In this work we study the ergodic magnetic limiters (EML) action on field lines from the point of view of a chaotic scattering process, considering the so-called exit basins, or sets of points in the chaotic region which originate field lines hitting the wall in some specified region. We divide the tokamak wall into three areas of equal poloidal angular length, corresponding to different exits for a chaotic field line. In order to obtain the exit basins we used a fine grid chosen inside a small rectangle which comprises a representative part of the chaotic region near the wall. Thus, exit basins were obtained for a tokamak wall with reversed magnetic shear. The nontwist mapping describes the perturbed magnetic field lines with two twin chains of magnetic islands and chaotic field lines in their vicinity. For a perturbing resonant magnetic field with a fixed helicity, the observed escape pattern changes with the perturbation intensity.
Gyrotropy-Induced Symmetry Breaking of Erosion Hot Spots on Antenna Limiters during High-Power Tokamak RF Operation: Mechanisms and Mitigation Strategies
Analytic solutions of the magnetohydrodynamic equilibrium equations for a cylindrically symmetric magnetically confined plasma with reversed magnetic shear, s < 0, and sheared flow are constructed by prescribing the safety factor-, poloidal velocity- and axial velocity- profiles consistently with experimental ones.
Toroidal rotation is well known to play significant roles in the edge transport and L-H transition dynamics of tokamaks. Our recent calculation finds that a sufficiently strong localized toroidal rotation can directly bring out the formation of edge pressure pedestal with reversed magnetic shear that is reminiscent of an H-mode plasma, purely through the effects of toroidal rotation on the tokamak MHD equilibrium itself. In particular, the enhanced edge toroidal rotation enables a substantial peaking of the parallel current profile near edge in higher $β$ regimes, which leads to the flattening…
The effect of a narrow sub-Alfvenic shear flow layer near the minimum q_min of the tokamak safety factor profile in a configuration with reversed central shear is analyzed. Sufficiently strong velocity shear gives rise to a broad spectrum of fast growing Kelvin-Helmholtz (KH)-like ideal magnetohydrodynamic (MHD) modes with dominant mode numbers m,n ~ 10. Nonlinear simulations with finite resistivity show magnetic reconnection near ripples caused by KH-like vortices, the formation of turbulent structures, and a flattening of the flow profile. The KH modes are compared to double tearing modes (D…
The aim of the present work is to investigate tokamak equilibria with reversed magnetic shear and sheared flow, which may play a role in the formation of internal transport barriers (ITBs), within the framework of two-fluid model. The study is based on exact self-consistent solutions in cylindrical geometry by means of which the impact of the magnetic shear, s, and the "toroidal" (axial) and "poloidal" (azimuthal) ion velocity components on the radial electric field, its shear and the shear of the ExB velocity is examined. For a wide parametric regime of experimental concern it turns out that …
First Observation of Fishbone-Driven Zonal Flows with Fine Reversed Structure in Tokamak Plasmas
School of Nuclear Science and Technology, University of Science and Technology of China（中国科学技术大学核科学与技术学院）；Institute of Plasma Physics, Chinese Academy of Sciences（中国科学院等离子体物理研究所）
In this paper we have studied the influence of reversed shear on the improvement of the confinement's quality in the plasma of tokamak and especially in reducing the anomalous transport. For that, we have used a special model for the drift wave fields. Comparison between particles trajectories for normal and reversed shear is carried out in 2 D and 3 D presentation. Also, the diffusion coefficient of particles for the two cases, normal and negative shear, is evaluated.
A novel channel for fuel ions heating in tokamak core plasma is proposed and analyzed using nonlinear gyrokinetic theory. The channel is achieved via spontaneous decay of reversed shear Alfven eigenmode (RSAE) into low frequency Alfven modes (LFAM), which then heat fuel ions via collisionless ion Landau damping. The conditions for RSAE spontaneous decay are investigated, and the saturation level and the consequent fuel ion heating rate are also derived. The channel is expected to be crucial for future reactors operating under reversed shear configurations, where fusion alpha particles are gene…
Some internal transport barriers in tokamaks have been related to the vicinity of extrema of the plasma equilibrium profiles. This effect is numerically investigated by considering the guiding-center trajectories of plasma particles undergoing ExB drift motion, considering that the electric field has a stationary nonmonotonic radial profile and an electrostatic fluctuation. In addition, the equilibrium configuration has a nonmonotonic safety factor profile. The numerical integration of the equations of motion yields a symplectic map with shearless barriers. By changing the parameters of the sa…
Weak and reversed magnetic shear effects on internal kink and fishbone modes
State Key Laboratory of Advanced Electromagnetic Technology（先进电磁技术国家重点实验室）；International Joint Research Laboratory of Magnetic Confinement Fusion and Plasma Physics（磁约束聚变与等离子体物理国际联合研究中心）
The effects that energetic trapped ions have on linear resistive magnetohydrodynamic (MHD) instabilities are studied in a reduced model that captures the essential physics driving or damping the modes through variations in the magnetic shear. The drift-kinetic orbital interaction of a slowing down distribution of trapped energetic ions with a resistive MHD instability is integrated to a scalar contribution to the perturbed pressure, and entered into an asymptotic matching formalism for the resistive MHD dispersion relation. Toroidal magnetic field line curvature is included to model trapping i…
The linear dynamics of Alfven modes in tokamaks is investigated here by means of the global gyrokinetic particle-in-cell code NEMORB. The model equations are shown and the local shear Alfven wave dispersion relation is derived, recovering the continuous spectrum in the incompressible ideal MHD limit. A verification and benchmark analysis is performed for continuum modes in a cylinder and for toroidicity-induced Alfven Eigenmodes. Modes in a reversed-shear equilibrium are also investigated, and the dependence of the spatial structure in the poloidal plane on the equilibrium parameters is descri…
The effect of magnetic perturbations (MPs) on the helical self-organization of shaped tokamak plasmas is discussed in the framework of the nonlinear 3D MHD model. Numerical simulations performed in toroidal geometry with the \textsc{pixie3d} code [L. Chacón, Phys. Plasmas {\bf 15}, 056103 (2008)] show that $n=1$ MPs significantly affect the spontaneous quasi-periodic sawtoothing activity of such plasmas. In particular, the mitigation of sawtooth oscillations is induced by $m/n=1/1$ and $2/1$ MPs. These numerical findings provide a confirmation of previous circular tokamak simulations, and are …
A general methodology is proposed to differentiate the likelihood of energetic-particle-driven instabilities to produce frequency chirping or fixed-frequency oscillations. The method employs numerically calculated eigenstructures and multiple resonance surfaces of a given mode in the presence of energetic ion drag and stochasticity (due to collisions and micro-turbulence). Toroidicity-induced, reversed-shear and beta-induced Alfven-acoustic eigenmodes are used as examples. Waves measured in experiments are characterized and compatibility is found between the proposed criterion predictions and …
The Hamiltonian representation of magnetic field lines enables one to study their confinement properties in tokamaks through the use of symplectic maps such as the symmetric tokamap and its bounded version, the latter being introduced here. In this time-independent purely magnetic framework, we observed the drastic improvement in the confinement of magnetic field lines produced by the local vanishing of the shear profile. This amounts to a non-twist condition that notably acts in the same way the safety profile being (non-strictly) monotonic or having a reversed shear. We single out the effect…
Hybrid MHD-gyrokinetic code simulations are used to investigate the dynamics of frequency sweeping reversed shear Alfvén eigenmode (RSAE) strongly driven by energetic particles (EPs) during plasma current ramp-up in a conventional tokamak configuration. A series of weakly reversed shear equilibria representing time slices of long timescale MHD equilibrium evolution is considered, where the self-consistent RSAE-EP resonant interactions on the short timescale are analyzed in detail. Both linear and nonlinear RSAE dynamics are shown to be subject to the non-perturbative effect of EPs by maximizin…
Following the analysis on linear spectra of shear Alfvén fluctuations excited by energetic particles (EPs) in the Divertor Tokamak Test (DTT) facility plasmas [T. Wang et al., Phys. Plasmas 25, 062509 (2018)], in this work, nonlinear dynamics of the corresponding mode saturation and the fluctuation induced EP transport is studied by hybrid magnetohydrodynamic-gyrokinetic simulations. For the reversed shear Alfvén eigenmode driven by magnetically trapped EP precession resonance in the central core region of DTT plasmas, the saturation is mainly due to radial decoupling of resonant trapped EPs. …
Heating of figure-8 ions by odd-parity rotating magnetic fields ($RMF_o$) applied to an elongated field-reversed configuration (FRC) is investigated. The largest energy gain occurs at resonances ($s \equiv ω_R/ ω$) of the $RMF_o$ frequency, $ω_R$, with the figure-8 orbital frequency, $ω$, and is proportional to $s^2$ for $s-even$ resonances and to $s$ for $s-odd$ resonances. The threshold for the transition from regular to stochastic orbits explains both the onset and saturation of heating. The FRC magnetic geometry lowers the threshold for heating below that in the tokamak by an order of magn…
A new non-disruptive error field (EF) assessment technique not restricted to low density and thus low beta was demonstrated at the EXTRAP-T2R reversed field pinch. Stable and marginally stable external kink modes of toroidal mode number n=10 and n=8, respectively, were generated, and their rotation sustained, by means of rotating magnetic perturbations of the same n. Due to finite EFs, and in spite of the applied perturbations rotating uniformly and having constant amplitude, the kink modes were observed to rotate non-uniformly and be modulated in amplitude. This behavior was used to precisely…
The impact of electromagnetic stabilization and flow shear stabilization on ITG turbulence is investigated. Analysis of a low-$β$ JET L-mode discharge illustrates the relation between ITG stabilization, and proximity to the electromagnetic instability threshold. This threshold is reduced by suprathermal pressure gradients, highlighting the effectiveness of fast ions in ITG stabilization. Extensive linear and nonlinear gyrokinetic simulations are then carried out for the high-$β$ JET hybrid discharge 75225, at two separate locations at inner and outer radii. It is found that at the inner radius…
Two-fluid boundary turbulence simulations in reversed field pinch plasmas
University of Padua（帕多瓦大学）；Consorzio RFX (CNR, ENEA, INFN, Università di Padova, Acciaierie Venete SpA)（RFX联盟（意大利国家研究委员会、国家新能源研究中心、意大利国家核物理研究所、帕多瓦大学、威尼斯钢铁公司））；Istituto per la Scienza e la Tecnologia dei Plasmi (ISTP), CNR（等离子体科学与技术研究所，意大利国家研究委员会）
Ray tracing codes are useful to study the electromagnetic wave propagation and absorption in the geometrical optics approximation. In magnetized fusion plasma community, most ray tracing codes assume the plasma density and temperature be functions of the magnetic flux and study waves only inside the last closed flux surface, which are sufficient for the present day tokamak. However, they are difficult to be used for configurations with open magnetic field line plasmas, such as mirror machine and field-reversed-configuration (FRC). We develop a ray tracing code in cylindrical coordinates $(r,ϕ,…
Turbulent dynamics in the scrape-off layer (SOL) of magnetic fusion devices is intermittent with large fluctuations in density and pressure. Therefore, a model is required that allows perturbations of similar or even larger magnitude to the time-averaged background value. The fluid-turbulence code GRILLIX is extended to such a global model, which consistently accounts for large variation in plasma parameters. Derived from the drift reduced Braginskii equations, the new GRILLIX model includes electromagnetic and electron-thermal dynamics, retains global parametric dependencies and the Boussines…
Present-days Reversed Field Pinches (RFPs) are characterized by quasi-laminar magnetic configurations in their core, whose boundaries feature sharp internal transport barriers, in analogy with tokamaks and stellarators. The abatement of magnetic chaos leads to the reduction of associated particle and heat transport along wandering field lines. At the same time, the growth of steep temperature gradients may trigger drift microinstabilities. In this work we summarize the work recently done in the RFP RFX-mod in order to assess the existence and the impact upon transport of such electrostatic and…
A general formulation of the problem of calculating the spectrum of stable and unstable eigenmodes of linearized perturbations about a magnetically confined toroidal plasma is presented. The analysis is based on a new hydromagnetic dynamical model, Multi-region Relaxed Magnetohydrodynamics (MRxMHD), which models the plasma-magnetic field system as consisting of multiple regions, containing compressible Euler fluid and Taylor-relaxed magnetic field, separated by flexible ideal-MHD current sheets. This is illustrated using a first-principles analysis of a two-region slab geometry, with periodic …
Classification of matter through topological phases and topological edge states between distinct materials has been a subject of great interest recently. While lattices have been the main setting for these studies, a relatively unexplored realm for this physics is that of continuum fluids. In the typical case of a fluid model with a point spectrum, nontrivial topology and associated edge modes have been observed previously. However, another possibility is that a continuous spectrum can coexist with the point spectrum. Here we demonstrate that a fluid plasma model can harbor nontrivial topology…
