Parallel Ion Flow Research Articles

Dimits transition in three-dimensional ion-temperature-gradient turbulence

We extend our previous work on the two-dimensional (2-D) Dimits transition in ion-scale turbulence (Ivanov et al., J. Plasma Phys., vol. 86, 2020, 855860502) to include variations along the magnetic field. We consider a three-field fluid model for the perturbations of electrostatic potential, ion temperature, and ion parallel flow in a constant-magnetic-curvature geometry without magnetic shear. It is derived in the cold-ion, long-wavelength asymptotic limit of the gyrokinetic theory. Just as in the 2-D model, a low-transport (Dimits) regime exists and is found to be dominated by a quasistatic staircase-like arrangement of strong zonal flows and zonal temperature. This zonal staircase is formed and maintained by a negative turbulent viscosity for the zonal flows. Unlike the 2-D model, the three-dimensional (3-D) one does not suffer from an unphysical blow up beyond the Dimits threshold where the staircase becomes nonlinearly unstable. Instead, a well-defined finite-amplitude saturated state is established. This qualitative difference between the 2-D and 3-D models is due to the appearance of small-scale ‘parasitic’ modes that exist only if we allow perturbations to vary along the magnetic field lines. These modes extract energy from the large-scale perturbations and provide an effective enhancement of large-scale thermal diffusion, thus aiding the energy transfer from large injection scales to small dissipative ones. We show that in our model, the parasitic modes always favour a zonal-flow-dominated state. In fact, a Dimits state with a zonal staircase is achieved regardless of the strength of the linear drive, provided the system is sufficiently extended along the magnetic field and sufficient parallel resolution is provided.

Ion temperature anisotropy model with cross‐field drifts in the scrape‐off layer

AbstractAn ion temperature anisotropy model including cross‐field drifts has been implemented in the 2D transport code UEDGE. Two ion temperature equations are solved in the model to give separate ion temperatures perpendicular and parallel to the magnetic field, which results in an additional mirror force for ion parallel transport and also leads to an additional curvature drift in the perpendicular direction. In our previous work, an ion temperature anisotropy model was implemented and applied to the full 2D version of UEDGE including recycled neutrals. The simulation results showed that the mirror force due to anisotropy reduces ion parallel flow velocity, however, the simulations were presented without cross‐field electric and magnetic drifts. Nevertheless, in present medium‐size tokamaks or future compact fusion devices, cross‐fields are important. In this work, the anisotropy model is extended to be compatible with the inclusion of cross‐field drifts. Preliminary results on comparison between the model solutions with and without cross‐field drifts are presented.

Free Energy Sources in Current Sheets Formed in Collisionless Plasma Turbulence

Abstract Collisionless dissipation of macroscopic energy into heat is an unsolved problem of space and astrophysical plasmas, e.g., solar wind and Earth’s magnetosheath. The most viable process under consideration is the turbulent cascade of macroscopic energy to kinetic scales where collisionless plasma processes dissipate the energy. Space observations and numerical simulations show the formation of kinetic scale current sheets in turbulent plasmas. Instabilities in these current sheets (CS) can provide collisionless dissipation and influence the turbulence. Spatial gradients of physical quantities and non-Maxwellian velocity distribution functions provide the free energy sources for CS plasma instabilities. To determine the free energy sources provided by the spatial gradients of plasma density and electron/ion bulk velocities in CS formed in collisionless turbulent plasmas with an external magnetic field B 0, we carried out two-dimensional particle-in-cell-hybrid simulations and interpret the results within the limitations of the simulation model. We found that ion-scale CS in a collisionless turbulent plasma are formed primarily by electron shear flows, i.e., electron bulk velocity inside CS is much larger than ion bulk velocity while the density variations through the CS are relatively small (<10%). The electron bulk velocity and, thus, the current density inside the sheets are directed mainly parallel to B 0. The shear in the perpendicular electron and ion bulk velocities generates parallel electron and ion flow vorticities. Inside CS, parallel electron flow vorticity exceeds the parallel ion flow vorticity, changes sign around the CS centers, and peaks near the CS edges. An ion temperature anisotropy develops near CS during the CS formation. It has a positive correlation with the parallel ion and electron flow vorticities. Theoretical estimates support the simulation results.

Prediction of average mobility of ions from corona discharge in air with respect to pressure, humidity and temperature

Pressure, temperature and humidity are the basic parameters of air, which affect the average mobility of ions in it. In this paper a series of the average mobilities of ions in corona discharge in air at different pressures, temperatures and humidities are measured using an apparatus for generating parallel plane ion flow field in a climatic test cabinet. The pressure, relative humidity, and temperature is from 80 to 110 kPa, 20 to 85%, and −10 to 40°C, respectively. The variation of the average mobility of ions in corona discharge in air, with respect to pressure, humidity and temperature, is discussed and calculated from the fundamental mobility equation.

Turbulence characteristics, energy equipartition, and zonal flow generation in coupled drift wave-parallel velocity gradient driven turbulence

We perform a computational study of characteristics of coupled drift wave (DW)-parallel velocity gradient (PVG) driven turbulence. The three-dimensional Hasegawa–Mima equation combined with ion parallel flow dynamics is used for this study. Energetic analyses, both analytic and computational, show the energy equipartition of the parallel Reynolds power (i.e. the free energy due to a gradient in equilibrium parallel velocity) in parallel and perpendicular directions. A considerable portion of the perpendicular energy that is transferred through the parallel coupling generates the perpendicular zonal flow (ZF), implying the increase of the ZF level when an equilibrium PVG is present. A careful analysis of parallel-perpendicular coupling dynamics shows that the vortex stretching-like term in this system plays a significant role in the ZF generation. This is in contrast to the neutral fluid turbulence where it hinders the inverse cascade process. However, the ZF generation from PVG turbulence is found to be less effective in comparison with that of DW turbulence.

The role of neutral friction in governing parallel flows in the HSX stellarator

Experimentally measured parallel ion flows in the standard quasihelically symmetric configuration of the HSX stellarator show a large discrepancy with previous neoclassical calculations, whereas flow in a symmetry degraded configuration is in reasonably good agreement with neoclassical theory. To examine this discrepancy, the neoclassical transport code PENTA has been modified to include collisions with background neutrals. It has been found that the flow damping due to ion-neutral friction significantly modifies the ion parallel flows in the standard configuration. This makes the modeling of the ion parallel flow agree better with the experimental measurements. In the symmetry degraded configuration, higher neoclassical viscosity makes the flow damping arising from neutral friction less important. The bootstrap current was found to be insensitive to the neutral friction as the decrease in ion flow was matched by an increase in the electron flow.

Radial electric field and ion parallel flow in the quasi-symmetric and Mirror configurations of HSX

The radial electric field and the ion mean parallel flow are obtained in the helically symmetric experiment stellarator from toroidal flow measurements of C+6 ion at two locations on a flux surface, using the Pfirsch–Schlüter effect. Results from the standard quasi-helically symmetric magnetic configuration are compared with those from the Mirror configuration where the quasi-symmetry is deliberately degraded using auxiliary coils. For similar injected power, the quasi-symmetric configuration is observed to have significantly lower flows while the experimental observations from the Mirror geometry are in better agreement with neoclassical calculations. Indications are that the radial electric field near the core of the quasi-symmetric configuration may be governed by non-neoclassical processes.

Ion heating and flows in a high power helicon source

We report experimental measurements of ion temperatures and flows in a high power, linear, magnetized, helicon plasma device, the Resonant Antenna Ion Device (RAID). Parallel and perpendicular ion temperatures on the order of 0.6 eV are observed for an rf power of 4 kW, suggesting that higher power helicon sources should attain ion temperatures in excess of 1 eV. The unique RAID antenna design produces broad, uniform plasma density and perpendicular ion temperature radial profiles. Measurements of the azimuthal flow indicate rigid body rotation of the plasma column of a few kHz. When configured with an expanding magnetic field, modest parallel ion flows are observed in the expansion region. The ion flows and temperatures are derived from laser induced fluorescence measurements of the Doppler resolved velocity distribution functions of argon ions.

Global 3D two-fluid simulations of the tokamak edge region: Turbulence, transport, profile evolution, and spontaneous E × B rotation

We present global two-fluid simulations of L-mode edge tokamak plasma turbulence and profile evolution including both closed field lines and the scrape-off-layer. We consider a shifted-circle magnetic configuration with realistic Alcator C-Mod inner wall limited discharge parameters. The dominant driver of turbulence in the simulations is the resistive ballooning mode. We observe spontaneous E × B rotation in the electron diamagnetic drift direction in the closed flux region in all cases. We explain this based on the steady state ion continuity relation ∇·nv→i≈0. We find that the E × B rotation in the closed flux region mostly cancels the ion diamagnetic drift as H-mode-like regimes are approached and exceeds it by a factor of 2 or more at lower temperatures due to parallel ion flows.

Total fluid pressure imbalance in the scrape-off layer of tokamak plasmas

Simulations using the fully kinetic neoclassical code XGCa (X-point included guiding- center axisymmetric) were undertaken to explore the impact of kinetic effects on scrape-off layer (SOL) physics in DIII-D H-mode plasmas. XGCa is a total-f, gyrokinetic code which self-consistently calculates the axisymmetric electrostatic potential and plasma dynamics, and includes modules for Monte Carlo neutral transport.Previously presented XGCa results showed several noteworthy features, including large variations of ion density and pressure along field lines in the SOL, experimentally relevant levels of SOL parallel ion flow (Mach number ∼ 0.5), skewed ion distributions near the sheath entrance leading to subsonic flow there, and elevated sheath potentials (Churchill 2016 Nucl. Mater. Energy 1–6).In this paper, we explore in detail the question of pressure balance in the SOL, as it was observed in the simulation that there was a large deviation from a simple total pressure balance (the sum of ion and electron static pressure plus ion inertia). It will be shown that both the contributions from the ion viscosity (driven by ion temperature anisotropy) and neutral source terms can be substantial, and should be retained in the parallel momentum equation in the SOL, but still falls short of accounting for the observed fluid pressure imbalance in the XGCa simulation results.

Determination of radial electric field from Pfirsch–Schlüter flows in the HSX stellarator

Inboard/outboard asymmetry in the impurity ion parallel flow is observed in the HSX stellarator using charge exchange recombination spectroscopy (CHERS). This observation shows the presence of counter-streaming Pfirsch–Schlüter flow predicted by neoclassical theory. The asymmetry of the flow is used to calculate the magnitude and direction of the radial electric field (Er), as well as the mean flow, using computed magnetic geometry factors. This method enables calculation of Er near the core of the HSX plasma where the Er obtained from the radial force balance equation has large uncertainties due to the relatively large width of the diagnostic neutral beam with respect to the plasma minor radius.

Electromagnetic theory of turbulent acceleration of parallel flow and momentum conservation

Intrinsic flow in plasma physics is a long-standing puzzle, since it is difficult to understand its origin without contradiction to momentum conservation in conventional wisdom. It is proved that the electromagnetic turbulent acceleration as a candidate for intrinsic parallel flow generation driven by pressure gradient along the total magnetic field line does not contradict the momentum conservation. The conserved quantity corresponding to axial symmetry is the total gyrocenter parallel canonical momentum carried by both species or the total gyrocenter parallel momentum including the ion gyrocenter kinematic momentum and electromagnetic fields momentum, but not the ion kinematic momentum, or even the ion parallel flow. A conservation equation of total parallel momentum including the ion particles' kinematic momentum and electromagnetic fields momentum is also presented.

Structure formation in parallel ion flow and density profiles by cross-ferroic turbulent transport in linear magnetized plasma

In this paper, we show the direct observation of the parallel flow structure and the parallel Reynolds stress in a linear magnetized plasma, in which a cross-ferroic turbulence system is formed [Inagaki et al., Sci. Rep. 6, 22189 (2016)]. It is shown that the parallel Reynolds stress induced by the density gradient driven drift wave is the source of the parallel flow structure. Moreover, the generated parallel flow shear by the parallel Reynolds stress is found to drive the parallel flow shear driven instability D'Angelo mode, which coexists with the original drift wave. The excited D'Angelo mode induces the inward particle flux, which seems to help in maintaining the peaked density profile.

Neoclassical parallel flow calculation in the presence of external parallel momentum sources in Heliotron J

A moment approach to calculate neoclassical transport in non-axisymmetric torus plasmas composed of multiple ion species is extended to include the external parallel momentum sources due to unbalanced tangential neutral beam injections (NBIs). The momentum sources that are included in the parallel momentum balance are calculated from the collision operators of background particles with fast ions. This method is applied for the clarification of the physical mechanism of the neoclassical parallel ion flows and the multi-ion species effect on them in Heliotron J NBI plasmas. It is found that parallel ion flow can be determined by the balance between the parallel viscosity and the external momentum source in the region where the external source is much larger than the thermodynamic force driven source in the collisional plasmas. This is because the friction between C6+ and D+ prevents a large difference between C6+ and D+ flow velocities in such plasmas. The C6+ flow velocities, which are measured by the charge exchange recombination spectroscopy system, are numerically evaluated with this method. It is shown that the experimentally measured C6+ impurity flow velocities do not contradict clearly with the neoclassical estimations, and the dependence of parallel flow velocities on the magnetic field ripples is consistent in both results.

New regime of low ion collisionality in the neoclassical equilibrium of tokamak plasmas

The neoclassical description of an axisymmetric toroidal plasma equilibrium is formulated for an unconventionally low ordering of the collisionality that suits realistic thermonuclear fusion conditions. This requires a drift-kinetic analysis to the second order of the ion Larmor radius, which yields a new contribution to the leading solution for the non-Maxwellian part of the ion distribution function if the equilibrium geometry is not up-down symmetric. An explicit geometrical factor weighs this second Larmor-radius order, low-collisionality effect that modifies the neoclassical ion parallel flow, and the ion contribution to the bootstrap current.

Verification of continuum drift kinetic equation solvers in NIMROD

Verification of continuum solutions to the electron and ion drift kinetic equations (DKEs) in NIMROD [C. R. Sovinec et al., J. Comp. Phys. 195, 355 (2004)] is demonstrated through comparison with several neoclassical transport codes, most notably NEO [E. A. Belli and J. Candy, Plasma Phys. Controlled Fusion 54, 015015 (2012)]. The DKE solutions use NIMROD's spatial representation, 2D finite-elements in the poloidal plane and a 1D Fourier expansion in toroidal angle. For 2D velocity space, a novel 1D expansion in finite elements is applied for the pitch angle dependence and a collocation grid is used for the normalized speed coordinate. The full, linearized Coulomb collision operator is kept and shown to be important for obtaining quantitative results. Bootstrap currents, parallel ion flows, and radial particle and heat fluxes show quantitative agreement between NIMROD and NEO for a variety of tokamak equilibria. In addition, velocity space distribution function contours for ions and electrons show nearly identical detailed structure and agree quantitatively. A Θ-centered, implicit time discretization and a block-preconditioned, iterative linear algebra solver provide efficient electron and ion DKE solutions that ultimately will be used to obtain closures for NIMROD's evolving fluid model.

Intrinsic toroidal rotation in the scrape-off layer of tokamaks

The origin and nature of intrinsic toroidal plasma rotation in the scrape-off-layer (SOL) of tokamaks is investigated both analytically and through numerical simulations. It is shown that the equilibrium poloidal E × B flow, the sheath physics, and the presence of poloidal asymmetries in the pressure profile act as sources of momentum, while turbulence provides the mechanism for the radial momentum transport. An equation for the radial and poloidal dependence of the equilibrium parallel ion flow is derived, and a simple analytical solution is presented. This solution reproduces and explains the main experimental trends for the Mach number found in the SOL of tokamaks. Global, three-dimensional fluid simulations of SOL turbulence in different limiter configurations confirm the validity of the analytical theory.

An assessment of ion temperature measurements in the boundary of the Alcator C-Mod tokamak and implications for ion fluid heat flux limiters

The ion temperature is not frequently measured in the boundary of magnetic fusion devices. Comparisons among different ion temperature techniques and simulations are even rarer. Here we present a comparison of ion temperature measurements in the boundary of the Alcator C-Mod tokamak from three different diagnostics: charge exchange recombination spectroscopy (CXRS), an ion sensitive probe (ISP), and a retarding field analyzer (RFA). Comparison between CXRS and the ISP along with close examination of the ISP measurements reveals that the ISP is space charge limited. It is thus unable to measure ion temperature in the high density (>1019 m−3) boundary plasma of C-Mod with its present geometry. Comparison of ion temperatures measured by CXRS and the RFA shows fair agreement. Ion and electron parallel heat flow is analyzed with a simple 1D fluid code. The code takes divertor measurements as input and results are compared to the measured ratios of upstream ion to electron temperature, as inferred respectively by CXRS and a Langmuir probe. The analysis reveals the limits of the fluid model at high Knudsen number. The upstream temperature ratio is under predicted by a factor of 2. Heat flux limiters (kinetic corrections) to the fluid model are necessary to match experimental data. The values required are found to be close to those reported in kinetic simulations. The 1D code is benchmarked against the 2D plasma fluid code UEDGE with good agreement.

Drift wave instability in a radially bounded dusty magnetoplasma with parallel ion velocity shear

AbstractProperties of the coupled dust ion-acoustic drift wave instability in a radially bounded dusty magnetoplasma with an equilibrium sheared parallel ion (SPI) flow are investigated. By using the two-fluid model for the electrons and ions, a wave equation for the low-frequency coupled dust ion-acoustic drift waves in a bounded plasma with stationary charged dust grains is derived. The wave equation admits a linear dispersion relation, which exhibits that the radial boundary affects the growth rate of the coupled ion-acoustic drift wave instability which is excited by the SPI flow. The results should be relevant to dusty magnetoplasma experiments with an SPI flow.

Numerical investigation of a compressible gyrofluid model for collisionless magnetic reconnection

Ion Larmor radius effects on collisionless magnetic reconnection in the presence of a guide field are investigated by means of numerical simulations based on a gyrofluid model for compressible plasmas. Compressibility along the magnetic field is seen to favour the distribution of ion guiding center density along the neutral line, rather than along the separatrices, unlike the electron density. On the other hand, increasing ion temperature reduces the intensity of localized ion guiding center flows that develop in the direction parallel to the guide field. Numerical simulations suggest that the width of these bar-shaped velocity layers scale linearly with the ion Larmor radius. The increase of ion temperature radius causes also a reduction of the electron parallel velocity. As a consequence, it is found that the cusp-like current profiles distinctive of non-dissipative reconnection are strongly attenuated. The field structures are interpreted in terms of the behavior of the four topological invariants of the system. Two of these are seen to behave similarly to invariants of simpler models that do not account for parallel ion flow. The other two exhibit different structures, partly as a consequence of the small electron/ion mass ratio. The origin of these invariants at the gyrokinetic level is also discussed. The investigation of the field structures is complemented by an analysis of the energetics of the system.