Thheoretical and Experimental, Studies Ok the Magnetic Fields of a Rotamak Discharge

THHEORETICAL AND EXPERIMENTAL, STUDIES OK THE MAGNETIC FIELDS OF A ROTAMAK DISCHARGE H.KIROLOUS Ph.THESIS DECEMBER 1986; THEORETICAL AND EXPERIMENTAL STUDIES OF THE MAGNETIC FIELDS OF A ROTAMAK DISCHARGE A Thesis Presented for the Degree of Doctor of Philosophy by Hanna Abd-el Malik Kirolous in the School of Physical Sciences The Flinders University of South Australia December 1986 (i) CONTENTS Summary (iv) Author's Publications (v) Statement (vi) Personal Statement (vii) Acknowledgements (viii) CHAPTER 1 Introduction 1 PARTI - in which a possible explanation for the observed self-generation of steady toroidal magnetic fields in rotamak discharges is advanced. CHAPTER 2 The Steady Currents Driven in a Conducting Sphere Placed in a Rotating magnetic Field 2.1 Introduction 5 2.2 Main Equations and Assumptions 9 2.3 Zeroth-order Fields and Currents 11 2.4 First-order Steady Current and Magnetic Field 12 2.5 Discussion 14 PART II - in which an experimental investigation of the magnetic properties of a rotamak discharge generated within a metal vessel is described. CHAPTER 3 Experimental Apparatus 3.1 Discharge vessel 1Q (ii) 3.2 The Vacuum System and Gas Handling 17 3.3 Preionization 17 3.4 The Applied Vertical field 18 CHAPTER 4 The Rotating Magnetic Field 4.1 Theoretical Considerations 20 4.1.1 The Exact Field Solution in Vacuum 21 4.1.2 The Series Approximation 22 4.1.3 The Field of a Bifilar Coil Surrounded by a Cylindrical Conducting Shell 24 4.1.4 The Fields of a Two-Phase System (Two Coils per Phase) Inside a Cylindrical Conducting Shell 28 4.2 Practical Considerations 4.2.1 The Coil Structure 33 4.2.2 R.F. Amplifiers 33 4.2.3 Impedance Matching 36 4.2.4 Calculation of Power Transfer to the Plasma Load 41 4.2.5 Calculation of Currents and Voltages 43 CHAPTER 5 Diagnostics and Data Acquisition 5.1 Magnetic Probes 46 5.2 Power Measurements 49 5.2.1 Voltage Measurements 50 5.2.2 Current Measurements 51 5.2.3 Phase Measurements 52 5.3 Data Acquisition System 52 CHAPTER 6 Experimental Results (iii) C.I Experimental Procedure 55 G.2 The Rotating Magnetic Field 56 6.3 Field Reversal During Rotamak Discharges 59 6.3.1 Influence of the Filling Gas Pressure 59 6.3.2 Influence of the Amplitude of the Vertical Field 60 6.4 Impedance Matching 60 6.5 Power Measurements 64 6.6 Measurements of the Penetration of the Rotating Field 67 6.7 The Steady Magnetic Field Structure of the Rotamak Discharge 69 6.7.1 Axial and Radial Field Profiles 70 6.7.2 Derivation of the Poloidal Flux Function, the Azimuthal Current Density and the Plasma Pressure 72 CHAPTER 7 Discussion of Experimental Results 7.1 General Observations 77 7.2 Speculation on the Origin of the Observed Negative Current Ring 78 7.3 Application of MHD Equilibrium Theory to the Observed Plasma/Field Configuration 80 7.4 Future Work 84 APPENDIX A A.I REFERENCES R.I (iv) SUMMARY In part I of this thesis, the self-generated bi-directional toroidal magnetic field structure which has been observed to exist in previous rotamak discharges is theoretically investigated. A possible explanation for the existence of this self-generated field, which relies on the presence of screening currents in the plasma, is advanced. Experimental studies of the magnetic field structure of a rotamak plasma configuration generated and sustained in a metal discharge vessel by means of a rotating magnetic field are described in part II. The rotating magnetic field was produced by feeding radio frequency (r.f.) currents, dephased by 90 degrees, through two or- thogonal coils which were located inside the metal chamber. High power amplifiers were used to supply the r.f. current pulses. The efficiency of the r.f. power transfer to the plasma was maximised by using impedance matching networks. The effect on the rotating magnetic field of eddy currents induced in the conducting vessel has been theoretically and experimentally investigated. Extensive magnetic field measurements have been undertaken on one particular rotamak discharge. Measurements of the penetration of the rotating magnetic field into the plasma were made at various axial positions. The steady magnetic field structure was measured at a matrix of 2640 points and a two dimensional least square polynomial fitting algorithm was used to smooth the measured data. This fitting procedure enabled reliable plots of the poloidal flux and current density contours to be constructed. An attempt has been made to apply MHD equilibrium theory to the observed plasma/field configuration. (v) AUTHOR'S PUBLICATIONS Some of the work presented in this thesis has already been presented in the following papers: 1. Hugrass, W. N., and Kirolous, H. A. (1984). The steady currents driven in a conducting sphere placed in a rotating magnetic field. Ausi. J. Phys. 37, 521. 2. Jones, I. R., and Kirolous, H. A. (1985). Long duration rotamak experiments. 12th. European Conference on Controlled Fusion and Plasma Physics, Budapest, Hungary, 2-6 September, 1985. 3. Trowse, J., and Kirolous, H. A. (1985). Recent results from the Flinders Uni- versity high power long duration rotamak discharges. 15th AINSE Plasma Physics Conference, Sydney, Australia, 4-6 February 1985. (unpublished). (vi) STATEMENT I certify that this thesis does not incorporate without acknowledgement any material previously submitted for a degree in any university ; and that to the best of my knowledge and belief it does not contain any material previously published or written by another person except where due reference is made in the text. Signed. Date.... (vii) PERSONAL STATEMENT Although formal recognition will be made in the next section, it is felt by the author that certain people have contributed to the work presented in this thesis to such a degree that they merit special acknowledgement. The first is Mr. Des Clift who designed and constructed the r.f. generators which have been used in a number of rotamak experiments including the present one. The second contributor is Dr. David Brotherton-Ratcliffe. To him I am grateful for help with the two-dimensional polynomial fitting algorithm. His aid was also invaluable for the application of MHD theory to the measured plasma/field configuration. The design and construction of the intermittent clock generator used to drive the LeCroy digitisers were done jointly with Mr. Andrew Knight and Mr. Geoff Cottrell whom I thank. (viii) ACKNOWLEDGEMENTS I wish to express my sincere gratitude to my supervisor Professor I. R. Jones for his inspiration and guidance throughout the course of this work. He has been most helpful in encouraging me to persevere and in particular with his careful reading of the drafts of this thesis and his numerous suggestions for improvement. I would also like to express my appreciation of the help and support provided by the entire plasma group at Flinders University. Special thanks must go to Dr. W. N. Hugrass for his invaluable help during the first two years of my can- didature. I am also grateful to Dr. D. B. Ratcliffe for his guidance in the analysis of the data. Thanks also go to Mr. K. Duldig and Mr. G. Cottrell for their excellent technical support. I would also like to thank members of the glass blowing and engineering workshops for their aid in the constuction of the experimental apparatus. The work in this thesis was supported by grants from the National Energy Re- search, Development and Demonstration Council of Australia, the Australian Insti- tute of Nuclear Science and Engineering, the Australian Research Grants Scheme and the Flinders University of South Australia research budget. A Flinders Uni- versity research scholarship was held during the course of this work and the author was on study leave from Cairo University. Finally I must thank my wife Lucie, who patiently understood and accepted the pressures involved in finishing the work. To her I dedicate this thesis. CHAPTER 1 INTRODUCTION The main contender in the search for a controlled nuclear fusion reactor is the tokamak. The performance of the present generation of tokamak devices has been improved to a stage where an attempt should be made to overcome the more funda- mental drawbacks inherent to this approach. These limitations are mainly related to the pulsed nature of the reactor and its inefficient use of magnetic energy. The tokamak vessel is toroidal (i.e. doughnut-like) in shape and it is a require- ment that a current be made to flow in the closed plasma ring contained within it. In the standard tokamak this ring current is induced by transformer action and this means that the tokamak reactor, as presently envisaged, cannot operate in a steady state manner. The plasma ring is created and destroyed in each pulse of the current transformer. A number of serious engineering difficulties, related to mechanical and thermal stressing, arise from this limitation. An important branch of contemporary fusion physics research is, consequently, concerned with a stuay of the various methods which are available to drive plasma currents continuously in toroidal systems. These methods mainly involve the use of radio-frequency (RF) techniques (see, for example, Start (1983)). A second major problem with the standard tokamak is that it is particularly wasteful in its use of magnetic energy. It has been recognized that the situation can be improved if the aspect ratio of the plasma ring is decreased, that is, if the 'hole in the centre of the doughnut' is shrunk. Taken to its limit, this procedure results in a device which, superficially, appears more spherical than toroidal but in which a plasma ring of D-shaped cross-section tightly encircles the central axis.

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