachi tokamak HT-2. Typical parameters are listed in Table I. Its poloidal cross

section is shown in Fig.1. A special feature of this

tokamak is its ability to generate various cross sectional plasmas (Fig. 2). It has three kinds of

poloidal coils: eight HY coils (HY1-HY8) , two B

coils (B1, B2) and two sets of horizontal field coils

(ACH and DH1, DH2). The HY coils are mainly

o. 6

c.4

o2

~ ~~

~~o

- O. 2

- o. 4

- 0.8

l ron

Core

t Plekup Coff

B8t . Flux Lcop DHI ~

~~1 HY3 HY2 ~l HY 4

~ Lf mi ter HY 1 ~e

~~ACH FptQidat Artete

,~~ Moveble Limitor

dg!

~ J~

ACH

Veeuvm Ve8･et

~~1 HYe HY7 ~~

B B2 ~ DH2

E~ HY8

Teroid･1 Coit

Fig. 1

Q.Q o.2 o.4 0.8 0.8 1.o M.i.. Rrdt~ R (~)

Poloidal cross section of the Hitachi tokamak

HT-2. Abbreviations are explained in the text (section 2.1 ). The arrows denote the magnetic

probes and the dots denote the flux loops. ,

353

30

20

10

o

-10

-20

-30

j~ ;~7 ･ ~~~~A';~~:~A~,p~~

I

f~ E o v N ~ ,o) ~5

I

1993~j~ 4 )il

limiter, Vaouum Vessel :

..r"t~"" ~1F

Plasma t

t,tb.. ,~4 -"'4'1'~"':

(a)

20

Circular

30

20

10

o

-1 o

-20

-30

35 50 65 Major radius R(cm)

shape

20 35 Major

(b) Highly

f¥ E o .~'

N ~' J: c, .~5

::

(c)

t:

,f* ~ e,

l t t ,,

tt ~ J' ,b ~~t~Ul~":

20 35 50 Major radiVS R(cm)

Slightly elongated shape displaced vertical position

before disruption.

Fig.2 Plasma cross tokamak.

50 ･ 65 radivs R(cm)

elongated shape.

l 65

with

j ust

sectional

20

(d)

35 50 65 Major radius R(cm)

Highly elongated shape divertor configuration.

shapes of the HT-2

with

magnetic field. A feature is that twelve pairs of

magnetic probes and one pair of Rogowski coils are

placed so as to make respective pairs inside and

outside of the vacuum vessel wall. This makes it

possible to measure the toroidal eddy currents on

the vacuum vessel wall. The magnetic analysis codes[13, 14] reconstruct the equilibrium magnetic

field using the data measured by these magnetic

sensors. The measured data are digitized by tr~nsient recorders which sampling time is 200lrs.

The power supplies for the HY coils are

transistor choppers with a maximum switching of

5kHz and condenserbank current source. The coil

and chopper connections are rather arbitrary. This enables the differently shaped plasmas (Fig.

2) to be produced. These include circular and

elongated plasmas, and even divertor configuration

is possible if lp is low (Ip < 15kA). The elonga-

tion parameter /~ (= b /a, a, plasma minor radius; b,

plasma minor radius in the vertical direction) can

be well controlled by changing the coil currents.

Experimentally, /c from 0.95 to 1.45 can be got.

Feedback control of the poloidal magnetic field can

be applied in the experiments, but it can modify the

lp decay rate and plasma movement even during the

disruption. However, to make the experimental

results simpler to interpret, feedback control gains

are set very low or switched off in this study. So

we can say that the poloidal magnetic field is not

feedback controlled during disruptions.

354

I

~~~*7~"-1~~~~l~~C Characteristics of Disruptive Plasma Current Decay in the HT-2 Tokamak

The cause of disruptions with the circular shape plasma is a low safety factor. Plasmas are vacuum vce8et

disrupted when the surface safety factor q* decreases to 3.0. The disruptions of elongated

plasmas (including the divertor configuration) are ~) due to the VDE'S. Rapid lp decay is usually @ observed when q~ drops to 2.0 because of the VDE.

Characteristics of disruptions with circularly ~ shaped plasmas and slightly elongated plasmas have

already been reported [12] . We have obtained the

toroidal eddy current on the vacuum vessel wall and

the magnetic field around the plasma by using the

SHP code[14]. The last phase of lp decay is not

well described by the SHP code. So, our magnetic analysis also uses the equilibrium code FITEQ [13]

with some modification to apply it to the disruptive

lp decay.

2. 2. Modifioation of FITEQ code and force

balanoe Magnetic field values corresponding to those

measured by the HT-2 magnetic sensors can be calculated from coil currents I., eddy current le and

plasma current density jp. The currents are

determined so as to minimize the following residual

E in the magnetic analysis [13, 14] ,

~ p E = ~ { P!yn ~ pj' ~p (R, ip), I., I*) }21(Tj2,

j=1 (1) where Pj', Pj~n ,aj and mp are the calculated field

values corresponding to the j-th magnetic sensor,

the measured field value of the j-th magnetic sensor,

the measurement error of the j-th magnetic sensor

and the number of magnetic sensors, respectively.

Once the currents are determined, the poloidal field

and electromagnetic forces can be calculated from

the currents.

The FITEQ is an MHD equilibrium code for a

steady state plasma and we modify it, so it can be

applied to the magnetic field during disruptive lp

decay. The modification includes assumption of

currents in the scrape off plasma area as well as in

the core plasma area. This situation is shown in

Fig. 3. There are three regions in the vacuum

vessel. Region I is the core area, in which all the

magnetic surfaces are closed without any interac-

tion with the limiter or the vacuum vessel wall.

Region 2 is the scrape-off area where current is on

the op~n magnetic surface. Region 3 is the scrape-

~~~~, f~~34~;

r

D < ~

(a) During steady state (b) During disruptive plasma

discharge. current decay.

Fig.3 Halo current region in poloidal cross section and

distributions of plasma current density jp as

functions of minor radius r.

off areawithout current. The original FITEQ code

ignores region 2, because it is applied to stable

plasmas like that of Fig. 3(a). However, during

disruptive lp decay with rapid plasma motions [12] ,

part of region I becomes region 2. Since the

current in the scrape-off area decays in less than

0.2ms, region 2 can be ignored, except during

disruptions. The modified equilibrium code FITEQD (FITEQ code for Disruption) assumes

toroidal current in the area in which the flux

function ip satisfies the equation,

ipa* > ip > ipH, (2) where ip.* is the flux function value at the magnetic

axis and ipH rs an input value which makes the

iterative calculation conyerge and E small.

The electron density of the HT-2 plasma is

about 3 x 1019m~3 and roughly an equivalent

density of H+ is in the plasma. The plasma weight

is estimated to be roughly 108kg because its volume

is 0.2m3. The electromagnetic force is estimated to

be in the order of 100N, because typically poploidal

field and plasma current is on the order of 0.01T

and 10kA. If the plasma is not at equilibrium, its'

acceleration rate is on the order of 10roms~2 and it

will collide with the vessel wall in several micro

seconds. However, disruptive lp decay occurs in

355

I

~f~ ;~7 ' ~~~:A*~~F~~~#*

about Ims,, so it can be said that the plasma is still at

an equilibrium. In this sense FITEQD is applic-

able to the disruptive lp decay phase.

During the disruptions, the plasma directly

touches the vacuum vessel wall and forces due to

thermal pressure and poloidal current as well as

due to the toroidal current can not be ignored

between the plasma and the vacuum vessel. The kinetic pressure Pk on the vessel wall is expressed

by,

(3) Pk = IeekTe + nikTi

where ne, ni, Te and Ti are the electron density, ion

density, electron temperature and ion temperatures

at scrape-off area, and k is the Boltzmann's constant. The pressure Pl due to poloidal current

is recognized as the difference of the magnetic

pressure of the toroidal field BT and is

P1 = (B~lN ~ B~oUT) / (2l/o) (4 )

where BTIN and BTOUT are the toroidal fields inside

and outside of the vessel wall, respectively, and !lo

is permeability in vacuum.

On the other hand, the plasma experiences a

force due to the toroidal current. The total force

FPT is obtained by the plasma surface integral

FPT = f B~ np / (2llo) dSp, (5)

and is estimated by the SHP code, where np is

the normal vector to the plasma surface directed

~~69~~~~ 4 I~* 1993~~ 4 J~

inward and FPT {= (F~T, FzPT)} is a vector on a

poloidal cross section. If the plasma is in a steady

state, FPT is zero. However, in the disruptive lp

decay phase, the force balance is,

FP = FPT + FPkl

FPT + f (p + p) nv dSv O (6)

where FP is the force acting on the plasma, nv is the

normal vector to the vacuum vessel wall directed

inward and the integral is calculated on the vacuum

vessel , wall. The force FPkl {= (FRPkl, FzPkl )

= f (Pk + pl) nvdSv} is the force acting on the

plasma due to thermal pressure and poloidal current and it is estimated by,

FPkl = _ FPT (7) using the SHP code in this study.

3. EXPERIMENTAL RESULTS 3. I . Eddy current distr,ibution during disruptive

lp decay The poloidal field strengths Bp are measured

during disruptions and results are plotted in Fig. 4,

including the time evolution of lp and net toroidal

current lv on the vacuum vessel. The lp decays in

0.5-1.5ms. In Fig. 4(a), showing the circular plas-

ma results, the plasma moves in the direction of the

small major radius side (6 = 180') .In Fis. 4(b), for

highly elongated plasma, it moves vertically

l

Fig. 4

50

_ 40 <J. 30

- 'a ~ " 10

O

p6 ~ bo C ~i -6

6

<'~'~,_;

!~0 210

(a)

Time evolutions of

IN and OUT mean respectively.

,

fl

f

1

,

IN ' , UT l

C=270'

:

11 12 13 15 17 18 19 20 21 1,

Time (ms) Time (ms) (b) Highly elongated plasma. Circularly shaped plasma.

plasma current lp,Poloidal field Bp, net vessel current lv during

the data are taken on the plasma side and atmospheric side

22

HT-2 disruptions.

ot the vessel wall,

356

I

~f -~ti~=,~~w~C

(toward the top: 6 = 270'). The poloidal fields

shown are the measured data in the direction in

which the piasmas are moving. The toroidal eddy

current density je on the vacuum vessel wall can be

estimated by

j* ~ (BpOUT ~ BplN) ///o, (8)

where BpOUT and BplN are outside and inside

poloidal fields. When plasmas are moving toward

the walls, the eddy current at the wall position in

which direction the plasma is moving, is in the

opposite direction of lp ~* < O) . However, the

eddy currents at this point become the same dirction

as lp ~* > O) at last. After that the eddy current

changes its direction, Ip decreases exponentially

and asymptotically reaches zero. The maximum lv

is observed to coincide with this change of direction.

Figure 5 plots the toroidal eddy current density j* calculated by the SHP code, as a function

of a for the circularly shaped plasma of Fig. 4(a).

Figure 5(a) is obtained at 13.4ms which is just

before the change of the eddy current direction and

> :S CO

c Of~ 1,E ~'¥ c< O~: L,J L:3 _,o

O' > lO =, UJ

40

o

Characteristics of Disruptive Plasma Current Decay in the HT-2 Tokamak

-10

13.4ms

1 .1 4m

> d+ .55

C O ~f~ 4JE ,: ¥d,

e~: L¥' :' O1)o

> U U LU

(a)

40

O 9Q 1 80 270 360 Poloidal an9le 6 (de9ree)

Just after the start ot I, decay.

~~~S, ~rP~l4~a

Fig. 5(b) is just after this change. The plasma

motion during disruptive lp decay is toward the

small major radius side (6 = 180' in Fig. 5). At

13.6ms, the eddy current direction changes from the

counter lp {j* (180 ) < O} direction to the lp

{je (180) > O} direction. The eddy current dis-

tribution of Fig. 5(a) is like that for a shell effect to

recover plasma displacement. However, the eddy current distribution in Fig. 5(b) pulls the plasma

toward the vessel wall and destabilizes the plasma

position. In spite of this j* distribution, an lp of

about 10kA does not vanish instantly. This means

that the plasma experiences forces FPT and FPkl

and FPkl should be a repelling force between the

plasma and the vacuum vessel wall. The discus-

sion so far means that characteristics of equilibrium

and force balance differ between plasmas before

and after the change of the eddy current distribu-

tion. Then, the equilibrium magnetic configura-

tions, force balance and lp decay rates should be

discussed taking this into account.

3. 2. Classifications of disruptive lp decay

wavefo rm s

Table 11 classifies the lp waveforms, which are

observed in the HT-2 disruption. The waveforms

can be divided into groups, depending on the plasma

cross sectional shape and initial plasma current I~,.

The waveform of lp decay consists of two parts. In

one lp decreases linearly with time, while in the

other it decreases exponentially. The linear lp

decay is only observed in the disruption of slightly

13,8ms

TableH Cta88ifle8tkm of Pbsma Current Waveforms during DisruDtions

Fig. 5

o

- 40 o 360 ' 90 1 80 270 Poloidal angle e (de9ree)

(b) Last phase of lp decay.

Toroidal eddy current distribution on the vacuum

vessel during disruptive piasma current decay of

circularly shaped plasma, caloulated by SHP code.

357

I

8

f~ ;~7 ･ ~~~!A*~~~~,---"*~

~ < J~

~ ,y~

~' c OL

L:-

o o co ,o

o >

,, < J, '~, ~? d~ =L(D

=0

o co (o

o >

6

4

2

o

6

4

2

(a) Elon9Gted

x ,C:::1.1

A ,C=1.2-1.4 A Divertor

confi9uration

/ /

/ al /

/ ll la

/ /

/ /

,~

/ /

/ JL

JL

/

ll /// Iv=; I Io

~ I~

/ Pp

{ Iv=T

lp= Pp +0 4

v~2i '

(b) Circular shaDe lv=~Pp

/ /

/ /

p- ~ n / lv~~i:+3.v I e /

e I e ' ee ' ll,, e e' e ...,. le .. It .... / / _, '-~'~/ I~-~+0,4 i

.p ;1__"

/ /

O o I O 20 30 40 50 Initial Dlasma current ~o(kA)

Correlation between peak net vessel current 1~

and plasma cross sectional shapes as a function of initial plasma current I~.

(a) Elongated plasma including divertor con-figuration.

(b) Circu'larly shaped plasma.

~~69~~~~ 4 ~~ 1993~~ 4 ,~

I~ = Ip0/5 when lp < 20kA, but at lpo > 20kA,

AI~/ Alpo becomes small, i.e. 1114, which is the

same as for the slightly eiongated case. These data

show that classification of the relationship between

lvP and lpo is the same way as given in Table II,

suggesting that disruptive lp decay depends not

only on the plasma characteristics, but also on

electromagnetic interactions between plasma and

the vacuum vessel.

Generally,just before start of lp decay, plasma

position is displaced and sometimes a negative loop

voltage and increase of lp are observed[12] . In

this sense, disruptive lp decay can be divided into

three phases, i.e.

phase I : pre lp decay phase,

phase 11 : Iinear lp decay phase,

phase 111 : exponential lp decay phase.

However, in the circular shape (Ip < 20kA) and

cases, no ase 11 is

Fig. 6

elongated plasmas and circular shape plasmas with

lp > 20kA. The arrows in Table 11 show the timings for the eddy current direction change. All

disruptive lp decays have a final exponential lp

decay phase.

Table 11 has four categories of lp decay waveforms, and the relationship between the lpo and

peak toroidal vessel current lvP can be divided into

the same four groups as shown in Fig. 6. The lvP is

plotted as a function of lpo. Figure 6(a) is for

elongated plasmas and Fig. 6(b) is for circular ones.

The I~ is roughly lvP = Ip0/7 for the highly

elongated plasmas but for the slightly elongated

plasmas it is lvP = I~/14 + 0.4 (kA) . The plas-

mas with divertor configuration have roughly the

same If values as the highy elongated plasmas. For

the circular plasmas, I~ is proportional to lpo and

highly elongated plasma cases, no phase

observed, but the eddy current is smaller in phase II

than phase 111. Sometimes a slight decrease of lp is

observed during phase I, but it is so small, that it

can be distinguished from the phase 11 occurrence.

Thermal disruption takes place in phase I. The

arrows in Table 11 can be understood to show the

start of phase 111. Phase 111 is thought to be a key

to recognizing characteristics of disruptive lp decay

because it is observed in all disruptions.

3. 3. Force balance and magnetic configuration

during disruptive lp-decay

Although the phases were not discussed explicitly, ref [12] discussed mainly behavior

corresponding to phase 11 of circular and slightly

elogated plasmas. Then, we give greater consid-

erations to the characteristics of phase 111 here.

Figure 7 shows the waveforms of lp, Bp (inside and

outside), vertical plasma position Zp, the vertical

force acting on the plasma FZPT and the vertical force

acting on the vessel FzVT. The forces are calculated

from the toroidal current and poloidal field because

they are analyzed by the SHP code. Phase I occurs

from 17.8 to 18.4ms, during which time the pla~ma

current channel moves in the direction of the bottom

vessel wall and dlp/dt is small. Phase 11 is not

clearly seen in this disruption, because it is highly

elongated. Phase 111 starts at 18.4ms, after which

lp decays as the function exp (-t/r~) (Td Is

roughly 0.25ms) and the plasma current channel

358

l

I

~f~~f~;~~*---=,~~ ~

ao

Characteristics of Disruptive Plasma Current Decay in the HT-2 Tokamak

0.2

Fay~1S, it~l4~;

'~ < J~'

~

30

20

10

o

Plasma current

IN

__ ._ _ d- -~- -~*~ ~" ~ ~i~ OUT 'b' ~ ~ ~..

~,~__ Pobidal fleld ( 6 270' = )

E ~. N j~ ,O'_

q' :::

0.1

'**

h ~ L2i

o,03

o

-0.03

o

-0.1

-0.2

f' E~

o ~ '~l

r~ Z ~, r ,LN LL

h )N LL

Fig. 7

O

-4

-8 O

- 2GO

-400

O

-200

- 400

18 I9 Time (ms)

Vertical force balance during disruptive lp decay

ot elongated plasma. The disruption is due to the VDE. Plasma ourrent lp, Poloidal field Bp (lN

and OUT), plasma vertical position Zp, vertical

force on plasma FZFT and vertical force on vessel

FZVT are plotted. The forces are calculated by

the toroidal current only.

.~ E ~. N d~! J:: .a,_

a, =:

f~ S ~. N ~~ a' ,~

=

0,1

o

-0.1

-o. 2

O. 1

o

-0.1

l

.t

.::::i::' . .4 "

. . I . .*. .

':': :~-'~'1'r:~'¥'

!"!"' : r:¥" : '¥' : j; '1/~:;;;i ~~~:~~~:~,:¥{~:

: ' ?:/ :.･:~k:-i'~: .~:L t ,~::¥~

~ { ,~ it.:;/;.:* ~

s' ';,.,.t' s 'r:~' ~:~, : ' '

~ :"t'}-~i$' ~,,~ I .,~, '$1 't. t'J~' 'h'eslell :1~ I A: ' ~s.: ~'5 :. y:_'~ I ~ 1 !~t~.~tt¥;"" ~ " '. ' " ':~:/j:/'/

.J~. . ~ '/' I ' l_ . ¥. . J¥' ~:;;$

' "'~' '~~:?~is

.::::r .::::::l

' ~:'~11~:~; f

7 :;'~ : : : :.:!:".':~:~~ i :~:

""/~ ' ~: :: t~ : :¥:

:::':k,~' .::'::t~.:::

"':~¥i:.~~' :::::1.¥c:~i.:

~ """t'*:"" : :~i･:･: : : : '~ 'Y l:~:.:.* ...r.::i*~J" ':¥ . **: * . .

18.4ms

-0.2 I

changes its direction of motion. The Zp after

19.0ms is not plotted because the small lp and large

eddy current cause a large uncertainty with the

filamental model of the plasma.

During phase I, FZPT is roughly zero, but

becomes non-zero by the start _of phase 111. The

FZPT should be cancelled by the force due to the

poloidal current and thermal pressure, i.e. FzPkl of

Eq. (7) . The vacuum vessel experiences the counter force and the total force on trie vessel is the

sum of - FzPkl and F~T. It is plotted by a dashed

line in Fig. 7. Then we conclude that during phase

I, the force acting on the plasma is mainly due to the

toroidal current, but on entering the lp decay phase,

the force due to the poloidal current and th~ thermal

pressure become important.

Figure 8 shows the magnetic configuration and

plasma current density during disruptive lp decay

Fig. 8

0.28 0.38 O.48 0.58 4 3 2 1 O Major radius R(m) Plasma current denSity

Jp(1 06Alm2)

Magnetic configuration and plasma current density distribution during disruptive lp decay

analyzed by FITEQD. The dofted area shows where the plasma current is found.

as analyzed by FITEQD. The disruption is the same as in Fig. 7. The first one is got at 18.0ms

which is during phase I, the second is at 18.4ms

which is at the end of phase'l, ahd the third is at

18.8ms which is early in phase 111. The dotted area

shows where the current is found. At 18.0ms the

plasma vertical displacement is small and the scrape-off area with current is thin. At 18.4ms,the

vertical displacement has become large and the

scrape-off area carrying the current becomes thick.

Since the plasma directly touches the, vessel wall,

359

I

j~ ;~7 ' ~~;~~!A*~~:A~~~~~~*~

the force FzPkl of Eq. (7) has a rather large value as

discussed in Fig. 7. At 18.8ms, during phase 111,

there is no closed flux surface in the plasma area.

The magnetic axis has moved out of the plasma area

and the upper half of the initial plasma has

remained. At this time, Ip of 15-20kA is still

observed in the plasma area. The change of toroidal eddy current direction at the start of phase

III can be recognized as due to the displacement of

the magnetic axis from the plasma area to the

vacuum vessel wall.

The reason that the plasma current channel

changes its direction of motion at the start of phase

III is recognized as follows. The core part of the

plasma current is displaced from the plasma area to

the vessel wall at about 18.6ms with rapidly moving

magnetic axis, but the scrape-off plasma current

does not move and remains in the vacuum vessel.

Since the magnetic measurement system measures

the weighted center of the plasma current distribu-

tion, it measures the current center of the scrape-off

area. However, if the measured plasma cent-er is

defined by the magnetic axis, the plasma does not

change direction.

Figure 9 shows a disruptive lp decay of a

slightly elongated plasma. The parameters are the

same as in Fig.7, except for pp + Ii/2, where ~p is

the poloidal beta and li is the normalized internal

inductance. The pp + Ii/2 is not well analyzed

when lp becomes small. Phase 11 is from 16.4 to

17.4ms (strictly speaking, phase 11 starts just after

16.4ms) and phase 111 starts at 17.4ms. Decrease

of the ~p + Ii/2 value suggests thermal disruption

occurs at 16.4ms. During phase II, the plasma is

going up, FZPT has a non-zero value and BplN rs

larger than BpOUT at 6 = 90'. Then,the magnetic

axis is thought to be in the plasma area, and it is

moving toward the top wall. However, the motion

is suppressed by the shell effect of the toroidal eddy

currents and the force FPkl also suppresses the

motion because FZPT has a non zero value. The

plasma position is maintained by balancing FPT and

FPkl. The important difference between disrup-

tions of Fig. 7 (highly elongated) and Fig. 9

(slightly elongated) is the speed of the magnetic

axis motion. The magnetic axis arrives at the vessel wall instantaneously (less than 0.2ms) after

the lp decay starts in Fig. 7 but it takes about Ims in

< ~,¥_

J~

h ~a GO

l~ < ~'

~ r~i

h teN

40

30

2Q

10

O

0.05

1993~1~ 4 ;!

Verticel force (Plasma)

400

200

O

Verticel force (VesseD

400 __･* .,...

200 *_.,_ O

=1cv

1 ,o + o q~L

0.5

O

~N LL

Fig. 9

16 17

Time (ms)

18

Vertical force balance during disruptive plasma

current d,ecay of slightly elongated plasma. Plasma current lp, Poloidal field Bp ( IN and OUT)

, pp + Ii/2 value, plasma vertical position Zp, vertical force on plasma FZPT and vertical force on

vessel FZVT are plotted. The forces are calcu-

lated by the toroidal current only.

Fig. 9. In the highly elongated case, the plasma

experiences strong Zp instability and lp decay

enhances the instability even more, so the magnetic

configuration changes rapidly to phase 111. Howev-

er, in the slighly elongated case the Zp instability is

weak and Zp is maintained mainly by FPT and

partially and by temporarily FPkl, Since FPT and

FPkl decay in roughly Ims and 0.Ims respectively,

reproducing the forces is necessary to maintain Zp.

Then, the plasma continues to move toward the top

vessel wall, which scrapes away the current in

plasma.

However, the results analyzed by the SHP code

describes the plasma position of the weighted center

of plasma current. Magnetic analysis using the

FITEQD code was carried out to obtain the motion

of the magnetic axis. Figure 10 shows the magnetic

configuration and plasma current density of slightly

360

l

~~f*~ti~･~~~~'~il^~~ Characteristics of Disruptive Plasma Current Decay in the HT-2 Tokamak ~~~~, ~r~~4~

~ c _ 3 o -~ ~~ 2 o '~ 'o c~' ~~C 1 *, 'a ~9 1 O CL

O, 2

0.1

E

N O ~ c .a,_

~ -O 1

-0.2

1 6.4ms

.:i~k:;~;~~;.::'~~~~b~"**･*; ~~

. .'. d:r".~-. . 4 '$ '. .1 ' *~ V$ ~S:'/'/'1~:.-

. .~:¥'~.~~;.¥$~':¥

y~t""' ･ ･ ･ , .- ･ ･ ･)･~¥ ¥:,~~:¥;~

- /' '~ ･~:::::~t:ii ' ! :~: 3;'?::

~; "~ '~ '1~",L:-" ""' "~ '~* . .rTIT" "* *' /

*;~ If" ~~~~' -' "'t / '-" j ¥:~:::;~ "'1

18.8ms

"!'1lt"' I't'l :"I$rt" ~~~~ I;{;:~ tF . :' .:1 It. l 'l' 14rTl" " t t ' ,,. . . ~it;""I " lll"t'l' "I J'IilS:"'!"'1¥tl ~: {: S ~fJ

~ t i't "I"I"i:t' Y'It't' ,.. .,ll rll'It .:'t tl'll"I' ~::~::::h~~:.:i'::~ Itl! :~,~ ~1 1 I~" I ' t 'l

:t'::':~/

:1;'::i:/:"::/ : IS¥"'1" ;:::;,~'fl'JL'J'J"J'S 'I"'t' 'IIll'lJ"f' ' : : :1~.;: : I :1:~i : 'f: I : :': ' t I !

l'l~'-11" '~' I il"I IJI tlt J

'I:~"Itl::.L 'II l:l ll I I I l'l~1~"t I '4:" J'J' ' t'l "4 "e ~"I

"""" ' f I " ' 'r 'd ' t l" "$ " l ~1'1':"' '-'1111 " /

"'rt "i " I / $ ' I ' i t ' t " I l'!" t4 " ' Il {rr ~4 '1'1~1 "I J ll""IIlttl'll'4tt 1'1 ,..'a,, . . t I """I" 1"'$ ' / I t ~~~'~i~1~1 ' " I ;4" t' ' L:_~.::-'~::/: ;:?t'

17.4ms

:. ' ':7:ik : :~:c'd~:~~;;~~~$i ' i ~ ; ･ ~

･:'.::;;i;i';~;::i;;is'~-

:/~ .. . ;~:./"f/ :;:?~;;~~~":::"':"":g 'L"' """'f'::/""'1 ' " ' ' "' '!"h! ' """':';"I " 'F"::.....J....!::h' ,., 'h.'....._... "" !::l """'*"":,;"i'

:.'}' '/"'~':~$ ' :1:'* ' '::'.$'1"'/*'J"

' :;/" r' ~;;~:"' "'/~:::'::) '$""' """""'f : ~S : ";-' : ~:/:･~:.. j ,;;

. .J. '::;"~'i" "Js

Fig. 10

0.33 0.43 0.53 0.33 0.43 0.53 0.33 0.43 0.53 Maior radius R (m) Maior radius R (m) Major radius R (m)

Magnetic configuration and plasma current density during disruptive lp decay of slightly elongated plasmas.

I

elongated plasma during disruptive lp decay.

Three time slices are analyzed. The first one is at

16.4ms which is during phase I, the second is at

16.8ms w'hich is during phase 11 and the third is at

17.4ms which is end of phase II. Halo plasma

current in the scrape off area is necessary to

converge the iterative calculation of FITEQD.

Comparing with Fig. 8, the magnetic axis does not

vanish instantly in Fig. 10 as estimated from SHP

results in Fig. 9.. During phase II, the magnetic

axis exists and moves not only the vertical but also

the radial direction, but the area with closed flux

surfaces become small. The scrape off area with

halo current become large but the position of the

area does not change so much.

We conclude that the presence of phase II

depends on the existence of magnetic axis during lp

decay phase. When the position stability of the

plasma is strong as highly elongated case, the

magnetic axis vanishes instantly and no phase 11 is

observed. In the highly elongated case like Fig. 7,

reproduction of FPT and FPkl is not enough to

maintain magnetic axis position against the instabil-

ity, ev,en temporarily.

The thermal disruption can be observed clearly

in Fig. 9 slightly elongated case, while there is no

clear thermal disruption in highly elongated case.

This also can be understood by the position instability. Since the vertical position instability

is strong in highly elongated case, the thermal

disruption is thought to be occurred in coincidence

with the vanish of magnetic axis and rapid lp decay

start, which make it difficult to observe the thermal

disruption. However, in the slightly elongated

case, since the position instability is not strong,

magnetic axis stays for a while and lp decay does

not coincide with the thermal disruption. This

situation makes it easy to observe the thermal

disruption.

The process of disruptive lp decay can be

recognized as a process of magnetic axis displace-

ment from the plasma area to the vessel wall.

When the axis arrives at the wall, the plasma current channel is supported by the forces FPT and

FPkl. Then,phase 111 is an equilibrium condition in

which the plasma is supported by the magnetic field

and vacuum vessel wall. Interactions due to the

kinetic pressure and poloidal current are present

between the plasma and the vessel wall.

3. 4 Time constant of disruptive lp decay

The lp decay time Td is usually defined by the

average of dlp/dt divided by the lpo [12]. Howev-

er, we have just shown that the lp decay ph.ase can

be divided into three phases, so it is reasonable to

discuss Td for each phase. The lp decay rate for

phase I can be ignored because the rate dlp/dt is

very small. Phase 11 has linear lp decay and dlp/dt is constant with time. The decay time 1,Idl

for phase 11 is defined by

rdl = _ I~)/(dlp/dt). (9) Phase 111 has exponential lp decay and the decay

361

I

j ~? ;~? ･ ~~~~A*~~fA**#*

time r~ is defined by

lp oc exp (- tlr~) . (10) Figure 11 shows the waveform of disruptive lp

decay for circular shaped plasma and a way to calculate Td of Eqs.(9) and (lO) . Phase I is very

short, from 12.8 to 13.0ms. A negative loop voltage

and a small increase of lp are observed. Phase 11 is

from 13.0 to 13.6ms and dlp/dt is a roughly constant value of - 4.5 x 107A/s, as shown Fig. 11

(a). The T~ is 0.93ms with lpo = 42kA. Phase 111

occurs after 13.6ms and the waveform can be well

approximated by an exponential function and rd' is

190/Is as shown in Fig. 11(b).

Figure 12(a) plots the absolute value of dlp/dt

versus lpo for Phase II. Since the sampling interval

is 0.2ms and the duration of phase 11 is less than

Ims, uncertainty of I dlpldtl is rather large. The

slightly elongated plasma have data only in the

region of lp < 32kA and have rdl = 1.6ms. the

circular shape plasmas have phase 11 only with lp >

20kA and have r~ = Ims. We conclude that rdl

depends on the plasma cross section shape or the

poloidal magnetic field configuration.

Figure 12(b) plots r~ of phase 111 versus lpo.

There are four kinds of plasma cross sectional

shapes and r~'s are from O 18 to O 4ms. No clear

difference in T:d* between these plasma shapes can be

observed. This differs from the situation of phase

II. We conclude that the decay time depends on the

plasma cross sectional shape only during phase II.

In phase 111, all of the magnetic surface

interacts with the limiter or vacuum vessel wall and

no closed flux surface is present. The ions and

electrons move along the flux surfaces and collide

with the vessel wall. Then, they are cooled and

become neutral particles. However, Joule heating

still occurs and the neutral particles can be reionized. The T* is the ionization level (13.6eV)

or less. If we assume T* = 5eV, the plasma loop

resistance Qp becomes 7.0mQ (if T* = 10eV, then it

is 2.2m9) with ap = 0.Im and Rp = 0.44m. Dur-

ing phase 111, the plasma stays roughly at the same

position and lp is decayed only by resistivity. The

approximate plasma inductance Lp is 1.0 X 10-6H

and T~ is estimated by Lp /Qp to be from 150 P s (T*

= 5eV) to 450 P s (T* = 10eV) . These values

agree roughly with the experimental data of Fig. 12

50

1993~~ 4 )~

db ~T~

-45kA/ms

* ~

< ~'

o Pl8sma current

5,ao

a.OO

3.00

2 .OO

1 .oo

0.0

11

Fig. 1 1

b*exD(- t 190Ps )

lz IS 13.6 u.o 14.4 1, 8 14 15

Time (ms) Time (ms) (a) Phase ll (b) Plase 111

Definitions of lp decay rate and time constant tor the

phases 11 and 111 of disruptive lp decay.

5

o d +' L,D

> CD

o-o'Q 3 ¥ 1'< ~'~ =0 O-LL ~ 8 ~l~ 2

co~ E cb ,D

~: t

~ CD

o o ~ 4' ,ca'

L :'

o 'o

E 'o ~o

Q '~ o ~ c 'u 1' ~ o o o e F:

f~ ,O

E ~*' ~:1'

o

0.4

0.3

0,2

8.1

o

(a)

T{d=-b/(d_･d_dl~)

,c

,

~'1

xx

, e

t~ - I ms

rdt -1 .6ms

(b )

A

A

}

AA

e

A A

bceex p( - t/ Zi~)

J~dLAJL J~A J~

JL~( JL IL dlLe JL '~re I JIL

A A ee Plasma shaoe

Circular

Ebn9ated(/C=1.05) Elongated(,c>1.2)

Divertor Confi9ur8tion

,

Fig. 1 2

O I O 20 30 40 50 Initial plasrha current l~(kA)

Time constants of disruptive lp decay of HT-2 tokamak. Data ~are clarified by the plastna cross

sectional shape and lpo. (a) phase ll. (b) Phase lll.

362

I

I

~~f~~~t~~'-~~"~i+Ro~ Characteristics of Disruptive Plasma Current Decay in the HT-2 Tokamak ~~~1S, i~rF~l4~~

(b), we conclude that the lp decay of phase 111 is

simply due to the high resistivity of the plasma

which is cooled to be T* = 5 - 10eV, The cause of

such low temperatures is that there is no closed flux

surface during phase 111 and the plasma touches the

vessel wall directly.

4. DISCUSSION 4. I . Phase 111 and vessel loop resistance

The plasma current channel does not move

during phase 111. The plasma and the vacuum vessel can be recognized as a simple parallel circuit.

The relationship of lv and lp during phase 111 is

roughly,

lp/Iv = 9v/1~)p (11) and 9p is calculated at T* = 5 - 10eV in phase 111.

The sum of lp and lv Should be less than lpO even at

the beginning of phase 111. Then, the lp during

phase 111 is,

lp < Ipo 1~)v/(9v + 9p) (during phase 111) .

(12)

where 9p is a value calculated at T* = 5 - lOeV.

The HT-2 has quite a large 12v Value, i.e. ~v > 1~)p

and at the beginning of phase 111, Ip is a rather large

value of 10 - 20kA. In this case, rd* is equal to

Lp 19p.

However, a tokamak with low 9v (12v < 9p)

should have a small lp at the beginning of phase 111,

suggesting that the phase 11 period becomes longer

due to low 9v. The r~ should be equal to the decay

time of lv (rd' = Lv/~v : Lv is the inductance of net

vessel current lv) with low 9v.

The waveform of disruptive lp decay depends

on the 9v Value and 9v/9p Should be taken into

account, when the results of this research are

compared with disruptions in other tokamak

devices. However, usually tokamak devices are designed so that 9v rs larger than 9p (T* = 5 -

10eV) . This is true of the HT-2. Then it is

expected that the waveform of HT-2 disruptive lp

decay is similar to that of other tokamak disrup-

tions, except for those with insulation in the toroidal

direction.

4. 2. Comparison with disruptive lp decay of

large tokamaks Several reports on disruptive lp decay, espe-

cially that due to VDE's has been published from

large tokamak experiments. Here, we consider the

common characteristics of disruptive lp decay in

large and small (HT-2) tokamaks.

The DIILD tokamak_ experiment[16] reported

that disruptive lp decay includes two phases. In

the first, the plasma moves vertically without lp

decay and in the second. Ip Starts to decay and a

vertical force due to poloidal current is observed.

These are the same characteristics as phases I and

II shown in the HT-2 disruptions. However, no phase 111 is identified, although exponential lp decay

occurs in the reported waveform. Then, phase 111

also occurs in DIII-D.

The JET tokamak experiments did not identify

phases but many common characteristics can be drawn from the Harris report[171. The direction

of vertical movement changes during disruptive lp

decay. After this, Ip decays exponentially and T*

decreases to less than 100eV coinci,ding with the

change of plasma movement direction. In JET disruption, Td' is calculated to be 12ms (T* = 5eV)

and this value is consistent with the experimental

result. These characteristics are shared with the

HT-2 experiments. Then,we can say that phaseIII

occurs in the JET disruptive lp decay and T* is

roughly 5eV during the this phase, because phase 111

is a phase during which no closed flux surface is

present and plasma is cooled by the vessel wall

.directly.

5. CONCLUSION Characteristics of disruptive lp decay have

been studied experimentally in the Hitachi tokamak

HT-2. The plasmas studied were vertically elon-

gated and circularly shaped. The disruptive lp

decay occurred with three phases. During phase I,

large displacement of plasma position without lp

decay was observed. A rapid lp decay was observed during phase 11 and the decay rate was

almost constant with time. The eddy current distribution was like that of a shell effect which

creates a poloidal field to reduce the plasma

displacement. Phase 11 was observed in slightly elongated and high lp (> 20kA) circularly shaped

plasmas, which did not have strong plasma position

instability. During phase 111, Ip decayed exponen-

tially and no closed flux surface was present in the

363

I

j~ ;~:7 ' ~;~~~~~~~A~*#*

plasma area. The lp decay rates in phase II

depended on the plasma cross sectional shape, but

they did not in phase 111. The plasmas directly

touched the vessel wall during phase 11 and 111.

Then, the plasma position was maintained by the

forces of poloidal current and thermal pressure as

well as toroidal current. The poloidal currents

flowed in the scrape-off area and the vessel wall

during phase 11 and 111. The magnetic axis was

displaced from the plasma area to the vacuum vessel

wall between phase 11 and 111.

ACKN OWLEDG EM ENTS We would like to thank Drs. Doi, Ozaki, Oomae

and Murai for their encouragement throughout this

work.

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364