Nonlinear Evolution Of Tearing Modes Research Articles

Multi-harmonic Rutherford island theory

Rutherford island theory, which governs the nonlinear evolution of tearing modes in tokamak plasmas, is generalized to take into account situations in which the conventional one-harmonic approximation is not valid. The analysis incorporates non-inductive currents driven by radio frequency (RF) electromagnetic waves injected into the plasma. A multi-harmonic tearing mode dispersion relation is derived that takes the form of a nonlinear inhomogeneous matrix eigenvalue problem. The dispersion relation is solved in the so-called two-harmonic approximation, in which only the principal Fourier harmonic of the perturbed magnetic flux and its first overtone are included in the calculation. In the absence of RF current drive, the nonlinear behavior of a tearing mode predicted in the two-harmonic approximation does not differ substantially from that predicted in the one-harmonic approximation. On the other hand, RF current drive that is sufficiently localized in the vicinity of the O-points of the mode's magnetic island chain is capable of triggering bifurcations of the O-points (which is impossible in the one-harmonic approximation). However, the current drive is incapable of triggering bifurcations of the island X-points. This finding is significant because Bardóczi and Evans [Phys. Rev. Lett. 126, 085003 (2021)] recently observed bifurcations of magnetic island chain O-points in the presence of RF current drive in the DIII-D tokamak but did not observe bifurcations of the X-points. Finally, the changes in the topology of the magnetic island flux-surfaces induced by RF current drive are found to facilitate the stabilization of the tearing mode.

Nonlinear study of tearing modes and plasma flows around magnetic islands in tokamak plasmas

The behavior of non-linear tearing modes and the plasma flows around magnetic islands is studied numerically in a cylindrical geometry using the method of reduced magneto-hydro-dynamic simulation. The results show that the single tearing mode (STM) becomes stable in a short time. The magnetic islands of double tearing modes (DTMs) first develop to a sufficiently large scale and then couple together when entering the non-linear phase. It is also shown that, before the non-linear growth stage, the perturbed kinetic energy and magnetic energy of both the STM and DTM have a process from different signs to constant positive values. For the STM island and plasma flow, it is demonstrated that the shear flow is formed on both sides of the islands and the poloidal flow velocity around the O-point is larger than that around the X-point. For the DTM island and plasma flow, we found that the peak of the poloidal flow velocity is mainly distributed at the O-point edge and the X-point of the magnetic island and the plasma flow velocities at the magnetic island edges are opposite. In addition, the process of plasma flow accompanying the nonlinear evolution of tearing modes is also presented.

Study of nonlinear evolution of tearing modes induced by anomalous electron viscosity

The nonlinear development of double tearing modes (DTMs) induced by anomalous electron viscosity, which may be present in magnetically confined plasmas due to electromagnetic turbulence and structures such as braiding of magnetic field lines, in a periodic cylinder is simulated. Comparing the evolution of the helical magnetic flux contours, the nonlinear development of magnetic reconnection of the DTMs is studied for different distances between the two resonant rational flux surfaces. There are three clear phases in the nonlinear evolution of DTMs when the distance between the two resonant flux surfaces is large: linear growing, nonlinearly driven growing, and saturation. There are four phases when the distance is medium: linear growing, nonlinearly driven growing, fast growing, and decaying. Finally, there are three phases of evolution when the distance is quite small, which are different from the phases when the distance is large: linear growing, nonlinearly driven growing, and decaying,. The coupling between the fastest-growing modes at the two resonant surfaces drives the nonlinear evolution of the system.

The nonlinear evolution of tearing mode with electron viscosity in electron magnetohydrodynamics

The general time evolution of tearing mode due to electron viscosity μe from linear to nonlinear phase in the framework of electron magnetohydrodynamics (EMHD) is derived by quasilinear theory. Tearing mode grows exponentially in the linear phase and slows to an algebraic growth behavior Ψ1∝(μet)2/3 (Ψ1 is the magnetic flux) in the nonlinear phase. These two phases are separated by a transition during which the growth behavior is much different from that in the linear and nonlinear phases. It behaves as Ψ1∝μe5/8t1/2 approximately.

The influence of mode coupling on the non-linear evolution of tearing modes

On the basis of tearing mode theory a simple but physically explicit model of the evolution of toroidally coupled rotating magnetic islands has been developed. The basic mechanism identified by the model in the island evolution is the locking in phase of rotating islands that leads to rapid destabilisation of an initially stable mode. Destabilisation of marginally stable (2, 1) and (3, 1) modes is analysed in several scenarios. It is shown that mode coupling is an effective way of destabilising a m = 3 island in a low-β plasma. The numerical examples presented show the individual roles of coupling, inertia and a resistive wall. The model was applied for the analysis of MHD observations of an ASDEX discharge.

Nonlinear self-reinforced growth of tearing modes with multiple rational surfaces

The nonlinear evolution of tearing modes with multiple rational surfaces is discussed. It is demonstrated that, in the presence of small differential rotation, the nonlinear growth might be faster than exponential. This growth occurs as the rotation frequencies of the plasma at the different rational surfaces equilibrate.

Effect of Sheared Flow on Resistive Tearing Instability and the Triggering of Flare

AbstractThe nonlinear evolution of tearing modes in the presence of sheared mass flow is studied in the cylindrical geometry. It is demonstrated that a sufficient large sheared mass flow can destabilize the development of resistive tearing instability. It is suggested that the coupling of sheared mass flow with shear magnetic field may be a triggering of solar flares.

Oscillating magnetic islands in a rotating plasma

The nonlinear evolution of tearing modes in the presence of sheared mass flow is studied as an initial value problem. Under certain conditions, when the mode is driven unstable primarily by the mass flow, the nonlinear evolution leads to a dynamic state in which the size and shape of the magnetic islands are oscillatory.

RESISTIVE FLUID INSTABILITY AT THE NONMONOTONOUS CURRENT PROFILE

It can be shown that the dynamics of magnetic perturbation at the nonmonoto-nous profile of a current in tokamak is qualitatively different from that of normal profiles. Behaviour of the perturbation depends on the helical magnetic currents localized mainly between the two singular surfaces. In this paper the numerical method developed to study the non-linear evolution of tearing modes is described in detail.

Magnetic reconnection: A problem of general physical and astrophysical interest, with special implications in solar physics

The astrophysical applications of magnetic reconnection are addressed. MHD flows involving reconnection are considered for various situations and different media, and the importance of thermal and gravitational effects in plasma MHD flows is argued. The nature of reconnection where the plasma is not collisional enough to be regarded as an MHD medium is addressed, and microturbulence in reconnection processes is discussed. Phenomena related to the nonlinear evolution of tearing modes in time-dependent reconnection are considered, including magnetic braiding, internal disruptions involving an apparently unique helical mode, and situations resulting when the primary periodicity of the tearing perturbation is inapplicable or where finite resistivity is included.

Effects of toroidal coupling on the non-linear evolution of tearing modes and on the stochastisation of the magnetic field topology in plasmas

The resistive MHD equations have been handled in toroidal geometry following the tokamak ordering, in order to obtain a simplified set of non-linear equations. This system of equations is compact, closed, consistent and exact to the first two orders in the expansion in the inverse aspect ratio. Studies of the non-linear evolution of tearing modes in the real geometry of tokamak discharges are now in progress, and quite significant results have been obtained from the numerical code REVE of Fontenay based on our above model. From the analytical results, strong linear coupling between neighbouring modes is expected as is demonstrated by the numerical results in the linear, and non-linear regimes. Moreover, coupling exhibits a stochastic structure of the magnetic field lines, the threshold of which is seen to be easily computed by a simple analytical criterion.