Multi-fluid Plasma Research Articles

Application of a fourth-order accurate finite-volume method with adaptive refinement in space and time to multifluid plasma simulations

Application of a fourth-order accurate finite-volume method with adaptive refinement in space and time to multifluid plasma simulations

Experimental confirmation of the linear relation between plasma current and external vertical magnetic field in EXL-50 spherical torus energetic electron plasmas

A three-fluid equilibrium plasma with bulk plasma and energetic electrons has been observed on the Xuanlong-50 (EXL-50) spherical torus, where the energetic electrons play a crucial role in sustaining the plasma current and pressure. In this study, the equilibrium of a multi-fluid plasma was investigated by analyzing the relationship between the external vertical magnetic field (B V), plasma current (I p), the poloidal ratio (β p) and the Shafranov formula. Remarkably, our research demonstrates some validity of the Shafranov formula in the presence of multi-fluid plasma in EXL-50 spherical torus. This finding holds significant importance for future reactors as it allows for differentiation between alpha particles and background plasma. The study of multi-fluid plasma provides a significant reference value for the equilibrium reconstruction of burning plasma involving alpha particles.

Modeling of tungsten impurity transport and distribution in EAST based on multi-fluid and kinetic Monte Carlo simulations

In recent years, the materials of plasma facing components, such as divertor target plates, domes, and outer walls of tokamaks, such as ASDEX Upgrade, WEST, JET, EAST, and ITER, have been changed from carbon to tungsten because of its lower erosion and tritium retention rates. Impurities are produced by interactions between the plasma and the first wall. This study provides an investigation to simulate the transport and distribution of tungsten impurities in the edge plasma on EAST. The 2D multi-fluid edge plasma transport code SOLPS-ITER and 2D kinetic Monte Carlo impurity transport code DIVIMP were used in the simulations. The multi-fluid model in SOLPS-ITER and the kinetic Monte Carlo model in DIVIMP were employed to treat tungsten impurity ions. The 2D density contour distributions in the computational region and the 1D density radial profiles at the inner and outer midplanes of tungsten impurity particles with ionization states (W0–W+74) and the total tungsten particles with all charge states were obtained. With the heating power 1.5 MW and the line-averaged plasma density 2 × 1019 m−3, the results from SOLPS-ITER and DIVIMP show that the maximum density of tungsten ion with single ionization state is about 1014 m−3 and the total density of tungsten impurities with all charge states is about 1015 m−3 at the core boundary. To the best of our knowledge, the simulation results from SOLPS-ITER and DIVIMP are compared for the first time to benchmark SOLPS-ITER with the multi-fluid mode and DIVIMP with the kinetic model for tungsten impurity transport. The density distributions of tungsten impurities with different ionization states from SOLPS-ITER and DIVIMP are highly similar, and good agreement can be found under similar conditions involved in the calculation. From the comparison benchmark between SOLPS-ITER and DIVIMP for tungsten impurity transport, it can be concluded that the impurity transport approximation used by DIVIMP is good.

Solar wind effect on the multi-fluid plasma expansion in the Venusian upper ionosphere

Inspired by the observations suggesting that at altitudes of about 1000 km the interaction between solar wind streams and Venus’ ionosphere plasma leads to ions acceleration and outflow, the influence of different solar wind physical parameters, such as densities, temperatures and initial streaming velocities, has been studied. The ionosphere plasma system consists of two positive ion populations O+, H+ and electrons along with the solar wind streaming protons and electrons. We calculated the generated oxygen and hydrogen ions flow velocities and the electric fields. In addition, we calculated rough estimates for the escaping flux of ion populations (O+, H+) from Venus’ ionosphere and compared them to observations. To a large extent, we found that the estimates match. We also discuss the relevance of ionospheric ion acceleration and outflow from Venus’ upper.

The magnetised plasma Richtmyer–Meshkov instability: elastic collisions in an ion–electron multifluid plasma

The influence of an applied magnetic field on the collisional plasma Richtmyer–Meshkov instability (RMI) is investigated through numerical simulation. The instability is studied within the five-moment multifluid plasma model without any simplifying assumptions such as infinite speed of light, negligible electron inertia or quasineutrality. The plasma is composed of ion and electron fluids, and elastic collisions are modelled with the Braginskii transport coefficients. A collisional regime is investigated and the magnetic field is applied in the direction of shock propagation, which is perpendicular to the density interface. The primary instability is influenced by several terms affecting the evolution of circulation, the most significant of which are the baroclinic, magnetic field torque and intraspecies collisional terms. The applied magnetic field results in a reduction of interface perturbation growth, agreeing qualitatively with previous numerical simulations for the case of an ideal multifluid plasma RMI. The only major difference in the present case's instability mitigation by applied magnetic field, relative to the ideal case with applied magnetic field, is that the elastic collisions replace and obstruct the secondary vorticity suppression mechanism through collisional dissipation of vorticity. Additionally the collisions, influenced by the combination of self-generated and the applied magnetic field, introduce anisotropy to the problem. The primary suppression mechanism for the RMI is unchanged relative to the ideal case, i.e. the magnetic field torque resisting baroclinic deposition of vorticity in the ion fluid.

An alternative method to mimic mode conversion for ion cyclotron resonance heating

Ion cyclotron range of frequency waves in hot plasmas exhibit spatial dispersion effects and the wave equation takes the integro-differential form. Under the local plasma model assumption, the wave equation can be simplified to the differential form and adapts to the numerical scheme of the finite element method (FEM). Even though direct absorption of fast waves by ions and electrons can be described well by the local plasma model, linear mode conversion associated with non-local effects is absent. To deal with this issue, an alternative method is put forward in this paper where quasi-electrostatic fluid waves based on the multi-fluid warm plasma model are employed to take the place of ion Bernstein waves in mode conversion. On this basis, an interative fluid-kinetics (INTFLUK) code based on the FEM is developed for full-wave simulation in hot plasmas. Derivation of the wave equations as well as benchmarking of the INTFLUK code against other wave simulation codes are carried out. In both one- and two-dimensional cases, the validity of the INTFLUK code was verified by comparison of the wave field distributions and power deposition. As a useful illustration of the INTFLUK code including the scrape-off layer and a realistic antenna, the influence of the poloidal antenna phasing difference on ion cyclotron resonance heating is analyzed. Finally, it should be noted that the method in this paper has the potential to be extended to the three-dimensional case, which will be considered in the near future.

Electrostatic solitary waves in a bi-ion plasma with two suprathermal electron populations – application to Saturn’s magnetosphere

ABSTRACT Non-thermal particle distributions characterized by a high-energy tail are ubiquitous in space plasmas. They are usually described by a kappa distribution function, that has been shown to be an excellent fit in most real circumstances. Among other space missions, Cassini and Voyager have both recorded evidence of a coexistence of non-thermal electron populations (with different characteristics) in Saturn’s magnetosphere, and subsequent studies showed that these are well-described by using different tailor-fit realizations of the (parametrized) kappa distribution. Motivated by these observations we have formulated a multifluid plasma model incorporating two types of (positive) ions and two distinct kappa-distributed electron populations, in order to study electrostatic solitary waves (ESWs) in Saturn’s magnetosphere from first principles. Our analysis reveals that the spectral index (in fact, the κ parameter value related to the cold electron population mainly) is vital in explaining the difference among different types of non-linear structures. A comparison with spacecraft observations suggests that our theoretical model provides an efficient framework for the interpretation of ESW observations in Saturn’s magnetosphere. Our qualitative predictions may also apply to other planetary magnetospheres, where a similar multispecies plasma composition may be present.

Numerical studies of plasma edge in W7-X with 3D FINDIF code

Abstract Modelling of the plasma transport for inherently three-dimensional (3D) problems as in stellarators requires dedicated complex codes. FINDIF is a 3D multifluid plasma edge transport code that has been previously successfully used for the analysis of energy transport in the TEXTOR-DED tokamak [1], where 3D perturbations led to an ergodic structure of field lines in the plasma edge. The ongoing efforts to apply it meaningfully to Wendelstein 7-X (W7-X) plasma problems resulted in advancements in the main model and accompanying tools for mesh generation and post-processing. In order to verify the applicability of the code and to compare with the reported simulation (EMC3-EIRENE) and experimental (OP1.1) results, a series of simulations for varying plasma density, temperature and anomalous transport coefficients as well as for fixed input power were performed. The connection length pattern of FINDIF traced magnetic field lines on the limiter was reproduced and its impact on heat loads was confirmed. An increase in the peak heat load on the limiter with a rise in plasma density, temperature and anomalous plasma transport coefficients was observed. The decay lengths of density, electron temperature and heat flux did not change with density, and were decreasing with temperature and increasing with anomalous plasma transport coefficient, which was compared to the simple scrape-off layer (SOL) model.

Fourth-order accurate numerical modeling of the multi-fluid plasma equations with adaptive mesh refinement

This work develops a multi-fluid plasma modeling capability in extension of a parallel, adaptive, fourth-order, finite-volume method, computational fluid dynamics algorithm. The governing equations of the multi-fluid plasma model are derived from moments of the Boltzmann equation, under the assumption of local thermodynamic equilibrium. Maxwell's equations describe the electromagnetic field evolution and are coupled to the fluid equations of charged species. The present work concentrates on two, charged, collisionless fluids as the first step, although the algorithm is designed to accommodate more fluids, both charged and neutral, and collisions between fluids; the extension to multiple fluids is straightforward. The numerical algorithm featuring parallel, high-order (≥4 for smooth flows), adaptive mesh refinement is expected to help cope with the inherent stiffness of the physics involved. The standard, fourth-order Runge-Kutta scheme is used to evolve the solution in time. The current study is primarily focused on verification and testing of the new, adaptive algorithm; we demonstrate 4th-order accuracy using problems with exact solutions and benchmark our solutions for common plasma simulations against references from literature. Using the 4th-order scheme, our multi-fluid model is shown to provide accurate solutions to plasma problems using half the cell count as traditional, 2nd-order methods. Furthermore, adaptive mesh refinement is successfully applied to three, plasma test problems, providing a significant reduction in mesh size. In subsequent work, an optimized version of our multi-fluid plasma algorithm will be applied to plasma test cases with more practical configurations, with a rigorous assessment of the improvements to computational efficiency afforded by our adaptive, higher-order scheme.

Computationally efficient high-fidelity plasma simulations by coupling multi-species kinetic and multi-fluid models on decomposed domains

A numerical method is developed for coupling a multi-species kinetic plasma model with a 5N-moment multi-fluid plasma model. The simulation domain is decomposed such that the local conditions satisfy the corresponding plasma model's region of validity. The method allows for hybrid simulations by formulating each model as a set of conservation laws and using a continuum numerical method to solve each model's governing equations in the subdomains of the decomposed domain. The models are coupled through fluxes across subdomain interfaces. Two methods are explored for the formulation of the fluxes that can be self-consistently represented by both plasma models. One method allows for flux calculations consistent with the 5N-moment multi-fluid plasma model and assumes thermodynamic equilibrium within each species of the kinetic plasma model. The second method ensures conservation of the distribution function as well as mass, momentum, and energy by formulating the fluxes using a composite underlying distribution function at the subdomain interfaces. The methods are compared in 1D1V simulations of a double rarefaction wave and a plasma sheath using the WARPXM framework, which solves each model using the discontinuous Galerkin finite element method. Both methods for formulating the fluxes perform well as the subdomain interface distribution function approaches a Maxwellian, with the consistent method being more robust to larger deviations. A simulation of the magnetized Kelvin-Helmholtz instability in 2D2V is also performed using the consistent method, which demonstrates the potential of the domain-decomposed hybrid method in facilitating speedup and reduction in required computational resources for high-fidelity plasma simulations, allowing for the investigation of problems that are beyond current capabilities.

Evolution of Negative Corona in the Discharge-Current Limitation Mode: Transition from the Pulsed-Periodic Mode to Steady-State Burning

The evolution of burning modes of a weak-current corona discharge in a diode filled with atmospheric air, having a pointed cathode and a flat anode, has been investigated. A theoretical description is performed in terms of an axisymmetric multifluid plasma model, including the kinetics of 9 types of particles and 25 plasma-chemical reactions. A discharge in a gap 10 mm long, with a needle-like cathode having a tip curvature radius of 100 μm, a source voltage of 8 kV, a ballast capacitance of 100 pF and a circuit ballast resistance of 1 MΩ, is described in detail. It is shown, both experimentally and theoretically, that the discharge has a lifetime of 180 μs and occurs in four clearly different stages under these conditions: (1) dark breakdown delay phase (0–20 μs); (2) Trichel pulse phase with a variable on–off time ratio and quasi-steady-state corona current component (20–80 μs); and (3) intermediate phase of monotonically rising weak current (80–130 μs), which ends with a vibrational transition to the (4) steady-state phase (130–180 μs), having a typical structure of glow discharge. The tendencies to a change in the corona discharge parameters with a variation in the feed voltage are analyzed. The results of theoretical calculations are in good agreement with the experimental data.

The effect of collisions on the multi-fluid plasma Richtmyer–Meshkov instability

The Richtmyer–Meshkov instability (RMI) results from the impulsive acceleration of a density interface where the RMI itself or the acceleration is perturbed. The RMI is ubiquitous in shock environments and may arise due to an interface of fluid species, isotopes, temperature, or more. The plasma RMI can be significantly influenced by electromagnetic effects and can be modeled more accurately by a multi-fluid plasma (MFP) model rather than conventional magnetohydrodynamics, though with increased computational expense. MFP modeling of the plasma RMI has revealed many phenomena but has only been completed within the ideal regime. Modeling the effects of elastic collisions is vital for understanding the behavior of the instability in a dense plasma. The Braginskii transport coefficients provide theoretically based relations modeling thermal equilibration, inter-species drag, viscous momentum- and energy-transfers, and thermal conductivity. Our numerical simulations of the MFP RMI with these relations show that the key changes from the ideal case are (1) reduction of relative motion between the ion and electron fluids (consequently affecting the self-generated electromagnetic fields), (2) introduction of anisotropy in momentum and energy via transport coefficients, and (3) damping of high frequency electromagnetic waves and plasma waves. Under the conditions studied, the net effect is a reduction in the MFP RMI amplitude width and the growth rate to levels approaching the neutral fluid instability, as well as a reduction in large scale perturbations along the ion fluid density interface, a positive for inertial confinement fusion efforts. There are, however, two important caveats: small-scale density interface perturbations remain, and the conditions simulated are a few relevant points in a large parameter space that requires further investigation.

The Richtmyer–Meshkov instability of thermal, isotope and species interfaces in a five-moment multi-fluid plasma

The Richtmyer–Meshkov instability (RMI) results from the impulsive acceleration of a density interface where either it or the acceleration is perturbed. Density interfaces may arise due to a change in gas species, isotope, temperature or a combination of these. We computationally investigate the effect of interface type on the plasma RMI, which is relevant for a range of applications, including inertial confinement fusion. We simulate the evolution of single-mode perturbed thermal, species and isotope interfaces in an ideal ion–electron plasma using the multi-fluid plasma (MFP) model. We find that, in the MFP model, the evolution of different types of interface differs significantly, in contrast to single-fluid models where they behave similarly if the Atwood number is matched. The thermal and species interfaces produce the most severe response to shock acceleration, experiencing the secondary instabilities and enhanced primary mode growth. The isotope interface evolution is restrained in comparison with the former cases, resembling the response predicted by single-fluid models. The determining factor in the severity of the MFP RMI is the density ratio across the initial interface in the electron fluid, which is unity for an isotope interface. We observe that, as the density ratio across the electron interface decreases, so do the magnitudes of the self-generated fields and consequently the severity of the growth amplification. Generally, the evolution of the RMI with different types of interface becomes more similar as the level of coupling between the ion and electron fluids is increased, characterised by reducing the plasma non-dimensional skin depth.

On the morphology of electrostatic solitary waves in the Earth’s aurora

Electrostatic solitary waves (ESWs) have been detected in abundance in Space plasma observations, both by satellites in near-Earth plasma environments as well as by planetary missions, e.g. Cassini in Saturn or MAVEN in Mars. In their usual form, these are manifested as a bipolar electric field corresponding to a bell-shaped pulse in the electrostatic potential. Recent studies have suggested the existence of alternative forms of ESWs, including flat-top solitary waves (FTSWs) and supersolitary waves (SSWs), both of which are often encountered in Space observations such as in polar cap boundary layer, the auroral acceleration region and elsewhere. This article focuses on the existence and characterization of different types of electrostatic solitary waves in multicomponent Space plasmas. Relying on a multi-fluid plasma model, comprising two types of ions and two different electron populations, we have identified the conditions for existence of flat-top solitary waves and supersolitons, in contrast to “standard" solitary waves. Both ion species are models as cold fluids, for simplicity. Our analysis reveals that the coexistence of the two electron populations is pivotal for the formation of such non-standard electrostatic structures, and that their characteristic parameters (temperature, density ratio) plays a decisive role in their generation and structural characteristics. Nonetheless, while supersolitary waves may exist in a wide range of parameter values (as confirmed by earlier theoretical studies), it appears that flat-top solitary waves will occur in a narrow window in the parameter region, which may explain their scarce (but non-negligible) frequency of observation. Our theoretical findings confirm and validate the existence of alternative (non-conventional) ESW waveforms in auroral plasma (in addition to the ubiquitous bipolar electric field form), where such an electron coexistence is typically observed.

An implicit monolithic AFC stabilization method for the CG finite element discretization of the fully-ionized ideal multifluid electromagnetic plasma system

This study considers an implicit finite element formulation for an ideal fully-ionized multifluid electromagnetic plasma system. The formulation is based on fully-implicit Runge-Kutta time discretizations and a monolithic discrete algebraic flux corrected (AFC) continuous Galerkin (CG) spatial discretization of the coupled system. The AFC approach adds scalar artificial diffusion to the high-order, semi-discrete Galerkin method and uses mass lumping in the time derivative term. The result is a low-order method that attempts to enforce local-extremum-diminishing properties for the hyperbolic system. An element-based iterative limiter is applied to reduce the amount of artificial diffusion that is used in regions where the solution is smooth and the additional stabilization is not required. Two models are considered for the electromagnetics portion of the system: an electrostatic model, and a full Maxwell system with a parabolic divergence cleaning approach that enforces the required involutions on the electric and magnetic fields. Results are presented that demonstrate the accuracy and robustness of the formulation for smooth and discontinuous solutions to challenging plasma physics problems. This includes a demonstration that the solution of the full multifluid system yields the expected behavior in the ideal shock-MHD limit.

The Heliosheath Plasma Flow Downstream of the Solar Wind Termination Shock in a Consistent Two-Fluid View

In this article, we shall take it serious what has come out from recent theoretical studies on the plasma conditions in the heliosheath, namely downstream of the solar wind termination shock the total plasma pressure is dominated by the pressure of the electrons. We shall respect these results and try to develop the corresponding theoretical basis for an authentic multi-fluid description of the plasma flow downstream of the shock, starting with the dominant pressure action of the local electrons on the mass- and momentum flow of the multi-fluid plasma. It turns out that the usual claim made by Voyager-1 and-2 experimentalists that the bulk velocity of the upwind plasma flow is decreasing with distance from shock, would require that, in reaction to that bulkplasma momentum loss, the electron pressure even increases downstream of the shock. The alternative possibility would be that Voyager-1/-2 data up to now are misinterpreted, and that in fact solar wind bulk velocities in the upwind heliosheath downstream of the shock are increasing opposite to present understandings.

B2.5-Eunomia simulations of Magnum-PSI detachment experiments: II. Collisional processes and their relevance

Detachment is achieved in Magnum-PSI by increasing the neutral background pressure in the target chamber using gas puffing. The plasma is studied using the B2.5 multi fluid plasma code B2.5 coupled with Eunomia, a Monte Carlo solver for neutral species. This study focuses on the effect of increasing neutral background pressure to the plasma volumetric loss of particle, momentum and energy. The plasma particle and energy loss almost linearly scale with the increase of neutral background pressure, while the momentum loss does not scale as strongly. Plasma recombination processes include molecular activated recombination (MAR), dissociative attachment, and atomic recombination. Atomic recombination, which includes radiative and three-body recombination, is the most relevant plasma process in reducing the particle flux and, consequently, the heat flux to the target. The low temperature where atomic recombination becomes dominant is achieved by plasma cooling via elastic H+−H2 collisions. The transport of vibrationally excited H2 molecules out of the plasma serves as an additional electron cooling channel with relatively small contribution. Additionally, the transport of highly vibrational H2 has a significant impact in reducing the effective MAR and dissociative attachment collision rates and should be considered properly. The relevancy of MAR and atomic recombination occupy separate electron temperature regimes, respectively, at eV and eV, with dissociative attachment being relevant in the intermediary. Plasma cooling via elastic H+−H2 collisions is effective at eV.

B2.5-Eunomia simulations of Magnum-PSI detachment experiments: I. Quantitative comparisons with experimental measurements

Detachment experiments have been carried out in the linear plasma device Magnum-PSI by increasing the gas pressure near the target. In order to have a proper detailed analysis of the mechanism behind momentum and power loss in detachment, a quantitative match is pursued between B2.5-Eunomia solutions and experimental data. B2.5 is a multi fluid plasma code and Eunomia is a Monte Carlo solver for neutral particles, and they are coupled together to provide steady-state solution of the plasma and neutral distribution in space. B2.5-Eunomia input parameters are adjusted to produce a close replication of the plasma beam measured in the experiments without any gas puffing in the target chamber. Using this replication as an initial condition, the neutral pressure near the plasma beam target is exclusively increased during simulation, matching the pressures measured in the experiments. Reasonable agreement is found between the electron temperature of the simulation results with experimental measurements using laser Thomson scattering near the target. The simulations also reveal the effect of increased gas pressure on the plasma current, effectively reducing the current penetration from the plasma source. B2.5-Eunomia is capable of reproducing detachment characteristics, namely the loss of plasma pressure along the magnetic field and the reduction of particle and heat flux to the target. The simulation results for plasma and neutrals will allow future studies of the exact contribution of individual plasma-neutral collisions to momentum and energy loss in detachment in Magnum-PSI.

Octonic Maxwell-type multifluid plasma equations

Stimulating from octonic reformulation of the Maxwell-type equations of compressible fluids, this paper aims to extend this effort to derive the compact and elegant expressions that reflect both the fluid and electromagnetic behavior of plasma. Using theorems and techniques of octon algebra, a single equation is proposed for the Maxwell-type field equations of multifluid plasma. Moreover, the wave equations in terms of generalized vorticity and Lamp vector are formulated in a similar form to electromagnetic and fluidic counterparts previously derived by using algebra of octons.

Four-fluid axisymmetric plasma equilibrium model including relativistic electrons and computational method and results

A non-relativistic multi-fluid plasma axisymmetric equilibrium model [A. Ishida et al., “Three-fluid axisymmetric equilibrium model and application to spherical torus plasmas sustained by RF electron heating,” Plasma Fusion Res. 10, 1403084 (2015)] was developed recently to account for the presence of an energetic electron fluid in addition to thermal electron and ion fluids. The equilibrium formulation of a multi-fluid plasma with relativistic energetic electrons is developed and reported in this paper. Relativistic effects in a fluid model approximation can appear in two ways: due to a large macroscopic fluid velocity comparable to the speed of light and a large particle's microscopic random motion which becomes significant if the temperature becomes comparable to or larger than the electron rest mass energy. It is found that the axial component of relativistic generalized angular momentum can be used to describe relativistic axisymmetric equilibrium. The formulation is applied to a four-fluid plasma composed of a relativistic energetic electron fluid, a thermal electron fluid, and fluids of two thermal ion species (e.g., proton and boron ions). The four-fluid density expression which is consistent with the electrostatic potential is obtained and applied in the computation. An example equilibrium approximating a four-fluid plasma recently observed in a solenoid-free ECRH sustained spherical torus plasma [Y.-K. M. Peng et al., “Initial results of the EXL-50 experiment,” (to be published)] is calculated and presented. A second equilibrium that extends the energetic electron temperature of the first example to 679 keV is calculated revealing significant relativistic effects.