Designing a Sine-Coil for Measurement of Plasma Displacements in IR-T1 Tokamak

Transcription

1 Designing a Sine-Coil fo Measuement of Plasma Displacements in IR-T Tokamak Pejman Khoshid, M. Razavi, M. Ghoanneviss, M. Molaii, A. TalebiTahe, R. Avin, S. Mohammadi and A. NikMohammadi Dept. of Physics, Islamic Azad Univesity, Mashhad, Ian Plasma Physics Reseach Cente, Islamic Azad Univesity, Tehan, Ian pkhoshid@gmail.com Abstact. A method fo the measuement of the plasma position in the IR-T tokamak in tooidal coodinates is developed. A sine-coil, which is a Rogowski coil with a vaiable wiing density is designed and fabicated fo this pupose. An analytic solution of the Biot Savat law, which is used to calculate magnetic fields ceated by tooidal plasma cuent, is pesented. Results of calculations ae compaed with the expeimental data obtained in no-plasma shots with a tooidal cuent-caying coil positioned inside the vessel to simulate the plasma movements. The esults ae shown a good linea behavio of plasma position measuements. The eo is less than.5% and it is compaed with othe methods of measuements of the plasma position. This method will be used in the feedback position contol system and tests of feedback contolle paametes ae ongoing. Keywods: plasma diagnostic, tokamaks. PACS: 5.7.m, 5.55.Fa INTRODUCTION In seveal configuations of magnetically confined plasmas, the position of the plasma column is a majo deteminant of plasma behavio fo contolling the plasma equilibium. Seveal methods ae employed fo displacement measuements, such as optical and magnetic methods. Fo the magnetic method, almost it is used sine-coil. The Ampee s theoem and the Biot Savat law ae well known tools used to calculate magnetic fields ceated by cuent distibutions [-4]. The fome is often used in high-symmety poblems of magnetisms. At fist section of this wok, an analytic solution of the Biot Savat law, which is used to calculate magnetic fields ceated by tooidal cuent-caying coil positioned inside the vessel to simulate the plasma movements, is pesented. In the second section a sine-coil, which is a Rogowski coil with a vaiable wiing density is designed and fabicated fo measuement of no-plasma shot expeiments with cicle coil of adius R =.45 m. The last section contain expeiments on the ohmically heated ai coe tokamak IR-T with a majo adius R=.45 m and a mino adius a =.5 m measuement of plasma position with the sine-coil. The vacuum chambe is a stainless steel welding stuctue with two tooidal beaks and a mino adius b=.5 m.

2 FIGURE. Tooidal stuctue of plasma cuent and sine- coil. ANALYSIS AND RESULTS Now we ty to use the Biot-Savat law to calculate the field in the tooidal coodinate of the cicula wie coil of adius =.45 cm as shown in figue. Accoding to Maxwell equation the magnetic field, B, is given by B = µ J, since the. B = and using expession of.( F v ) =, we can wite B = A, whee J is cuent density and A is vecto potential so that the above expession yields, ' µ J ( ) A( ) = dv' ' () 4π and by defining J ( ) dv = Idl, B() leads to, µ I dl ( ) B( ) = c 3 4π This equation has been solved using a numeical method, and the topology of the whole magnetic fields calculated. Figue shows the cicula wie used fo ou calculation. () z x dl y FIGURE. An electical cuent I flows in the wie. The magnetic field is ceated at point. Fo using the Biot-Savat law in numeical calculation accoding to simulated coil and tokamak stuctue, we defined equation paametes as below, dl = [.45 sin( u ), +.45 cos( u ),] = [.45 cos( u ),.45 sin( u ), ] (3) (4)

3 = [ x, y, z] (5) p = [.45 cos( u) z,.45 sin( u) z, (6).45 sin( u ) ( y.45 sin( u) ).45 cos( u ) ( x.45 cos( u ))] q = ( x.45 cos( u ) + y.45 sin( u ) + z ) ( 3 / ) (7) S =.45 cos ( u ) z ( x.45 cos ( u ) + y.45 sin ( u ) + ).45 sin ( u ) z ( x.45 cos ( u ) + y.45 sin ( u ) + ), z ( 3 / ), z ( 3 / ).45 sin( u ) ( y.45 sin( u )).45 cos( u ) ( x.45 cos( u )) ( x.45 cos( u ) + y.45 sin( u ) + z ) ( 3 / ) (8) whee P = dl ( ), q=( ) 3 and S is integand of magnetic field components [ B x, By, Bz ] unde paamete of u which vaies fom to π, and electic cuent is 3 Amps. The magnetic field calculated in mid-plane of tooidal cuent-caying coil fo high field side and low field side is shown in figue 3. Now, a sine-coil, which is a Rogowski coil with a vaiable wiing density is designed and fabicated fo measuement of position of cuent-caying coil as illustated in figue. The equation of path fo this coil with espect to a efeence point in lab intoduced as below, R{ a + bcos( mθ )sin( θ ), a + bcos( mθ )cos( θ ), b sin( mθ ) } (9) HFS LFS FIGURE 3. The magnetic field calculated in mid-plane of cuent-caying coil, high field side and low field side, R=.45 m accoding to figue. The flux induced in the sine-coil fom cuent coil calculated with Φ = B n. ds is shown in figue 4. Hee we defined a paamete fo adios of each tun of sine-coil suface as v, which vaied fom to.5 metes and paamete of t, that vaied fom to π, the aea with low numbe of tuns. The flux calculated at the mid-plane stongly depends on the position of the

4 wie loop inside the sine-coil as shown in Figue 5. The cuve shows a linea behavio inside the sine-coil fom R=.5 m to R=.59 m. FIGURE 4. The flux induced in the sine-coil fom cuent loop in suface of coil in the all points. The esult has been investigated fo measuement of cuent caying coil position with espect to sine-coil position. In this calculation, we fixed the sine-coil position and moved the cuent coil in the R diection. The esults of flux calculation by Biot-Savat law is compaed with expeimental data (figue 6). They show a good ageement with theoy. a b FIGURE 5. The flux induced in sine-coil in the mid-plane of cuent wie accoding to figue configuation, the adius of sine-coil hee is =.7 m. a and b indicate the sine- coil limits, and dash line indicates the cuent loop position. Relative H-Displacement Biot-Savat Calculation Expeimental Measuement Radius [Cm] FIGURE 6. Compaison of calculations with actual plasma position. The ectangle and the tiangle symbols show the Biot Savat law calculation and the measuements with the sine-coil, espectively.

5 The signal induced fom plasma cuent in Sine-coil and Rogowski coil is shown in figue 7. The plasma displacement can be detemined as the ation of the sine-coil signal and the plasma cuent measued by the Rogowski coil. The esult is shown in figue 8. Voltage [a.u.]..9.6 Sine Coil Rogowski Coil (Ip) Time [ms] FIGURE 7. The signal induced fom plasma cuent in Sine-coil and Rogowski coil. Plasma Displacement [cm] - In Out Displacement Time [ms] FIGURE 8 The plasma displacement measued by this signals. In conclusion, compaing the esults of the model expeiment with the equation (4) we conclude that the sine-coil can be exploited fo measuement of plasma displacement in the IR-T tokamak. The eo is less than.5% and it has been compaed with othe methods of measuements of the plasma position. In addition, this method will be used in the feedback position contol system and tests of feedback contolle paametes. ACKNOWLEDGMENTS The authos would like to thanks IT cente of IAU of Mashhad fo thei nice coopeation. REFERENCES. L. Chen, Q. Zhao, Y. Zhu, Z. Fang, H. Fan, Measuement of plasma position on HT-7 tokamak Jounal of Fusion Engineeing and Design, (996) 7.. M.H. Choudhuy, Electomagnetism John Wiley and Sons, New Yok (989). 3. T. Chaitat and F. Gane, About the magnetic field of a finite wie, Eu. J. Phys. 4 (3) G. Cavalleiy, G. Spavieiz and G. Spinelli, The Ampee and Biot Savat foce laws Eu. J. Phys. 7 (996) 5.