Determination of confinement efficiency in tokamaks based on current independent flux loops technique

Determination of confinement efficiency in tokamaks based on current independent flux loops technique Results in Physics 7 (2017) 175–177 Contents lists available at ScienceDirect Results in Physics j[.]

Determination of confinement efficiency in tokamaks based on current

independent flux loops technique

A Salar Elahi ⇑ , M Ghoranneviss

Plasma Physics Research Center, Science and Research Branch, Islamic Azad University, Tehran, Iran

a r t i c l e i n f o

Article history:

Received 25 November 2016

Received in revised form 15 December 2016

Accepted 18 December 2016

Available online 24 December 2016

Keywords:

Tokamak

Confinement efficiency

Poloidal flux loops

a b s t r a c t

In this contribution we presented a current independent approximation of the combination of poloidal beta and internal inductance (confinement efficiency) only based on poloidal flux loops measurement

in IR-T1 tokamak The main advantage of this technique is that it based only on the one diagnostic (only flux loops and not need to plasma current measurement) Based on this method, two flux loops were designed, constructed, and installed on outer surface of the IR-T1 tokamak chamber and then the Shafranov parameter was measured from them Also the result of this technique was compared with con-ventional magnetic probes technique and found in good agreement with each other

Ó 2016 The Author Published by Elsevier B.V This is an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/)

Introduction

Equilibrium of the plasma within the vessel of the tokamak

requires a suitably structured magnetic fields configuration These

magnetic fields will act as a magnetic tube only as long as especial

conditions are satisfied The confinement and equilibrium of the

plasma within the discharge chamber of tokamak can be thought

of as a problem of controlling the equilibrium position of the

plasma column and the position of the plasma column with respect

to its equilibrium position [1–20] If the equilibrium position of the

plasma column can be made to be at the cross sectional center of

the vacuum chamber, then a necessary condition for the plasma

to be well confined is that the position of the plasma column from

the center of the vacuum chamber be maintained to be less than a

suitably small displacement In the low beta tokamaks as IR-T1,

radial pressure balance is achieved by the poloidal field, and

dal force balance is achieved by the Lorentz force But, in the

toroi-dal force balance problem, if the two opposite forces are not equal,

then plasma intend to shift inward or outward, which is dangerous

for tokamak plasma equilibrium Therefore, plasma equilibrium

study is one of the fundamental problems of the magnetically

con-fined plasmas [21–45] There are many available experimental

methods and analytical solutions of the steady state

Magnetohy-drodynamics (MHD) equations, in particular, the Grad-Shafranov

equation Determination of the combination of poloidal beta and

internal inductance (Shafranov parameter) (which is one of the

tokamak plasma equilibrium parameters, K ) is essential for toka-mak experiments Very of plasma information can be deduced from this parameter, such as the poloidal beta, plasma equilibrium state, plasma energy, plasma confinement time, plasma toroidal current profile, and Magnetohydrodynamics (MHD) instabilities

[46–57] In this paper we presented a current independent mea-surement of the Shafranov parameter only using poloidal flux loops in the IR-T1 tokamak, which is a small, air core, low beta, and large aspect ratio tokamak with a circular cross section (see

Table 1 ) Details of this technique for the measurement of the Shafranov parameter will be presented in ‘Current independent measurement of the Shafranov parameter’ section Experimental results and comparison with conventional magnetic probes tech-nique also will be presented in ‘Experimental result and compar-ison with conventional magnetic probes technique’ section Also summary and conclusion will be discussed in last section.

Current independent measurement of the Shafranov parameter The poloidal flux loops are a simple toroidally loops which mea-sures the poloidal magnetic flux and an array of loops is usually used in control and reconstruction of plasma equilibrium states The magnetic flux passing through such a loop is equal to 2 p w, where w represents magnetic poloidal flux In the ohmically heated tokamaks, ohmic coils field is the main fraction of poloidal flux which passing through the flux loop Therefore to obtain net poloi-dal flux due to plasma, compensation is required for all excessive flux Because of large area of the flux loop, the inductive voltage

is also large and then it consists of usually one turn According to

http://dx.doi.org/10.1016/j.rinp.2016.12.015

2211-3797/Ó 2016 The Author Published by Elsevier B.V

⇑ Corresponding author

E-mail address:Salari_phy@yahoo.com(A Salar Elahi)

Contents lists available at ScienceDirect

Results in Physics

j o u r n a l h o m e p a g e : w w w j o u r n a l s e l s e v i e r c o m / r e s u l t s - i n - p h y s i c s

relation for frequency response, it is obvious that because of small

self-inductance, frequency response of flux loop usually is higher

than which desired The magnetic probes are suitable for the

mea-surement of equilibrium parameters only in circular cross section

plasma and not for elongated one, but the flux loops can be used

in both elongated and circular section tokamaks The plasma

boundary in tokamaks is usually defined by Last Closed Flux

Sur-face (LCFS) At the LCFS poloidal magnetic flux is constant, if we

install some flux loops at some distance in vicinity of LCFS, then

we can find plasma equilibrium parameters from the difference

in poloidal fluxes that received by the flux loops In the

quasi-cylindrical coordinates ðr; h; /Þ for the poloidal magnetic flux we

have [1]

wðr;hÞ ¼ l0R0Ip 2  ln 8R0

r

þ l0Ip

2 ln

r

a þ K þ 1 2

1  a2

r2

r cosh;

ð1Þ

where

K ¼ bpþ li

2  1;

and where Ip; R0; a; bp; li are the plasma current, major and minor

plasma radiuses, poloidal beta and internal inductance of the

plasma The current independent relation between poloidal

mag-netic flux and the Shafranov parameter can be obtained:

K ¼ b

2

b2 a2 2 R0

b 2  ln 8R0

b

wout win

woutþ win

þ ln a b

 1

2 ; ð2Þ

where b is the radial position of the measurement instrumentation

(flux loops), and where the desired poloidal fluxes at low field side

(LFS) and high field side (HFS) are:

wout¼ wðb; h0Þ;

respectively In the IR-T1 tokamak two poloidal flux loops were

designed and installed on outer surface of the vacuum chamber in

polar angles h1¼ 0 and h2¼ p , with radiuses r1¼ 61cm and

r2¼ 29cm, respectively (see Table 2 ) It is must be mentioned that

the excessive fields such as toroidal field is the fraction of the

poloi-dal flux which passing through the flux loops, therefore essentially

compensation is needed Compensation is done with dry runs

tech-nique Experimental result for the measurement of the Shafranov

parameter using this technique will be presented in the next

section.

Experimental result and comparison with conventional

magnetic probes technique

In order to determination of the Shafranov parameter based on

this technique, we needed for measurements of the poloidal

mag-netic flux around the plasma As mentioned, we designed and

installed two poloidal flux loops on outer surface of the IR-T1

chamber Results of measurement of the time history of the Shafra-nov parameter based on flux loops are presented in the Fig 1 b In order to comparison of this result we presented the result of con-ventional magnetic probes technique as shown in the Fig 1 c Also plasma current is presented in the Fig 1 a These figures show that the results are in good agreement with each other The acceptable difference between them is because of possible error in compensa-tion of the excessive fluxes.

Summary and conclusions

We presented a current independent approximation of the combination of poloidal beta and internal inductance (Shafranov parameter) only based on poloidal flux loops measurement in IR-T1 tokamak The main advantage of this technique is that it based only on the one diagnostic (only flux loops and not need to plasma current measurement) Based on this method, two flux loops were designed, constructed, and installed on outer surface of the IR-T1 tokamak chamber and then the Shafranov parameter was mea-sured from them Also the result of this technique was compared with conventional technique (magnetic probes technique) and found in agreement with each other The acceptable difference

Table 1

Parameters of the IR-T1 tokamak

Parameters Value

Major radius 45 cm

Minor radius 12.5 cm

Toroidal field <1.0 T

Plasma current <40 kA

Discharge time <35 ms

Electron density 0.7–1.5 1013

cm3

Table 2 Parameters of the poloidal flux loops

Two flux loops parameters Values

R (resistivity) 3X

6X

2 mH

S (SENSITIVITY) 11, 31 mV/G

f (frequency response) 3 kHz

3 kHz

1.17 m2

d (wire diameter) 1 mm

r (loops average radius) 290 mm

610 mm

Fig 1 Time history of the (a) Plasma current, (b) Shafranov parameter measured by the current independent flux loops technique, and (c) Shafranov parameter

A Salar Elahi, M Ghoranneviss / Results in Physics 7 (2017) 175–177

between them is because of possible error in compensation of the

excessive fluxes.

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A Salar Elahi, M Ghoranneviss / Results in Physics 7 (2017) 175–177