Magnetic Separatrix Research Articles

Čerenkov emission of quasiparallel whistlers by fast electron phase-space holes during magnetic reconnection.

Kinetic simulations of magnetotail reconnection have revealed electromagnetic whistlers originating near the exhaust boundary and propagating into the inflow region. The whistler production mechanism is not a linear instability, but rather is Čerenkov emission of almost parallel whistlers from localized moving clumps of charge (finite-size quasiparticles) associated with nonlinear coherent electron phase space holes. Whistlers are strongly excited by holes without ever growing exponentially. In the simulation the whistlers are emitted in the source region from holes that accelerate down the magnetic separatrix towards the x line. The phase velocity of the whistlers vφ in the source region is everywhere well matched to the hole velocity vH as required by the Čerenkov condition. The simulation shows emission is most efficient near the theoretical maximum vφ=half the electron Alfven speed, consistent with the new theoretical prediction that faster holes radiate more efficiently. While transferring energy to whistlers the holes lose coherence and dissipate over a few local ion inertial lengths. The whistlers, however, propagate to the x line and out over many 10's of ion inertial lengths into the inflow region of reconnection. As the whistlers pass near the x line they modulate the rate at which magnetic field lines reconnect.

On applicability of the “thermalized potential” solver in simulations of the plasma flow in Hall thrusters

In Hall thrusters, the potential distribution plays an important role in discharge processes and ion acceleration. This paper presents a 2D potential solver in the Hall thruster instead of the “thermalized potential”, and compares equipotential contours solved by these two methods for different magnetic field conditions. The comparison results reveal that the expected “thermalized potential” works very well when the magnetic field is nearly uniform and electron temperature is constant along the magnetic field lines. However for the case with a highly non-uniform magnetic field or variable electron temperature along the magnetic field lines, the “thermalized potential” is not accurate. In some case with magnetic separatrix inside the thruster channel, the “thermalized potential” model cannot be applied at all. In those cases, a full 2D potential solver must be applied. Overall, this paper shows the limit of applicability of the “thermalized potential” model.

Analysis of the diamagnetic effect in multipole Galatea traps

The toroidal current emerging after the injection of a plasmoid through the magnetic shell of the Trimyx-3M (microwave) multipole trap is measured using the Rogowski loop. This current is due to diamagnetism of the plasma. The relation between the diamagnetic current and the maximal plasma pressure produced at the magnetic field separatrix is obtained. It is shown hence that magnetic measurements in a multi-pole trap for a known concentration make it possible to determine the plasma temperature in the trap and the energy confinement time.

The role of drifts in the plasma transport at the tokamak core–SOL interface

The interface between the core (inside the magnetic separatrix in X-point configurations) and the scrape-off layer (SOL) of tokamaks is a delicate region of the magnetic topology transition from closed to open field lines where neither the standard neoclassical theory nor the SOL physics fully apply. Sharp gradients of plasma parameters in the outer core, caused by the proximity of divertor sinks in the near SOL, invalidate some ordering assumptions of the neoclassical theory. At the same time, the existence of closed flux surfaces in the core enforces ambipolarity of radial plasma flows, in difference to the situation in the SOL where the current loop may close through the divertor. Detailed analysis of the plasma transport and flows with the emphasis on the outer core region, just inside the separatrix, is carried out in the paper, based on EDGE2D modelling and analytical formulas.

QUADRATURE OBSERVATIONS OF WAVE AND NON-WAVE COMPONENTS AND THEIR DECOUPLING IN AN EXTREME-ULTRAVIOLET WAVE EVENT

We report quadrature observations of an extreme-ultraviolet (EUV) wave event on 2011 January 27 obtained by the Extreme Ultraviolet Imager (EUVI) onboard \emph{Solar Terrestrial Relations Observatory} (\emph{STEREO}), and the Atmospheric Imaging Assembly (AIA) onboard the \emph{Solar Dynamics Observatory} (\emph{SDO}). Two components are revealed in the EUV wave event. A primary front is launched with an initial speed of $\sim$440 km s$^{-1}$. It appears significant emission enhancement in the hotter channel but deep emission reduction in the cooler channel. When the primary front encounters a large coronal loop system and slows down, a secondary much fainter front emanates from the primary front with a relatively higher starting speed of $\sim$550 km s$^{-1}$. Afterwards the two fronts propagate independently with increasing separation. The primary front finally stops at a magnetic separatrix, while the secondary front travels farther before it fades out. In addition, upon the arrival of the secondary front, transverse oscillations of a prominence are triggered. We suggest that the two components are of different natures. The primary front belongs to a non-wave coronal mass ejection (CME) component, which can be reasonably explained with the field-line stretching model. The multi-temperature behavior may be caused by considerable heating due to the nonlinear adiabatic compression on the CME frontal loop. For the secondary front, most probably it is a linear fast-mode magnetohydrodynamic (MHD) wave that propagates through a medium of the typical coronal temperature. X-ray and radio data provide us with complementary evidence in support of the above scenario.

Revealing the sub-structures of the magnetic reconnection separatrix via particle-in-cell simulation

Magnetic separatrix is an important boundary layer separating the inflow and outflow regions in magnetic reconnection. In this article, we investigate the sub-structures of the separatrix region by using two-and-half dimensional electromagnetic particle-in-cell simulation. The separatrix region can be divided into two sub-regions in terms of the ion and electron frozen-in conditions. Far from the neutral sheet, ions and electrons are magnetized in magnetic fields. Approaching the neutral sheet, ion frozen-in condition is broken in a narrow region (∼c/ωpi) at the edge of a density cavity, while electrons are frozen-in to magnetic fields. In this region, electric field Ez is around zero, and the convective term –(vi × B) is balanced by the Hall term in the generalized Ohm’s law because ions carry the perpendicular current. Inside the density cavity, both ion and electron frozen-in conditions are broken. The region consists of two sub-ion or electron-scale layers, which contain intense electric fields. Formation of the two sub-layers is due to the complex electron flow pattern around the separatrix region. In the layer, Ez is balanced by a combination of Hall term and the divergence of electron pressure tensor, with the Hall term being dominant. Our preliminary simulation result shows that the separatrix region in guide field reconnection also contains two sub-regions: the inner region and the outer region. However, the inner region contains only one current layer in contrast with the case without guide field.

Bootstrap current for the edge pedestal plasma in a diverted tokamak geometry

The edge bootstrap current plays a critical role in the equilibrium and stability of the steep edge pedestal plasma. The pedestal plasma has an unconventional and difficult neoclassical property, as compared with the core plasma. It has a narrow passing particle region in velocity space that can be easily modified or destroyed by Coulomb collisions. At the same time, the edge pedestal plasma has steep pressure and electrostatic potential gradients whose scale-lengths are comparable with the ion banana width, and includes a magnetic separatrix surface, across which the topological properties of the magnetic field and particle orbits change abruptly. A drift-kinetic particle code XGC0, equipped with a mass-momentum-energy conserving collision operator, is used to study the edge bootstrap current in a realistic diverted magnetic field geometry with a self-consistent radial electric field. When the edge electrons are in the weakly collisional banana regime, surprisingly, the present kinetic simulation confirms that the existing analytic expressions [represented by O. Sauter et al., Phys. Plasmas 6, 2834 (1999)] are still valid in this unconventional region, except in a thin radial layer in contact with the magnetic separatrix. The agreement arises from the dominance of the electron contribution to the bootstrap current compared with ion contribution and from a reasonable separation of the trapped-passing dynamics without a strong collisional mixing. However, when the pedestal electrons are in plateau-collisional regime, there is significant deviation of numerical results from the existing analytic formulas, mainly due to large effective collisionality of the passing and the boundary layer trapped particles in edge region. In a conventional aspect ratio tokamak, the edge bootstrap current from kinetic simulation can be significantly less than that from the Sauter formula if the electron collisionality is high. On the other hand, when the aspect ratio is close to unity, the collisional edge bootstrap current can be significantly greater than that from the Sauter formula. Rapid toroidal rotation of the magnetic field lines at the high field side of a tight aspect-ratio tokamak is believed to be the cause of the different behavior. A new analytic fitting formula, as a simple modification to the Sauter formula, is obtained to bring the analytic expression to a better agreement with the edge kinetic simulation results.

Secondary Magnetic Islands Generated by the Kelvin-Helmholtz Instability in a Reconnecting Current Sheet

Magnetic islands or flux ropes produced by magnetic reconnection have been observed on the magnetopause, in the magnetotail, and in coronal current sheets. Particle-in-cell simulations of magnetic reconnection with a guide field produce elongated electron current layers that spontaneously produce secondary islands. Here, we explore the seed mechanism that gives birth to these islands. The most commonly suggested theory for island formation is the tearing instability. We demonstrate that in our simulations these structures typically start out, not as magnetic islands, but as electron flow vortices within the electron current sheet. When some of these vortices first form, they do not coincide with closed magnetic field lines, as would be the case if they were islands. Only after they have grown larger than the electron skin depth do they couple to the magnetic field and seed the growth of finite-sized islands. The streaming of electrons along the magnetic separatrix produces the flow shear necessary to drive an electron Kelvin-Helmholtz instability and produce the initial vortices. The conditions under which this instability is the dominant mechanism for seeding magnetic islands are explored.

Numerical simulations of separatrix instabilities in collisionless magnetic reconnection

Electron scale dynamics of magnetic reconnection separatrix jets is studied in this paper. Instabilities developing in directions both parallel and perpendicular to the magnetic field are investigated. Implicit particle-in-cell simulations with realistic electron-to-ion mass ratio are complemented by a set of small scale high resolution runs having the separatrix force balance as the initial condition. A special numerical procedure is developed to introduce the force balance into the small scale runs. Simulations show the development of streaming instabilities and consequent formation of electron holes in the parallel direction. A new electron jet instability develops in the perpendicular direction. The instability is closely related to the electron MHD Kelvin-Helmholtz mode and is destabilized by a flow, perpendicular to magnetic field at the separatrix. Tearing instability of the separatrix electron jet is modulated strongly by the electron MHD Kelvin-Helmholtz mode.

Identification of edge-localized moments of the current density profile in a tokamak equilibrium from external magnetic measurements

The flux surface topology of a toroidal plasma bounded by a magnetic separatrix allows edge moments of the toroidal current density profile to be identified in an MHD equilibrium reconstruction code using only external magnetic measurements. This is demonstrated analytically for simple plasma shapes and applied to experimental data on the ASDEX Upgrade tokamak where CLISTE reconstructions from magnetic data are shown to be consistent with those obtained from a more complete set of diagnostic data. An independent demonstration of edge current profile recoverability is obtained by analysing the reconstruction errors for a database of Monte Carlo-generated equilibria.

Investigations of high-energy electrons of the microwave discharge plasma at configuration of the “Magnetor” Bi-dipole magnetic confinement system by X-ray radiation analyses

The results of the investigations of a group of fast electrons in a microwave discharge plasma in the “Magnetor” magnetic trap are presented. The data on the presence and location of this group of electrons is important for estimating the total plasma pressure taking the previous probe measurements into account. Fast electrons are found to be localized within the magnetic separatrix in the region of confinement of the main plasma. The maximal energy of fast electrons is higher than 25 keV.

Free-boundary magnetohydrodynamic equilibria with flow

The finite-element M3D code [W. Park et al., Phys. Plasmas 6, 1796 (1999)] has been modified to include a free-boundary equilibrium solver with arbitrary toroidal and poloidal flows. With this modification, the M3D code now has the capability to self-consistently model two essential ingredients necessary for equilibrium calculations in the edge region, namely, free-boundary and arbitrary flow. As a free-boundary code, M3D includes the separatrix and scrape-off layer regions in the equilibrium calculation. Poloidal flows in the subsonic, supersonic, and transonic regimes can be calculated with the new version of the M3D code. Calculation results show that the presence of equilibrium flows, in particular those next to the plasma boundary, can considerably influence the position of the X-point and magnetic separatrix shape/location and hence the position of the strike point on the divertor plates. Moreover, it is shown that poloidal flow is not a rigid-body rotation, with the fastest flows occurring on the inboard side of the plasma. A numerical confirmation of the “de Laval nozzle” model of Betti and Freidberg [R. Betti and J. P. Freidberg, Phys. Plasmas 7, 2439 (2000)] for free-boundary equilibrium calculations is obtained, with the formation of the predicted discontinuities between regions of subsonic and supersonic flows (with respect to the poloidal sound speed). Finally, a detailed comparison between isentropic and isothermal equilibria is presented, showing qualitative analogies and quantitative differences.

“Crater” flux transfer events: Highroad to the X line?

We examine Cluster observations of a so‐called magnetosphere crater FTE, employing data from five instruments (FGM, CIS, EDI, EFW, and WHISPER), some at the highest resolution. The aim of doing this is to deepen our understanding of the reconnection nature of these events by applying recent advances in the theory of collisionless reconnection and in detailed observational work. Our data support the hypothesis of a stratified structure with regions which we show to be spatial structures. We support the bulge‐like topology of the core region (R3) made up of plasma jetting transverse to reconnected field lines. We document encounters with a magnetic separatrix as a thin layer embedded in the region (R2) just outside the bulge, where the speed of the protons flowing approximately parallel to the field maximizes: (1) short (fraction of a sec) bursts of enhanced electric field strengths (up to ∼30 mV/m) and (2) electrons flowing against the field toward the X line at approximately the same time as the bursts of intense electric fields. R2 also contains a density decrease concomitant with an enhanced magnetic field strength. At its interface with the core region, R3, electric field activity ceases abruptly. The accelerated plasma flow profile has a catenary shape consisting of beams parallel to the field in R2 close to the R2/R3 boundary and slower jets moving across the magnetic field within the bulge region. We detail commonalities our observations of crater FTEs have with reconnection structures in other scenarios. We suggest that in view of these properties and their frequency of occurrence, crater FTEs are ideal places to study processes at the separatrices, key regions in magnetic reconnection. This is a good preparation for the MMS mission.

Plasma transport in stochastic magnetic field caused by vacuum resonant magnetic perturbations at diverted tokamak edge

A kinetic transport simulation for the first 4 ms of the vacuum resonant magnetic perturbations (RMPs) application has been performed for the first time in realistic diverted DIII-D tokamak geometry [J. Luxon, Nucl. Fusion 42, 614 (2002)], with the self-consistent evaluation of the radial electric field and the plasma rotation. It is found that, due to the kinetic effects, the stochastic parallel thermal transport is significantly reduced when compared to the standard analytic model [A. B. Rechester and M. N. Rosenbluth, Phys. Rev. Lett. 40, 38 (1978)] and the nonaxisymmetric perpendicular radial particle transport is significantly enhanced from the axisymmetric level. These trends agree with recent experimental result trends [T. E. Evans, R. A. Moyer, K. H. Burrell et al., Nat. Phys. 2, 419 (2006)]. It is also found, as a side product, that an artificial local reduction of the vacuum RMP fields in the vicinity of the magnetic separatrix can bring the kinetic simulation results to a more detailed agreement with experimental plasma profiles.

Formation of Field-Reversed-Configuration Plasma with Punctuated-Betatron-Orbit Electrons

We describe ab initio, self-consistent, 3D, fully electromagnetic numerical simulations of current drive and field-reversed-configuration plasma formation by odd-parity rotating magnetic fields (RMF{o}). Magnetic-separatrix formation and field reversal are attained from an initial mirror configuration. A population of punctuated-betatron-orbit electrons, generated by the RMF{o}, carries the majority of the field-normal azimuthal electrical current responsible for field reversal. Appreciable current and plasma pressure exist outside the magnetic separatrix whose shape is modulated by the RMF{o} phase. The predicted plasma density and electron energy distribution compare favorably with RMF{o} experiments.

Experimental studies of edge turbulence and confinement in Alcator C-Mod

The steep gradient edge region and scrape-off-layer (SOL) on the low-field-side of Alcator C-Mod [I. H. Hutchinson, R. Boivin, F. Bombarda et al., Phys. Plasmas 1, 1511 (1994)] tokamak plasmas are studied using gas-puff-imaging diagnostics. In L-mode plasmas, the region extending ∼2 cm inside the magnetic separatrix has fluctuations showing a broad, turbulent spectrum, propagating in the electron diamagnetic drift direction, whereas features in the open field line region propagate in the ion diamagnetic drift direction. This structure is robust against toroidal field strength, poloidal null-point geometry, plasma current, and plasma density. Global parameter dependence of spectral and spatial structure of the turbulence inside the separatrix is explored and characterized, and both the intensity and spectral distributions are found to depend strongly on the plasma density normalized to the tokamak density limit. In H-mode discharges the fluctuations at and inside the magnetic separatrix show fundamentally different trends compared to L-mode, with the electron diamagnetic direction propagating turbulence greatly reduced in ELM-free [F. Wagner et al., Proceedings of the Thirteenth Conference on Plasma Physics and Controlled Nuclear Fusion Research (IAEA, Vienna, 1982), Vol. I, p. 277], and completely dominated by the modelike structure of the quasicoherent mode in enhanced D-alpha regimes [A. E. Hubbard, R. L. Boivin, R. S. Granetz et al., Phys. Plasmas 8, 2033 (2001)], while the normalized SOL turbulence is largely unaffected.

Generic magnetic field model in poloidal divertor tokamaks in the presence of resonant magnetic perturbations

A generic analytical model for the description of magnetic field lines in poloidal divertor tokamaks in the presence of external resonant magnetic perturbations is proposed. It is based on the Hamiltonian description of magnetic field lines in tokamaks. The safety factor and the spectra of magnetic perturbations are chosen by the requirement to satisfy their generic behaviour near the magnetic separatrix and at the magnetic axis. The field line equations are integrated by the construction of two symplectic and computationally efficient mappings of field lines. The model for internal MHD modes is also proposed. The mapping procedure for field lines which includes the MHD modes is described. It is shown that the numerically calculated diffusion and convection coefficients of field lines are in close agreement with the quasilinear ones. It is found that in the presence of internal MHD modes at the plasma edge the convectional outward transport of field lines may reverse its direction to inward convectional transport.

Stabilization of pressure-driven magnetohydrodynamic modes by separatrix in dipole plasma confinement

The eigenvalue problem is solved for the short-wavelength pressure-driven magnetohydrodynamic modes in configuration with closed magnetic field lines in the poloidal direction. Here we show that the magnetic separatrix (which determines the boundary of the confinement region) provides a substantial stabilizing effect by which the total volume inside the separatrix becomes stable even for very high beta values. The plasma inertia and compressibility are properly formulated to give the correct growth rate of the mode.

The distributions of plasma parameters in the "Magnetor" device with hot cathode discharge

The dipole magnetic configuration as realized in planet magnetospheres is of interest for controlled fusion plasma confinement. This type of magnetic trap is free of convective instability. Distributions of plasma parameters in "Magnetor" device with double dipole magnetic configuration that allows restrict considerable volume of confined plasma are investigated. The comparison of plasma parameters distribution inside the trap for two plasma generation methods: microwave discharge at 2,45GHz and hot cathode discharge in crossed E and B fields are made. It is shown that plasma is localized inside the magnetic separatrix for both types of discharges. To determine possible additional plasma movements caused by the presence of the electric field in the magnetic configuration measurements of plasma flows in discharge with the hot cathode in crossed E and B fields are carried out. Two directions of plasma flows with flux density 1016÷1017cm−2s−1 inside the magnetic trap are determined: the flow along the axis leading particles leaving from a trap through weak magnetic field region and the flow caused by plasma azimuth drift.

Stationary nontearing inertial scale electron magnetohydrodynamic instability

Two-dimensional stationary nontearing inertial scale electron magnetohydrodynamic (EMHD) instability is described. The physical mechanism of the instability is illustrated. Analytical asymptotic estimate of the growth rate is provided and verified with a numerical calculation of the instability, also describing the characteristic structure of the eigenmode. Natural occurrence of the instability is demonstrated in a nonlinear EMHD simulation of a system undergoing magnetic reconnection, where the instability manifests itself on the outflow side of the magnetic field separatrix and may affect the self-determined length of the layer.