Macroarea di Scienze MM FF NN Corso di Laurea in Fisica Master Thesis Study of three-dimensional Magnetic Reconnection Phenomena in the experiment PROTO-SPHERA Student: Supervisor: Samanta Macera Prof. Marco Tavani Co-Supervisor: Dott. Franco Alladio Academic Year 2019/2020 Contents Introduction 4 1 Magnetic Reconnection 6 1.1 General theory of reconnection . 6 1.2 Steady state reconnection . 9 1.3 Fast Magnetic Reconnection . 14 1.4 Collisionless reconnection . 17 1.5 Three-dimensional reconnection . 24 1.6 Magnetic Reconnection in Astrophysics . 27 2 Laboratory Plasma 34 2.1 Experimental setup to study reconnection . 34 2.1.1 Magnetic Confinement . 35 2.1.2 Tokamak . 39 2.1.3 Reversed Field Pinch (RFP) and Spheromak . 41 2.2 Magnetic Reconnection and kink instability . 43 2.3 Experimental evidence of reconnection . 46 3 PROTO-SPHERA 51 3.1 From the screw pinch to the spherical torus . 54 3.1.1 Phase 1.0 . 55 3.1.2 Phase 1.25 (January 2018 - September 2019) . 57 3.1.3 Phase 1.5 (September 2019 - December 2021) . 58 3.1.4 The role of magnetic reconnection . 59 3.1.5 Towards phase 2.0 and beyond . 59 4 Data Analysis 63 4.1 Hall sensor . 63 4.2 Langmuir probe . 64 4.3 Fast cameras . 66 4.4 Fast camera image analysis . 68 4.5 Cross Correlations analysis . 74 4.6 Plasma phenomenology . 81 2 Conclusions 85 Bibliography 89 Ringraziamenti Introduction In the last eighty years, a lot of efforts have been made in Plasma Physics in order to understand magnetic reconnection, which is a physical process consisting of a topological rearrangement of magnetic field lines in a plasma. Magnetic fields pervade the most of the objects throughout the Universe. Depending on the object, the magnetic field will have different features and complexity. For example, the ones emanating from the planets in our s So- lar System are essentially dipolar and are relatively weak compared to the strengths that can be found on the Sun's magnetic field. Reconnection oc- curs in regions of strong magnetic shear, that are regions in which the direc- tion of the magnetic field changes significantly over a short distance. Under certain circumstances, magnetic field lines can \break" and re-assemble in order to minimize the magnetic energy stored in the magnetic field and in order to achieve a new equilibrium configuration with lower energy. The big amount of energy released during the process is converted into kinetic energy through acceleration or heating of charged particles in the plasma: the electrons through Ohmic heating and the ions through acceleration of Alfv´enicjets. Reconnection can be both collisional or collisionless, depending on the char- acteristics of the magnetized plasma. Collisional reconnection is usually too slow to explain the data observed from both astrophysical and laboratory plasmas. Therefore, fast magnetic reconnection requires collisionless mod- els. This process is of great importance in many astrophysical processes such as the heating of stellar coronae, the acceleration of stellar winds and astrophysical jets, γ-ray burst and magnetospheric substorms, being the mechanism behind the auroras. Earth's tear-shaped magnetic field contin- uously oscillates and responds to the changing intensity of the solar wind. The solar wind particles funnel around to the long tail of the magnetosphere, where they become trapped. When magnetic reconnection occurs, the par- ticles are accelerated toward Earth's poles. Reconnection could be involved also in the formation of stars. Stellar activity is magnetically driven, and raconnections can be expected also in strongly magnetized neutron stars (classed as anomalous X-ray pulsars and as soft gamma repeaters). More- over the observed hard X-ray variability of some accretion disks could be due to flares powered by reconnection. It is also of fundamental important 4 Contents in laboratory plasma, since it has been observed in numerous laboratory ex- periments and it seems to be the key process for self-organization of fusion plasmas in devices as tokamaks, spheromaks and reversed field pinches. Although it concerns several phenomena in nature, this process is challeng- ing to observe. In fact reconnection might not always have the signatures which we expect. Moreover, a change of the magnetic structure might also occur with a lower energy output or on a slower time scale. Over the years, several models have been proposed: two-dimensional, three- dimensional, collisional and collisionless models and so on. In this thesis work, the data obtained from the PROTO-SPHERA (PROTOtype of a Spherical Plasma for HElicity Relaxation Assessment) fusion experiment, located at the CR Enea in Frascati were analyzed. This experiment has a magnetic setup that exploits magnetic reconnection mechanisms to confine the plasma in a spherical torus. The purpose of this thesis is to characterize the episodes of magnetic reconnection within the experiment. In chapter 1 the theory of magnetic reconnections is presented. Collisional reconnec- tion models, such as Sweet Parker and Petschek model, and collisionless models are explored. Some applications in Astrophysics are exposed in sec- tion 1.6. Chapter 2 describes laboratory experiments aimed at studying nuclear fusion, in which reconnection processes can be studied. Different types of magnetic configurations used to confine plasmas and the role of magnetic reconnections in these laboratory plasmas are presented. In Sec- tion 2.2 kink instability and its connection with Astrophysics are exposed. In chapter 3 the PROTO-SPHERA experiment and its differences from the configurations described in Chapter 2 are described. Chapter 4 presents the diagnostics used and the data analysis. Finally, section 4.6 presents the PROTO-SPHERA plasma phenomenological description that derives from this analysis. 5 Chapter 1 Magnetic Reconnection 1.1 General theory of reconnection Magnetic reconnection is a topological rearrangement of magnetic field that converts magnetic energy to plasma energy. This phenomenon affects plasma dynamics, energetics and transport, and it couples global and local scales. There is a unique relationship between the topology of a magnetic field and the corresponding equilibrium: any change in topology has a significant im- pact on the entire equilibrium [1]. Therefore, all equilibria are characterized by their own topology. If the current topology of the plasma is character- ized by an equilibrium with energy E, and a change in the aforementioned topology would lead to an equilibrium with energy E0 < E , the plasma will evolve towards this latter state of equilibrium by modifying the topology of the magnetic field through magnetic reconnection processes. A topological change of the magnetic structure can release huge amounts of the energy stored in the magnetic field. During this process there is a rapid conversion of magnetic energy by viscous processes into heat, radiation and particle acceleration. Therefore, in its most general formulation, magnetic reconnection requires only a change in the magnetic connectivity of plasma elements. In the ideal case of highly conducting plasma the electric field is given by Ohm's law E + v × B = 0 (1.1) where v is the bulk plasma velocity field. In this condition Alfv´en theorem holds: without dissipation terms on the right hand side of the previous equation, the topology of field lines is left invariant, which means that the flux is invariant for all the times, and therefore magnetic field lines are frozen to the plasma. Hence magnetic flux and magnetic field lines are conserved [2]. By taking the curl of ideal Ohm's law (equation 1.1), the induction equation for the magnetic field can be obtained: @B = r × (v × B): (1.2) @t 6 1.1. General theory of reconnection In order to allow field lines to change their connection, there must be a dissipative term which breaks the frozen-in condition, even if only in a small diffusion region. In fact, a change in a region small compared to the size of the system still has global effects. A non ideal term R must be added to the right side of Ohm's law 1.1: E + v × B = R (1.3) where R can contain resistivity, Hall current, electron inertia and pressure and ambipolar diffusion. If R can be represented as R = rφ + u × B; (1.4) equation 1.3 becomes E + (u + v) × B = rφ (1.5) and equation 1.2 becomes dB − r × w × B = 0 (1.6) dt with w = u + v. So even if the connection of plasma elements might change (the field lines move with velocity u, different from the velocity of plasma element v), the topology of field lines remains the same since the field is frozen-in respect to the velocity w, so no reconnection can occour, provided that u and w are globally regular. As already mentioned, R can be the resitive term in Ohm's law ηj, or can contain the electron inertia or the electron pressure tensor. Depending on the terms it contains, different reconnection models can be obtained. R can be decomposed in the two direction parallel and orthogonal to the magnetic field: Rk = rkφ (1.7) R? = r?φ + u × B: (1.8) We can now solve 1.7 by integrating the potential φ along magnetic field lines and then use this solution to determine u from 1.8. It can be shown that the solution for u is B × (R − rφ) u = : (1.9) B2 At magnetic null points the direction of B is undefined. Here the splitting into 1.7 and 1.8 breaks down. An analysis of flow u near the null point shows that certain R require diverging derivatives of u at the null (Hornig and Schindler, 1996). A bifurcation of null points is a change of topology and requires an infinite velocity u at the time of the bifurcation.