Publisher's Note: “Three-dimensional two-fluid Braginskii simulations of the large plasma device” [Phys. Plasmas 22, 092121 (2015)]
No abstract prepared.
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Kinetic simulation of capacitively coupled plasmas driven by trapezoidal asymmetric voltage pulses
A kinetic Particle-In-Cell simulation with Monte Carlo Collisions was performed of a geometrically symmetric capacitively coupled, parallel-plate discharge in argon, driven by trapezoidal asymmetric voltage pulses with a period of 200 ns. The discharge was electrically asymmetric, making the ion energy distributions at the two electrodes different from one another. The fraction of the period (α), during which the voltage was kept at a constant (top-flat) positive value, was a critical control parameter. For the parameter range investigated, as α increased, the mean ion energy on the grounded electrode increased and the ions became more directional, whereas the opposite was found for the ions striking the powered electrode. The absolute value of the DC self-bias voltage decreased as α increased. Plasma instabilities, promoted by local double layers and electric field reversals during the time of the positive voltage excursion, were characterized by electron plasma waves launched from the sheath edge.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Applying the Gyrokinetic Formulation of Magnetized Plasma Dynamics to Z-pinch plasmas
This project adapts and applies the gyrokinetic Eulerian code COGENT to an emerging area of highly-magnetized Z-pinch plasma systems. Simulation efforts for these plasmas currently use either magneto-hydrodynamic (MHD) fluid codes, which suffer from fidelity being restricted to narrow plasma conditions, or fully kinetic particle-in-cell (PIC) methods, which suffer from the run-time needed to resolve the very small spatial and temporal scales required for the plasma conditions. The progress with achieving detailed theoretical understanding of Z-pinch plasma systems can be greatly expedited using some combination of gyrokinetic and drift-ordered MHD models, developed in the tokamak community and implemented in the COGENT code. These formulations are applicable to a much larger parameter space than standard MHD models, while providing a substantial speed-up in run-time over fully kinetic codes. In particular, the gyrokinetic formalism is successfully applied to a flow-stabilized Z pinch (FSZP) system – a promising fusion concept where a sheared axial flow is used to provide stability against large-scale ideal-MHD modes. Results of gyrokinetic simulations with COGENT agree well with those from fully kinetic simulations, while requiring ~500x less run-time.
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Monte Carlo simulation of the classical two-dimensional one component plasma
Monte Carlo simulation, lattice dynamics in the harmonic approximation, and solution of the hypernetted chain equation were used to study the classical two-dimensional one component plasma. The system consists of a single species of charged particles immersed in a uniform neutralizing background. The particles interact via a l/r potential, where r is the two dimensional separation. Equations of state were calculated for both the liquid and solid phases. Results of calculation of the thermodynamic functions and one and two particle correlation functions are presented.
Gann, R. C.↗
Geometric electrostatic particle-in-cell algorithm on unstructured meshes
We present a geometric particle-in-cell (PIC) algorithm on unstructured meshes for studying electrostatic perturbations with frequency lower than electron gyrofrequency in magnetized plasmas. In this method, ions are treated as fully kinetic particles and electrons are described by the adiabatic response. The PIC method is derived from a discrete variational principle on unstructured meshes. To preserve the geometric structure of the system, the discrete variational principle requires that the electric field is interpolated using Whitney 1-forms, the charge is deposited using Whitney 0-forms and the electric field is computed by discrete exterior calculus. The algorithm has been applied to study the ion Bernstein wave (IBW) in two-dimensional magnetized plasmas. The simulated dispersion relations of the IBW in a rectangular region agree well with theoretical results. In a two-dimensional circular region with fixed boundary condition, the spectrum and eigenmode structures of the IBW are obtained from simulations. We compare the energy conservation property of the geometric PIC algorithm derived from the discrete variational principle with that of previous PIC methods on unstructured meshes. The comparison shows that the new PIC algorithm significantly improves the energy conservation property.
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Induction plasma heating - System performance, hydrogen operation and gas core reactor simulator development
Induction plasma heating system for hydrogen-argon simulated gas cooled reactor studies
Thorpe, M. L.↗
Simulation of electron Bernstein waves using FullWave with a 2D non-local hot plasma model
Hot plasma wave simulation capability is expanded in the FullWave code by updating the hybrid iterative solver in the code with a semi-implicit time stepping method. The new approach is used to simulate Electron Bernstein Wave (EBW) heating in over-dense spherical tokamak plasmas. The code’s hybrid iterative solver circumvents the prohibitive memory cost of direct methods by combining a time evolution of Maxwell’s equations with frequency-domain relaxation, while the conductivity kernel, calculated via 3D particle tracking, captures the essential non-local wave–particle interactions. One-dimensional EBW simulations verify the algorithm’s accuracy by demonstrating mode conversion from X-mode wave to EBW at the upper hybrid resonance and a strong cyclotron damping near the plasma core. Two-dimensional simulation reproduces the predicted short EBW wavelength and quantitatively matches the hot-plasma dispersion relation. This study demonstrates the fidelity of the hybrid solver for the electron cyclotron frequency range.
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Verification of gyrokinetic particle simulation of current-driven instability in fusion plasmas. II. Resistive tearing mode
In this work, global gyrokinetic particle simulation of resistive tearing modes has been developed and verified in the gyrokinetic toroidal code (GTC). GTC linear simulations in the fluid limit of the kink-tearing and resistive tearing modes in the cylindrical geometry agree well with the resistive magnetohydrodynamic eigenvalue and initial value codes. Ion kinetic effects are discovered to reduce the radial width of the tearing modes. GTC simulations of the resistive tearing modes in the toroidal geometry find that the toroidicity reduces the growth rates.
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Impact of collisionality on turbulence in the edge of tokamak plasma using 3D global simulations
Collisionality is one of the key parameters in determining turbulent transport in the plasma edge, regulating phenomena such as 'shoulder formation', separation of scale lengths in the scrape-off layer (SOL), turbulence damping and zonal flow dynamics. Understanding its role is therefore of primary importance for future reactors like ITER. Getting reliable predictions and a better characterization of plasma flow properties when varying collisionality remains, however, a critical challenge for the simulations. This paper focuses on the impact of varying collisionality in a non-isothermal three-dimensional fluid model of the plasma edge. A high field side limited configuration encompassing open and closed magnetic field lines with parameters typical of a medium-sized tokamak is considered. The present model can consistently account for the variations of collisionality and its impact on both the parallel resistivity η ∥ and the ion and electron parallel thermal conductivities χ ∥e,i . Details on mean flow and turbulence properties are given. Changing collisionality leads to significant changes in the flow properties both on the mean and fluctuating quantities. In particular, lowering collisionality decreases the size of coherent structures, the fluctuation levels of turbulence, and steepens the density and temperature equilibrium profiles around the separatrix leading to a global reduction of the turbulent transport. The SOL width is observed to increase with collisionality, eventually resulting in the disappearance of the scale lengths separation between near and far SOL, consistently with previous experimental observations. At low collisionality, where the presence of narrow feature is well-established, a contribution of heat conduction increases up to compete with heat convection.
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Nonlinear coupling of whistler waves to oblique electrostatic turbulence enabled by cold plasma
Kinetic simulations and theory demonstrate that whistler waves can excite oblique, short-wavelength fluctuations through secondary drift instabilities if a population of sufficiently cold plasma is present. The excited modes lead to heating of the cold populations and damping of the primary whistler waves. The instability threshold depends on the density and temperature of the cold population and can be relatively small if the temperature of the cold population is sufficiently low. Furthermore, this mechanism may thus play a significant role in controlling amplitude of whistlers in the regions of the Earth's magnetosphere where cold background plasma of sufficient density is present.
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Modulations of the plasma uniformity by low frequency sources in a large-area dual frequency inductively coupled plasma based on fluid simulations
As the wafer size increases, dual frequency (DF) inductively coupled plasma (ICP) sources have been proposed as an effective method to achieve large-area uniform plasma processing. A two-dimensional (2D) self-consistent fluid model, combined with an electromagnetic module, has been employed to investigate the influence of the low frequency (LF) source on the plasma radial uniformity in an argon DF discharge. When the DF antenna current is fixed at 10 A, the bulk plasma density decreases significantly with the LF due to the less efficient heating, and the best radial uniformity is obtained at 3.39 MHz. As the LF decreases to 2.26 MHz, the plasma density is characterized by an edge-high profile, and meanwhile the maximum of the electron temperature appears below the outer two-turn coil. Moreover, the axial ion flux at 3.39 MHz is rather uniform in the center region except at the radial edge of the substrate, where a higher ion flux is observed. When the inner five-turn coil frequency is fixed at 2.26 MHz, the plasma density profiles shift from edge-high over uniform to center-high as the LF coil current increases from 6 A to 18 A, and the best plasma uniformity is obtained at 14 A. In addition, the maximum of the electron temperature becomes lower with a second peak appears at the radial position of r = 9 cm at 18 A.
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A parallel-kinetic-perpendicular-moment model for magnetised plasmas
We describe a new model for the study of weakly collisional, magnetised plasmas derived from exploiting the separation of the dynamics parallel and perpendicular to the magnetic field. This unique system of equations retains the particle dynamics parallel to the magnetic field while approximating the perpendicular dynamics through a spectral expansion in the perpendicular degrees of freedom, analogous to moment-based fluid approaches. In so doing, a hybrid approach is obtained that is computationally efficient enough to allow for larger-scale modelling of plasma systems while eliminating a source of difficulty in deriving fluid equations applicable to magnetised plasmas. We connect this system of equations to historical asymptotic models and discuss advantages and disadvantages of this approach, including the extension of this parallel-kinetic-perpendicular moment beyond the typical region of validity of these more traditional asymptotic models. This paper forms the first of a multi-part series on this new model, covering the theory and derivation, alongside demonstration benchmarks of this approach that include shocks and magnetic reconnection.
astrophysical plasmas↗
Role of ion acoustic instability in magnetic reconnection
We report on a first-principles numerical study of magnetic reconnection in plasmas with different initial ion-to-electron temperature ratios. In cases where this ratio is significantly below unity, we observe intense wave activity in the diffusion region, driven by the ion-acoustic instability. Our analysis shows that the dominant macroscopic effect of this instability is to drive substantial ion heating. In contrast to earlier studies reporting significant anomalous resistivity, we find that anomalous contributions due to the ion-acoustic instability are minimal. These results shed light on the dynamical impact of this instability on reconnection processes, offering new insights into the fundamental physics governing collisionless reconnection.
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A model distribution function for relativistic bi-Maxwellian with drift
A model distribution function for relativistic bi-Maxwellian with drift is proposed, based on the maximum entropy principle and the relativistic canonical transformation. Since the obtained expression is compatible with the existing distribution functions and has a relatively simple form as well as smoothness, it might serve as a useful tool in the research fields of space or high temperature fusion plasmas.
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A multi-dimensional Vlasov-Fokker-Planck code for arbitrarily anisotropic high-energy-density plasmas
To study the kinetic physics of High-Energy-Density Laboratory Plasmas, we have developed the parallel relativistic 2D3P Vlasov-Fokker-Planck code Oshun. The numerical scheme uses a Cartesian mesh in configuration-space and incorporates a spherical harmonic expansion of the electron distribution function in momentum-space. The expansion is truncated such that the necessary angular resolution of the distribution function is retained for a given problem. Finite collisionality causes rapid decay of the high-order harmonics, thereby providing a natural truncation mechanism for the expansion. The code has both fully explicit and implicit field-solvers and employs a linearized Fokker-Planck collision operator. Oshun has been benchmarked against well-known problems, in the highly kinetic limit to model collisionless relativistic instabilities, and in the hydrodynamic limit to recover transport coefficients. The performance of the code, its applicability, and its limitations are discussed in the context of simple problems with relevance to inertial fusion energy.
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Response of a partial wall to an external perturbation of rotating plasma
In this paper, we present the response of a 3D thin multiply connected wall to an external kink mode perturbation in axisymmetric tokamak configurations. To calculate the contribution of the plasma perturbed magnetic field in the vacuum region, we have made use of the concept of surface currents [following C. V. Atanasiu, A. H. Boozer, L. E. Zakharov, and A. A. Subbotin, Phys. Plasmas 6, 2781 (1999)]. The wall response is expressed in terms of a stream function of the wall surface currents, which are obtained by solving a diffusion type equation, taking into account the contribution of the wall currents themselves iteratively. The use of stream function makes the approach applicable for both well-studied earlier Resistive Wall Modes and for Wall Touching Kink Modes, which were discovered recently as a key phenomenon in disruptions [L. E. Zakharov, S. A. Galkin, and S. N. Gerasimov, Phys. Plasmas 19, 055703 (2012)]. New analytical expressions, suitable for numerical calculations of toroidal harmonics of the vacuum magnetic fields from the surface currents on axisymmetric shells, are derived.
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Charge exchange and ionization cross sections of H{sup +}+H collision in dense quantum plasmas
The plasma screening effects of dense quantum plasmas on H{sup +}+H charge exchange and ionization cross sections are calculated by the classical trajectory Monte Carlo method. For charge exchange cross sections, it is found that the screening effects reduce cross sections slightly in weak screening conditions. However, cross sections are reduced substantially in strong screening conditions. For ionization cross sections, with the increase of screening effects, cross sections for low energies increase more rapidly than those for high energies. When the screening effects are strong enough, it is found that ionization cross sections decrease with the increase of incident H{sup +} energy. In addition, the cross sections have been compared with those in weakly coupled plasmas. It is found that in weak screening conditions, plasma screening effects in the two plasmas are approximately the same, while in strong screening conditions, screening effects of dense quantum plasmas are stronger than those of weakly coupled plasmas.
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Modeling of the influences of electron cyclotron current drive on neoclassical tearing modes
Influences of external current drive on neoclassical tearing modes are studied numerically with a set of compressible magnetohydrodynamics equations. By considering the effects of driven current parameters and its deposition timing, and by examining the relationship between driven current and the missing bootstrap current, the basic requirements of deposition width and external current density for effectively suppressing neoclassical tearing modes are investigated. When the driven current density is able to compensate the missing bootstrap current and the deposition region is comparable with the saturated island, the suppression results are notable. Meanwhile, the pre-emptive strategy of current deposition reported experimentally is also evaluated, and the results agree with the experimental ones that early current deposition can enhance suppression effectiveness greatly. In addition, the deficiencies of continuous driven current are discussed when the plasma rotation has been taken into account, and the application of modulated current drive, which is synchronized in phase with the rotating island, can restore the stabilizing role under some conditions. The favorable parameters of modulation such as duty cycle are also addressed.
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