arXiv subjects

Yi-Min Huang

Publications and source records attributed to Yi-Min Huang.

At least 19 recordsLinked to original sources

arXiv2026

Transition of Magnetic Reconnection Regimes in Partially Ionized Plasmas

Magnetic reconnection in partially ionized plasmas plays a crucial role in a wide range of solar, astrophysical, and laboratory environments. While reconnection in such plasmas is commonly characterized by the ion-neutral coupling strength and the ionization fraction $χ=n_{i}/(n_{i}+n_{n})$, most previous studies have focused primarily on the former. A systematic exploration of the ionization fraction, particularly in combination with ion-neutral coupling, is still lacking. This study presents the first systematic scan of the two-dimensional parameter space defined by ion-neutral collisionality and ionization fraction, enabling investigation of the transition from strongly coupled reconnection to faster, decoupled reconnection. To achieve this, we employ a new three-fluid, five-moment numerical model that treats electrons, ions, and neutrals as separate species on an equal footing. We find that in the strongly coupled regime, the reconnection rate is consistent with a $χ^{1/4}$ scaling. As collisionality decreases, the system transitions to a fast, ionization-independent regime. On the other hand, in the weakly coupled and fast-reconnection regimes, the current sheet approaches an ion-inertial-scale thickness rather than the expanded hybrid scale $d_{i}χ^{-1/2}$ predicted by fully coupled analytic fluid theories. The identified critical thickness and the resulting onset of fast reconnection agree reasonably well with recent fully kinetic simulations and laboratory experiments. In addition, we show that, over a wide range of coupling strengths, the ion outflow velocities remain Alfvénic, scaling with the appropriate ion or hybrid Alfvén speed, while the hybrid outflow velocity scales as $χ^{1/2}$ when normalized by ion Alfvén speed.

physics.plasm-ph↗

arXiv2026

System Size Dependence of Collisionless Reconnection Rate

It is a widely accepted paradigm that collisionless magnetic reconnection proceeds at a universal fast rate of $\sim0.1$ when normalized to a properly defined reconnecting magnetic field and Alfvén speed, effectively independent of the macroscopic system size. This conclusion, derived primarily from kinetic simulations of classical Harris current sheets with kinetic-scale thickness, stands in contrast to results from forced reconnection and island coalescence, where the rate significantly depends on the system size. Here, we reconcile this disparity by performing a rigorous scaling study using both particle-in-cell and Hall magnetohydrodynamic simulations. We demonstrate that when the global magnetic configuration is self-consistently preserved by scaling the initial current sheet thickness proportionally with the system size, the ``universal'' fast rate disappears. Instead, the reconnection rate decreases as the system size increases. These results indicate that dependence on macroscopic scales is not peculiar to specific geometries but is a fundamental property of collisionless reconnection, effectively unifying the Harris sheet with other configurations exhibiting size-dependence.

physics.plasm-ph↗

arXiv2026

Forced Reconnection in Voigt-Regularized MHD

Forced reconnection in Voigt-regularized MHD is investigated in the Hahm-Kulsrud-Taylor problem. It is shown that Voigt regularization introduces an early linear phase of reconnection that partially bypasses the ideal current sheet formation phase. A Rutherford-like model of nonlinear island growth and saturation is introduced, including time-dependent spatial variation in the island current distribution and the braking effects of regularization and viscosity. It is conjectured, with numerical justification, that the inclusion of drag in the momentum equation results in precise MHS equilibria in the long-time limit.

physics.plasm-ph↗

arXiv2025

Computation of Magnetohydrodynamic Equilibria with Voigt Regularization

This work presents the first numerical investigation of using Voigt regularization as a method for obtaining magnetohydrodynamic (MHD) equilibria without the assumption of nested magnetic flux surfaces. Voigt regularization modifies the MHD dynamics by introducing additional terms that vanish in the infinite-time limit, allowing for magnetic reconnection and the formation of magnetic islands, which can overlap and produce field-line chaos. The utility of this approach is demonstrated through numerical solutions of two-dimensional ideal and resistive test problems. Our results show that Voigt regularization can significantly accelerate the convergence to solutions in resistive MHD problems, while also highlighting challenges in applying the method to ideal MHD systems. This research opens up new possibilities for developing more efficient and robust MHD equilibrium solvers, which could contribute to the design and optimization of future fusion devices.

physics.plasm-ph↗

arXiv2024

Centrifugal Confinement Fusion Thruster

Centrifugal confinement fusion, a promising alternative to toroidal confinement devices like tokamaks and stellarators, leverages supersonic plasma rotation within a magnetic mirror configuration to achieve simplified coil design, compactness, and enhanced stability. This brief article explores the potential of centrifugal confinement fusion for propulsion applications. A previous concern regarding the escape of energetic ions, essential for propulsion, is addressed through test-particle simulations. The results indicate that the earlier estimate based on adiabatic invariance was overly pessimistic, and the underlying physics is clarified.

physics.plasm-ph↗

arXiv2024

Three-dimensional plasmoid-mediated reconnection and turbulence in Hall magnetohydrodynamics

Plasmoid instability accelerates reconnection in collisional plasmas by transforming a laminar reconnection layer into numerous plasmoids connected by secondary current sheets in two dimensions (2D) and by fostering self-generated turbulent reconnection in three dimensions (3D). In large-scale astrophysical and space systems, plasmoid instability likely initiates in the collisional regime but may transition into the collisionless regime as the fragmentation of the current sheet progresses toward kinetic scales. Hall MHD models are widely regarded as a simplified yet effective representation of the transition from collisional to collisionless reconnection. However, plasmoid instability in 2D Hall MHD simulations often leads to a single-X-line reconnection configuration, which significantly differs from fully kinetic particle-in-cell simulation results. This study shows that single-X-line reconnection is less likely to occur in 3D compared to 2D. Moreover, depending on the Lundquist number and the ratio between the system size and the kinetic scale, Hall MHD can also realize 3D self-generated turbulent reconnection. We analyze the features of the self-generated turbulent state, including the energy power spectra and the scale dependence of turbulent eddy anisotropy.

physics.plasm-ph↗

arXiv2024

Direct prediction of saturated neoclassical tearing modes in slab using an equilibrium approach

We demonstrate for the first time that the nonlinear saturation of neoclassical tearing modes (NTMs) can be found directly using a variational principle based on Taylor relaxation, without needing to simulate the intermediate, resistivity-dependent dynamics. As in previous investigations of classical tearing mode saturation (Loizu et al. 2020; Loizu & Bonfiglio 2023), we make use of SPEC (Hudson et al. 2012), an equilibrium solver based on the variational principle of the Multi-Region relaxed MHD, featuring stepped pressure profiles and arbitrary magnetic topology. We work in slab geometry and employ a simple bootstrap current model $J_\textrm{bs} = C \nabla p$ to study the bootstrap-driven tearing modes, scanning over the asymptotic matching parameter $Δ'$ and the bootstrap current strength. Saturated island widths produced by SPEC agree well with the predictions of an initial value resistive MHD code (Huang & Bhattacharjee 2016) while being orders of magnitude faster to calculate. Additionally, we observe good agreement with a simple analytical Modified Rutherford Equation, without requiring any fitting coefficients. The match is obtained for both linearly unstable classical tearing modes in the presence of bootstrap current, and neoclassical tearing modes, which are linearly stable but nonlinear-unstable due to the effects of the bootstrap current

physics.plasm-ph↗

arXiv2024

Structure of pressure-gradient-driven current singularity in ideal magnetohydrodynamic equilibrium

Singular currents typically appear on rational surfaces in non-axisymmetric ideal magnetohydrodynamic equilibria with a continuum of nested flux surfaces and a continuous rotational transform. These currents have two components: a surface current (Dirac $δ$-function in flux surface labeling) that prevents the formation of magnetic islands and an algebraically divergent Pfirsch--Schlüter current density when a pressure gradient is present across the rational surface. At flux surfaces adjacent to the rational surface, the traditional treatment gives the Pfirsch--Schlüter current density scaling as $J\sim1/Δι$, where $Δι$ is the difference of the rotational transform relative to the rational surface. If the distance $s$ between flux surfaces is proportional to $Δι$, the scaling relation $J\sim1/Δι\sim1/s$ will lead to a paradox that the Pfirsch--Schlüter current is not integrable. In this work, we investigate this issue by considering the pressure-gradient-driven singular current in the Hahm\textendash Kulsrud\textendash Taylor problem, which is a prototype for singular currents arising from resonant magnetic perturbations. We show that not only the Pfirsch--Schlüter current density but also the diamagnetic current density are divergent as $\sim1/Δι$. However, due to the formation of a Dirac $δ$-function current sheet at the rational surface, the neighboring flux surfaces are strongly packed with $s\sim(Δι)^{2}$. Consequently, the singular current density $J\sim1/\sqrt{s}$, making the total current finite, thus resolving the paradox.

physics.plasm-ph↗

arXiv2023

Numerical study of $δ$-function current sheets arising from resonant magnetic perturbations

General three-dimensional toroidal ideal magnetohydrodynamic equilibria with a continuum of nested flux surfaces are susceptible to forming singular current sheets when resonant perturbations are applied. The presence of singular current sheets indicates that, in the presence of non-zero resistivity, magnetic reconnection will ensue, leading to the formation of magnetic islands and potentially regions of stochastic field lines when islands overlap. Numerically resolving singular current sheets in the ideal MHD limit has been a significant challenge. This work presents numerical solutions of the Hahm-Kulsrud-Taylor (HKT) problem, which is a prototype for resonant singular current sheet formation. The HKT problem is solved by two codes: a Grad-Shafranov (GS) solver and the SPEC code. The GS solver has built-in nested flux surfaces with prescribed magnetic fluxes. The SPEC code implements multi-region relaxed magnetohydrodynamics (MRxMHD), where the solution relaxes to a Taylor state in each region while maintaining force balance across the interfaces between regions. As the number of regions increases, the MRxMHD solution approaches the ideal MHD solution assuming a continuum of nested flux surfaces. We demonstrate excellent agreement between the numerical solutions obtained from the two codes through a thorough convergence study.

physics.plasm-ph↗

arXiv2022

Do chaotic field lines cause fast reconnection in coronal loops?

Over the past decade, Boozer has argued that three-dimensional (3D) magnetic reconnection fundamentally differs from two-dimensional (2D) reconnection due to the fact that the separation between any pair of neighboring field lines almost always increases exponentially over distance in a 3D magnetic field. According to Boozer, this feature makes 3D field-line mapping chaotic and exponentially sensitive to small non-ideal effects; consequently, 3D reconnection can occur without intense current sheets. We test Boozer's theory via ideal and resistive reduced magnetohydrodynamic simulations of the Boozer-Elder coronal loop model driven by sub-Alfvenic footpoint motions [A. H. Boozer and T. Elder, Physics of Plasmas 28, 062303 (2021)]. Our simulation results significantly differ from their predictions. The ideal simulation shows that Boozer and Elder under-predict the intensity of current density due to missing terms in their reduced model equations. Furthermore, resistive simulations of varying Lundquist numbers show that the maximal current density scales linearly rather than logarithmically with the Lundquist number.

physics.plasm-ph↗

arXiv2022

Reconnection-Driven Energy Cascade in Magnetohydrodynamic Turbulence

Magnetohydrodynamic turbulence regulates the transfer of energy from large to small scales in many astrophysical systems, including the solar atmosphere. We perform three-dimensional magnetohydrodynamic simulations with unprecedentedly large magnetic Reynolds number to reveal how rapid reconnection of magnetic field lines changes the classical paradigm of the turbulent energy cascade. By breaking elongated current sheets into chains of small magnetic flux ropes (or plasmoids), magnetic reconnection leads to a new range of turbulent energy cascade, where the rate of energy transfer is controlled by the growth rate of the plasmoids. As a consequence, the turbulent energy spectra steepen and attain a spectral index of -2.2 that is accompanied by changes in the anisotropy of turbulence eddies. The omnipresence of plasmoids and their consequences on, e.g., solar coronal heating, can be further explored with current and future spacecraft and telescopes.

astro-ph.SR↗

arXiv2019

Scalings Pertaining to Current Sheet Disruption Mediated by the Plasmoid Instability

Analytic scaling relations are derived for a phenomenological model of the plasmoid instability in an evolving current sheet, including the effects of reconnection outflow. Two scenarios are considered, where the plasmoid instability can be triggered either by an injected initial perturbation or by the natural noise of the system (here referred to as the system noise). The two scenarios lead to different scaling relations because the initial noise decays when the linear growth of the plasmoid instability is not sufficiently fast to overcome the advection loss caused by the reconnection outflow, whereas the system noise represents the lowest level of fluctuations in the system. The leading order approximation for the current sheet width at disruption takes the form of a power-law multiplied by a logarithmic factor, and from that, the scaling relations for the wavenumber and the linear growth rate of the dominant mode are obtained. When the effects of the outflow are neglected, the scaling relations agree, up to the leading order approximation, with previously derived scaling relations based on a principle of least time. The analytic scaling relations are validated with numerical solutions of the model.

physics.plasm-ph↗

arXiv2019

Magnetohydrodynamical equilibria with current singularities and continuous rotational transform

We revisit the Hahm-Kulsrud-Taylor (HKT) problem, a classic prototype problem for studying resonant magnetic perturbations and 3D magnetohydrodynamical equilibria. We employ the boundary-layer techniques developed by Rosenbluth, Dagazian, and Rutherford (RDR) for the internal $m=1$ kink instability, while addressing the subtle difference in the matching procedure for the HKT problem. Pedagogically, the essence of RDR's approach becomes more transparent in the simplified slab geometry of the HKT problem. We then compare the boundary-layer solution, which yields a "DC" current singularity at the resonant surface, to the numerical solution obtained using a flux-preserving Grad-Shafranov solver. The remarkable agreement between the solutions demonstrates the validity and universality of RDR's approach. In addition, we show that RDR's approach consistently preserves the rotational transform, which hence stays continuous, contrary to a recent claim that RDR's solution contains a discontinuity in the rotational transform.

physics.plasm-ph↗

arXiv2018

Boundary layers and noise in magnetized plasmas line-tied at conducting surfaces

In magnetized plasma situations where magnetic fields intersect massive conducting boundaries, "line-tied" boundary conditions are often used, analytically and in numerical simulations. For ideal MHD plasmas, these conditions are arrived at given the relatively long time scales for magnetic fields penetrating resistively into good conductors. Under line-tied boundary conditions, numerical simulations often exhibit what could be construed as numerical "noise" emanating from the boundaries. We show here that this "noise" is real. By combining numerical and analytical methods, we highlight the existence of boundary layers near the conductors and confirm the appearance of short wavelength structures riding on long wavelength features. We conclude that for numerical fidelity the boundary layers need to be resolved. Boundary layer widths scale as the square root of the plasma \b{eta}.

physics.plasm-ph↗

arXiv2018

Role of the Plasmoid Instability in Magnetohydrodynamic Turbulence

The plasmoid instability in evolving current sheets has been widely studied due to its effects on the disruption of current sheets, the formation of plasmoids, and the resultant fast magnetic reconnection. In this Letter, we study the role of the plasmoid instability in two-dimensional magnetohydrodynamic (MHD) turbulence by means of high-resolution direct numerical simulations. At sufficiently large magnetic Reynolds number ($R_m=10^6$), the combined effects of dynamic alignment and turbulent intermittency lead to a copious formation of plasmoids in a multitude of intense current sheets. The disruption of current sheet structures facilitates the energy cascade towards small scales, leading to the breaking and steepening of the energy spectrum. In the plasmoid-mediated regime, the energy spectrum displays a scaling that is close to the spectral index $-2.2$ as proposed by recent analytic theories. We also demonstrate that the scale-dependent dynamic alignment exists in 2D MHD turbulence and the corresponding slope of the alignment angle is close to 0.25.

physics.plasm-ph↗

arXiv2018

Energy spectrum of tearing mode turbulence in sheared background field

The energy spectrum of tearing mode turbulence in a sheared background magnetic field is studied in this work. We consider the scenario where the nonlinear interaction of overlapping large-scale modes stirs up a broad spectrum of small-scale modes, generating tearing mode turbulence. The spectrum of such turbulence is of interest since it is relevant to the small-scale back-reaction to the large-scale field. The turbulence we discuss here differs from traditional MHD turbulence mainly in two aspects, one being the existence of many linearly stable small-scale modes which cause an effective damping during energy cascade; the other being the scale independent anisotropy induced by the large scale modes tilting the sheared background field, as opposed to the scale dependent anisotropy frequently encountered in traditional weak turbulence or critically balanced turbulence theory. These two differences result in the deviation of energy spectrum from a simple power law behavior, taking the form of a power law multiplied by an exponential falloff. Numerical simulation is carried out using viscous resistive MHD equations to verify our theoretical prediction, and reasonable agreement is found between numerical result and our model.

physics.plasm-ph↗

arXiv2018

Constructing current singularity in a 3D line-tied plasma

We revisit Parker's conjecture of current singularity formation in 3D line-tied plasmas using a recently developed numerical method, variational integration for ideal magnetohydrodynamics in Lagrangian labeling. With the frozen-in equation built-in, the method is free of artificial reconnection, and hence it is arguably an optimal tool for studying current singularity formation. Using this method, the formation of current singularity has previously been confirmed in the Hahm--Kulsrud--Taylor problem in 2D. In this paper, we extend this problem to 3D line-tied geometry. The linear solution, which is singular in 2D, is found to be smooth for arbitrary system length. However, with finite amplitude, the linear solution can become pathological when the system is sufficiently long. The nonlinear solutions turn out to be smooth for short systems. Nonetheless, the scaling of peak current density versus system length suggests that the nonlinear solution may become singular at finite length. With the results in hand, we can neither confirm nor rule out this possibility conclusively, since we cannot obtain solutions with system length near the extrapolated critical value.

physics.plasm-ph↗

arXiv2017

Plasmoid Instability in Evolving Current Sheets and Onset of Fast Reconnection

The scaling of plasmoid instability maximum linear growth rate with respect to Lundquist number $S$ in a Sweet-Parker current sheet, $γ_{max}\sim S^{1/4}$, indicates that at high $S$, the current sheet will break apart before it approaches the Sweet-Parker width. Therefore, a proper description for the onset of the plasmoid instability must incorporate the evolving process of the current sheet. We carry out a series of two-dimensional simulations and develop diagnostics to separate fluctuations from an evolving background. It is found that the fluctuation amplitude starts to grow only when the linear growth rate is sufficiently large ($γ_{max}τ_{A}>O(1)$) to overcome convective losses. The linear growth rate continues to rise until the sizes of plasmoids become comparable to the inner layer width of the tearing mode. At this point the current sheet is disrupted and the instability enters the early nonlinear regime. The growth rate suddenly decreases, but the fluctuation amplitude continues to grow until it reaches nonlinear saturation. We identify important time scales of the instability development, as well as scalings for the linear growth rate, current sheet width, and dominant wavenumber at current sheet disruption. These scalings depend on not only the Lundquist number, but also the initial noise amplitude. A phenomenological model that reproduces scalings from simulation results is proposed. The model incorporates the effect of reconnection outflow, which is crucial for yielding a critical Lundquist number $S_{c}$ below which disruption does not occur. The critical Lundquist number $S_{c}$ is not a constant value but has a weak dependence on the noise amplitude.

physics.plasm-ph↗