arXiv subjects

Xian-Zhu Tang

Publications and source records attributed to Xian-Zhu Tang.

At least 37 records · Page 2Linked to original sources

arXiv2023

Denoising Particle-In-Cell Data via Smoothness-Increasing Accuracy-Conserving Filters with Application to Bohm Speed Computation

The simulation of plasma physics is computationally expensive because the underlying physical system is of high dimensions, requiring three spatial dimensions and three velocity dimensions. One popular numerical approach is Particle-In-Cell (PIC) methods owing to its ease of implementation and favorable scalability in high-dimensional problems. An unfortunate drawback of the method is the introduction of statistical noise resulting from the use of finitely many particles. In this paper we examine the application of the Smoothness-Increasing Accuracy-Conserving (SIAC) family of convolution kernel filters as denoisers for moment data arising from PIC simulations. We show that SIAC filtering is a promising tool to denoise PIC data in the physical space as well as capture the appropriate scales in the Fourier space. Furthermore, we demonstrate how the application of the SIAC technique reduces the amount of information necessary in the computation of quantities of interest in plasma physics such as the Bohm speed.

math.NA↗

arXiv2023

Stand-off runaway electron beam termination by tungsten particulates for tokamak disruption mitigation

Stand-off runaway electron termination by injected tungsten particulates offers a plausible option in the toolbox of disruption mitigation. Tungsten is an attractive material choice for this application due to large electron stopping power and high melting point. To assess the feasibility of this scheme, we simulate runaway collisions with tungsten particulates using the MCNP program for incident runaway energies ranging from 1 to 10 MeV. We assess runaway termination from energetics and collisional kinematics perspectives. Energetically, the simulations show that 99% of runaway beam energy is removed by tungsten particulates on a timescale of 4-9 $μ$s. Kinematically, the simulations show that 99% of runaways are terminated by absorption or backscattering on a timescale of 3-4 $μ$s. By either metric, the runaway beam is effectively terminated before the onset of particulate melting. Furthermore, the simulations show that secondary radiation emission by tungsten particulates does not significantly impact the runaway termination efficacy of this scheme. Secondary radiation is emitted at lower particle energies than the incident runaways and with a broad angular distribution such that the majority of secondary electrons emitted will not experience efficient runaway re-acceleration. Overall, the stand-off runaway termination scheme is a promising concept for last-ditch runaway mitigation in ITER, SPARC, and other future burning-plasma tokamaks.

physics.plasm-ph↗

arXiv2023

Electromagnetic turbulence simulation of tokamak edge plasma dynamics and divertor heat load during thermal quench

The edge plasma turbulence and transport dynamics, as well as the divertor power loads during the thermal quench phase of tokamak disruptions are numerically investigated with BOUT++'s flux-driven, six-field electromagnetic turbulence model. Here a transient yet intense particle and energy sources are applied at the pedestal top to mimic the plasma power drive at the edge induced by a core thermal collapse, which flattens core temperature profile. Interesting features such as surging of divertor heat load (up to 50 times), and broadening of heat flux width (up to 4 times) on the outer divertor target plate, are observed in the simulation, in qualitative agreement with experimental observations. The dramatic changes of divertor heat load and width are due to the enhanced plasma turbulence activities inside the separatrix. Two cross-field transport mechanisms, namely the $E\times B$ turbulent convection and the stochastic parallel advection/conduction, are identified to play important roles in this process. Firstly, elevated edge pressure gradient drives instabilities and subsequent turbulence in the entire pedestal region. The enhanced turbulence not only transports particles and energy radially across the separatrix via $E\times B$ convection which causes the initial divertor heat load burst, but also induces an amplified magnetic fluctuation $\tilde{B}$. Once the magnetic fluctuation is large enough to break the magnetic flux surface, magnetic flutter effect provides an additional radial transport channel. In the late stage of our simulation, $|\tilde{B}_r/B_0|$ reaches to $10^{-4}$ level that completely breaks magnetic flux surfaces such that stochastic field-lines are directly connecting pedestal top plasma to the divertor target plates or first wall, further contributing to the divertor heat flux width broadening.

physics.plasm-ph↗

arXiv2023

A mimetic finite difference based quasi-static magnetohydrodynamic solver for force-free plasmas in tokamak disruptions

Force-free plasmas are a good approximation where the plasma pressure is tiny compared with the magnetic pressure, which is the case during the cold vertical displacement event (VDE) of a major disruption in a tokamak. On time scales long compared with the transit time of Alfven waves, the evolution of a force-free plasma is most efficiently described by the quasi-static magnetohydrodynamic (MHD) model, which ignores the plasma inertia. Here we consider a regularized quasi-static MHD model for force-free plasmas in tokamak disruptions and propose a mimetic finite difference (MFD) algorithm. The full geometry of an ITER-like tokamak reactor is treated, with a blanket module region, a vacuum vessel region, and the plasma region. Specifically, we develop a parallel, fully implicit, and scalable MFD solver based on PETSc and its DMStag data structure for the discretization of the five-field quasi-static perpendicular plasma dynamics model on a 3D structured mesh. The MFD spatial discretization is coupled with a fully implicit DIRK scheme. The algorithm exactly preserves the divergence-free condition of the magnetic field under the resistive Ohm's law. The preconditioner employed is a four-level fieldsplit preconditioner, which is created by combining separate preconditioners for individual fields, that calls multigrid or direct solvers for sub-blocks or exact factorization on the separate fields. The numerical results confirm the divergence-free constraint is strongly satisfied and demonstrate the performance of the fieldsplit preconditioner and overall algorithm. The simulation of ITER VDE cases over the actual plasma current diffusion time is also presented.

physics.plasm-ph↗

arXiv2023

Resolving the mystery of electron perpendicular temperature spike in the plasma sheath

A large family of plasmas has collisional mean-free-path much longer than the non-neutral sheath width, which scales with the plasma Debye length. The plasmas, particularly the electrons, assume strong temperature anisotropy in the sheath. The temperature in the sheath flow direction ($T_{e\parallel}$) is lower and drops towards the wall as a result of the decompressional cooling by the accelerating sheath flow. The electron temperature in the transverse direction of the flow field ($T_{e\perp}$) not only is higher but also spikes up in the sheath. This abnormal behavior of $T_{e\perp}$ spike is found to be the result of a negative gradient of the parallel heat flux of transverse degrees of freedom ($q_{es}$) in the sheath. The non-zero heat flux $q_{es}$ is induced by pitch-angle scattering of electrons via either their interaction with self-excited electromagnetic waves in a nearly collisionless plasma or Coulomb collision in a collisional plasma, or both in the intermediate regime of plasma collisionality.

physics.plasm-ph↗

arXiv2023

On the collisional damping of plasma velocity space instabilities

For plasma velocity space instabilities driven by particle distributions significantly deviated from a Maxwellian, weak collisions can damp the instabilities by an amount that is significantly beyond the collisional rate itself. This is attributed to the dual role of collisions that tend to relax the plasma distribution toward a Maxwellian and to suppress the linearly perturbed distribution function. The former effect can dominate in cases where the unstable non-Maxwellian distribution is driven by collisionless transport on a time scale much shorter than that of collisions, and the growth rate of the ideal instability has a sensitive dependence on the distribution function. The whistler instability driven by electrostatically trapped electrons is used as an example to elucidate such a strong collisional damping effect of plasma velocity space instabilities, which is confirmed by first-principles kinetic simulations.

physics.plasm-ph↗

arXiv2022

The constraint of plasma power balance on runaway avoidance

In a post-thermal-quench plasma, mitigated or unmitigated, the plasma power balance is mostly between collisional or Ohmic heating and plasma radiative cooling. In a plasma of atomic mixture $\{n_α\}$ with $α$ labeling the atomic species, the power balance sets the plasma temperature, ion charge state distribution $\{n_α^i\}$ with $i$ the charge number, and through the electron temperature $T_e$ and ion charge state distribution $\{n_α^i\},$ the parallel electric field $E_\parallel.$ Since the threshold electric field for runaway avalanche growth $E_{av}$ is also set by the atomic mixture, ion charge state distribution and its derived quantity, the electron density $n_e,$ the plasma power balance between Ohmic heating and radiative cooling imposes a stringent constraint on the plasma regime for avoiding and minimizing runaways when a fusion-grade tokamak plasma is rapidly terminated.

physics.plasm-ph↗

arXiv2022

Staged cooling of a fusion-grade plasma in a tokamak thermal quench

In tokamak disruptions where the magnetic connection length becomes comparable to or even shorter than the plasma mean-free-path, parallel transport can dominate the energy loss and the thermal quench of the core plasma goes through four phases (stages) that have distinct temperature ranges and durations. The main temperature drop occurs while the core plasma remains nearly collisionless, with the parallel electron temperature $T_{e\parallel}$ dropping in time $t$ as $T_{e\parallel}\propto t^{-2}$ and a cooling time that scales with the ion sound wave transit time over the length of the open magnetic field line. These surprising physics scalings are the result of effective suppression of parallel electron thermal conduction in an otherwise bounded collisionless plasma, which is fundamentally different from what are known to date on electron thermal conduction along the magnetic field in a nearly collisionless plasma.

physics.plasm-ph↗

arXiv2022

Runaway electron current reconstitution after a non-axisymmetric magnetohydrodynamic flush

Benign termination of mega-ampere (MA) level runaway current has been convincingly demonstrated in recent JET and DIII-D experiments, establishing it as a leading candidate for runaway mitigation on ITER. This comes in the form of a runaway flush by parallel streaming loss along stochastic magnetic field lines formed by global magnetohydrodynamic instabilities, which are found to correlate with a low-Z injection that purges the high-Z impurities from a post-thermal-quench plasma. Here we show the competing physics that govern the post-flush reconstitution of the runaway current in a ITER-like reactor where significantly higher current is expected. The trapped ``runaways'' are found to dominate the seeding for runaway reconstitution, and the incomplete purge of high-Z impurities helps drain the seed but produces a more efficient avalanche, two of which compete to produce a 2-3~MA step in current drop before runaway reconstitution of the plasma current.

physics.plasm-ph↗

arXiv2022

Efficient training of artificial neural network surrogates for a collisional-radiative model through adaptive parameter space sampling

Reliable plasma transport modeling for magnetic confinement fusion depends on accurately resolving the ion charge state distribution and radiative power losses of the plasma. These quantities can be obtained from solutions of a collisional-radiative (CR) model at each time step within a plasma transport simulation. However, even compact, approximate CR models can be computationally onerous to evaluate, and in-situ evaluations of these models within a coupled plasma transport code can lead to a rigid bottleneck. A way to bypass this bottleneck is to deploy artificial neural network surrogates for rapid evaluations of the necessary plasma quantities. However, one issue with training an accurate artificial neural network surrogate is the reliance on a sufficiently large and representative data set for both training and validation, which can be time-consuming to generate. In this study we further explore a data-driven active learning and training scheme to allow autonomous adaptive sampling of the problem parameter space that ensures a sufficiently large and meaningful set of training data assembled for the surrogate training. Our numerical experiments show that in order to produce a comparably accurate CR surrogate, the proposed approach requires a total number of data samples that is an order-of-magnitude smaller than a conventional approach.

physics.plasm-ph↗

arXiv2022

Cooling flow regime of a plasma thermal quench

A large class of Laboratory, Space, and Astrophysical plasmas is nearly collisionless. When a localized energy or particle sink, for example, in the form of a radiative cooling spot or a black hole, is introduced into such a plasma, it can trigger a plasma thermal collapse, also known as a thermal quench in tokamak fusion. Here we show that the electron thermal conduction in such a nearly collisionless plasma follows the convective energy transport scaling in itself or in its spatial gradient, due to the constraint of ambipolar transport. As the result, a robust cooling flow aggregates mass toward the cooling spot and the thermal collapse of the surrounding plasma takes the form of four propagating fronts that originate from the radiative cooling spot, along the magnetic field line in a magnetized plasma. The slowest one, which is responsible for deep cooling, is a shock front.

physics.plasm-ph↗

arXiv2022

Bohm criterion of plasma sheaths away from asymptotic limit

The plasma exit flow speed at the sheath entrance is constrained by the Bohm criterion. The so-called Bohm speed regulates the plasma particle and power exhaust fluxes to the wall, and it is commonly deployed as a boundary condition to exclude the sheath region in quasi-neutral plasma modeling. Here the Bohm criterion analysis is performed in the intermediate plasma regime away from the previously known limiting cases of adiabatic laws and the asymptotic limit of infinitesimal Debye length in a finite-size system, using the transport equations of an anisotropic plasma. The resulting Bohm speed has explicit dependence on local plasma heat flux, temperature isotropization, and thermal force. Comparison with kinetic simulations demonstrates its accuracy over the plasma-sheath transition region in which quasineutrality is weakly perturbed and Bohm criterion applies.

physics.plasm-ph↗

arXiv2022

An adaptive scalable fully implicit algorithm based on stabilized finite element for reduced visco-resistive MHD

The magnetohydrodynamics (MHD) equations are continuum models used in the study of a wide range of plasma physics systems, including the evolution of complex plasma dynamics in tokamak disruptions. However, efficient numerical solution methods for MHD are extremely challenging due to disparate time and length scales, strong hyperbolic phenomena, and nonlinearity. Therefore the development of scalable, implicit MHD algorithms and high-resolution adaptive mesh refinement strategies is of considerable importance. In this work, we develop a high-order stabilized finite-element algorithm for the reduced visco-resistive MHD equations based on the MFEM finite element library (mfem.org). The scheme is fully implicit, solved with the Jacobian-free Newton-Krylov (JFNK) method with a physics-based preconditioning strategy. Our preconditioning strategy is a generalization of the physics-based preconditioning methods in [Chacon, et al, JCP 2002] to adaptive, stabilized finite elements. Algebraic multigrid methods are used to invert sub-block operators to achieve scalability. A parallel adaptive mesh refinement scheme with dynamic load-balancing is implemented to efficiently resolve the multi-scale spatial features of the system. Our implementation uses the MFEM framework, which provides arbitrary-order polynomials and flexible adaptive conforming and non-conforming meshes capabilities. Results demonstrate the accuracy, efficiency, and scalability of the implicit scheme in the presence of large scale disparity. The potential of the AMR approach is demonstrated on an island coalescence problem in the high Lundquist-number regime ($\ge 10^7$) with the successful resolution of plasmoid instabilities and thin current sheets.

physics.comp-ph↗

arXiv2021

A parallel cut-cell algorithm for the free-boundary Grad-Shafranov problem

A parallel cut-cell algorithm is described to solve the free-boundary problem of the Grad-Shafranov equation. The algorithm reformulates the free-boundary problem in an irregular bounded domain and its important aspects include a searching algorithm for the magnetic axis and separatrix, a surface integral along the irregular boundary to determine the boundary values, an approach to optimize the coil current based on a targeting plasma shape, Picard iterations with Aitken's acceleration for the resulting nonlinear problem, and a Cartesian grid embedded boundary method to handle the complex geometry. The algorithm is implemented in parallel using a standard domain-decomposition approach and a good parallel scaling is observed. Numerical results verify the accuracy and efficiency of the free-boundary Grad-Shafranov solver.

math.NA↗

arXiv2020

An adaptive discontinuous Petrov-Galerkin method for the Grad-Shafranov equation

In this work, we propose and develop an arbitrary-order adaptive discontinuous Petrov-Galerkin (DPG) method for the nonlinear Grad-Shafranov equation. An ultraweak formulation of the DPG scheme for the equation is given based on a minimal residual method. The DPG scheme has the advantage of providing more accurate gradients compared to conventional finite element methods, which is desired for numerical solutions to the Grad-Shafranov equation. The numerical scheme is augmented with an adaptive mesh refinement approach, and a criterion based on the residual norm in the minimal residual method is developed to achieve dynamic refinement. Nonlinear solvers for the resulting system are explored and a Picard iteration with Anderson acceleration is found to be efficient to solve the system. Finally, the proposed algorithm is implemented in parallel on MFEM using a domain-decomposition approach, and our implementation is general, supporting arbitrary order of accuracy and general meshes. Numerical results are presented to demonstrate the efficiency and accuracy of the proposed algorithm.

math.NA↗

arXiv2020

Neural network representability of fully ionized plasma fluid model closures

The closure problem in fluid modeling is a well-known challenge to modelers aiming to accurately describe their system of interest. Over many years, analytic formulations in a wide range of regimes have been presented but a practical, generalized fluid closure for magnetized plasmas remains an elusive goal. In this study, as a first step towards constructing a novel data based approach to this problem, we apply ever-maturing machine learning methods to assess the capability of neural network architectures to reproduce crucial physics inherent in popular magnetized plasma closures. We find encouraging results, indicating the applicability of neural networks to closure physics but also arrive at recommendations on how one should choose appropriate network architectures for given locality properties dictated by underlying physics of the plasma.

physics.comp-ph↗

arXiv2019

Impact of a minority relativistic electron tail interacting with a thermal plasma containing high-atomic-number impurities

A minority relativistic electron component can arise in both laboratory and naturally-occurring plasmas. In the presence of high-atomic-number ion species, the ion charge state distribution at low bulk electron temperature can be dominated by relativistic electrons, even though their density is orders of magnitude lower. This is due to the relativistic enhancement of the collisional excitation and ionization cross sections. The resulting charge state effect can dramatically impact the radiative power loss rate and the related Bethe stopping power of relativistic electrons in a dilute plasma.

physics.plasm-ph↗

arXiv2016

Comparison of dust charging between Orbital-Motion-Limited theory and Particle-In-Cell simulations

The Orbital-Motion-Limited (OML) theory has been modified to predict the dust charge and the results were contrasted with the Whipple approximation [Tang and Delzanno, Phys. Plasmas 21, 123708 (2014)]. To further establish its regime of applicability, in this paper the OML predictions (for a non-electron-emitting, spherical dust grain at rest in a collisionless, unmagnetized plasma) are compared with Particle-In-Cell simulations that retain the absorption radius effect. It is found that for large dust grain radius $r_d$ relative to the plasma Debye length $λ_D$, the revised OML theory remains a very good approximation as, for the parameters considered ($r_d/λ_D\le10$, equal electron and ion temperatures), it yields the dust charge to within $20\%$ accuracy. This is a substantial improvement over the Whipple approximation. The dust collected currents and energy fluxes, which remain the same in the revised and standard OML theories, are accurate to within $15-30\%$.

physics.plasm-ph↗