Ambipolar Radial Electric Field Research Articles

Gyrokinetic simulation of the toroidal rotation driven by the ambipolar radial electric field induced by stochastic magnetic perturbations in a tokamak plasma

Gyrokinetic simulation of the toroidal rotation driven by the ambipolar radial electric field induced by stochastic magnetic perturbations in a tokamak plasma

Excitation of radially propagating electrostatic shear Alfvén wave during the formation of ambipolar radial electric field in a stochastic magnetic field

A radially propagating electrostatic shear Alfvén wave (ωH mode) is found during the formation of ambipolar radial electric field in a magnetic stochastic layer through gyrokinetic simulation. It is found that the times scale of the ambipolar radial electric field formation is the damping time of the ωH mode. The frequency and damping rate of the ωH mode are theoretical derived, which are in good agreement with the simulation results.

Role of the edge stochastic layer in density pump-out by resonant magnetic perturbations

The role of the edge stochastic layer on particle transport is addressed in DIII-D plasmas with applied resonant magnetic perturbations (RMPs) causing density pump-out (a term used to denote the density reduction at the top of the pedestal due to the applied RMPs). Using an analytical model that adds the stochastic parallel transport of electrons (Harvey et al 1981 Phys. Rev. Lett. 47 102) to the fluid equations, the ambipolar radial electric field and particle flux are calculated simultaneously. In this model the nonambipolar electron particle flux, driven by the stochastic magnetic field, is predominantly balanced by the nonambipolar perpendicular ion flux, driven by toroidal viscosity, across a narrow stochastic layer of order two percent of the plasma radius (0.98 < ψ n < 1). The model reproduces the level of density pump-out and its dependence on RMP amplitude near the separatrix for three plasma discharges for which the pedestal foot is at medium to high collisionality . The experimentally observed and numerically tested inverse density dependence of density pump-out (Hu et al 2020 Nucl. Fusion 60 076001) is accurately captured by the model: an increase in collisionality with density in the pedestal foot results in a decrease in stochastic diffusivity, and hence a decrease in the level of pump-out.

Study on impurity hole plasmas by global neoclassical simulation

An impurity hole observed in the large helical device (LHD) is a hollow density profile of an impurity ion species formed in the core plasma where the negative (inward-pointing) ambipolar radial electric field (E r) exists. Although local neoclassical models have predicted that the sign of E r in impurity hole plasmas is negative for the entire minor radius, an experimental measurement of an impurity hole plasma has shown that the E r changes the sign from negative to positive along the minor radius. In the present work, we investigate neoclassical impurity transport in an impurity hole plasma using a global neoclassical simulation code FORTEC-3D. The variation of electrostatic potential on each flux surface (Φ1) is evaluated from the quasi-neutrality condition in multi-ion-species plasma by the global simulation. The ambipolar E r and neoclassical fluxes are determined in solving a global drift-kinetic equation including the effect of Φ1. By the global simulation, we show that an E r which changes the sign along the radius is obtained as a solution of the ambipolar condition and with such an E r, impurity carbon flux can be outwardly directed even where E r < 0 and the carbon density profile is hollow around the magnetic axis. Furthermore, it is found that the outward carbon flux is only a factor 2–3 from balancing the modeled inward turbulent flux. Our result indicates that we have moved one step closer to reproducing the impurity transport in impurity hole plasmas by kinetic simulation.

Turbulence Mechanisms of Enhanced Performance Stellarator Plasmas

We theoretically assess two mechanisms thought to be responsible for the enhanced performance observed in plasma discharges of the Wendelstein 7-X stellarator experiment fueled by pellet injection. The effects of the ambipolar radial electric field and the electron density peaking on the turbulent ion heat transport are separately evaluated using large-scale gyrokinetic simulations. The essential role of the stellarator magnetic geometry is demonstrated, by comparison with a tokamak.

Investigation of the neoclassical ambipolar electric field in ion-root plasmas on W7-X

The role of the radial electric field in high-performance ion-root plasmas on Wendelstein 7-X (W7-X) is examined and compared with neoclassical predictions. The W7-X stellarator is the world’s first large-scale optimized stellarator. One of the important targets chosen for optimization during the W7-X design process was the reduction of core neoclassical heat transport. This optimization was targeted for reactor-relevant high-density plasmas with in which the neoclassical ambipolar radial electric field is expected to be negative throughout the plasmas core.Measurements of the core radial electric field (Er) have confirmed that ion-root conditions (negative Er in the plasma core) have been achieved in W7-X with high-density plasmas and central ECRH. These measured Er profiles agree well with the neoclassical ambipolar Er predicted by the code sfincs. This good agreement provides confidence in the validity of neoclassical calculations in high-density ion-root conditions, and enables initial studies on the role of neoclassical transport in the optimized high-density regime of W7-X.Profile measurements of electron temperature (Te), ion temperature (Ti) and electron density (ne) along with approximations for the average value of have been used as inputs to the sfincs code to calculate the ambipolar Er profile along with neoclassical ion and electron energy flux profiles (, ). Finally the total experimental energy input to the plasma from ECRH heating has been compared to the neoclassical energy fluxes to provide a first estimate for the fraction of transport that can be attributed to neoclassical processes in reactor-relevant high-density ion-root conditions.

Effects of island chains on transport through changes in the radial electric field (TJ-II stellarator)

The opening of island chains in magnetically confined fusion plasma is a natural and common process. The effects on transport, however, are difficult to assess because of the complexity of the phenomenon, which often happens dynamically. In this work we investigate one basic way in which transport may be altered due to the presence of magnetic islands: the modification of the ambipolar radial electric field Er due to the distortion of the flux surfaces and the presence of a separatrix. For the latter, we first adapt the metric coefficients to a new configuration that excludes the island region; then we also perturb the original Er with a neoclassical scaling taken from Shaing’s formulation [Phys. Plasmas 9 3470 (2002)]. Some examples are shown for TJ-II plasmas with dynamic configuration scans, i.e., with some low-order rational of the rotational transform moving through the plasma minor radius during one discharge. It is suggested that a modification of transport properties other than neoclassical is necessary in order to explain the experimental results.

Flux-surface variations of the electrostatic potential in stellarators: impact on the radial electric field and neoclassical impurity transport

Flux-surface variations of the electrostatic potential are typically neglected in standard neoclassical theory, but in 3D devices they can be large enough to affect the radial particle flux of impurities. The radially local drift-kinetic equation solver SFINCS (stellarator Fokker–Planck iterative neoclassical conservative solver) (Landreman et al 2014 Phys. Plasmas 21 042503) has been updated to account for these variations. In the present work we use SFINCS to perform a novel study of neoclassical particle transport in stellarators, where we simultaneously account for the flux-surface potential variations, several kinetic species including non-adiabatic electrons and non-trace impurities, and the full linearized Fokker–Planck–Landau collision operator for self- and inter-species collisions (with no expansion made in mass ratio). We also make a self-consistent calculation of the ambipolar radial electric field, to analyze how it is affected by the flux-surface variations and the presence of non-trace impurities. In a simulated Wendelstein 7-X plasma, we find that the impact of the flux-surface variations on the radial particle fluxes of all plasma species is small. In contrast, for an experimental impurity hole discharge in the Large Helical Device (LHD) the carbon flux can be strongly modified by the flux-surface potential variation and also the calculated ambipolar radial electric field can change. However, around mid radius the potential variations cause enhanced inward neoclassical carbon fluxes, rather than causing outward fluxes, thus suggesting that the role of flux-surface potential variations in neoclassical transport may not be the explanation for the impurity hole phenomenon observed in LHD plasmas.

Neoclassical transport benchmark of global full-f gyrokinetic simulation in stellarator configurations

A global full-f gyrokinetic simulation code, GT5D, is extended to incorporate stellarator equilibria, provided by a widely used three-dimensional equilibrium code, VMEC [S. P. Hirshman and O. Betancourt, J. Comput. Phys. 96, 99 (1991)]. An interface code is newly developed, in which the so-called VMEC coordinates are transformed into the coordinates of GT5D. The following benchmark calculations in a typical LHD equilibrium are carried out for the numerical verification of GT5D in stellarator configurations. First, zonal flow damping tests are performed, and good agreement in the residual levels with an analytical theory is confirmed. Second, the neoclassical transport and the ambipolar radial electric field computed by a global δf neoclassical transport code, FORTEC-3D [S. Satake et al., Plasma Fusion Res. 3, S1062 (2008)], are successfully reproduced.

Observation of the ECH effect on the impurity accumulation in the LHD

Recent experiments in the Large Helical Device (LHD) clearly show the ability of electron cyclotron heating (ECH) to control accumulation of impurities, as demonstrated by external injection of a tracer-encapsulated solid pellet (TESPEL). The impurity introduced locally into the core region of the LHD plasma by the TESPEL has strongly accumulated in a high-density LHD plasma, as well as an intrinsic impurity, such as a carbon. When a high-power (1.5 MW) ECH is applied just after the TESPEL injection for such a plasma, the accumulation of the impurity injected by the TESPEL was almost completely suppressed. This result indicates that applying ECH enhances the outward radial impurity flux. Although a neoclassical ambipolar radial electric field in stellarators has a stronger impact on the transport, particularly on the impurity transport, than in tokamaks, the sign of the radial electric field measured and calculated is directed to a negative even in the 1.5 MW ECH case, resulting in the inward impurity flux. By revisiting the neoclassical formulation, an increment of ion temperature and its gradient could be one of the candidates for the explanation, since the ion temperature is also increased globally by ECH.

Boundary plasma response in RFX-mod to 3D magnetic field perturbations

The edge of the RFX-mod (R=2m, a=0.46m) Reversed Field Pinch device is characterized by weak magnetic chaos affecting ion and electron diffusion. Edge particle transport is strongly influenced by a toroidal and poloidal asymmetry caused by magnetic islands and an ambipolar radial electric field ensures local neutrality. At higher plasma current (Iϕ>1MA) a spontaneous resonant dominant mode m/n=1/7, slowly rotating, develops in the inner region. The edge electron pressure Pe and floating potential Vf show a shape of the Plasma Wall Interaction (PWI) with the same toroidal periodicity, which follows the edge local ideal magnetic displacement Δ1,7.Detailed measurements along the poloidal direction of Pe and Vf have been undertaken newly, their time behavior present respect to Δ1,7 a time lag, which depends on the poloidal angle θ. The mode analysis in terms of helical angle reveals a role of the 0/7 mode in determining a poloidal phase lag respect to Δ1,7 of Pe and Vf. Since the 0/7 is the largest toroidal sideband of the 1/7 mode, this work suggests a role of toroidal coupling in determining the plasma response to a MP.

Ambipolar radial electric field generated by anomalous transport induced by magnetic perturbations

The anomalous particle transport induced by magnetic perturbations in a tokamak is investigated. The correlation between the radial position and the kinetic energy of electrons, DrK=−eErDrr, is predicted theoretically and is verified by simulations in the presence of a mean radial electric field. This correlation leads to a radial particle flux produced by the radial electric field. The ambipolar radial electric field can thus be predicted by using the ambipolarity condition Γri=Γre.

Effect of suprathermal electrons flux on the ambipolar electric field in stellarators

Low collisionality plasmas in non-axisymmetric toroidal magnetic devices have significant radial particle fluxes due to trapped particles in the magnetic ripples. The associated ambipolar radial electric field cannot be quantitatively reproduced by standard neoclassical models since the measured values are systematically larger. Here the contribution of suprathermal electrons is included in the radial electric field. The radial flux of suprathermal particles is calculated following a kinetic analysis of the particle transport in which a non-Maxwellian velocity distribution is assumed for the high velocity electrons in the low collisionality regime. The electric field modification produced by the suprathermal electrons is then obtained and an analytical expression for the radial electric field is found which is compared with the one obtained from the thermal particles. An estimate of the needed contribution of the suprathermal electrons is given. Experimental data of the TJ-II Heliac-stellarator are taken for the computations since good Heavy Ion Beam Probe measurements are available.

Impurities in a non-axisymmetric plasma: Transport and effect on bootstrap current

Impurities cause radiation losses and plasma dilution, and in stellarator plasmas the neoclassical ambipolar radial electric field is often unfavorable for avoiding strong impurity peaking. In this work we use a new continuum drift-kinetic solver, the SFINCS code (the Stellarator Fokker-Planck Iterative Neoclassical Conservative Solver) [M. Landreman et al., Phys. Plasmas 21, 042503 (2014)] which employs the full linearized Fokker-Planck-Landau operator, to calculate neoclassical impurity transport coefficients for a Wendelstein 7-X (W7-X) magnetic configuration. We compare SFINCS calculations with theoretical asymptotes in the high collisionality limit. We observe and explain a 1/ν-scaling of the inter-species radial transport coefficient at low collisionality, arising due to the field term in the inter-species collision operator, and which is not found with simplified collision models even when momentum correction is applied. However, this type of scaling disappears if a radial electric field is present. We also use SFINCS to analyze how the impurity content affects the neoclassical impurity dynamics and the bootstrap current. We show that a change in plasma effective charge Zeff of order unity can affect the bootstrap current enough to cause a deviation in the divertor strike point locations.

On collisional impurity transport in nonaxisymmetric plasmas

The presence of impurity species in magnetic confinement fusion devices leads to radiation losses and plasma dilution. Thus it is important to analyze impurity dynamics, and search for means to control them. In stellarator plasmas the neoclassical ambipolar radial electric field often points radially inwards (referred to as the ion root regime), causing impurities to accumulate in the core. This can limit the performance of nonaxisymmetric devices.In the present work we analyze neoclassical impurity transport in stellarator plasmas using a recently developed continuum drift-kinetic solver, the SFINCS code (the Stellarator Fokker- Planck Iterative Neoclassical Conservative Solver). The study is performed for a case close to the edge of W7-X using the standard configuration magnetic geometry. We investigate the sensitivity of impurity transport to impurity charge, main species density and temperature gradients, as well as ion temperature.At the studied radial location we find that the neoclassical impurity peaking factor can be very large, particularly for high-Z impurities. The ambipolar radial electric field is in the ion root regime, and impurity accumulation can thus be expected. The accumulation is strengthened by the large main species density and temperature gradients. Moreover we find that the size of the bootstrap current is affected by the value of the plasma effective charge, suggesting that employing a realistic ion composition can be important when calculating the bootstrap current.

Edge plasma physics modifications due to magnetic ripple in RFX-mod

The edge of the RFX-mod (R=2m, a=0.46m) Reversed Field Pinch is characterized by weak magnetic chaos affecting ion and electron diffusion. Edge particle transport is strongly influenced by a toroidal asymmetry caused by magnetic islands. An ambipolar radial electric field ensures local neutrality and possesses the same symmetry as the parent magnetic ripple: the result is the modulation of the perpendicular flow, with a slowing-down at the island X-point.In this paper we present a complete statistical analysis, over a large database of RFX-mod discharges, of the edge properties as they are modified by the magnetic topology: the plasma wall footprint follows the helical shape of the dominant central mode (m/n=1/7), with an increase of Hα emission and electron density corresponding to the O-point of the inner magnetic island. Edge turbulence is modified by the magnetic topology, being generated in the O-point region and damped near the X-point.

On neoclassical impurity transport in stellarator geometry

The impurity dynamics in stellarators has become an issue of moderate concern due to the inherent tendency of the impurities to accumulate in the core when the neoclassical ambipolar radial electric field points radially inwards (ion root regime). This accumulation can lead to collapse of the plasma due to radiative losses, and thus limit high performance plasma discharges in non-axisymmetric devices.A quantitative description of the neoclassical impurity transport is complicated by the breakdown of the assumption of small E × B drift and trapping due to the electrostatic potential variation on a flux surface compared with those due to the magnetic field gradient. This work examines the impact of this potential variation on neoclassical impurity transport in the Large Helical Device heliotron. It shows that the neoclassical impurity transport can be strongly affected by . The central numerical tool used is the δf particle in cell Monte Carlo code EUTERPE. The used in the calculations is provided by the neoclassical code GSRAKE. The possibility of obtaining a more general self-consistently with EUTERPE is also addressed and a preliminary calculation is presented.

Inter-machine validation study of neoclassical transport modelling in medium- to high-density stellarator-heliotron plasmas

A comparative study of energy transport for medium- to high-density discharges in the stellarator-heliotrons TJ-II, W7-AS and LHD is carried out. The specific discharge parameters are chosen to apply a recently concluded benchmarking study of neoclassical (NC) transport coefficients (Beidler et al 2011 Nucl. Fusion 51 076001) to perform this validation study. In contrast to previous experiments at low densities for which electron transport was predominant (Yokoyama et al 2007 Nucl. Fusion 47 1213), the current discharges also exhibit significant ion energy transport. As it affects the energy transport in 3D devices, the ambipolar radial electric field is addressed as well. For the discharges described, ion-root conditions, i.e. a small negative radial electric field were found. The energy transport in the peripheral region cannot be explained by NC theory. Within a ‘core region’(r/a < 1/2 ∼ 2/3), the predicted NC energy fluxes comply with experimental findings for W7-AS. For TJ-II, compliance in the core region is found for the particle transport and the electron energy transport. For the specific LHD discharges, the core energy transport complied with NC theory except for the electron energy transport in the inward-shifted magnetic configuration. The NC radial electric field tends to agree with experimental results for all devices but is measured to be more negative in the core of both LHD and TJ-II. As a general observation, the energy confinement time approaches the gyro-Bohm-type confinement scaling ISS04 (Yamada et al 2005 Nucl. Fusion 45 1684). This work is carried out within the International Stellarator-Heliotron Profile Database (www.ipp.mpg.de/ISS and http://ishpdb.nifs.ac.jp/index.html).

Neoclassical transport simulations for stellarators

The benchmarking of the thermal neoclassical transport coefficients is described using examples of the Large Helical Device (LHD) and TJ-II stellarators. The thermal coefficients are evaluated by energy convolution of the monoenergetic coefficients obtained by direct interpolation or neural network techniques from the databases precalculated by different codes. The temperature profiles are calculated by a predictive transport code from the energy balance equations with the ambipolar radial electric field estimated from a diffusion equation to guarantee a unique and smooth solution, although several solutions of the ambipolarity condition may exist when root-finding is invoked; the density profiles are fixed. The thermal transport coefficients as well as the ambipolar radial electric field are compared and very reasonable agreement is found for both configurations. Together with an additional W7-X case, these configurations represent very different degrees of neoclassical confinement at low collisionalities. The impact of the neoclassical optimization on the energy confinement time is evaluated and the confinement times for different devices predicted by transport modeling are compared with the standard scaling for stellarators. Finally, all configurations are scaled to the same volume for a direct comparison of the volume-averaged pressure and the neoclassical degree of optimization.

Considerations from the Viewpoint of Neoclassical Transport Towards Higher Ion Temperature Heliotron Plasmas

AbstractThe neoclassical (NC) transport analyses have been performed to elucidate the plausible approaches towards higher ion‐temperature heliotron plasmas. Avoidance of the ripple transport is the key issue, for which the neoclassical ambipolar radial electric field (Er) can be utilized. The ion‐root scenario and the electron‐root scenario are expected to be effective according to the experimental situation (especially, the temperature ratio between ions and electrons). The impact of the ion mass on the neoclassical ambipolar Er is also investigated to reveal the easier realization of electron‐root Er in heavier ion plasmas (© 2010 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)