Magnetic Separatrix Research Articles

Role of turbulent separatrix tangle in the improvement of the integrated pedestal and heat exhaust issue for stationary-operation tokamak fusion reactors

The magnetic separatrix surface is designed to provide the final and critical confinement to the hot stationary-operation core plasma in modern tokamak reactors in the absence of an external magnetic perturbation (MP) or transient magneto-hydrodynamic perturbation, while diverting the exhaust heat to divertor plates. All the stationary operational boundary plasma studies and reactor designs have been performed under this assumption. However, there has been a long-standing suspicion that a stationary-operation tokamak plasma even without external MPs or edge localized modes (ELMs) activities may not have a stable closed separatrix surface, especially near the magnetic X-point. Here, the first gyrokinetic numerical observation is reported that the divertor separatrix surface, due to homoclinic tangles caused by intrinsic electromagnetic turbulence, is not a stable closed surface in a stationary operation phase even without MPs or ELMs. Unlike the MP- or ELM-driven homoclinic tangles that could cause deleterious effects to core confinement or divertor plates, it is found that the micro-turbulence driven homoclinic tangles could connect the divertor plasma to the pedestal plasma in a constructive way by broadening the divertor heat-exhaust footprint and weakening the pedestal slope to the ELM-safe direction. Micro-turbulent homoclinic tangles can open a new research direction in understanding and controlling these two most troublesome and non-locally connected edge-plasma issues in a tokamak fusion reactor.

Effect of resonant magnetic perturbation on edge–core turbulence spreading in a tokamak plasma

Turbulence spreading from the edge to the core region of a tokamak with a resonant magnetic perturbation (RMP) is investigated using an electromagnetic Landau-fluid model in a toroidal geometry. As a RMP field with an appropriate amplitude is applied, long-wavelength fluctuations around the resonance surface can be excited due to forced magnetic reconnection. Strong shear flow at the magnetic island separatrix is observed, which can break the radially elongated vortex structures of the turbulent fluctuation. Inward turbulence spreading can be blocked by this shear flow, and the saturation level of turbulence intensity in the core region declines.

Numerical analysis for the free-boundary current reversal equilibrium in the AC plasma current operation in a tokamak

In recent decades, tokamak discharges with zero total toroidal current have been reported in tokamak experiments, and this is one of the key problems in alternating current (AC) operations. An efficient free-boundary equilibrium code is developed to investigate such advanced tokamak discharges with current reversal equilibrium configuration. The calculation results show that the reversal current equilibrium can maintain finite pressure and also has considerable effects on the position of the X-point and the magnetic separatrix shape, and hence also on the position of the strike point on the divertor plates, which is extremely useful for magnetic design, MHD stability analysis, and experimental data analysis etc. for the AC plasma current operation on tokamaks.

Influence of the position relationship between the cathode and magnetic separatrix on the discharge process of a Hall thruster

Previous studies have shown that there is an obvious coupling relationship between the installation location of the external cathode and the magnetic separatrix in the plume region of a Hall thruster. In this paper, the particle-in-cell simulation method is used to compare the thruster discharge process under the conditions of different position relationships between the cathode and the magnetic separatrix. By comparing the distribution of electron conduction, potential, plasma density and other microscopic parameters, we try to explain the formation mechanism of the discharge difference. The simulation results show that the cathode inside and outside the magnetic separatrix has a significant effect on the distribution of potential and plasma density. When the cathode is located on the outer side of the magnetic separatrix, the potential above the plume region is relatively low, and there is a strong potential gradient above the plume region. This potential gradient is more conducive to the radial diffusion of ions above the plume, which is the main reason for the strong divergence of the plume. The distribution of ion density is also consistent with the distribution of potential. When the cathode is located on the outer side of the magnetic separatrix, the radial diffusion of ions in the plume region is enhanced. Meanwhile, by comparing the results of electron conduction, it is found that the trajectories of electrons emitted from the cathode are significantly different between the inner and outer sides of the magnetic separatrix. This is mainly because the electrons are affected by the magnetic mirror effect of the magnetic tip, which makes it difficult for the electrons to move across the magnetic separatrix. This is the main reason for the difference in potential distribution. In this paper, the simulation results of macroscopic parameters under several conditions are also compared, and they are consistent with the experimental results. The cathode is located on the inner side of the magnetic separatrix, which can effectively reduce the plume divergence angle and improve the thrust. In this paper, the cathode moves from R = 50 mm to R = 35 mm along the radial direction, the thrust increases by 3.6 mN and the plume divergence angle decreases by 23.77%. Combined with the comparison of the ionization region and the peak ion density, it is found that the main reason for the change in thrust is the change in the radial diffusion of ions in the plume region.

Interplay of plasma resistivity and rotation on β limits in free boundary diverted tokamaks

A plasma resistivity-β driving mechanism aimed at explaining the appearance of long wavelength global instabilities in free boundary high-β tokamak plasmas with a divertor is presented. These perturbations resemble very closely the resistive wall mode phenomenon. Performing a proper toroidal analysis, we show that the magnetohydrodynamic stability is worsened by the interplay of plasma β and resistivity. By modelling the effect of a magnetic separatrix through a careful positioning of the resonant surfaces, we find that in an ideal plasma wall effects are effectively screened, so that the ideal β limit becomes independent of the wall position/physics. A lower wall dependent critical β is found if plasma resistivity is allowed. We find that global stability can be improved with a toroidal flow, small enough not to induce equilibrium modification. The rotation stabilisation effectiveness depends upon the proximity of the plasma equilibrium parameters to the resistive marginal boundary.

Drift kinetic theory of neoclassical tearing modes in tokamak plasmas: polarisation current and its effect on magnetic island threshold physics

A nonlinear 4-dimensional drift island theory derived in (Imada et al 2019 Nucl. Fusion 59 046016 and references therein) provides qualitative predictions of the plasma response to a stationary neoclassical tearing mode (NTM) magnetic island in a low beta, large aspect ratio tokamak plasma. (Dudkovskaia et al 2021 Plasma Phys. Control. Fusion 63 054001) refines a model for the magnetic drift frequency and exploits the limit of rare collisions, reducing this theory to 3-dimensional and thus providing a more accurate treatment of the trapped-passing boundary layer. The drift island theory is further improved in (Dudkovskaia et al 2023 Nucl. Fusion 63 016020) by introducing plasma shaping and finite beta effects. In the present paper, an improved model is adopted to resolve the drift island separatrix boundary layer, allowing one to investigate the polarisation current contribution that exists around the magnetic island separatrix, including in the presence of the background electric field. In particular, different magnetic topologies from both sides of the separatrix generate a radial discontinuity in the distribution function gradient there, when collisions are neglected. Allowing for collisional dissipation in the leading order distribution function around the separatrix resolves this discontinuity, smoothing the density distribution. The overall effect of the polarisation current on the NTM threshold is then combined from the outer contributions that exist outside the layer, as well as the separatrix layer piece, and self-consistently accounts for the electrostatic potential reconstructed from plasma quasi-neutrality. The corresponding NTM threshold is quantified and compared with previous predictions of (Dudkovskaia et al 2021 Plasma Phys. Control. Fusion 63 054001, Dudkovskaia et al 2023 Nucl. Fusion 63 016020).

Penetration properties of applied resonant magnetic perturbation in HL-2A tokamak

Any arbitrary perturbation on a magnetic field separatrix can cause a structure named homoclinic tangle in tokamaks. Both an edge localized mode (ELM) and a resonant magnetic perturbation (RMP) can lead to a perturbation of the magnetic field on the separatrix. Under the appropriate circumstances, RMP could alleviate or even completely suppress a rapid collapse process of an ELM. The simulation results using the CLTx code, the extended version of the three-dimensional toroidal magnetohydrodynamic (MHD) code (CLT (Ci-Liu-Ti, which means MHDs in Chinese)) with a scrape-off layer, show the structure of the homoclinic tangle with a borderline stochastic region resulting from RMP in HL-2A tokamak. Strongly distorted magnetic field lines with the homoclinic tangle could connect to the tokamak divertors. The footprints of these magnetic field lines on the divertors are consistent with the energy deposit spots in the experiment. From Poincaré plots of escaped magnetic field lines, it is found that the depth of the plasma edge region penetrated by these field lines depends on the RMP coil current, the rotation frequency of the RMP field, and the plasma resistivity.

Optimization of a Long-Lifetime Hall Thruster with an Internally Mounted Cathode

Hall thrusters with an internal cathode are widely used due to their ability to enhance efficiency, minimize plume divergence, and eliminate plume asymmetry. In addition, the long-lifetime technology of Hall thrusters typically relocates the intense magnetic-field region outside the channel, known as an “aft-loaded magnetic field,” to mitigate erosion of the discharge channel caused by high-energy ions. However, this exacerbates plume divergence and diminishes overall performance. Therefore, this research focuses on optimizing a Hall thruster with an aft-loaded magnetic field and internal cathode. Given that electrons emitted by the internal cathode initially diffuse onto the magnetic separatrix and subsequently couple with the ion beam in the plume, this study experimentally investigates the impact of the magnetic separatrix shape on the discharge characteristics and plume behavior of the Hall thruster. The experimental findings indicate that expanding the envelope of the magnetic separatrix contributes to improved plume focusing and enhanced performance. Thus, the results of this study highlight the significance of the magnetic field outside the channel as a crucial design factor for long-lifetime Hall thrusters.

Strong Nonideal Electric Fields and Energy Dissipation Observed by MMS within Field-Aligned Current Layers in the Plasma Sheet of the Earth’s Magnetotail

We report the MMS observations of the intense spikes of field-aligned current (FAC) produced by magnetic reconnection at the plasma sheet (PS) field lines. The MMS was located tailward of a near-Earth X-line and the most intense spike of FAC with an electric current density of ∼70 nA/m2 was observed near the magnetic separatrix. The FAC structures located deeper in the PS were strongly filamented and consisted of several spikes with a thickness of ∼(1–2)ρe (ρe is the gyroradius of thermal electrons). We found that the FAC in these structures was carried by unmagnetized thermal and suprathermal electron populations (≥ 1 keV), which were ∼(20–80)% of the entire electron population. Strong nonideal electric fields up to ∼100 mV/m were detected in the FAC spike near the magnetic separatrix. The generation of these fields was mainly due to the anomalous resistivity, possibly caused by the electrostatic fluctuations. As a result, a significant energy dissipation of up to 1.3 nW/m3 occurred within the electron-scale FAC structure, which caused an increase in the electron temperature by a factor of two compared with that outside the FAC. Thus, MMS observations demonstrate that during the interval of the active X-line, the outer part of the PS consists of multiple electron-scale FAC layers/filaments in which a significant energy exchange between electrons and fields occurs. To investigate the stability of these filaments and estimate their lifetime, additional observations and theoretical studies are needed.

Study on the ionization and acceleration of a microwave discharge cusped field thruster

The microwave discharge cusped field thruster is a novel concept electric micro propulsion device, also a candidate thruster for the gravitational detection mission. A coaxial transmission line resonator is utilized to feed the microwave into the thruster to generate Xe plasma steadily with a mass flow rate as low as 0.1 sccm. Due to the separation of ionization and acceleration, the thruster performs high operation mode stability over a wide range of voltage in low mass flow conditions. Experimental and simulation methods are carried out to study the ionization and ion acceleration of the thruster. The results show that in operating conditions with a mass flow rate of 0.1 sccm, an anode voltage of 0 V to 1000 V, and a microwave power of 2 W, the right-hand circularly polarized wave (R wave) and the ordinary wave (O wave) play the most important role in the ionization process. The ion acceleration region locates around the exit magnetic separatrix, and the acceleration region tends to converge toward the separatrix as the anode voltage increases, resulting in an increased focus of the thruster plume and concentration of the ion energy distribution. Due to the separation of the ionization and acceleration regions, the thruster performs a divergence efficiency of 0.5–0.8, and an acceleration efficiency of 0.9.

A reduced-model (nSOLT) simulation of neutral recycling effects on plasma turbulence in the divertor region of MAST-U

The 2D scrape-off-layer turbulence code (nSOLT), which includes 1D kinetic neutral–plasma interactions, is applied to study effects of neutral recycling on plasma turbulence for parameters illustrative of the MAST-U divertor region. Neutral recycling is modeled by injecting a fraction of the parallel plasma flux to the divertor back into the simulation domain as a source of Franck–Condon-distributed neutrals. Stationary sources, concentrated at the magnetic separatrix, model plasma streaming into the divertor region from the upstream scrape-off-layer and sustain plasma turbulence absent neutral recycling. Starting from one such no-neutrals equilibrium, we initiate recycling in a numerical experiment designed to diagnose and identify the effects of various neutral–plasma interactions on the divertor plasma, divertor turbulence, and plasma exhaust. The onset of recycling triggers an initial burst of enhanced cross field plasma transport that is quelled by ionization cooling and charge–exchange (CX) friction, with growing neutral pressure, leading to a quiescent, turbulence-free state. Diagnosis of this transient burst reveals that (1) the sudden increase in plasma density due to ionization dominates the onset of the burst, (2) electron cooling due to ionization increases collisionality and disconnects blob filaments from the sheath, and (3) CX friction drives tripole polarization of a blob that can dominate the curvature-driven dipole polarization, leading to the stagnation of blob propagation and reduced radial turbulent transport. It is shown that CX friction is negligible compared to sheath physics in determining equilibrium mean flow shearing rates, for parameters considered herein (specifically a short connection length to the divertor target), while it can significantly reduce interchange-instability growth rates.

Direct observations of a complex coronal web driving highly structured slow solar wind

The solar wind consists of continuous streams of charged particles that escape into the heliosphere from the Sun, and is split into fast and slow components, with the fast wind emerging from the interiors of coronal holes. Near the ecliptic plane, the fast wind from low-latitude coronal holes is interspersed with a highly structured slow solar wind, the source regions and drivers of which are poorly understood. Here we report extreme-ultraviolet observations that reveal a spatially complex web of magnetized plasma structures that persistently interact and reconnect in the middle corona. Coronagraphic white-light images show concurrent emergence of slow wind streams over these coronal web structures. With advanced global magnetohydrodynamics coronal models, we demonstrate that the observed coronal web is a direct imprint of the magnetic separatrix web (S-web). By revealing a highly dynamic portion of the S-web, our observations open a window into important middle-coronal processes that appear to play a key role in driving the structured slow solar wind.

Electromagnetic total-f algorithm for gyrokinetic particle-in-cell simulations of boundary plasma in XGC

The simplified δf mixed-variable/pullback electromagnetic simulation algorithm implemented in XGC for core plasma simulations by Cole et al. [Phys. Plasmas 28, 034501 (2021)] has been generalized to a total-f electromagnetic algorithm that can include, for the first time, the boundary plasma in diverted magnetic geometry with neutral particle recycling, turbulence, and neoclassical physics. The δf mixed-variable/pullback electromagnetic implementation is based on the pioneering work by Kleiber and Mischenko et al. [Kleiber et al., Phys. Plasmas 23, 032501 (2016); Mishchenko et al., Comput. Phys. Commun. 238, 194 (2019)]. An electromagnetic demonstration simulation is performed in a DIII-D-like, H-mode boundary plasma, including a corresponding comparative electrostatic simulation, which confirms that the electromagnetic simulation is necessary for a higher fidelity understanding of the electron particle and heat transport even at the low-β pedestal foot in the vicinity of the magnetic separatrix.

Analytic theory of ideal-MHD vertical displacements in tokamak plasmas

An analytic derivation of the relevant dispersion relation for vertical displacements in shaped tokamak plasmas is presented, valid for arbitrary values of the ellipticity parameter. The theory is developed within the framework of the reduced ideal-MHD model. A nearby, perfectly conducting wall can provide passive feedback stabilization of vertical displacements on the ideal-MHD timescale. The mechanism for passive stabilization relies on image currents induced on the metallic wall. However, if the plasma extends to the magnetic separatrix, where magnetic X-points are located, as in the case of a divertor tokamak configuration, perturbed axisymmetric currents carried by the plasma in the vicinity of the X-points are triggered. It is shown that these X-point currents can provide passive feedback stabilization, even in the absence of a nearby wall. X-point currents are excited due to the resonant nature of magnetic X-points with respect to toroidal axisymmetric perturbations. An intermediate case, where the plasma boundary is located just inside the magnetic separatrix, is also analyzed, providing additional insight into the stabilization mechanism.

Experimental observation of the transport induced by ion Bernstein waves near the separatrix of magnetic nulls

The waves in a magnetic null could play important roles during 3D magnetic reconnection. Some preliminary clues in this paper show that the ion Bernstein wave (IBW) may be closely related to transport process in magnetic null region. The magnetic null configuration experiment reported here is set up in a linear helicon plasma device, Peking University plasma test device (PPT). The wave modes with frequencies between the first and third harmonics of local ion cyclotron frequency () are observed in the separatrix of magnetic null, which are identified as the IBW based on the dispersion relation. Further analysis shows that IBW could drive substantial particle flux across the magnetic separatrix. The theoretical radial particle flux driven by IBW and the measured parallel flow in PPT device are almost on the same order, which shows that IBW may play an important role during 3D reconnection process.

Magnetic Force-Free Theory: Nonlinear Case

In this paper, a theory of force-free magnetic field useful for explaining the formation of convex closed sets, bounded by a magnetic separatrix in the plasma, is developed. This question is not new and has been addressed by many authors. Force-free magnetic fields appear in many laboratory and astrophysical plasmas. These fields are defined by the solution of the problem ∇×B=ΛB with some field conditions B∂Ω on the boundary ∂Ω of the plasma region. In many physical situations, it has been noticed that Λ is not constant but may vary in the domain Ω giving rise to many different interesting physical situations. We set Λ=Λ(ψ) with ψ being the poloidal magnetic flux function. Then, an analytic method, based on a first-order expansion of ψ with respect to a small parameter α, is developed. The Grad–Shafranov equation for ψ is solved by expanding the solution in the eigenfunctions of the zero-order operator. An analytic expression for the solution is obtained deriving results on the transition through resonances, the amplification with respect to the gun inflow. Thus, the formation of spheromaks or protosphera structure of the plasma is determined in the case of nonconstant Λ.

FEQ: a new flux coordinates based equilibrium solver including both magnetic axis and separatrix

Accurate tokamak plasma equilibrium solution in flux coordinates is crucial for many stability and transport studies. Different approaches for dealing with singularities in solving the nonlinear Grad–Shafranov (GS) equation in flux coordinates or also known as straight field line coordinates are proposed in this paper. The GS equation is solved by iterating the position of grids directly in flux coordinates, and hence, no additional errors are introduced due to mapping process for a convergent solution. The singularity at magnetic axis in flux coordinates is removed by using a novel coordinate transform technique. Different from other techniques previously developed, no assumption in boundary condition at magnetic axis is used. This is consistent with the fact that there is no physical boundary at the magnetic axis. A flux coordinate system with poloidal coordinate chosen as the geometric poloidal angle is proposed. It conquers the difficulty in no definition of poloidal coordinate in flux coordinates at separatrix because of the singularity at x-point(s) in a divertor configuration. It also simplifies the process for computing poloidal flux coordinate during the iteration for solving the nonlinear GS equation. Non-uniform grids can be applied in both radial and poloidal coordinates, which allows it to increase the spacial resolution near x-point(s) in a divertor configuration. Based on the model proposed in this paper, a new Flux coordinates based EQuilibrium solver (FEQ) in tokamaks is developed. The numerical solutions from this code agree well with both the analytic Solov’ev solution and the numerical one from the EFIT code for a divertor configuration in the EAST tokamak. This code can be applied for simulating different equilibria with prescribed shape, pressure and current profiles, i.e. including both limiter and divertor configurations, positive triangularity and negative triangularity, different β, arbitrary magnetic shear profile etc. It provides a powerful and convenient fixed-boundary inverse equilibrium solver including both magnetic axis and separatrix in the solution for tokamak researches.

Edge harmonic oscillations in plasmas with a separatrix and the effect of edge magnetic shear

This work presents an extension of exfernal mode theory, where the effects of edge magnetic shear and plasma separatrix are investigated and applied to edge harmonic oscillations (EHOs). Linear analytical modelling is performed on a large aspect ratio tokamak with circular cross section, from which a set of three coupled differential equations describing the dispersion relation are derived. To correctly assess the effect of edge shear on exfernal modes, higher order corrections need to be retained in the expansion of the safety factor around the rational surface. The equations are solved numerically for equilibrium pressure and safety factor profiles containing the key features for the excitation of exfernal modes, including a model of a plasma separatrix. The current-driven branch of the instability is significantly reduced by the inclusion of the separatrix, but the mode remains unstable through coupling with the pressure-driven infernal drive. The obtained parameter space for the instability without the effect of the separatrix is compared with the growth rates calculated using the KINX code, and with the nonlinear plasma displacement calculated using the VMEC free-boundary code. From the comparison it was found that the edge shear can be of order unity and still excite exfernal modes, implying that EHOs can be excited even with weak flattening of the local safety factor at the edge, which is in line with some current experimental observations, but contrary to previous simpler analytic theory.

Impact of magnetic X-points on the vertical stability of tokamak plasmas

The ideal-magneto-hydro-dynamic (MHD) theory of axisymmetric modes with toroidal mode number n = 0 in tokamak plasmas is developed. These modes are resonant at the magnetic X-points of the tokamak divertor separatrix. As a consequence, current sheets form along the separatrix, which profoundly affect the stability of vertical plasma displacements. In particular, current sheets at the magnetic separatrix lead to stabilization of n = 0 modes, at least on the ideal-MHD time scale, adding an important ingredient to the mechanism of passive feedback stabilization.

On Cathode Position and Inclination Angle in Magnetically Shielded Hall Thrusters

This study systematically investigated the influence of the position and inclination angle of an externally mounted hollow cathode in 1.35 kW magnetically shielded Hall thrusters to establish the relationship between thruster performance, plume state, and cathode placement. For this purpose, a combined motor driver with a three-degree-of-freedom movement was designed to move the cathode over a wide range of positions and inclination angles. In an experiment performed on a thruster with outer magnetic columns, placing the cathode inside the magnetic separatrix resulted in a considerable amount of thrust. However, an extremely small distance between the cathode and thruster can cause a sharp increase in the discharge current; hence, the optimal cathode position should be determined. It was also found that a small inclination angle was favorable for obtaining high performance. In addition, a strong correlation was found between the plume image and thruster performance. Under improved performance conditions, the visible light region of the plume had a shorter axial length and a broader pink halo. Finally, a comparative experiment was conducted on a thruster with an outer magnetic shell. The thruster of this structure was observed to be insensitive to the cathode position; hence, to protect the cathode from ion sputtering, the distance between the cathode and thruster can be appropriately increased.