J. Plasma Fusion Res. SERIES, Vol. 3 (2000) 489493

Helicity Injection Experiment in the slNp rokamak
BHATTACHARYYA Krishnendu and RAy Nihar Ranjan*
Plasma Physics Division, Saha Institute Of Nuclear Physics, I/AF, Bidhannagar, Calcufta-700064 (India)(Received: 18 January 2000 / Accepted: 7 April 2000)

Abstract
The current drive or sustainment in magnetized toroidal resistive plasmas can be thought of as a"balance" between helicity injection and dissipation. In the present work, the mechanisms of the"balance" in the fluctuating magnetized resistive plasmas of the SINP tokamak, have been studied
experimentally. The result shows that the oscillatory vertical magnetic field and oscillatory plasmas'
velocity in a definite phase relationship causes the balancing effect between helicity injection anddissipation and thus sustainment of plasma current for a longer period of time has been observed in theresistive plasmas of the SINP tokamak.

1. Introduction

rapid penetration of skin currents induced at the plasmaedge. There is ample experimental evidence that such a

Recently there has been considerable interest in theidea of driving current in various fusion experiments byflux conversion mechanism is present in the RFP's andis responsible for maintaining the reversed state [4-5].
This mechanism of flux conversion is not studied verymeans of oscillating current drive helicity injection [131. The method originally proposed for RFP's by Bevir

and Gray [1] and called F-0 pumping, involves oscillat-

well experimentally in a tokamak plasmas accompanied
by fluctuations, although there are attempts to drive current (externally) in a tokamak by oscillating the toroidaling the current in the ohmic heating circuit and in thetoroidal field circuit in a definite phase relationship. Essential to this proposal is the idea that magnetic helicity

and poloidal fields [6] (AC helicity injection) or by injecting magnetized coaxial plasma gun (Spheromak in-(K; in the plasma, which is closely related to the amountof plasma current sustained in a magnetized plasma, decays resistively as the current decays and by transporting helicity flux into the plasma, compensation ofhelicity loss can be made and the plasma might be indefinitely maintained close to its original state and thus
helicity injection provides possible means of current
drive in resistive plasmas. Since the magnetic helicity(K) is a linkage between toroidal and poloidal magnetic
flux, therefore in a magnetically confined toroidal plasmas, the current drive or current sustainment can bethought of as a balance between helicity injection andhelicity dissipation. As a mechanism, for the process of
this "balance", the fluctuating magnetized plasma is as-jection), into the Encore tokamak [7]. For transporting
helicity flux into the resistive plasmas, it seems that confining magnetic field is to be generated partially byplasma fluctuations within the plasma as an effect ofhelicity injection [4] and this effect can be effectively
treated in a cylindrical plasma using resistive magnetohydrodynamics (MHD), called resistive MHD dynamo.
The boundary of the plasma plays a key role on theMHD dynamo in laboratory plasmas and this has been

sumed to have flux conversion mechanisms that convert

pare the observed experimental results with the predic-one component of magnetic field to another, leaving thetion of the model of Jarobe and Alper. In short, thepredicted in the helicity dissipation model by Jarobe andAlper [8]. The motivation of the present work is to study
the process of helicity "balance" in the low B SINP
tokamak accompanied by fluctuating plasma and com-plasma in a preferred state, and in the process causing*Corresponding author's

e-mail: nihar@ hp2.saha.ernet.in489@2000 by The Japan Society of Plasma
Science and Nuclear Fusion ResearchBhattacharyya K. et aI., Helicity Injection Experiment in the SINP Tokamak

deliver unidirectional currents to the toroidal andpoloidal field coils and the primary coil of the ohmic

model is described below: Using the helicity balance assumption, the time rate of change of helicity is given bytransformer. The base pressure is around I x l0-7 torr inthe vacuum chamber. The plasma current 1, is measured
by Rogowoskii coil, toroidal loop voltage Vr by an one[8]:dK tdt =-2[ E.B d(vot)+2[ ur",d(vot)(1)

turn flux loop along the major circumference of thetorus surface, whereas there is an one turn flux loop

where Eu and Bu are values of electric and magnetic
fields that would be produced in a vacuum by the sameflux, linking the boundary, that are present in theplasma. The E and B are the fields in the plasmas. Thealong the minor circumference to measure the toroidal

flux and the poloidal loop voltage Ve. In the present
experiment, we operated the SINP tokamak with limiterradius a1 of 0.07 m, gas (hydrogen) filling pressure of0.2 to 0.3 mTorr, applied Vrof 27 volts and applied 8u""'is l5 to 50 Gauss. Typical parameters of the discharges
are: peak current Iq= 54 kAmp, fl" = 3 x 1018 m-3, Z, -first term on the right is the "dissipation" and the second
term is the "injection". For a tokamak having vacuum
region between plasma and conducting wall, the injec-tion may be assumed as 2V, @, where Q and Vt are thetoroidal flux and loop voltage. In the steady state dKldl

10-15 eV, Spitzer resistivity tl = 5 x l0-5 Q-m and Br=
0.15 T.

= 0. thus.

I ,' t d(vot)=vrQ

3. Results and Discussionsa)

The interesting observations come from the effectof variation of the magnitude of vertical magnetic field,B,", keeping all other operating parameters fixed. When8,",, was above 60 gauss the plasma current rose to apeak value around 12 kAmp and showed its usual
behavior (see Fig. 1b), i.e., it rose towards the peakvalue, stayed nearly constant and decayed slowly
thereafter. Total duration of the discharges under thisFrom the assumption that helicity dissipation takes placein the cold plasma regions where E11 = constant = q,pitz",
j110, where jq10 equilibrium current density parallel to Bp,
and using equation (2) one can write:

vr= (Euv" e)/fio2 +IRk

(3)

Where V" is the volume of the edge region as defined bylimiters and field errors; 0 is pinch parameter (- a/R);

condition were not more than 3 msecs. However, as 8,",1R1{ represents the dissipation in the bulk of the plasma.

oscillatory nature in the plasma current I, occurring

Some interesting predictions can be made from the eq.

spontaneously. Though the peak current did not rise as
high, the discharge duration increased substantially. The
number of intrinsic oscillation cycles increased moreand more as 8u",, was lowered further in the range of20-50 gauss. The observations were highly reproducible
and a typical one with B,"n = 30 gauss is shown in Fig.

was gradually lowered we started observing an(3): for the given values of E11, V" , 0 and a, the helicity
dissipation IRIQ can be compensated by increasing theloop voltage l.e. increasing the helicity injection rate.
We did experiment to explore this phenomenon in thelow p SINP tokamak accompanied by fluctuating plas-la. The important features of the experimentalmas.

measurements on oscillatory plasma current and loop
voltages (toroidal & poloidal) shown in Fig.2 are thatthe plasma current rose to a peak value of about 6 kAmp
at about / = 0.5 msec from the beginning of the current
rise (Fig. 2c), after which it started decaying fast in atime scale - several hundreds of microsecs. This is thenfollowed by repetitive slow current rise and fast crashfor several cycles and the discharge was sustained for

2. Apparatus and Experiments
The SlNP-tokamak is a small iron core tokamak(R = 0.3 ryt, as = 0.085 m, volt-sec = 0.12; stainless steel

vacuum chamber wall thickness = 5 mm with two
ceramic breaks at two toroidal locations 180' apart; twomovable poloidal limiters, mounted at vertically up anddown ports at the same toroidal location, adjust theplasma minor radius to a maximum of 0.075 m, one
fixed poloidal limiter of minor radius = 0.075 m; themachine has a aluminum shell with minor radius of0.109 m and thickness of i mm surrounding the vacuum
vessel, the shell has two poloidal and four toroidal cuts
for field penetration). Three independent power supplies

more than 5 msecs. Similar oscillatory nature wasobserved in the signals of V, and yo respectively (Figs.
2a & 2b). In order to study the helicity balance, aspredicted in the model of Jarobe & Alper, plasma's
helicity was measured using internal magnetic probes atdifferent minor radius r and using the formula:490

Bhattacharyya K. et al., Helicity Injection Experiment in the SINp Tokamak

(a)

(a)
1tE

Y.4x10{E 1.2x1}a=g
10+-0.000.0x10'

8.0x10-50.001 0.002 0.003

0.055

0.004

0.060

r,mTime, sec(b)6.0x t 0's(b)5.0x10{Eo<A:z-8=
4.0x10'Y"
3.0x1050.050 0.05s 0.060 0.065 0.070
r.m

00.0000 0.0005 0.0010 0.0015 0.0020 0.0025

Fig. 3 Helicity (r0 per unit length vs. Radius (r): (a)During peak plasma current, (b) After the crash ofplasma current.

Time, sec

Fig. 1 Plasma current (/,) vs. Time

m=1. f=S.SkHz

45930

(a)

Sis

o=0'0.00

E -o.osrrr.(b)lLn ,[ .d J r.r .ri}^d''rlilf-,'F,d 0.00
aa.

dl>t -0.10
o-0.05

6E4Y20.@@ 0.0m1 0.0m2 0.0003 0.0004 0.0ms

0.000 0.001 0.002 0.003 0.004 0.005

0.0006

Time, sec

Fig 4. Poloidal magnetic field (4) vs. Time at (a) 0 = 0'probe and {b) 0= 90'probe.

Time, sec

Fig 2. (alToroidal loop Voltage (%), (b) Poloidal loop
voltage {VJ and (c} Plasma current (/,} vs. Time.

the crash of current, are shown in Fig. 3. The result (Fig.

IIK (r)=lAr(r) B r(r)+Ae t)Be Q)ln r'/ Wb'm-r (4)3) shows that there is decrease ofKby about 707o in theinner region of plasma and about 6OVo in the outer region of plasma during crash of plasma current. The result (Fig. 2a) shows that the loop voltage V, is increasedtransiently during the fast crash of plasma current (Fig.

tl

Where A's are components of vector potential and B'sare components of magnetic fields. The typical estimated values of K ( r) at peak 1, and at minimum I , after491

Bhattacharyya K. et al., Helicity Injection Experiment in the SINP Tokamak

900 lo 1 1 00 Hz Band Pass FiltergH
5EoE>

EoFUE,o6.=6H.o
6:'6oFo'*'t,r",ooo4o"""

oo2rlr" ("itoo 006

Fig.5 (a) Fluctuating plasma velocity 4 and (b)Fig. 6 Toroidal electric field vs. time. Dotted curve
estimated from v,x B*and solid curve from Vr.

2c) i.e. helicity injection rate is increasedby aboutTUVoto 807o. Here the vacuum region = l%o, 0 = 0.23, E1 =10 V/m and the volt-sec consumption during the transient crash period of current = l5Vo (the stored volt-sec= 0.12). That helicity dissipation during current crash is
associated with tearing activity is shown in Fig. 4, asmeasured by two magnetic probes 0 = 0o and 0 = 90o.

(solid curve of Fig. 6) incorporates all other contributions (i.e. j x B, Vp", etc.) besides that from vrx B'en.

Therefore the present result shows that under the typicaloperating condition of the tokamak discharge, thehelicity dissipation in the resistive plasma is being com-the plasma and helicity injection is approximately
according to the model of Jarobe and Alper and thevertical magnetic field B,"n plays a key role in thisbalancing process. Also it is observed that due tooutward particle transport, inward helicity transPort ispossible, provided vertical magnetic field and plasma's
velocity are oscillated at low frequency with a definite

Fluctuating vertical magnetic fild 8,"' vs. Time.

4. Conclusions
In the helicity injection experiment at the low B
SINP tokamak accompanied by fluctuating plasma it isobserved that the balance between helicity dissipation inpensated by the transiently increased helicity injection

rate, as predicted in the model. In order to find out thekey role of the vertical magnetic field we have estimatedthe vertical electric field from the measured value of
top-bottom floating potential by Langmuir probes (as-phase relationship. The experiment also shows increaseof duration of plasma current i.e. sustainment of plasma
due to balancing effect between helicitydissipation andinjection. Therefore helicity dissipation due to tearing

suming temperature constant). The result shows that imbalance between 8,"1x B q and E q x 8n",, forces causes
fluctuating plasma velocity v". Now the fluctuating r"
and fluctuating Bn"nin the plasma with a definite phase

activity may be balanced by helicity injection in

relationship, as shown in Fig. 5, may cause the generation of confining magnetic field in the plasma according
to Ohm's law Er=v,xB,rn, which we call a flux con-resistive plasmas by means of v,x B,"n force and current
can be driven for a longer period of time in the tokamak,provided there is sufficient amount of stored volt-sec inversion mechanism due to fluctuating magnetizedplasma. Therefore, due to outward particle transport

the tokamak.

Referencescausing up-down asymmetry (observed in tokamaks
very often [9]) the flux conversion mechanism can betriggered by oscillating the vertical magnetic field 8,",,and oscillating the plasmas' velocity u, and as a result
helicity transport from outward to inward may be possible in a tokamak accompanied by fluctuating plasma.
The estimated value of toroidal electric field -8" fromthe measured values of v, and Br"n @ig. 5) is shown in
Fig. 6 (dotted curve) and the estimated value of toroidal
electric freld E, from the measured value of V, (Fig. 2a)is shown in Fig. 6 (solid curve). The magnitude of E,[1] M. Bevir and J. Gray, Proc. RFP workshop, Los
Alamos Report LA,-8944-C, p.176 (1981).

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[4] E.J. Caramana and D.A. Baker, Nucl. Fusion, 24,423 (1984').
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[6] P. Bellan, Nucl. Fusion,29 (l),78 (1989).
492

Bhattacharyya K. et al., Helicity Injection Experiment in the SINp Tokamak

t7l M.R. Brown, P.M. Bellan, Nucl. Fusion, 32, ll25

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