i ii~~=!~""""~~ ~~=~~" ~-.~~~~C

Measurement of Halo Current in the HT-2 Tokamak and Investigation of a Scallng Law

ABE Mitsushi, TADOKORO Takahiro, DOI Akira, NAKAYAMA Takeshi, OTSUKA Michio and NISHIO Satoshil)

Power & Industrial Systems R&D Division. Hitachi Ltd.

Hitachi 319-1221, Japan

1) Naka Fusion Research Establishment. Japan Atomic Energy Research Institute,

lbaraki 311-01 93, Japan

(Received 8 May 1997/Accepted 7 January 1998)

Abstract The halo current, which flows between the plasma and plasma facing components in a vacuum

vessel during disruptions, was measured in the Hitachi tokamak HT-2 and the scaling law of the magni-

tude was examined based on the balance of the electromagnetic forces. Electrode plates were placed

where they touched the plasma during the disruptions. A halo current flowed through the electrodes

and the electrode currents were measured by Rogowski coils. The measurements showed the followings.

(1) The halo current intensity IHL is large during vertical displacement event (VDE) with rapid lp decay

and high toroidal field BT. (2) The product of IHL and duration time increases with lp but have no de-

pendence on BT. (3) The halo current reduces the shell effect, destabilizing the plasma position. (4) A

scaling law, based on a force balance on the plasma, gives an approximate estimation of the halo current

magnitudes for various tokamaks.

Keywords: tokamak, disruption, VDE, halo current

1. Introduction

The next step in magnetic fusion research will be

experiments on a large scale fusion device like the

ITER (International Thermonuclear Experimental Re-

actor) [1]. The most important point in designing such

a large magnetic fusion device is to design a machine

which withstands the strong electromagnetic forces. The

most important electromagnetic force on the vacuum

vessel is that during a disruption including a VDE

(Vertical Displacement Event) [ 2] . In designing existing

tokamak, the force was estimated by calculating magni-

tudes of the eddy current on the vacuum vessel and in-

teraction with magnetic field. The eddy current is

induced by the rapid disruptive plasma current (Ip)

decay. However experiments on the JET tokamak

showed that the force on the vacuum vessel is not only

due to eddy currents but also due to poloidal current

which is known as an halo current [3]･ The current

flows between the plasma and the vacuum vessel. A va-

cuum vessel design must take into account the halo cur-

rent [4]. Then, experiments to understand the electro-

magnetic force due to the halo current are being carried

out in large tokamaks [5-9]. On the other hand, a small

tokamak has an advantage of easy modification of the

vacuum vessel. So we have carried out experiments on

the HT-2 to understand characteristics and scaling of

the halo currents, and present the finding in this paper.

Experiments to understand the characteristics of

disruptive lp decay were previously carried out in the

HT-2, by using magnetic analysis, which reconstructed

corresponding author~ e-mail: abem@ erl.hitachi. co.jp

49 1

j~ ~7 ･ ~~~~~~AD ~'j~~~--._~d~~

the poloidal field distribution from the measured mag-

netic field data [4,10,11] . These results showed that the

electromagnetic force due to the halo currents can be a

major force during a disruption. Now we discuss the

disruptive plasma current decay, especially the force

balance on the plasma taking into account of halo cur-

rent, using the magnetic analysis at first. Then, we de-

scribe halo current measurements. Finally, we discuss a

scaling law of the halo current magnitude.

2. Experimental Device HT-2 Experiments were carried out on the Hitachi To-

kamak HT-2, which is a small tokamak with parameters

listed on Table 1. Figure I shows the poloidal cross sec-

tion of HT-2. There are two types of poloidal field coils

(PFCs). One is the HY-coils. They (HYI to HY8) are

multivariablly controlled poloidal field coils HPFC

[ 12] . The other is single functional PFCS such as hori-

zontal field coil (DH-coil), rapid control horizontal

field coil (AH-coil) and biasing coil (B-coil) for iron

core magnetization. The power supplies are transistor

choppers which are operated by up to 5 kHZ pulse

width modulated (PWM) pulses. The choices of con-

nections between HY-coils and the power supplies are

rather arbitrary. In this experimental series, two kind of

connections were used. Their plasma cross-sectional

shapes are shown in Fig. 2. Figure 2(a) is a plasma cre-

ated by a hybrid type poloidal field coil (A-connec-

tion). Figure 2(b) is a plasma created by B-connection

which is useful to create a plasma with high elongation.

In the A-connection, usually six HY-coils (HY2 to

HY7) are used for a plasrna discharge with six inde-

pendently controlled power supplies. Each coil current

can be controlled independently and variation of the

current distribution on the HY-coils can change the

index of vertical field nv = -(R/Bv) (aBvlaR) (then,

the plasma elongation) and plasma triangularity, as well

Table I Parameters of HT-2.

1998~~ 5 ~]

0.6

o .4

E O,2 ~.

N c:

o ~'

co o o a co ~2 ~:s

L (D > ~O 2

E

~: o) a)

l:

-0.4

-0.6

o.o

Fig. 1

02

ol

o

-o 1

-o.2

0.2 0.4 0.6 0.8 1 .o Maior radius R (m)

Poloidal cross section of the HT-2 tokamak.

(b)

~~~~~~

o 25 o 45 o 65 o 25 o 45 o 65 Major radius (m)

Fig. 2 Plasma cross sectional shapes with vertical elonga-

tion in HT-2 experiments. (a) Plasma created by 6

independent PFCs. (b) Plasma created by independ-

ent OH coil and 8 PFC driven by 4 power supplies.

as plasma positions (vertical position Zp and major

radius position Rp). In the B-connection, eight coils

(HYI to HY8) are used with four independently con-

trolled power supplies. The degree of freedom is less

than the A-connection and triangularity is not controll-

able.

The HT-2 is well equipped with poloidal magnetic

field sensors, which are 15 flux loops, 36 magnetic

probes for poloidal field measurements and two Ro-

gowski coils for plasma current measurements. Among

them, one Rogowski coil and 12 magnetic probes are

492

~~~~5tt;"--'1~~'~~FB)~ Measurement of Halo Current in the HT-2 Tokamak and Investigation of the Scaling Law F~ ~~ , EEI~"p~f4~

placed inside the vacuum vessel. This arrangement

allows sensing of the eddy currents on the vacuum

vessel wall flowing in the toroidal direction. Recon-

struction of the poloidal magnetic field is carried out

using two techniques. One is a technique described in

Refs. [ 10,13] and based on the algorithm developed by

Swain et al. [14], but our reconstruction includes the

magnetic field due to eddy currents on the vacuum

vessel [13]. The other is a technique based on MHD

equilibrium computation and the algorithm developed

by Lao et al. [15]. However, our reconstruction con-

tains the eddy current and poloidal field due to TFC

error field [16].

While the iron core produces a significant mag-

netic field and can not be ignored, the magnetic field

can be calculated assuming a circular cross section with

infinite length. The accuracy of this assumption was

confirmed by an experiment in the former Hitachi To-

kamak HT-1 [17].

Experiments were carried out with vertically

elongated plasmas, which vertical position Zp Was sta-

bilized by an active feedback control. However in order

to trigger VDE, the control was stopped during a dis-

charge. Then, the VDE developed and we measured

halo currents.

Electrodes had been placed in the vacuum vessel,

facing the plasma, in order to measure the halo current.

The placements of the electrodes and Rogowski coils

on the poloidal cross section are shown in Fig. 3. Six

toroidal rows of electrodes were placed and bottom two

rows of electrodes had Rogowski coils to measure halo

Voltage measurement

[t_~ ~} vacuum vessel

ll

currents. Top two rows were insulated electrically from

the vacuum vessel and voltage between these electrodes

could be measured. Each row was divided into four

electrodes in the toroidal direction, and halo currents

were measured in every 90 degrees toroidal section on

bottom two rows. Electrodes numbered 1,3,5,7 were

placed on the small major radius (R) row and those

numbered 2,4,6,8 were placed on large R row. During

the VDE in the experimental series, plasma position

was tuned to disrupt between the bottom two electrode

rows as shown in Fig. 3. In order to optimize the

plasma position, the vertical field offset was changed

shot by shot. Then, the electrode currents IEI to IE8

were measured. The halo current intensity IHL may be

defined as integrated value on plasma facing wall. How-

ever, total electrode currents as shown by the equations

below are used in the following parts of this paper,

IEI = IEI + IE3 + IE5 + IE7 , (1)

IEO = IE2 + IE4 + I + IE8 , (2) E6

where subscripts show the electrode number for identi-

fication. Usually, we take IEO as IHL in the following

part of this research. The plasma positions at which

plasmas disrupted were confirmed by the magnetic ana-

lysis.

E E, ~r cT)'

co

3. Characteristics of Halo Current in HT-2

Since our final objective of this paper is to obtain a

scaling law of the IHL, we discuss the characteristics

necessary to understand the law. The experimental data

discussed in this section are not only measured halo

current (IEI' IEo) but also information obtained by the

magnetic analysis in the HT-2.

Electrode ¥l

L (Insulated) l

¥¥¥ // ~ i h'/

1: '~_-/ ¥ /¥/¥

~¥

--~ /

If ¥l 1 )l /

!

I

l

plasma I

~

,t

'RO owski coil

Fig. 3 Placements of electrodes in HT-2

for halo current measurements.

.

.

-L

vacuum vessel

3.1 Force balance and results of magnetic analysis

A tokamak plasma has not only toroidal current

but also poloidal current component, and the plasma

experiences a vertical electromagnetic force FzP de-

scribed by,

FzP = FzPpl + FZPE + FZPPFC (3)

where FzPpl is due to interaction between toroidal field

and poloidal current, FZPE is due to poloidal field of

eddy current on vacuum vessel and FZPPFC is due to po-

loidal field of PFCs. The reaction force against FZPE is

on the vacuum vessel and

FZPE ~ (4) . -FZVE

where FZVE is a force on vacuum vessel due to eddy

493

j~ ;~:7 ･ f^k-~~l~~~:~~--**#< ~~74~~~i~ 5 ~* 1998~~ 5 )~

current induced by plasma movement. The FZVE (or

FzPE) and FZPPFC can be obtained from the toroidal cur-

rent calculated by magnetic analysis based on measured

poloidal field data [4,10,11]. However, since the

plasma is in equilibrium condition, the FzP is estimated

to be roughly zero and the FzPpl can be calculated by,

FzPpl = =(FzPE + FzPPFC) = Fzv* _ Llz ' ' ~ r' PPFC (5)

Figure 4 shows results of magnetic analysis for a

VDE with plasma cross sectional shape of Fig. 2(b).

Time evolutions of lp, Poloidal field Bp at poloidal

angle 270 degrees, Zp as current center, vertical forces

on plasma and vacuum vessel FzPT, FZVT are plotted in

Fig. 4(a), and Fig. 4(b) shows flux contours during dis-

ruptive lp decay. The superscripts P and V means that

the forces are acting on the plasma and vacuum vessel

respectively, and superscript T means that the forces

are calculated from toroidal currents only. The forces

FzPT, FZVT are obtained by magnetic analysis and the

forces due to halo currents are not included, i.e., FZPT

FZPE + FzPPFc, and FZVT _ FzPpl is the real force on va-

cuum vessel. Since no toroidal current other than eddy

current flows on vacuum vessel, the FZVT is equal to

FzVE' The plasma current flows in the dotted area. Two

Bp's are for inside (IN) and outside (OUT) of the va-

cuum vessel. In normal magnetic configuration (before

18.6 ms), the Bp's are positive. However, during VDE,

the signals change their signs, showing that the mag-

netic axis moved out of the plasma region after 18.8

ms .

As discussed in Ref. [4], the disruption occurs

with two lp decay phases. During the first decay phase,

lp decays roughly constant decay rate (dlp/dt) and dur-

ing second decay phase it decays exponentially. Total

decay time is around I ms in the HT-2. During the first

phase, the magnetic axis exists in the plasma and hot

core plasma still exists in the closed flux surface as

shown in Fig. 4 upper figure, while the scrape off layer

(SOL) current develops. Entering the second phase,

magnetic axis moves on the vacuum vessel wall and all

(a) 40

30

< ~1 20 ~ *

10 plasma current

O

(b)

0.1

IN

0.03

~ --~--~ ~ ~-H - - * ~ OUT O ~~' ~ o* cO

-0.03 poloidal field (e=270')

. 1~

lb,~..,_

/-h E ~l N +J O ~: o)' a)

I -0.1

E~ O o ~ ~ -4

-8

- O Z ~ h -200 ,L

N LL _400

- O Z ~ ~N 200

LL -400

18 19

-0.2

0.1

~ E ~ N +' O Jc o)

o I -0.1

-0.2

1 8.4ms

'l

' ' :_1~ : . : :;'-

' '/'~ ' ' ' I ""' ' '/'~'~'1~1"" '¥

. * * . ¥' ' '¥' '

/' "r:~:~:~1~:~¥' : :¥' '

' '/' ' '*' ;¥" ::!: :~ ;/' "(:;r'++4+' h ' ~. ,¥' t

' t j' :/:;1 : :*.*: ~~+:¥:¥ ¥ 1'¥::¥;¥;t

'!' ; ' "' :'r' ;¥'."~: . .1_ . ' '7,,.f"' ..:;~.,~. ~~: { :f ' ~ ~ ~

:/: ~{i{

" ; /'/'1'i' :¥: i¥~~:¥:¥a*~*' ' I "',f':/: : ; )

' ' : ~ : :-: :f~'77tT:)~:., ~ ' ' i~ * "¥' ~'~~t*' '+

18.8ms

: r'

"::l . .1F*'

' 'l'

'/' ' ' '/~~' ' ' ' l¥ ' ' ' ' ;¥" I :¥;

':/

':: : :~ : : '

~~: : : [¥{ : :¥:

' ' [ ~: : :

¥ " ' ' l¥{ : :¥; ;¥:

..¥""""" ~ ' ' I : :¥: :¥; '¥

;" ' ' I'~ : : ' :

[

Fig. 4

0.28 0.38 0.48 0.58

Time (ms) MaiOr radiuS R(m) Typical VDE in HT-2 analyzed by magnetic analysis. (a) Time evolution of p]asma current /p and forces. FZPT and FZVT

are vertical forces acting on plasma and vacuum vessel calcu]ated by toroidal current only. FzPPI and Fzvpl are vertical

forces acting on plasma and vacuum vessel due to po[oidal current. (b) Magnetic surfaces during disruptive /p decay.

Time 18.4 ms has magnetic axis during the first phase and time 18.8 ms has no magnetic axis during the second

phase.

494

~~-7~~"~~~^)~ Measurement of Halo Current in the HT-2 Tokamak and Investigation of the Scaling Law ~~**"~, EEIF~"~f 4ti~

magnetic surfaces in the plasma are open as shown in

Fig. 4 Iower figure. Then, plasma is cooled down in-

stantly to several eV temperature. During the first

phase the decay rate dlp/dt depends on the poloidal

magnetic field configuration, while during the second

phase no explicit dependence is observed. This is be-

cause, during the first phase the plasma moves and the

motion depends on the poloidal configuration and a

rapid motion is related to a rapid lp decay [4] ･ The

highly elongated plasma has a rapid lp decay in the first

phase. The second phase has no magnetic axis and no

movement is observed for all kinds of initial plasma

shapes and the decay time constant of the exponential

decay has no dependence on the poloidal magnetic

field configuration.

The arrows on Fig. 4(a) are forces due to the halo

current calculated by Eq. (5). Estimated actual electro-

magnetic forces on the plasma and vacuum vessel are

shown by dotted lines. Assuming the current path

length on the vacuum vessel is 0.12 m which is consist-

ent with magnetic analysis, 3.75 kA halo current is esti-

mated from BT = 1.0 T and 450 N force from Fig. 4.

This current corresponds to 90/. of initial plasma cur-

rent lpo = 42 kA. According to the magnetic analysis

results, following halo current characteristics could be

understood.

(1) Halo current and total force become peak values

at start time of the second phase.

(2) Halo current is large during lp decay phase.

(3) Halo current flow direction is same as TFC current

direction on a poloidal cross section.

A tokamak should be designed to withstand the

peak electromagnetic force, which is observed at the

start of the second phase. The force on the vessel FZVE

calculated by toroidal current is roughly zero at the

start of the second phase, at which time FzPpl has its

peak value. This is consistent with the fact that during

the second phase, no significant motion of plasma cur-

rent center is observed. The force balance at this time

is,

FZPpl = _FZPPFC (6)

meaning that, the PFCS push plasma on the open flux

surface through poloidal magnetic field, while the

plasma is supported by vacuum vessel through the halo

current. The fact that the largest FzPpl is observed at the

start of the second phase means that the open flux sur-

face plays a major role for the halo current. We can

assume that the path length on vacuum vessel in

poloidal direction is equal to Al (= 1.0ap roughly, the

ap is a plasma minor radius) and FZPPFC is equal to

-2JrRpB~FClp. Equation (6) become,

Al IPEAKBT = ~2JTR BPFClpS , PR HL

(7)

where superscript s of lpS means the lp Value is at start

of second phase. This force balance shows the IHPLEAK is

proportional to B~FC which is a radial component of

equilibrium vertical field due to PFCs. Since B~FC is

equal to -nvB~FCZp/Rp, where nv is a decay index of

the vertical field, it can be understood that a VDE of

high I nvl (high elongation) has a large halo current. We

discuss this characteristics by direct poloidal SOL cur-

rent measurements in the following section.

3.2 Results of halo current measurements

We have discussed halo current characteristics

from magnetic analysis based on poloidal magnetic field

measurement in the former section and in this section

we will discuss the characteristics by the direct

measurement of the halo current, which was measured

as the summation of the electrode currents. Typical

time evolutions of lp, halo current IHL (= IEO : in the

following part of this paper, a waveform of IHL is rep-

resented by IEo), electrode currents (IE1' IE2), Zp and

visible light intensity (CIII, ionization energy is 24 eV)

are plotted in Fig. 5. Positive electrode current means

that the halo current is flowing from the plasma

through the electrode into the vacuum vessel. Since the

electrode currents (IE1' IE2) are roughly same magni-

tude with opposite direction, we believe that the plasma

disrupted at radial position just between these two elec-

trodes as shown in Fig. 3. From these measured data

and total electrode current IEO thought to be equal to

IHL, following facts can be read.

(1) The halo current flows only during disruptive lp

decay.

(2) The halo current takes its peak value at start time

of the second phase.

(3) The halo current flows toward the same direction

as the TFC coil current on a poloidal cross-section.

Considering the flux contour on Fig. 4 and electrode

placement on Fig. 3 , this shows that halo current flows

along magnetic force lines.

(4) Step increases of electrode currents are observed

in coincident with positive lp spikes, which occur at

same time as negative loop voltage Vl spikes. This

makes plasma current distributions flat and the plasma

current flow in the scraped off layer.

(5) Oscillating signals are observed in first phase.

These oscillational signal characteristics are considered

to be representing the MHD oscillation in the plasma.

However, since the typical oscillating frequency is

495

j~ ;~7 ･ ~~~~~~Arl~"~~~~-pd~~ 1998~P 5 ~l

~ ~ ~ o*

~ ~ J I

20

10

o

_ o O uJ c, -1 .o

~ O.5

UJ O

~ ~ c¥:

UJ

o

-0.5

O

:) -4 ~ I

Z

-< 2 1 ,L N O

21 .6 22.4 23.2 24.0 Time (ms)

Fig. 5 Typical downward disruption with halo current in

HT-2 at BT = 0.8 T. P[asma current /p, halo current

/H~' electrode currents /E1･ /E2. vertical plasma posi-

tion Zp and light intensity from CHI(C2+) are plotted.

The vertical dashed line is a time that the second

phase (ll) of disruptive /p decay start. The first

phase is shown by I. Positive electrode current

means the current flows from plasma into vacuum vessel.

40

< ~:: 2C ~~

~~ O ~ O J I - -1 <~ 0.5

Lu O ~ -0.5

< ~ 0.5 ~-~J O

-0.5

<~e,+_ 0.5

(c' O UJ

~ -0.5

<x ,0.5

~ O -O 5

Plasma current 21 27 BT=0.6T

higher than 50 kHZ in HT-2 and a few kHZ in large to-

kamaks, such short force pulse can be ignored in the

mechanical design.

The results (1-3) are consistent with the results

from magnetic analysis (Fig. 4), in which electromag-

netic forces were discussed. Other than electrode cur-

rent waveforms, the intensity of Clll is decreased in the

second phase, suggesting that plasma is cooled down to

a very low temperature, which is consistent with the

magnetic analysis again, i.e. no closed flux in the

plasma during second phase. According to these results

of section 3.1 and 3.2, we will pay attentions on the

halo current at the start time of second phase to

examine the IHP~AK-

3.3

and

Dependence of halo current magnitude on toroidal field and plasma current

Halo current is suggested to be affected by BT, IP

B~FC, as discussed on section 3.1. Equation (7)

Fig. 6

Halo current

o 6ms 0.6ms Time (0.3ms/div)

Comparison of two VDES with different BT' (a) Left

VDE is with BT = 0.6 T. (b) Right VDE is with BT = 1.1

T. The halo current is large with high BT and high

frequency components are stabilized at high BT.

suggests that the IHPLEAK is proportional to these parame-

ters. However, the plasma minor radius ap is considered

to be a function of lp and BT through the safety factor

q,

q = 2gTap2BT/ (/loRlp) , (8)

and at start of lp decay, the q is at roughly the same

value of q = 3. Then, IHPLEAK may not be simply propor-

tional to the parameters. Following part of this paper

discusses the relation of halo current with these param-

eters.

3.3.1 Dependence on the tOroidal field Strength BT

The electrode currents during VDE were measured with changing BT from 0.6 T to 1.1 T. The

results are shown in Fig. 6, which shows waveforms of

halo current IHL (= IEo), four electrode currents (IE2,

IE4, IE6, IE8 : summation is IEO as Eq. (2) ) and lp at BT

= 0.6 and 1.1 T. The lp decays in 0.6 ms in both VDE.

Large BT increases IHL, while it decreases duration time

tHL. Another feature is that the large BT suppresses the

oscillational signal amplitudes.

The IHPLEAK and duration time tHL are plotted

against of BT in Fig. 7 . The tHL is defined as the period

that halo current is larger than half of the peak magni-

tude. The IHPLEAK increases as BT become strong, while

tHL becomes short.

Equatron (7) suggests that IHPLEAK decrease with BT

increment, as far as the right side of the equation and

496

~~~~5t~~*-'-1~~'~~EE~~ Measurement of Halo Current in the HT-2 Tokamak and Investigation of the Scaling Law p~ ~~ , EEIF'~"~f{~

~2 ~_

~

~ a'

(Q

> ~: 1 (U (1)

~ ~ c (1'

::l

o ~2 (o

:C: o

><

- - tHL x

x x

e

e

IHLPEAK e

o

X'~ .~ x

0.6 0.7 0.8 0.9 i.O i 1 Toroidal fi~ld strength BT(T)

0.5:

0.4.

031 ~~ E_ JI

0.2* -

o. 1

o

Dependence of halo current on toroidal field strength BT. The halo current has a positive de-

pendence on BT.

becomes small with increasing BT With constant q = 3

and this results in large Zp displacement at start of the

second phase and large B~FC in Eq. (7). This fact can

change the BT dependence of the IHPLEAK. For weak BT,

the lp starts to decrease when vertical displacement and

B~Q are still small, meaning that the destabilizing force

is weak, plasma movement is slow and the tHL is ex-

pected to be long.

Fig. 7

A I are constant. However, this idea conflicts with the

experimental results, which can be explained as follows.

The lp decay starts with roughly q = 3 and the plasma

cross sectional area is considered not to change much

during lp decay as Fig. 4. The halo current flows on the

SOL and the flow is on the open flux surface during lp

decay along half circular shaped magnetic surface at

about r = 0.5 ap (ap : at start of lp decay). The ap

3.3.2 Dependence of halO Current on the ini-tial plasma current

The VDE experiments with lpo = 25, 20, 15, 10

kA were carried out in order to obtain the relation be-

tween lp and IHL and the results are shown in Fig. 8 .

The decay rates dlp/dt's of the two phases are roughly

same for these VDEs, except lpo = 10 kA case in which

the first phase is not clear. The VDES With lpo = 25, 20,

1 5 kA have peak IHPLEAK of roughly I kA, while lpo = 10

kA VDE has very small IHPLEAK and large lpo VDE has

long tHL. The parameter IHPLEAKtHL can be roughly ex-

pressed by,

IHPLEAK tHL = 0.037(l~ - 8 [kA]) [AS] (9)

The reason why halo current is small at ~ = 10

40 -2 s OT O.= Plasma current

21 29

< 20 ~ ~ O

r'

-< O ~:

~ -1

40

< ~･:

~ ~ 20

_ o < ~ J o ~

l -1

lp0=25kA

1 ms

-2 s OT O lp0= I OkA

21 32

1 ms

Fig. 8 Dependence of ha]o current on plasma current ~. The peak current does not depend on ~ at ~ > 15 kA but product

of peak current and duration time has positive dependence on ~.

497

j~ ;~~7 ･ ~~~~~i~~~~~~~-"~.*.

kA and expected to be zero at around lpo = 8 kA, can

be recognized as follows. The halo current considered

to be originally a poloidal component of plasma cur-

rent, which component is small at a condition of poloi-

dal beta fip = 1.0, at which plasma kinetic pressure P

and poloidal magnetic pressure B~/(2l/o) are balanced.

Such low lp Plasma can be at this condition during

VDE. For example, electron density n* = 6XI019 m~3

and electron temperature T* = 7 eV give plasma pres-

sure of P = 78 Pa, while B~/(2/lo) was 78 Pa at lp = 7

kA assuming ap = 0.1 m. We consider that the reason

why halo current is small at lpo = 10 kA is that poloidal

component current in plasma is small.

'~,

< ~: ,,'~,

~

15

O

(a)H ~2 s OT r'o'= '997 O. 24ms BT::1. IT

~ plasma current I fp i =51 MA/s

'~,

< !~ ¥j J I

o Halo current

-800 (Large R side)

~ <!~ 75

~ CL

'~ < ~: *~, J I

'~ < ~( ¥l CL

'~,

< ~: ,~' J I

O

o

-800

15

o

O

-800

O. 6mS

Fig.9 Halo currents in three different d/p/dt VDEs. The

halo currents have strong invert dependence on decay time of /p. The plasma movement velocities just before /p decay starts are I dZpldtl = 72 m/s, 50

m/s and 29 m/s {from top (a) to bottom (c)} respec-

tively and have a strong correlation with lp decay

rate and halo current.

~~74~~~~ 5 ~~+ 1998~j~ 5 ~J

The VDES in Fig. 8 had roughly same values of

dlp/dt. Then, we tested the IHPLEAK, changing the nv

{=-(R/Bv) aBVlaRJ and the dlp/dt at lpo = 15 kA.

Figure 9 shows the three VDES With different dlp/dt

rates. Time evolutions of lp and IHTL for three VDES

with different dZp/dt and dlp/dt are plotted. From

these VDEs, the tendency that rapid lp decay has short

tHL and large IHPLEAK, can be read. These VDES have dif-

ferent tHL due to variation of nv, showing that slow lp

decay VDE has small halo current and slow plasma

movement. This is consistent with large tokamak ex-

periment of Ref. [18] .

3.4 Relation between shell effect and halo

current Discussion so far shows that the IHPLEAK is roughly

proportional to I dlp/dtl and I dZp/dt]. This is consist-

ent with Eq. (7), because large I nv I gives plasma a

large vertical destabilizing force and rapid plasma

movement. However, rapid plasma movement gives a

large shell effect to stabilize plasma position, while Fig.

4 has shown that shell effect is small at time of peak

halo current. Why the shell effect becomes less effective

during VDE should be recognized.

Figure 10 shows relation between shell effect and

vertical force FzPpl due to halo current calculated by the

magnetic anlysis and Eq. (5). The eddy current compo-

nent IBHI which produces horizontal field is taken as a

parameter of the shell effect. The magnetic field con-

figurations and lpo (20 kA) were roughly same and BT

was 0.8 T. The black solid circles are data for the insu-

lated electrodes and crosses are data for conducted

electrodes. The IBHI = 5 kA corresponds to B~FC =

3.5xl0-3 T and gives plasma repelling force from wall

Z ~ N LL

i50

100

50

o

)<

x

X

X X

x

x

- IHL~FlkA

e o x><

Fig. 10 -1 4 5 1 3

O 2 IBHI (kA)

Relation between force due to halo current and shell effect eddy current at start of the second

phase during /p decay. Crosses (x) denote normal

VDE and closed circles (e) denote suppressed halo

current VDE.

498

Measurement of Halo Current in the HT-2 Tokamak and Investigation of the Scaling Law F~~"~, EEIF'~'=~?4til

of 1 10 N at lps = 13 kA. The data points are roughly on

the line from IBHI = O kA, FzPpl = 100 N to IBHI = 5

kA, FzPpl = O N. This means that forces from shell effect

and halo current are in a tradeoff relation. We claim

that the halo current decreases the shell effect and ac-

celerates the plasma motion and lp decay.

There are two reasons that decrease the shell ef-

fect. One is that, Iarge IHL (or FzPpl) means that the SOL

current is large, and the plasma current in the core

plasma is relatively small, while the current which is ef-

fective for the shell effect is that in the core because the

current position is moving. The other is that the halo

current is the plasma current which penetrates into the

vacuum vessel and the current on the vessel is in oppo-

site toroidal direction of the shell effect. The halo

current produces a stabilizing force on SOL plasma,

however it has no effect on the core plasma of the first

phase. The core plasma can be stabilized by the shell

effect, on which the halo current has no effect. The

movement of the core plasma, then lp decay is faster

with halo current than without it.

The maximum halo current is observed with IBHI =

O kA. This is a condition for Eq. (7) and consistent

with Fig. 4. This fact can be a help to discuss the halo

current intensities in tokamaks.

Figure 1 1 compares lp decay characteristics of

VDE on insulated electrodes and conducted electrodes.

The lp decayed in 1.6 ms on insulated electrodes (Fig.

1 1(a)), while 0.8 ms on conducted electrodes (Fig.

11(b)). Insulated electrodes are placed at top as illus-

trated in Fig. 3 and VTL Was measured there, while halo

current was measured at bottom. The differences in

waveforms of VTL and IHTL between Fig. 1 1(a) and Fig.

1 1(b) are due to the direction of VDE or conductive

condition of electrodes. It can be clearly understood

that reduction of halo current results in slow plasma

movement and slow lp decay during VDE.

4. Formulation of Halo Current Scaling Law

The experimental results discussed in the former

section can be summarized as follows.

( 1) The characteristics of halo current estimated from

force balance based on magnetic analysis are consistent

with directly measured halo current.

(2) Peak halo current IHPLEAK is observed at start of the

second phase, at which time, electromagnetic force due

to poloidal field by PFCS are balanced with force due

to halo current and shell effect is weak.

~ <~ 20

~ o

- 600 < H~ O J -:: -600

~> 30 ~ >~

,~ > ,~' J H >

CO

300

O

-300

~I

8

~ 4 E o ~ ONCL

-4

-8

Fig. 1 1

Time 2ms Time 1 ms

Plasma current lp decay and plasma vertical position Zp (O) movement during VDE to insulated electrode and con-

ducted electrode. Halo current and e]ectrodes currents were measured at bottom and top respectively. The /p decay

rate and measured /HTL, VTL values depended on VDE direction. (a) Upward VDE toward insulated electrodes which is

iocated at top. (b) Downward VDE toward conducted eiectrodes which is located at bottom.

499

j~ ;~7 ･ ~~~~~ki~~~:A*--_~*~ 1998~j~ 5 ~j

(3) A VDE with rapid plasma vertical movement and

lp decay has large halo current, which is due to large

destabilizing force.

We discuss a scaling law for halo current with

above experimental results. The term (2) supports force

balance equation of Eq. (7), which we use to get the

law in this paper. The balance is shown in Fig. 12 sche-

matically. Plasma cross sectional shape during normal

operation is shown by a dotted line and the solid lines

show flux surfaces at start of the VDE second phase.

The force FZPPFC which pushes down the plasma, while

FzPpl pushes up it. These two forces are balanced each

other in peak halo current condition at the start of the

second phase.

4.1 Discussion on scaling law of halo current

magnitude As discussed so far, Eq. (7) is a basic scaling law

for the halo current. However, it is necessary to change

such parameters as B~FC and lp into machine parame-

ters like maj or and minor radii of the plasma or vacuum

vessel. Since we are considering the force balance at

start time of the second phase and the plasma area on

/ ¥ //p~ma ~fore VDE ¥¥

Current oenter before VDE

X

E

poloidal section does not change much during VDE,

the plasma current center position Zp is approximated

by,

~

Plas

~

FHL ' ll

><C ent c

/

~PFC ~

current

-'-'F IHL

;~* C::l

~:

A model for a halo current scaling law. Forces due

to halo current and PFC fie!d are balanced at start

of the second phase in disruptive /p decay. Scrape-

off plasma current is flowing in dashed area. Forces due to eddy current can be ignored at this

timing.

Zp = -(hv a ) (10) where hv is a vertical minor radius of the vacuum vessel

and ap can be understood a distance from plasma

center to vessel wall, as shown in Fig. 1 2. Using the

decay index of the vertical field, B~FC can be expressed

by,

BPFC = _nv(Bv/Rp)(hv ~ ap) (11) R

In this equation, the vertical field Bv can be easily cal-

culated for lpo by Shafranov's equation. The plasma

current lp in Eqs. (10) and (11) is that at start of the

second phase, which is estimated to be,

lpS = IpoQv/(Qp[5 eV] + Qv) ' ( 1 2)

at maximum [ 1 1]. The largest lpS is calculated to be 0.7

lpo in the HT-2 because of Qp(5 eV) = 6 m~ and Qv =

14 m~~. As Al is assumed to be about ap and using Eqs.

(11) and (12), the force balance Eq. (7) at start time of

disruptive lp decay second phase, yields IHPLEAK of,

IHPLEAK = 2JcnvBvlpS(hv ~ ap)1(ap BT) (13)

where ap is related to q by Eq. (8), and we adopt values

of just before disruptive lp decay for ap and around q =

3, i.e. ap is calculated by Eq. (8) with lp = Ipo. Since the

Bv is a function of lpo, the peak halo current IHPLEAK of

Eq. (13) is a function of BT and lpo. Figure 13 shows IHL

as a function of BT With a lpo of 20 kA, which is consist-

ent with the experimental results of Fig. 7. The IHPLEAK'S

are calculated with three q values of 2.5, 3.0 and 3.5.

Equation (13) represents the positive dependence on

~ ~ J :C:

i. 5

l. O

o. 5

Fig. 12 o

A

~

A

x

--~--~;-*=e-

A X

q L 2.5 1.0

3.5 O.75

3.0 1.0

A X

A X

lp0=20kA.

ap0=0. I m

nv=-1 .9

A X

Fig. 13

o. 6 o. 8 o. 9 l. o o. 7

BTCr)

Simu]ated haio current peak vaiues against toroidal field strength BT for HT-2

means Al/apo.

l. l

plotted

The L

500

Measurement of Halo Current in the HT-2 Tokamak and Investigation of the Scaling Law FD! ~~~ ,

Q EHF'~'=~f 4L~

BT and we can conclude that Eq. ( 1 3) roughly explains

the experimental results with around q = 3, claiming

that the halo current magnitude can be explained by the

force balance on the plasma.

The scaling law of Eq. (13) was adopted to other

tokamaks. The number nv is estimated from geometri-

cal magnetic field configuration as

nv = ~(R/Bv)(aBvlaR) = -(R/Bv)(aBR/ aZ)

~~ RBR/(BvhNL) , (14) where we assume that the plasma has a divertor con-

figuration and null point is at Z = -hNL. In this equa-

tion Bv, BR are poloidal magnetic fields due to PFCS at

the vacuum vessel center and null point respectively.

The hNL is a vertical distance from magnetic axis to null

point of poloidal field and is approximately equal to hv'

Since the BR is canceled by the field due to plasma cur-

rent at the null point, we use BR = /40lpo/(2Jthv) at Z =

-hNL. The Zp at start of the second phase is -(hv ~

ap). Assumption of linear dependence of BR on vertical

position yields BR = /lolpo(hv ~ ap)/(2Jth~) at Zp =

-(hv ~ ap). Then, FZPFC is,

FZPFC = /loRplpOlpS (hv ~ ap)/(h~) .

and halo current is

IHPLEAK = /loRplpOlpS (hv ~ ap)/(apBThv2)

(15)

(16)

where ap is a minor radius with q = 3 with lpo and this

equation gives halo current magnitude of plasma with

null point.

Table 2 shows scaled halo currents for several to-

kamaks, where the lpS was assumed to be lp0/2. The

scaled IHPLEAK'S are consistent with experimental results

for tokamaks other than ITER. Then we can say that

the scaling law of Eq. (16) can provide a good estima-

tion of the IHPLEAK for various tokamaks' VDES and the

scaling law is useful equation for estimation of halo cur-

rent magnitude. This scaling law gives 3.1 MA halo

current for ITER and the magnetic force is estimated to

be 64 MN. In the Table 2 estimation, Iarge uncertain-

ties are due to the uncertainty of lpS. We assume that lps

is lp0/2 for all tokamaks in Table 2 estimation. However

our experimental results showed that lpS is small with

low Qv [11]. Then we can say that low Qv tokamak

like ITER is expected to have a smaller halo current

magnitude than the table 2 values.

5. Conclusion In order to examine characteristics and a scaling

law of halo current which flows between plasma and

vacuum vessel, an experimental study of force balance

on plasma and halo current measurements during

VDES Were carried out in the Hitachi Tokamak HT-2.

The former was based on magnetic analysis using

measured poloidal magnetic field data and the latter

was based on the direct measurements using electrodes

facing the plasma. The following findings were ob-

tained.

(a) The halo current becomes its peak value at start of

the second phase of disruptive lp decay.

(b) The peak current of IHL is large in high toroidal

field BT and in rapid lp decay VDE.

(c) The product of IHL and duration time increases

with lp but had no dependence on BT.

(d) The halo current reduces the shell effect, destabi-

lizing the plasma position.

(e) The lp decay rate can be reduced by insulated first

wall.

Table 2 Estimation of halo currents using the scaling law.

501

~~74~~~~~ *o =~. 1998~~ 5 ~

(D At the time that halo current takes its peak value,

the electromagnetic force on plasma due to PFCS is bal-

anced with force due to halo current.

Following the experimental results, a scaling law

based on the force balance of plasma was proposed.

The scaling law gives approximate estimations of the

halo current magnitudes for various tokamaks and pre-

dicts 3.1 MA halo current with 64 MN vertical force

for the ITER.

Acknowledgments The authors thank Dr. Yoshino and Dr.

of JAERI for fruitful discussions.

Neyatani

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502