Evolution of the IR-T1 Tokamak Plasma Local and Global Parameters

REVIEW ARTICLE

Evolution of the IR-T1 Tokamak Plasma Local and GlobalParameters

A. Salar Elahi • M. Ghoranneviss

Published online: 26 September 2013

� Springer Science+Business Media New York 2013

Abstract In this contribution, an attempt is made to

investigate of evolution of some local and global plasma

parameters in IR-T1 tokamak. For this purpose, four

magnetic pickup coils were designed, constructed and

installed on outer surface of the tokamak and then asym-

metry factor is obtained from them. On the other hand,

diamagnetic loop were designed and installed on IR-T1 and

poloidal beta is determined from it. Therefore, the internal

inductance and effective edge safety factor measured. Also,

time evolution of the energy confinement time is measured

using the diamagnetic loop. Experimental results show that

maximum energy confinement time (which correspond to

minimum collisions, minimum microinstabilities and

minimum transport), relate to the low values of effective

edge safety factor and also relate to the low values of

internal inductance.

Keywords Tokamak � Plasma � Diagnostics

Introduction

One of the major research efforts in the area of controlled

thermonuclear fusion, especially in tokamaks research, is

focused on the confinement of hot plasmas by means of

strong magnetic fields. Confinement time which is one of

the main parameters of the ignition condition is limited by

thermal conduction and convection processes, but radiation

is also a source of energy loss. Maximum energy con-

finement time is determined by the microscopic behavior of

the plasma as collisions and microinstabilities. This

behavior ultimately leads to macroscopic energy transport

which can be either classical or anomalous depending on

the processes involved. In the absence of instabilities the

confinement of toroidally symmetric tokamak plasma is

determined by Coulomb collisions. Since these phenomena

require knowledge of individual particle motion on short

length and time scales, they are usually treated by kinetic

models, but including only limited geometry because of the

complexity of the physics. To achieve thermonuclear

condition (ignition condition) in a tokamaks (n T sE [ 3�1021m�3KeV s), it is necessary to confine the plasma for a

sufficient time. The global energy confinement time sE is

defined byR

3=2n ðTe þ TiÞ d3x=P, were n is the plasma

density, T is the plasma particles temperature and P is the

total input power. In the absence of a theoretical under-

standing of confinement and given the need to predict the

confinement properties of future tokamaks, it has been

necessary to resort to empirical methods. The simplest of

these is to accumulate data from a number of tokamaks,

each operated under a range of conditions and to use sta-

tistical methods to determine the dependence of the con-

finement time on the parameters involved. This provides

scaling expressions which, within some error, allow

extrapolation to projected tokamaks [1–65]. In this paper

we presented an investigation of time evolution of the

energy confinement time, internal inductance and effective

edge safety factor, in IR-T1 tokamak, which is a small,

large aspect ratio, low beta, ohmically heated tokamak,

with circular cross section (see Table 1). This paper is

arranged as follows: In Sect. 2 we will be presented mag-

netic probe method for determining the Shafranov param-

eter. In Sect. 3 we will be presented the diamagnetic loop

method for measurement of the poloidal beta. In Sect. 4 we

A. Salar Elahi (&) � M. Ghoranneviss

Plasma Physics Research Center, Science and Research Branch,

Islamic Azad University, Tehran, Iran

e-mail: [email protected]

123

J Fusion Energ (2014) 33:1–7

DOI 10.1007/s10894-013-9634-9

will be presented experimental results of measurements of

the internal inductance and edge safety factor. We also will

be presented experimentally in Sect. 5 results of determi-

nation of the energy confinement time and effects of the

internal inductance and edge safety factor on it. Also, the

turbulence of the plasma has been studied by using the

movable Langmuir probe array in the plasma edge will be

presented in Sect. 6. Summary and conclusion are will be

presented in Sect. 7.

Determination of the Shafranov Parameter

(Asymmetry Factor) Using the Magnetic Pickup coils

Combination of poloidal beta and internal inductance relate

to the distribution of magnetic fields around the plasma

current. Therefore, those can be written in terms of the tan-

gential and normal components of the magnetic field on the

chamber surface. Distribution of magnetic fields is can be

written in the first order of the inverse aspect ratio as follows:

Bh ¼l0Ip

2p b� l0Ip

4p R0

�

lna

bþ 1

n� Kþ 1

2

� �a2

b2þ 1

� �

� 2R0Ds

b2

�

cos h;

Bq ¼ �l0Ip

4p R0

�

lna

bþ Kþ 1

2

� �a2

b2� 1

� �

þ 2R0Ds

b2

� �

sin h;ð1Þ

where R0 is the major radius of the vacuum vessel, Ds is the

Shafranov shift, Ip is the plasma current, a and b are the

minor plasma radius and minor chamber radius

respectively and li is the plasma internal inductance.

These equations accurate for low beta (bp) and circular

cross section tokamaks as IR-T1 and where:

K ¼ bp þ li=2� 1

¼ lna

bþ p R0

l0Ip

ðhBhi þ hBqiÞ;ð2Þ

where

hBhi ¼ Bhðh ¼ 0Þ � Bhðh ¼ pÞ;

hBqi ¼ Bqðh ¼p2Þ � Bqðh ¼

3p2Þ;

and where subscripts h and q represents the tangential and

normal components. We can obtain poloidal and normal

components of the magnetic field from the output signals of

the magnetic probes after compensation and integration.

Therefore we can be to calculate the Shafranov parameter

from the Eq. (2). The compensation done by fields dis-

charge without plasma and receives output signals of the

magnetic probes and subtract those from total output sig-

nals from the probes (dry runs technique). Moreover in our

work we used the Rogowski coil and the poloidal flux loop

for the measurements of plasma current and the plasma

voltage, respectively, but only we will be presented their

data.

Determination of the Poloidal Beta Using

the Diamagnetic Loop

Diamagnetic loop measure the plasma diamagnetic flux for

the purpose of measurements of the plasma parameters e.g.

poloidal beta and thermal energy of the plasma. The dia-

magnetic loop consists of a simple loop that links the

plasma column, ideally located in a poloidal direction in

order to minimize detecting the poloidal field. In cases of

the ohmically heated tokamaks (low beta) where the

plasma energy density is small compared to the energy

density of the magnetic field, the change in the total

toroidal magnetic flux is small. Therefore a reference sig-

nal equal to the vacuum toroidal magnetic flux is usually

subtracted from it, giving a net toroidal flux equal to the

diamagnetic flux DUD produced by the circular plasma.

Relation between the diamagnetic flux and the poloidal

beta derived from simplified equilibrium relation [12, 13]:

bp ¼ 1� 8pBu0

l20I2

p

DUD; ð3Þ

where

Uvacuum ¼ UT þ UO þ UV þ UE;

and where Bu0 is the toroidal magnetic field in the absence

of the plasma which can be obtained by the magnetic probe

or diamagnetic loop, Ip is the plasma current which can be

obtained by the rogowski coil, UT is the toroidal flux

because of toroidal field coils, UO and UV are the passing

flux through loop due to possible misalignment between

ohmic field and vertical field and the diamagnetic loop and

UE is the toroidal field due to eddy current on the vacuum

chamber. These fluxes can be compensated either with

compensation coil or dry runs technique. It must be noted

Table 1 Main parameters of the IR-T1 Tokamak

Parameters Value

Major radius 45 cm

Minor radius 12.5 cm

Toroidal field h1.0 T

Plasma current h40 kA

Discharge duration h35 ms

Electron density 0.7–1.5 9 1013 cm-3

2 J Fusion Energ (2014) 33:1–7

123

that compensating coil for diamagnetic loop is wrapped out

of the plasma current and only the toroidal flux (which is

induced by the change of toroidal field coil current when

plasma discharges) can be received. As shown in Eq. (3)

the diamagnetic loop signal contains two parts, plasma

diamagnetic flux and the vacuum toroidal flux. So the

diamagnetic flux DUD caused by plasma current can be

measured from the diamagnetic loop and compensating

coil using subtraction.

Experimental Results for Measurements of the Internal

Inductance and Effective Edge Safety Factor

In the IR-T1 tokamak, array of four magnetic probes were

designed, constructed and two of them were installed on

the circular contour C of the radius b = 16.5 cm in angles

of h = 0 and h = p to detect the tangential component of

the magnetic field Bh and two magnetic probes are also

installed above, h ¼ p=2 and below, h ¼ 3p=2, to detect

the normal component of the magnetic field Bq.

After measurements hBhi and hBqi from magnetic

probes and Ip from rogowski coil and substituting them into

Eq. (2) Shafranov parameter were obtained. Design

parameters of the magnetic pickup coils present in Table 2.

Diamagnetic loop and its compensating coil also were

constructed and installed on the IR-T1 tokamak. Its char-

acteristics are also shown in Table 2.

Therefore, combination of the magnetic probe and dia-

magnetic loop measurements give us the value of the

internal inductance:

li ¼ 2 Kþ 1� bp

� �; ð4Þ

also the effective safety factor at the edge is defined by [8]:

qeff ¼2pa2Bu

l0R0Ip

1þ e2 1þ Kþ 1ð Þ2

2

! !

ð5Þ

According to these relations and also values of the Sha-

franov parameter and poloidal Beta [Eqs. (2),(3)], which

measured using the magnetic probes and diamagnetic loop,

we plotted time history of the internal inductance and

effective edge safety factor in target shot, as shown in

Figs. 1, 2, respectively.

Determination of the Energy Confinement Time

Before we want to derive relation for the energy confine-

ment time, we must determine the volume averaged plasma

kinetic pressure ph i, and then the plasma thermal energy U.

ph i is can be measured directly from the definition of the

poloidal beta:

ph i ¼ bp

B2h að Þ2l0

¼l0I2

pbp

8p2a2ð6Þ

where a is the plasma minor radius.

For measurement of the plasma thermal energy we start

from the plasma state equation:

ph i ¼X

i

niTi ¼2

3

X

i

Ei ¼2

3E; ð7Þ

where subscript i indicate the plasma species i and E

indicate the plasma thermal energy density, therefore the

plasma thermal energy U and also plasma temperature is

obtained:

Table 2 Design parameters of the magnetic probes and diamagnetic

loop

Parameters Magnetic probe Diamagnetic loop

R (Resistivity) 33 X 100 X

L (Inductance) 1.5 mH 20 mH

n (Turns) 500 170

S (Sensitivity) 0.7 mV/G 0.5 V/G

f (Frequency response) 22 kHz 5 kHz

Effective nA 0.022 m2 16 m2

d (Wire diameter) 0.1 mm 0.2 mm

dm(Coil average radius) 3 mm 175 mm

Fig. 1 Combination of the Diamagnetic Loop and Magnetic Probe

Results: a Plasma Current, b Internal Inductance obtained by

Subtraction of Poloidal Beta (c), from Shafranov Parameter (d)

J Fusion Energ (2014) 33:1–7 3

123

U ¼ 3

2

X

a

naTa

!

V ¼ 3

2ph iV ; ð8Þ

where V is the plasma volume. The plasma specific

resistance in the steady state plasma is can be written as:

qp ¼1

rp

¼ A

lRp ¼

a2

2R0

VR

Ip

; ð9Þ

where rp is the plasma conductivity, Rp is the plasma

resistance and VR is the resistive component of the loop

voltage (poloidal flux loop).

But most important of these measurements is the

determination of the plasma thermal energy confinement

time which defined by equation:

dU

dt¼ POhmic �

U

sE

; ð10Þ

where sE is the plasma energy confinement time, and Pohmic

is the rate of input heating power. Rearranging Eq. (10), the

ohmic heating power is:

POhmic ¼ VRIp �d

dt

1

2LI2

p

� �

: ð11Þ

If the plasma is in thermal equilibrium ( _L ¼ 0 and_I ¼ 0), then from Eqs. (8), (10) we have:

POhmic ¼ VRIp ¼ RpI2p ¼

U

sE

;

sE ¼3

8

l0R0Ipbp

VR

¼ 3

8

l0R0bp

Rp

:

ð12Þ

Also if dU=dt is not negligible, then from Eqs. (8), (10)

we have:

1

sE

¼ 8Rp

3l0R0bp

� 2 _I

I�

_bp

bp

: ð13Þ

In the flat region of the tokamak plasma current, time

variations is very small and Eq. (12) is indefeasible.

Therefore according to above discussion we can find

plasma energy confinement time and also effects of the

internal inductance and effective edge safety factor on it,

by the magnetic probe, diamagnetic loop and with helping

the Rogowski coil and poloidal flux loop. Experimental

results can be observed in the Figs. 3 and 4.

Electrical Measurements

In this work, the effect of biasing and RHF on the multi-

fractal property of Is, Vf, poloidal electric field (Ep), the

radial particle flux (Cr) and the Magneto Hydro Dynamics

(MHD) behavior and the type of their correlation were

studied. The turbulence of the plasma has been studied by

Fig. 2 Combination of the Diamagnetic Loop and Magnetic Probe

Results: (a) Plasma Current, (b) Effective Edge Safety Factor,

(c) Toroidal Magnetic Field and (d) Shafranov Parameter

Fig. 3 a Plasma Current, b Plasma Resistance, c Energy Confine-

ment Time and d Plasma Particles Temperature


123

using the movable Langmuir probe array at the plasma

edge in the IR-T1 tokamak. The experiment was done in

the three different conditions as described in the previous

section. The limiter biasing was applied at r/a = 0.9 with

Vbias = 200 v and RHF had L = 3. To characterize the

fluctuations of the signals we used MF-DFA method. The

time evolution of Is, Vf, Ep and Cr were shown in Fig. 5.

Suddenly after applied biasing to the plasma at t = 15 ms,

Is, Vf, Ep and Crreduced about 25, 90, 70, 50 % respectively

compared to the situation with no biasing. Also they were

reduced about 15, 90, 35 and 25 % respectively by

applying RHF. The power spectrum amplitude of Is, Vf, Cr

and MHD fluctuation signal were reduced in the all range

of frequency by applying biasing or RHF (Fig. 6). It means

that the biasing and RHF can modify the plasma fluctua-

tions. With applied biasing, the radial electric field and so

E 9 B flow was generated. It can decorate the turbulence.

Also the structure of the edge fluctuations was affected by

RHF. To characterize the effect of biasing and RHF on the

turbulence of the edge plasma, we used the MF-DFA

method for the experimental signals. We follow this

method for understanding a deviation from pure self-sim-

ilarity. The MF-DFA method represents a modern time

series technique of investigation.

Summary and Conclusion

Diamagnetic loop and also array of magnetic probes have

been designed and installed on the outer surface of the IR-

T1 tokamak. The poloidal and radial components of the

magnetic fields and also diamagnetic flux signal obtained.

Then, from the value of K which obtained from the mag-

netic probes and the poloidal beta which obtained from the

diamagnetic loop, the values of the internal inductance li

and also the effective edge safety factor were obtained.

Also, energy confinement time is measured from the dia-

magnetic loop and then the effects of internal inductance

Fig. 4 a Plasma Current, b Plasma Internal Inductance, c Safety

Factor and d Energy Confinement Time. As shown, Maximum

Energy Confinement Time is at region of low values of effective edge

safety factor (2:5 hqeff ðaÞ h2:8), and also at low values of internal

inductance (0:61 h li h 0:72)

Fig. 5 Time evolution of a Plasma current, b ion saturation current,

c fluctuation of floating potential, d poloidal electric field, f radial

particle flux, for plasma discharges with bias or RHF and without

them. Limiter bias applied at r/a = 0.9 with Vbias = 200v and RHF

had L = 3


123

and effective edge safety factor on it presented. Experi-

mental results on IR-T1, show that maximum energy

confinement time (which correspond to minimum colli-

sions, minimum microinstabilities and minimum transport)

relate to the low values of effective edge safety factor

(2:5 \qeff ðaÞ\2:8) and also relate to the low values of

internal inductance (0:61 \ li \ 0:72). Results are in

agreement with theoretical approach [1–5]. To characterize

the fluctuations of the signals we used MF-DFA method.

The time evolution of Is, Vf, Ep and Cr were shown in

Fig. 5. Suddenly after applied biasing to the plasma at

t = 15 ms, Is, Vf, Ep and Cr reduced about 25, 90, 70, 50 %

respectively compared to the situation with no biasing.

Also they were reduced about 15, 90, 35 and 25 %

respectively by applying RHF. The power spectrum

amplitude of Is, Vf, Cr and MHD fluctuation signal were

reduced in the all range of frequency by applying biasing or

RHF (Fig. 6). It means that the biasing and RHF can

modify the plasma fluctuations.

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Evolution of the IR-T1 Tokamak Plasma Local and Global Parameters