The role of a runaway current in a post-disruption plasma is investigated through numerical simulations in an asymmetric magnetic reconnection event. We first reproduce the known linear results on the growth rate, the rotation frequency, and the formation of a microlayer smaller than the resistive one as found in Liu et al. [Physics of Plasmas 27, 092507 (2020)] and then focus on the nonlinear regime where are our main findings. We find that while the resistive layer controls the transition of the island from the linear to the nonlinear stage, the microlayer width controls the transition of the runaway current from the linear to the nonlinear phase. This latter transition is accompanied by a redistribution of runaways according to a spiral-like structure within the island. The same structure is also found in the thermal electron distribution when the electron inertia effects into the Ohm's law are taken into account. Finally, nonlinear simulations show that the island rotation frequency tends toward zero when the saturation is reached

In the vicinity of the poles of the planets of the solar system, ordered crystals of vortices and intermittency are observed. The formation of vortex structures in the vicinity of the poles of the planets of the solar system is investi-gated. The conditions for the formation of vortexes are considered. A nonlinear equation was found describing the vortex dynamics and structures were studied.

In this work, the development of two-dimensional current sheets with respect to tearing modes, in collisionless plasmas with a strong guide field, is analysed. During their nonlinear evolution, these thin current sheets can become unstable to the formation of plasmoids, which allows the magnetic reconnection process to reach high reconnection rates. We carry out a detailed study of the effect of a finite, which also implies finite electron Larmor radius effects, on the collisionless plasmoid instability. This study is conducted through a comparison of gyrofluid and gyrokinetic simulations. The comparison shows in general a good capability of the gyrofluid models in predicting the plasmoid instability observed with gyrokinetic simulations. We show that the effects of promotes the plasmoid growth. The effect of the closure applied during the derivation of the gyrofluid model is also studied through the comparison among the variations of the different contributions to the total energy

We investigate the problem of the tearing stability of a post-disruption weakly collisional plasma where the current is completely carried by runaway electrons. We adopt here a two fluid model which takes into account also ion sound Larmor radius and electron inertia effects in the description of the reconnection process. In the past, it has been demonstrated in [Helander et al. Phys. Plasmas 14, 12, (2007)] that in the purely resistive regime the presence of runaway electrons in plasma has a significant effect on the saturated magnetic island width. In particular, runaway electrons generated during disruption can cause an increase of 50% in the saturated magnetic island width with respect to the case with no runaway electrons. These results were obtained adopting a periodic equilibrium magnetic field that limited the analysis to small size saturated magnetic islands. Here we present our results to overcome this limitation adopting a non-periodic Harris' type equilibrium magnetic field. Preliminary results on the effects of the ion sound Larmor radius effects will also be presented

Noncollisional current sheets that form during the nonlinear development of spontaneous magnetic reconnection are characterized by a small thickness, of the order of the electron skin depth. They can become unstable to the formation of plasmoids, which allows the magnetic reconnection process to reach high reconnection rates. In this work, we investigate the marginal stability conditions for the development of plasmoids when the forming current sheet is purely collisionless and in the presence of a strong guide field. We analyze the geometry that characterizes the reconnecting current sheet, and what promotes its elongation. Once the reconnecting current sheet is formed, we identify the regimes for which it is plasmoid unstable. Our study shows that plasmoids can be obtained, in this context, from current sheets with an aspect ratio much smaller than in the collisional regime, and that the plasma flow channel of the marginally stable current layers maintains an inverse aspect ratio of 0.1.

The linear and nonlinear evolutions of the tearing instability in a collisionless plasma with a strong guide field are analysed on the basis of a two-field Hamiltonian gyrofluid model. The model is valid for a low ion temperature and a finite ?e. The finite ?e effect implies a magnetic perturbation along the guide field direction, and electron finite Larmor radius effects. A Hamiltonian derivation of the model is presented. A new dispersion relation of the tearing instability is derived for the case ?e = 0 and tested against numerical simulations. For ?e 1 the equilibrium electron temperature is seen to enhance the linear growth rate, whereas we observe a stabilizing role when electron finite Larmor radius effects become more relevant. In the nonlinear phase, stall phases and faster than exponential phases are observed, similarly to what occurs in the presence of ion finite Larmor radius effects. Energy transfers are analysed and the conservation laws associated with the Casimir invariants of the model are also discussed. Numerical simulations seem to indicate that finite ?e effects do not produce qualitative modifications in the structures of the Lagrangian invariants associated with Casimirs of the model

The plasmoid formation in collisionless plasmas, where magnetic reconnection within turbulence may take place driven by the electron inertia, is analyzed. We find a complex situation in which, due to the presence of strong velocity shears, the typical plasmoid formation, observed to influence the energy cascade in the magnetohydrodynamic context, has to coexist with the Kelvin-Helmholtz (KH) instability. We find that the current density layers may undergo the plasmoid or the KH instability depending on the local values of the magnetic and velocity fields. The competition among these instabilities affects not only the evolution of the current sheets, that may generate plasmoid chains or KH-driven vortices, but also the energy cascade, that is different for the magnetic and kinetic spectra.

Recent progress about helical self-organization studies is reported. Extensive exploita5on of 3D nonlinear visco-resistive modeling, SpeCyl code, which describes current-driven dynamics typical of pinch configura5ons in cylindrical geometry. Magnetic topology studies are based on the Field Line Tracing code NEMATO and a new refined tool to detect Lagrangian Coherent Structures is compared with results from a temperature equa/on solver. The following Physics Issues in helical self-organization are addressed: o Boundary Conditions and dimensionless parameters impact, (RFP, and circular Tokamak) o Forma5on of internal transport barriers, (RFP) o Temporary loss of opera5onal point, reconnec5on events, (RFP and circular Tokamak), o Alfvén waves excitation (RFP and circular Tokamak), RESULTS show: o Reasonable comparison (validation) with RFP experimental observations, o Similarities between RFP and Tokamak-like configuration.

Recent progress about helical self-organization studies is reported. Extensive exploita5on of 3D nonlinear visco-resistive modeling, SpeCyl code, which describes current-driven dynamics typical of pinch configura5ons in cylindrical geometry. Magnetic topology studies are based on the Field Line Tracing code NEMATO and a new refined tool to detect Lagrangian Coherent Structures is compared with results from a temperature equation solver. The following Physics Issues in helical self-organization are addressed: o Boundary Condi5ons and dimensionless parameters impact, (RFP, and circular Tokamak) o Formation of internal transport barriers, (RFP) o Temporary loss of opera5onal point, reconnec5on events, (RFP and circular Tokamak), o Alfvén waves excitation (RFP and circular Tokamak), RESULTS show: o Reasonable comparison (validation) with RFP experimental observa/ons, o Similarities between RFP and Tokamak-like configura/on.

We derive and analyze a dispersion relation for the growth rate of collisionless tearing modes, driven by electron inertia and accounting for equilibrium electron temperature anisotropy in a strong guide field regime. For this purpose, a new gyrofluid model is derived and subsequently simplified to make the derivation of the dispersion relation treatable analytically. The main simplifying assumptions consist in assuming cold ions, neglecting electron finite Larmor radius effects, decoupling ion gyrocenter fluctuations, and considering \beta_{perp}_ e << 1, with \beta_{perp}_ e indicating the ratio between the perpendicular electron thermal pressure and the magnetic pressure exerted by the guide field. This simplified version of the gyrofluid model is shown to possess a noncanonical Hamiltonian structure. The dispersion relation is obtained by applying the theory of asymptotic matching and does not predict an enhancement of the growth rate as the ratio \Theta_e between perpendicular and parallel equilibrium electron temperatures increases. This indicates a significant difference with respect to the case of absent or moderate guide field. For an equilibrium magnetic shear length of the order of the perpendicular sonic Larmor radius and at a fixed \beta_{perp}_ e, we obtain that the tearing mode in the strong guide field regime gets actually weakly damped, as \Theta_e increases. In the isotropic limit \Theta_e = 1, the dispersion relation reduces to a previously known formula. The analytical predictions are tested against numerical simulations, showing a very good quantitative agreement. We also provide a detailed discussion of the range of validity of the derived dispersion relation and of the compatibility among the different adopted assumptions.

In the framework of the studies on magnetic reconnection, much interest has been recently devoted to asymmetric magnetic configurations, which can naturally be found in solar and astrophysical environments and in laboratory plasmas. Several aspects of this problem have been investigated, mainly in a two-dimensional geometry and by means of particle-in-cell (PIC) simulations. Still, there are open questions concerning the onset and the effects of secondary instabilities in the nonlinear phase of an asymmetric reconnection process. In this work, we focus on the conditions that lead to the appearance of the Kelvin-Helmholtz instability following an asymmetric reconnection event in a collisionless plasma. This investigation is carried out by means of two-dimensional numerical simulations based on a reduced fluid model assuming a strong guide field. We show that, unlike the symmetric case, in the presence of asymmetry, a Kelvin-Helmholtz-like instability can develop also for a finite equilibrium electron temperature. In particular, simulations indicate the formation of steep velocity gradients, which drive the instability, when the resonant surface of the equilibrium magnetic field is located sufficiently far from the peak of the equilibrium current density. Moreover, a qualitative analysis of the vorticity dynamics shows that the turbulent behavior induced by the secondary instability not only is confined inside the island but can also affect the plasma outside the separatrices. The comparison between simulations carried out with an adiabatic closure and a Landau-fluid closure for the electron fluid indicates that the latter inhibits the secondary instability by smoothing velocity gradients.

In recent years the use of dynamical techniques to investigate the transport features in magnetized plasmas assumed an important role, especially in plasmas with low collisionality. In this regime transport is highly anisotropic, collisions are no longer the main actors and, as it has been shown, e.g. in Reversed Field Pinch (RFP) and Stellarator studies1,2, the magnetic topology plays a very important role: neglecting the finite Larmor radius and drifts, in this regime thermal particles move essentially along magnetic field lines. The transport properties in such systems are usually analyzed drawing the Poincaré map of the magnetic field. Unfortunately, especially when strong chaos affects the system, the Poincaré map gives only a general picture of the transport neglecting that there exist coherent patterns governing the transport process. Moreover, the Poincaré map can be applied only under some circumstances: the system has to be periodic and thus, for an evolving 3D magnetic configuration, this means to study the confinement properties at fixed time instant. The goal of the present work is to go beyond these limits applying Lagrangian Coherent Structures (LCS) technique3, borrowed from the study of Dynamical Systems, to magnetic field configurations in order to underline coherent patterns and thus regions of the system having different transport characteristics. In our work the LCS technique has been applied to carry on three studies. The first study focuses on a simplified model that allows us to consider explicitly the case where the magnetic field evolves in time on timescales comparable to the particles transit time through the configuration4,5. In contrast with previous works on this topic6, this analysis requires that a system that is aperiodic in time be investigated. The second study, expanding previous works7, extends our analysis to realistic numerical reproduction of a RFP configuration. In particular we focus in two different situations with resonant and non resonant dominant mode. In this two frame, a further distinction regards the amplitude of the dominant mode respect to the others: two time instants, with different level of field line chaos, are analyzed. Finally in the third part, starting from the cases of previous study, an effective magnetic field8,9 for non-thermal particles is constructed and analyzed. This allows us to show the different coherent patterns that determinates the transport of thermal and non-thermal particles and thus how different energy particles obey to different transport.

A new kind of magnetic reconnection process that is associated with the presence of finite electron temperature [1] gradients on rational magnetic surfaces of an axisymmetric confinement configuration, is presented. This is relevant to regimes where the electron thermal conductivity is relatively large and the reconnection layer is smaller than the "thermal" layer where the transverse thermal conductivity plays a key role. When referring to fusion burning plasmas the excitation of the considered modes is associated with the nuclear heating of the electron population. This "thermonuclear instability" [2] can then develop more easily around closed magnetic field lines, than on nonrational magnetic surfaces.

The concept of Lagrangian coherent structures (LCS) has been recently applied to complex magnetic configurations in plasmas in order to find and characterize their main structural features. LCS make it possible to separate regions inside these configurations where field lines exhibit a different kind of behavior. In the present article, first we review the main features and uses of this technique and then apply it to the study of configurations that evolve into a self-organized quasi-single helicity state referring in particular to results obtained in the reversed-field pinch experiment in Padua.

Magnetically confined plasmas of fusion interest display phenomena that find several analogies in astrophysics and other complex systems. This is the case of toroidal pinches where magnetic self-organization molds the plasma into a peculiar helical shape when the ratio of plasma current to toroidal magnetic flux exceeds the socalled Kruskal-Shafranov limit. In this case, a core kink instability ("sawtoothing" and/or "snake") tends to develop in Tokamaks 1 . Similarly, a global helical shape (so-called Quasi Single Helical, QSH, regimes) forms in Reversed Field Pinch experiments (RFP)2,3 , helically modulating the plasma up to the edge 4,5 . MHD modeling has been largely successful in capturing the basic features of such a phenomenon 6,7,8 , quite evading the famous Taylor's relaxation theory for RFP 9,10 . Nearly periodic relaxation events involving current sheet reconnection can be observed 6,9 , together with a magnetic chaos healing effect when the helical states are robustly achieved11,8 . The latter effect is presently the best candidate to explain the formation of internal electron transport barriers2 observed in RFP helical regimes. In particular, "hidden" magnetic field lines transport barriers have been recently detected in experimental-like numerical simulations, which are associated with "fine" topological structures like Cantori sets or Lagrangian Coherent Structures 12 . After summarizing these general features, we here discuss the recent successful MHD prediction of alternative helical regimes, obtained by seed edge magnetic perturbations with suitable choice of helical pitch. A first set of RFXmod experiments substantially confirms modeling predictions 13 . The new helical regimes obtained as plasma response to edge Magnetic Perturbations are predicted to favor magnetic chaos healing in the case of non-resonant seeds. After first indications obtained in RFX-mod experiment 13 , we expect to validate modeling predictions concerning transport properties in the modified device RFX-mod2 starting operation in 2020. The device, characterized by reduced plasma-wall/feedback coils distance, will provide efficient control action in order to negotiate at best with RFP helical magnetic self- organization.

The concept of Lagrangian Coherent Structures (LCS) has been introduced by G. Haller in the context of transport processes in complex fluid flows [1]. LCS are a generalization of the dynamical structures observed in autonomous and periodic systems to temporally aperiodic flows. They separate the flow domain into macro-regions inside which fast mixing phenomena take place. Over the finite time span which characterizes the LCS these macro-regions do not exchange fluid elements and thus act as transport barriers. In two recent articles [2, 3], we have applied this conceptual framework to the study of particle transport in a magnetized plasma by referring to a simplified model that uses magnetic field lines as a proxy for particle trajectories and that allows us to consider explicitly a magnetic configuration evolving in time on timescales comparable to the particle transit time through the configuration. © 45th EPS Conference on Plasma Physics, EPS 2018. All rights reserved.

This paper addresses one aspect of the problem of the suppression of tearing mode magnetic islands by electron cyclotron current drive (ECCD) injection, formulating the problem as the converse of a forced reconnection problem. New physical conditions are discussed which should be considered in the technical approach towards a robust control strategy. Limits on the ECCD deposition are determined to avoid driving the system into regimes where secondary instabilities develop. Numerical simulations confirming the theory are also presented.

An electromagnetic reduced gyrofluid model for collisionless plasmas, accounting for electron inertia, finite ion Larmor radius effects and Landau-fluid closures for the electron fluid is derived by means of an asymptotic expansion from a parent gyrofluid model. In the absence of terms accounting for Landau damping, the model is shown to possess a non-canonical Hamiltonian structure. The corresponding Casimir invariants are derived and use is made thereof, in order to obtain a set of normal field variables, in terms of which the Poisson bracket and the model equations take a remarkably simple form. The inclusion of perpendicular temperature fluctuations generalizes previous Hamiltonian reduced fluid models and, in particular, the presence of ion perpendicular gyrofluid temperature fluctuations reflects into the presence of two new Lagrangian invariants governing the ion dynamics. The model is applied, in the cold-ion limit, to investigate numerically a magnetic reconnection problem. The Landau damping terms are shown to reduce, by decreasing the electron temperature fluctuations, the linear reconnection rate and to delay the nonlinear island growth. The saturated island width, on the other hand, is independent of Landau damping. The fraction of magnetic energy converted into perpendicular kinetic energy also appears to be unaffected by the Landau damping terms, which, on the other hand, dissipate parallel kinetic energy as well as free energy due to density and electron temperature fluctuations.

In a pair of linked articles (called Papers I and II, respectively), we apply the concept of Lagrangian Coherent Structures borrowed from the study of Dynamical Systems to chaotic magnetic field configurations in order to separate regions where field lines have different kinds of behavior. In the present article, Paper II, by means of a numerical procedure, we investigate the Lagrangian Coherent Structures in the case of a two-dimensional magnetic configuration with two island chains that are generated by magnetic reconnection and evolve nonlinearly in time. The comparison with previous results, obtained by assuming a fixed magnetic field configuration, allows us to explore the dependence of transport barriers on the particle velocity. Published by AIP Publishing.

In a pair of linked articles (called Papers I and II, respectively), we apply the concept of Lagrangian Coherent Structures (LCSs) borrowed from the study of dynamical systems to magnetic field configurations in order to separate regions where field lines have a different kind of behaviour. In the present article, Paper I, after recalling the definition and the properties of the LCSs, we show how this conceptual framework can be applied to the study of particle transport in a magnetized plasma. Furthermore, we introduce a simplified model that allows us to consider explicitly the case where the magnetic configuration evolves in time on time scales comparable to the particle transit time through the configuration. In contrast with previous works on this topic, this analysis requires that a system that is aperiodic in time be investigated. Published by AIP Publishing.