Master Thesis Presentation Presentation December 2019 CITATIONS - PDF document

See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/339795979 Master Thesis Presentation Presentation · December 2019 CITATIONS READS 0 31 1 author: Yacopo Damizia Sapienza University of Rome 1 PUBLICATION 0 CITATIONS SEE PROFILE Some of the authors of this publication are also working on these related projects: Implementation of an optical tomography of the plasma on the PROTO-SPHERA experiment View project All content following this page was uploaded by Yacopo Damizia on 26 May 2020. The user has requested enhancement of the downloaded file.

Faculty of Mathematical, Physical and Natural Sciences Master Degree Course in Particle and Astroparticle Physics STUDY OF MAGNETIC RECONNECTION PHENOMENA ON THE PROTO-SPHERA EXPERIMENT THROUGH THE ANALYSIS OF FAST CAMERAS DATA Degree Dissertation Internal rapporteur: Candidate: Giovanni Montani Yacopo Damizia External rapporteur: Serial: 1388631 Franco Alladio Academic year 2018/2019

To my family 2

SUMMARY INTRODUCTION ............................................................................................................................... 5 CHAPTER 1: COMPACT TOROIDS ................................................................................................. 9 1.1 Spheromak ................................................................................................................................ 11 1.2 Field Reverse Configuration .................................................................................................... 13 1.3 Spherical Tokamak ................................................................................................................... 15 CHAPTER 2: PROTO-SPHERA PHYSICAL PRINCIPLES ........................................................... 16 2.1 Toroidal Plasma Formation ...................................................................................................... 17 2.2 Magnetic Helicity ..................................................................................................................... 18 2.3 Relative Magnetic Helicity ....................................................................................................... 19 2.3 Magnetic Reconnection ............................................................................................................ 21 2.4 DC Helicity Injection ............................................................................................................... 22 CHAPTER 3: MAGNETOHYDRODYNAMICS ............................................................................. 24 3.1 Two-fluid model ....................................................................................................................... 26 3.2 Single fluid model .................................................................................................................... 28 3.3 Ideal MHD ................................................................................................................................ 34 3.4 Balance in presence of magnetic forces ................................................................................... 36 3.4.1 θ -Pinch ............................................................................................................................... 37 3.4.2 Z-Pinch .............................................................................................................................. 38 3.4.3 Screw-Pinch ....................................................................................................................... 39 CHAPTER 4: CHANDRASEKHAR-KENDALL-FURTH .............................................................. 41 4.1 CKF Force-Free Fields ............................................................................................................. 42 4.2 Ideal MHD Stability of CKF Force-Free Fields ....................................................................... 44 4.3 Unrelaxed CKF Configurations ................................................................................................ 45 CHAPTER 5: MECHANIC DESIGN OF PROTO-SPHERA .......................................................... 46 5.1 Vacuum Vessel ......................................................................................................................... 47 5.2 Electrodes ................................................................................................................................. 49 5.3 Poloidal Field Coils .................................................................................................................. 50 5.4 Divertor .................................................................................................................................... 51 3

5.6 Assembly and Maintenance ...................................................................................................... 53 CHAPTER 6: DIAGNOSTICS .......................................................................................................... 54 6.1 Fast Cameras ............................................................................................................................ 55 6.2 Camera Calibration and 3D Layout .......................................................................................... 56 CHAPTER 7: EXPERIMENTAL SEQUENCE AND DAQ ............................................................ 60 7.1 Data Acquisition System .......................................................................................................... 60 7.2 Sequence ................................................................................................................................... 62 CHAPTER 8: IMPLEMETATION OF OPTICAL TOMOGRAPHY .............................................. 64 8.1 Zernike Polynomials ................................................................................................................. 64 8.1.1 Mathematical basis ............................................................................................................ 65 8.1.2 Tomographic inversion of Zernike .................................................................................... 67 8.2 Data analyses ............................................................................................................................ 69 8.2.1 Hydrogen ........................................................................................................................... 70 8.2.2 Argon ................................................................................................................................. 72 CONCLUSIONS ................................................................................................................................ 74 REFERENCES ................................................................................................................................... 77 ACKNOWLEDGEMENTS ............................................................................................................... 78 4

INTRODUCTION In the field of nuclear fusion the most commonly used machines for the study of magnetic confinement fusion reactions are the tokamaks. A tokamak is an experimental toroidal-shaped machine designed by Russian physicists in the 1950s, which through the magnetic confinement of hydrogen isotopes in the plasma state creates the conditions for the thermonuclear fusion to occur in a controlled manner. The main magnetic field in the tokamak is the toroidal field 𝐶 Ф (Fig.1a), but this alone cannot confine the plasma, because to have an equilibrium in which the plasma pressure is balanced by the magnetic force it is also necessary to have a poloidal magnetic field 𝐶 𝑞 . This field is mainly produced by the current flowing in the plasma itself along the toroidal direction. The poloidal magnetic fields are generally an order of magnitude lower than the toroidal field. The combination of these two fields generates field lines that have a helical trajectory around the torus (Fig.1b). Figure 1: Toroidal magnetic field 𝐶 Ф poloidal magnetic field 𝐶 𝑞 b) The combination of 𝐶 Ф and 𝐶 𝑞 generates lines of field that wrap around the plasma In the tokamaks, there is a central pole, containing the inner part of the toroidal magnet and the ohmic transformer, which produces and maintains the toroidal plasma current. The plasma pressure is the product of particle density and temperature. The fact that the reactivity of the plasma increases with both these quantities implies that the pressure must be high enough in a reactor. The plasma pressure is determined by stability considerations obtained through the equations of MagnetoHydroDynamics (MHD), and increases with the strength of the applied magnetic field. However, the magnitude of the toroidal field is limited by technological factors. For example in laboratory experiments with copper coils, both the cooling requirement and the magnetic forces impose a limit to the magnetic field that they can produce. Moreover, it is necessary to take into account the energy losses due to the Joule effect and today therefore, superconducting coils are envisaged which have a field limit lower than that of copper. In this case, there is the risk of a loss of superconductivity beyond a certain critical 5