arXiv subjects

Ping Zhu

Publications and source records attributed to Ping Zhu.

At least 73 records · Page 4Linked to original sources

arXiv2021

Data-Driven Multiscale Design of Cellular Composites with Multiclass Microstructures for Natural Frequency Maximization

For natural frequency optimization of engineering structures, cellular composites have been shown to possess an edge over solid. However, existing multiscale design methods for cellular composites are either computationally exhaustive or confined to a single class of microstructures. In this paper, we propose a data-driven topology optimization (TO) approach to enable the multiscale design of cellular structures with various choices of microstructure classes. The key component is a newly proposed latent-variable Gaussian process (LVGP) model through which different classes of microstructures are mapped into a low-dimensional continuous latent space. It provides an interpretable distance metric between classes and captures their effects on the homogenized stiffness tensors. By introducing latent vectors as design variables, a differentiable transition of stiffness matrix between classes can be easily achieved with an analytical gradient. After integrating LVGP with the density-based TO, an efficient data-driven cellular composite optimization process is developed to enable concurrent exploration of microstructure concepts and the associated volume fractions for natural frequency optimization. Examples reveal that the proposed cellular designs with multiclass microstructures achieve higher natural frequencies than both single-scale and single-class designs. This framework can be easily extended to other multi-scale TO problems, such as thermal compliance and dynamic response optimization.

cs.CE↗

arXiv2021

Destabilizing effects of edge infernal components on n = 1 resistive wall modes in CFETR 1GW steady-state operating scenario

The stability of the $n=1$ resistive wall modes (RWMs) is investigated using the AEGIS code for the newly designed China Fusion Engineering Test Reactor (CFETR) 1GW steady-state operating (SSO) scenario. Here, $n$ is the toroidal mode number. Due to the large fraction of bootstrap current contribution, the profile of safety factor q is deeply reversed in magnetic shear in the central core region and locally flattened within the edge pedestal. Consequently the pressure-driven infernal components develop in the corresponding q-flattened regions of both core and edge. However, the edge infernal components dominate the $n=1$ RWM structure and lead to lower $β_N$ limits than the designed target $β_N$ for the CFETR 1GW SSO scenario. The edge rotation is found the most critical to the stabilization due to the dominant influence of the edge infernal components, which should be maintained above $1.5\%Ω_{A0}$ in magnitude in order for the rotation alone to fully suppress the $n=1$ RWM in the CFETR 1GW SSO scenario.

physics.plasm-ph↗

arXiv2021

Transition from fishbone mode to $β$-induced Alfvén eigenmode on HL-2A tokamak

In the presence of energetic particles (EPs) from auxiliary heating and burning plasmas, fishbone instability and Alfvén modes can be excited and their transition can take place in certain overlapping regimes. Using the hybrid kinetic-magnetohydrodynamic model in the NIMROD code, we have identified such a transition between the fishbone instability and the $β$-induced Alfvén Eigenmode (BAE) for the NBI heated plasmas on HL-2A. When the safety factor at magnetic axis is well below one, typical kink-fishbone transition occurs as the EP fraction increases. When $q_0$ is raised to approaching one, the fishbone mode is replaced with BAE for sufficient amount of EPs. When $q_0$ is slightly above one, the toroidicity-induced Alfvén eigenmode (TAE) dominates at lower EP pressure, whereas BAE dominates at higher EP pressure.

physics.plasm-ph↗

arXiv2021

Effects of Helium massive gas injection level on disruption mitigation on EAST

In this study, NIMROD simulations are performed to investigate the effects of massive helium gas injection level on the induced disruption on EAST tokamak. It is demonstrated in simulations that two different scenarios of plasma cooling (complete cooling and partial cooling) take place for different amounts of injected impurities. For the impurity injection above a critical level, a single MHD activity is able to induce a complete core temperature collapse. For impurity injection below the critical level, a series of multiple minor disruptions occur before the complete thermal quench (TQ).

physics.plasm-ph↗

arXiv2021

Formation of edge pressure pedestal and reversed magnetic shear due to toroidal rotation in a tokamak equilibrium

Toroidal rotation is well known to play significant roles in the edge transport and L-H transition dynamics of tokamaks. Our recent calculation finds that a sufficiently strong localized toroidal rotation can directly bring out the formation of edge pressure pedestal with reversed magnetic shear that is reminiscent of an H-mode plasma, purely through the effects of toroidal rotation on the tokamak MHD equilibrium itself. In particular, the enhanced edge toroidal rotation enables a substantial peaking of the parallel current profile near edge in higher $β$ regimes, which leads to the flattening or reversal of the local $q$ (safety factor) profile. Here the formation of pressure pedestal along with the reversed magnetic shear region is shown to be the natural outcome of the MHD tokamak equilibrium in a self-consistent response to the presence of a localized toroidal rotation typically observed in H-mode or QH-mode.

physics.plasm-ph↗

arXiv2020

Quasi-linear theory of forced magnetic reconnection for the transition from linear to Rutherford regime

Using the in-viscid two-field reduced MHD model, a new analytical theory is developed to unify the Hahm-Kulsrud-Taylor (HKT) linear solution and the Rutherford quasi-linear regime. Adopting a quasi-linear approach, we obtain a closed system of equations for plasma response in a static plasma in slab geometry. An integral form of analytical solution is obtained for the forced magnetic reconnection, uniformly valid throughout the entire regimes from the HKT linear solution to the Rutherford quasi-linear solution. In particular, the quasi-linear effect can be described by a single coefficient $K_s\propto S^{8/5} ψ_c^2$, where $S=\frac{τ_R}{τ_A}$ and $ψ_c$ are the Lunquist number and amplitude of external magnetic perturbation, respectively. The HKT linear solution for response can be recovered when the index $K_s\rightarrow 0$. On the other hand, the quasi-linear effect plays a key role in the island growth when $K_s\sim1$. Our new analytical solution has also been compared with reduced MHD simulations with agreement.

physics.plasm-ph↗

arXiv2020

Data-Driven Topology Optimization with Multiclass Microstructures using Latent Variable Gaussian Process

The data-driven approach is emerging as a promising method for the topological design of multiscale structures with greater efficiency. However, existing data-driven methods mostly focus on a single class of microstructures without considering multiple classes to accommodate spatially varying desired properties. The key challenge is the lack of an inherent ordering or distance measure between different classes of microstructures in meeting a range of properties. To overcome this hurdle, we extend the newly developed latent-variable Gaussian process (LVGP) models to create multi-response LVGP (MR-LVGP) models for the microstructure libraries of metamaterials, taking both qualitative microstructure concepts and quantitative microstructure design variables as mixed-variable inputs. The MR-LVGP model embeds the mixed variables into a continuous design space based on their collective effects on the responses, providing substantial insights into the interplay between different geometrical classes and material parameters of microstructures. With this model, we can easily obtain a continuous and differentiable transition between different microstructure concepts that can render gradient information for multiscale topology optimization. We demonstrate its benefits through multiscale topology optimization with aperiodic microstructures. Design examples reveal that considering multiclass microstructures can lead to improved performance due to the consistent load-transfer paths for micro- and macro-structures.

cs.CE↗

arXiv2020

Deep Generative Modeling for Mechanistic-based Learning and Design of Metamaterial Systems

Metamaterials are emerging as a new paradigmatic material system to render unprecedented and tailorable properties for a wide variety of engineering applications. However, the inverse design of metamaterial and its multiscale system is challenging due to high-dimensional topological design space, multiple local optima, and high computational cost. To address these hurdles, we propose a novel data-driven metamaterial design framework based on deep generative modeling. A variational autoencoder (VAE) and a regressor for property prediction are simultaneously trained on a large metamaterial database to map complex microstructures into a low-dimensional, continuous, and organized latent space. We show in this study that the latent space of VAE provides a distance metric to measure shape similarity, enable interpolation between microstructures and encode meaningful patterns of variation in geometries and properties. Based on these insights, systematic data-driven methods are proposed for the design of microstructure, graded family, and multiscale system. For microstructure design, the tuning of mechanical properties and complex manipulations of microstructures are easily achieved by simple vector operations in the latent space. The vector operation is further extended to generate metamaterial families with a controlled gradation of mechanical properties by searching on a constructed graph model. For multiscale metamaterial systems design, a diverse set of microstructures can be rapidly generated using VAE for target properties at different locations and then assembled by an efficient graph-based optimization method to ensure compatibility between adjacent microstructures. We demonstrate our framework by designing both functionally graded and heterogeneous metamaterial systems that achieve desired distortion behaviors.

cs.CE↗

arXiv2020

Analytical model for quasi-linear flow response to resonant magnetic perturbation in resistive-inertial and viscous-resistive regimes

In this work, a quasi-linear model for plasma flow response to the resonant magnetic perturbation (RMP) in a tokamak has been rigorously developed in the resistive-inertial (RI) and viscous-resistive (VR) regimes purely from the two-field reduced MHD model. Models for plasma response to RMP are commonly composed of equations for the resonant magnetic field response (i.e. the magnetic island) and the torque balance of plasma flow. However, in previous plasma response models, the magnetic island and the torque balance equations are often derived separately from reduced MHD and full MHD equations, respectively. By contrast, in this work we derive both the magnetic island response and the torque balance equations in a quasi-linear model for plasma flow response entirely from a set of two-field reduced MHD equations. Such a quasi-linear model can recover previous plasma flow response models within certain limits and approximations. Furthermore, the physical origins of quasi-linear forces and moments in the flow response equation are also accurately calculated and clarified self-consistently.

physics.plasm-ph↗

arXiv2020

Kinetic Ballooning Instability of the Near-Earth Magnetotail in Voigt Equilibrium

For a long time, ballooning instabilities have been believed to be a possible triggering mechanism for the onset of substorm and current disruption initiation in the near-Earth magnetotail. Yet the stability of the kinetic ballooning mode (KBM) in a global and realistic magnetotail configuration has not been well examined. In this paper, stability of the KBM is evaluated for the two-dimensional Voigt equilibrium of the near-Earth magnetotail based on an analytical kinetic theory of ballooning instability in the framework of kinetic magnetohydrodynamic (MHD) model, where the kinetic effects such as the finite gyroradius effect, wave-particle resonances, particle drifts motions are included usually through kinetic closures. The growth rate of the KBM strongly depends on the magnetic field line stiffening factor $S$, which is in turn determined by the effects of the trapped electrons, the finite ion gyroradius, and the magnetic drift motion of charged particles. The KBM is unstable in a finite intermediate range of equatorial $β_{eq}$ and only marginally unstable at higher $β_{eq}$ regime for higher $T_e/T_i$ values. The finite ion gyroradius and the trapped electron fraction enhance the stiffening factor that tends to stabilize the KBM in the magnetotail far away from Earth. On the other hand, the current sheet thinning destabilizes KBM in the lower $β_{eq}$ regime and stabilizes KBM in the higher $β_{eq}$ regime.

physics.plasm-ph↗

arXiv2020

Plasma flow evolution in response to resonant magnetic perturbation in a tokamak

Externally applied non-axisymmetric magnetic fields such as error field and resonant magnetic perturbation (RMP) are known to influence the plasma momentum transport and flow evolution through plasma response in a tokamak, whereas the evolution of plasma response itself strongly depends on the plasma flow as well. The nonlinear interaction between the two have been captured in the conventional error field theory with a ``no-slip'' condition, which has been recently extended to allow the ``free-slip'' condition. For comparison with simulations, we solve for the nonlinear plasma response and flow evolution driven by a single-helicity RMP in a tokamak, using the full resistive MHD model in the initial-value code NIMROD. Time evolution of the parallel (to ${\mathbf k}$) flow or ``slip frequency'' profile and its asymptotic steady state obtained from the NIMROD simulations are compared with both conventional and extended nonlinear response theories. Here ${\mathbf k}$ is the wave vector of the propagating island. Good agreement with the extended theory with ``free-slip'' condition has been achieved for the parallel flow profile evolution in response to RMP in all resistive regimes, whereas the difference from the conventional theory with the ``no-slip'' condition tends to diminish as the plasma resistivity approaches zero.

physics.plasm-ph↗

arXiv2019

Low-$n$ global ideal MHD instabilities in CFETR baseline scenario

This article reports an evaluation on the linear ideal magnetohydrodynamic (MHD) stability of the China Fusion Engineering Test Reactor (CFETR) baseline scenario for various first-wall locations. The initial-value code NIMROD and eigen-value code AEGIS are employed in this analysis. A good agreement is achieved between two codes in the growth rates of $n=1-10$ ideal MHD modes for various locations of the perfect conducting first-wall. The higher-$n$ modes are dominated by ballooning modes and localized in the pedestal region, while the lower-$n$ modes have more prominent external kink components and broader mode profiles. The influences of plasma-vacuum profile and wall shape are also examined using NIMROD. In presence of resistive wall, the low-$n$ ideal MHD instabilities are further studied using AEGIS. For the designed first-wall location, the $n = 1$ resistive wall mode (RWM) is found unstable, which could be fully stabilized by uniform toroidal rotation above 2.9\% core Alfvén speed.

physics.plasm-ph↗

arXiv2019

Extended hybrid kinetic-magnetohydrodynamic model for ignited burning plasmas

A brief review of the existing kinetic-magnetohydrodynamic(MHD) hybrid models for the alpha particle physics in burning plasma demonstrates that the pressure-coupling scheme is equivalent to the current-coupling scheme only in a specific dynamic regime where the alpha particle density is much lower than the background ion and electron. A more comprehensive kinetic-multifluid model is proposed for a proper account of the dynamical regime of the burning plasma where both the energetic alpha and the helium ash particles are present. The Kinetic-multifluid model is further simplified into an extended hybrid kinetic-MHD model in the MHD limit. This reduction process demonstrates that the existing pressure-coupling scheme is more extensive than the current-coupling scheme and sufficient for the wide range of dynamical regimes. This analysis further shows a significant change in the model equations mainly the generalized Ohm's law due to the contributions of a significant amount of alpha particles in the system. These models can be used for studies of the impact of the alpha particles present in ignited burning plasma and space plasma.

physics.plasm-ph↗

arXiv2019

Analytical model of plasma response to external magnetic perturbation in absence of no-slip condition

Recent simulation and experimental results suggest that the magnetic island and flow on resonant surface often do not satisfy the "no-slip" condition in the steady state. A new theory model on nonlinear plasma response to external magnetic perturbation in absence of no-slip condition is proposed. The model is composed of the equations for the evolution of both width and phase of magnetic island due to forced reconnection driven by the external magnetic perturbation, and the force-balance equation for the plasma flow. When the island width is much less than the resistive layer width, the island growth is governed by the linear Hahm-Kulsrud-Taylor solution in presence of time-dependent plasma flow. In the other regime when the island width is much larger than the resistive layer width, the evolution of both island width and phase can be described using the Rutherford theory. The island solution is used to construct the quasi-linear electromagnetic force, which together with viscous one, contributes to the nonlinear variation in plasma flow. The no-slip condition assumed in the conventional error field theory is not imposed here, where the island oscillation frequency depends on but does not necessarily equal to the plasma flow frequency at the rational surface.

physics.plasm-ph↗

arXiv2019

Stabilizing effect of enhanced resistivity on peeling-ballooning instabilities on EAST

Previous stability analysis of NSTX equilibrium with lithium-conditioning demonstrates that the enhanced resistivity due to the increased effective charge number Zeff (i.e. increased impurity level) can provide a stabilizing effect on low-n edge localized modes (Banerjee et al 2017 Nucl. Fusion 24 054501). This paper extends the resistivity stabilizing effect to the intermediate-n peeling-ballooning (PB) instabilities with the linear stability analysis of EAST high-confinement mode equilibria in NIMROD two-fluid calculations. However, the resistivity stabilizing effect on PB instabilities in the EAST tokamak appears weaker than that found in NSTX. This work may give better insight into the physical mechanism behind the beneficial effects of impurity on the pedestal stability.

physics.plasm-ph↗

arXiv2019

Solving the Grad-Shafranov equation using spectral elements for tokamak equilibrium with toroidal rotation

The Grad-Shafranov equation is solved using spectral elements for tokamak equilibrium with toroidal rotation. The Grad-Shafranov solver builds upon and extends the NIMEQ code [Howell and Sovinec, Comput. Phys. Commun. 185 (2014) 1415] previously developed for static tokamak equilibria. Both geometric and algebraic convergence are achieved as the polynomial degree of the spectral-element basis increases. A new analytical solution to the Grad-Shafranov equation is obtained for Solov'ev equilibrium in presence of rigid toroidal rotation, in addition to a previously obtained analytical solution for a defferent set of equilibrium and rotation profiles. The numerical solutions from the extended NIMEQ are benchmarked with the analytical solutions, with good agreements. Besides, the extended NIMEQ code is benchmarked with the FLOW code [L. Guazzotto, R. Betti, et al., Phys. Plasma 11(2004)604].

physics.plasm-ph↗

arXiv2019

Numerical study of transition between even and odd toroidal Alfvén eigenmodes on EAST

Linear simulations of toriodal Alfvén eigenmodes (TAEs) driven by energetic particles (EPs) on EAST (Experimental Advanced Superconducting Tokamak) are performed using the hybrid-kinetic MHD (HK-MHD) model implemented in NIMROD code. The EAST equilibrium is reconstructed using the EFIT code based on experimental measurement. The "slowing down" distribution is adopted for modeling the equilibrium distribution of the energetic ions from the deuterium neutral beam injection on EAST. The frequency, the dominant poloidal mode number, the radial location and the detailed 2D mode structure of the TAE/RSAE/EPM modes are consistent between the eigenvalue analysis and the NIMROD simulation. As the $β$ fraction of EP increases, a transition between even and odd TAEs occurs, along with that between the ballooning and anti-ballooning mode structures. When the $β$ fraction of EP is close to the transition threshold, both types of TAEs coexist.

physics.plasm-ph↗

arXiv2019

Quasi-separatrix Layers Induced by Ballooning Instability in Near-Earth Magnetotail

Magnetic reconnection processes in the near-Earth magnetotail can be highly 3-dimensional (3D) in geometry and dynamics, even though the magnetotail configuration itself is nearly two dimensional due to the symmetry in the dusk-dawn direction. Such reconnection processes can be induced by the 3D dynamics of nonlinear ballooning instability. In this work, we explore the global 3D geometry of the reconnection process induced by ballooning instability in the near-Earth magnetotail by examining the distribution of quasi-separatrix layers associated with plasmoid formation in the entire 3D domain of magnetotail configuration, using an algorithm previously developed in context of solar physics. The 3D distribution of quasi-separatrix layers (QSLs) as well as their evolution directly follows the plasmoid formation during the nonlinear development of ballooning instability in both time and space. Such a close correlation demonstrates a strong coupling between the ballooning and the corresponding reconnection processes. It further confirms the intrinsic 3D nature of the ballooning-induced plasmoid formation and reconnection processes, in both geometry and dynamics. In addition, the reconstruction of the 3D QSL geometry may provide an alternative means for identifying the location and timing of 3D reconnection sites in magnetotail from both numerical simulations and satellite observations.

physics.space-ph↗