Yi-Min Huang | Princeton University (original) (raw)

Papers by Yi-Min Huang

Physical review. E, 2016

Recently a variational integrator for ideal magnetohydrodynamics in Lagrangian labeling has been ... more Recently a variational integrator for ideal magnetohydrodynamics in Lagrangian labeling has been developed. Its built-in frozen-in equation makes it optimal for studying current sheet formation. We use this scheme to study the Hahm-Kulsrud-Taylor problem, which considers the response of a 2D plasma magnetized by a sheared field under sinusoidal boundary forcing. We obtain an equilibrium solution that preserves the magnetic topology of the initial field exactly, with a fluid mapping that is non-differentiable. Unlike previous studies that examine the current density output, we identify a singular current sheet from the fluid mapping. These results are benchmarked with a constrained Grad-Shafranov solver. The same signature of current singularity can be found in other cases with more complex magnetic topologies.

Strong unipolar core magnetic fields and density compression are observed in the plasmoids which ... more Strong unipolar core magnetic fields and density compression are observed in the plasmoids which produce suprathermal electrons during magnetotail reconnection with a weak guide field (< 3% B0, where B0 is the reconnecting field strength)[1]. The in-plane electric fields in these plasmoids are localized near the plasmoid core and point toward the core. Hall MHD and PIC simulations show that these features are consistent with plasmoids generated in the reconnection electron current sheet. In particular, the strong density compression and unipolar core field can be generated under sufficiently low upstream beta (<=0.4) with a weak ambient guide field. The beta-dependence of the core-field generation allows us to infer the upstream condition of the observed magnetotail reconnection based on the observed plasmoid internal structures. [4pt] [1] Phys. Plasmas, 16, 056501 (2009)

Supra-arcade downflows (hereafter referred to as SADs) are low-emission, elongated, finger-like f... more Supra-arcade downflows (hereafter referred to as SADs) are low-emission, elongated, finger-like features observed in active region coronae above post-eruption flare arcades. Observations exhibit downward moving SADs intertwined with bright upward growing spikes. Whereas SADs are dark voids, spikes are brighter, denser structures. Although SADs have been observed for more than a decade, the mechanism of the formation of SADs remains an open issue. Using three-dimensional resistive magnetohydrodynamic simulations, we demonstrate that Rayleigh-Taylortype instabilities develop in the downstream region of a reconnecting current sheet. The instabilities result in the formation of low-density coherent structures that resemble SADs, and high-density structures that appear to be spike-like. Comparison between the simulation results and observations suggests that Rayleigh-Taylor-type instabilities in the exhaust of reconnecting current sheets provide a plausible mechanism for observed SADs.

ABSTRACT Magnetic reconnection, a ubiquitous phenomenon in astrophysics, space science and magnet... more ABSTRACT Magnetic reconnection, a ubiquitous phenomenon in astrophysics, space science and magnetic confinement research, frequently proceeds much faster than predicted by simple resistive MHD theory. Acceleration can result from the break-up of the thin Sweet–Parker current sheet into plasmoids, or from two-fluid effects decoupling mass and magnetic flux transport over the ion inertial length or the drift scale depending on the absence or presence of a strong magnetic guide field. We describe new results on the modelling of sawtooth reconnection in a simple tokamak geometry (circular cylindrical equilibrium) pushed to realistic Lundquist numbers for present day tokamaks. For the resistive MHD case, the onset criteria and the influence of plasmoids on the reconnection process agree well with earlier results found in the case of vanishing magnetic guide fields. While plasmoids are also observed in two-fluid calculations, they do not dominate the reconnection process for the range of plasma parameters considered in this study. In the two-fluid case they form as a transient phenomenon only. The reconnection times become weakly dependent on the S-value and for the most complete model—including two-fluid effects and equilibrium temperature and density gradients—agree well with those experimentally found on ASDEX Upgrade

Supra-arcade fans are bright, irregular regions of emission that develop during eruptive flares a... more Supra-arcade fans are bright, irregular regions of emission that develop during eruptive flares above flare arcades. The underlying flare arcades are thought to be a consequence of magnetic reconnection along a current sheet in the corona. At the same time, theory predicts plasma jets from the reconnection sites which are extremely difficult to observe directly because of their low densities. It has been suggested that the dark supra-arcade downflows (SADs) seen falling through supra-arcade fans may be low-density jet plasma. The head of a low-density jet directed toward higher-density plasma would be Rayleigh-Taylor unstable, and lead to the development of rapidly growing low-and high-density fingers along the interface. Using Solar Dynamics Observatory/Atmospheric Imaging Assembly 131 Å images, we show details of SADs seen from three different orientations with respect to the flare arcade and current sheet, and highlight features that have been previously unexplained, such as the splitting of SADs at their heads, but are a natural consequence of instabilities above the arcade. Comparison with three-dimensional magnetohydrodynamic simulations suggests that SADs are the result of secondary instabilities of the Rayleigh-Taylor type in the exhaust of reconnection jets.

The Astrophysical Journal, 2014

Magnetic fields without a direction of continuous symmetry have the generic feature that neighbor... more Magnetic fields without a direction of continuous symmetry have the generic feature that neighboring field lines exponentiate away from each other and become stochastic, hence the ideal constraint of preserving magnetic field line connectivity becomes exponentially sensitive to small deviations from ideal Ohm's law. The idea of breaking field line connectivity by stochasticity as a mechanism for fast reconnection is tested with numerical simulations based on reduced magnetohydrodynamics equations with a strong guide field line-tied to two perfectly conducting end plates. Starting from an ideally stable force-free equilibrium, the system is allowed to undergo resistive relaxation. Two distinct phases are found in the process of resistive relaxation. During the quasi-static phase, rapid change of field line connectivity and strong induced flow are found in regions of high field line exponentiation. However, although the field line connectivity of individual field lines can change rapidly, the overall pattern of field line mapping appears to deform gradually. From this perspective, field line exponentiation appears to cause enhanced diffusion rather than reconnection. In some cases, resistive quasi-static evolution can cause the ideally stable initial equilibrium to cross a stability threshold, leading to formation of intense current filaments and rapid change of field line mapping into a qualitatively different pattern. It is in this onset phase that the change of field line connectivity is more appropriately designated as magnetic reconnection. Our results show that rapid change of field line connectivity appears to be a necessary, but not a sufficient condition for fast reconnection.

Physics of Plasmas, 2010

An overview of some recent progress on magnetohydrodynamic stability and current sheet formation ... more An overview of some recent progress on magnetohydrodynamic stability and current sheet formation in a line-tied system is given. Key results on the linear stability of the ideal internal kink mode and resistive tearing mode are summarized. For nonlinear problems, a counterexample to the recent demonstration of current sheet formation by Low and Janse ͓Astrophys. J. 696, 821 ͑2009͔͒ is presented, and the governing equations for quasistatic evolution of a boundary driven, line-tied magnetic field are derived. Some open questions and possible strategies to resolve them are discussed.

The Astrophysical Journal, 2008

We present numerical simulations of the growth and saturation of the Kelvin-Helmholtz instability... more We present numerical simulations of the growth and saturation of the Kelvin-Helmholtz instability in a compressible fluid layer with and without a weak magnetic field. In the absence of a magnetic field, the instability generates a single eddy which flattens the velocity profile, stabilizing it against further perturbations. Adding a weak magnetic field -weak in the sense that it has almost no effect on the linear instability -leads to a complex flow morphology driven by MHD forces and to enhanced broadening of the layer, due to Maxwell stresses. We corroborate earlier studies which showed that magnetic fields destroy the large scale eddy structure through periodic cycles of windup and resistive decay, but we show that the rate of decay decreases with decreasing plasma resistivity η, at least within the range of η accessible to our simulations. Magnetization increases the efficiency of momentum transport, and the transport increases with decreasing η.

The Astrophysical Journal, 2012

The compression or expansion of a magnetic field that is initially potential is considered. It wa... more The compression or expansion of a magnetic field that is initially potential is considered. It was recently suggested by Janse & Low that, following the volumetric deformation, the relevant lowest energy state for the magnetic field is another potential magnetic field that in general contains tangential discontinuities (current sheets). Here, we examine this scenario directly using a numerical relaxation method that exactly preserves the topology of the magnetic field. It is found that, of the magnetic fields discussed by Janse & Low, only those containing magnetic null points develop current singularities during an ideal relaxation, while the magnetic fields without null points relax toward smooth force-free equilibria with finite nonzero current.

Physics of Plasmas, 2005

The ideal magnetohydrodynamic equations are usually derived under the assumption V A Ӷ c, where V... more The ideal magnetohydrodynamic equations are usually derived under the assumption V A Ӷ c, where V A is the Alfvén speed and c is the speed of light. This system of equations is extended to low density plasmas wherein V A can be comparable to or greater than c. This involves relaxation of the usual charge quasineutrality assumption and the inclusion of electromagnetic momentum on par with plasma momentum. The extended system is applied to interchange instabilities in "line-tied" slab geometry as well as to centrifugally confined plasmas. It is found that interchange growth rates are reduced by a factor of 1 + V A 2 / c 2 , corresponding to a larger effective mass resulting from the extra electromagnetic momentum. Line tying is unaffected.

Physics of Plasmas, 2004

Particle sources and resulting density profiles are shown to play an important role in the magnet... more Particle sources and resulting density profiles are shown to play an important role in the magnetohydrodynamic ͑MHD͒ stability of azimuthally rotating axially magnetized plasmas. In the absence of particle sources, density profiles relax under resistive diffusion to pile up to the outside of the system consistent with the outward centrifugal forces. In particular, particle sources would have to be placed appropriately to maintain desired density profiles for fusion applications of centrifugally confined systems. Tailoring of the density profiles could, however, be used to achieve control over MHD stability. Long wavelength Kelvin-Helmholtz modes as well as short wavelength interchange modes are studied in relation to profile tailoring and efficacy of velocity shear. It is concluded that judiciously placed particle sources could be used to enhance stability.

Physics of Plasmas, 2006

It is well known that the radial displacement of the m = 1 internal kink mode in a periodic screw... more It is well known that the radial displacement of the m = 1 internal kink mode in a periodic screw pinch has a steep jump at the resonant surface where k · B =0 ͓Rosenbluth, Dagazian, and Rutherford, Phys. Fluids 16, 1894 ͑1973͔͒. In a line-tied system, relevant to solar and astrophysical plasmas, the resonant surface is no longer a valid concept. It is then of interest to see how line-tying alters the aforementioned result for a periodic system. If the line-tied kink also produces a steep gradient, corresponding to a thin current layer, it may lead to strong resistive effects even with weak dissipation. Numerical solution of the eigenmode equations shows that the fastest growing kink mode in a line-tied system still possesses a jump in the radial displacement at the location coincident with the resonant surface of the fastest growing mode in the periodic counterpart. However, line-tying thickens the inner layer and slows down the growth rate. As the system length L approaches infinity, both the inner layer thickness and the growth rate approach the periodic values. In the limit of small ⑀ ϳ B / B z , the critical length for instability L c ϳ ⑀ −3 . The relative increase in the inner layer thickness due to line-tying scales as ⑀ −1 ͑L c / L͒ 2.5 .

Physics of Plasmas, 2003

The ideal magnetohydrodynamics stability of a Dean flow plasma supported against centrifugal forc... more The ideal magnetohydrodynamics stability of a Dean flow plasma supported against centrifugal forces by an axial magnetic field is studied. Only axisymmetric perturbations are allowed for simplicity. Two distinct but coupled destabilization mechanisms are present: flow shear ͑magnetorotational instability͒ and magnetic buoyancy ͑Parker instability͒. It is shown that the flow shear alone is likely insufficient to destabilize the plasma, but the magnetic buoyancy instability could occur. For a high Mach number (M S ), high Alfvén Mach number (M A ) system with M S M A տR/a (R/a is the aspect ratio͒, the Parker instability is unstable for long axial wavelength modes. Implications for the centrifugal confinement approach to magnetic fusion are also discussed.

Physics of Plasmas, 2013

Magnetic reconnection mediated by the hyper-resistive plasmoid instability is studied with both l... more Magnetic reconnection mediated by the hyper-resistive plasmoid instability is studied with both linear analysis and nonlinear simulations. The linear growth rate is found to scale as S 1/6 H with respect to the hyper-resistive Lundquist number S H ≡ L 3 V A /η H , where L is the system size, V A is the Alfvén velocity, and η H is the hyper-resistivity. In the nonlinear regime, reconnection rate becomes nearly independent of S H , the number of plasmoids scales as S * yiminh@princeton.edu

Physics of Plasmas, 2012

The effects of the initial upstream plasma b on the plasmoid instability are studied via twodimen... more The effects of the initial upstream plasma b on the plasmoid instability are studied via twodimensional resistive magnetohydrodynamic simulations. For cases with nonuniform b dependent initial plasma mass density and uniform temperature, our numerical results indicate that the critical Lundquist number for onset of the plasmoid instability depends on the initial plasma b. The critical Lundquist number is approximately 2000 À 3000 for b ¼ 50 and is 8000 À 10 000 for b ¼ 0:2. The higher the b, the smaller the critical Lundquist number is. Similar to previous studies of high-b systems, the average reconnection rate in low b systems is found to become weakly dependent on the Lundquist number in the plasmoid-unstable regime. However, the average reconnection rate, normalized to the asymptotic value of upstream BV A , is lower in a low b system than that in a high b system. The magnetic energy spectral index, which characterizes fragmentation of the reconnection layer, is approximately two and is insensitive to b in the high-Lunquist number regime. It is also found that the magnetic reconnection rate becomes similar for different b cases, if the initial forcebalance is provided by temperature gradient instead of density gradient. Therefore, it is concluded that the b-dependence mentioned above may be largely attributed to the density variation. V C 2012 American Institute of Physics. [http://dx.

Physics of Plasmas, 2013

ABSTRACT The results from guide field studies on the Magnetic Reconnection Experiment (MRX) are c... more ABSTRACT The results from guide field studies on the Magnetic Reconnection Experiment (MRX) are compared with results from Hall magnetohydrodynamic (HMHD) reconnection simulation with guide field. The quadrupole field, a signature of two-fluid reconnection at zero guide field, is modified by the presence of a finite guide field in a manner consistent with HMHD simulation. The modified Hall current profile contains reduced electron flows in the reconnection plane, which quantitatively explains the observed reduction of the reconnection rate. The present results are consistent with the hypothesis that the local reconnection dynamics is dominated by Hall effects in the collisionless regime of the MRX plasmas. While very good agreement is seen between experiment and simulations, we note that an important global feature of the experiments, a compression of the guide field by the reconnecting plasma, is not represented in the simulations. V C 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4805244]

Physics of Plasmas, 2013

Our understanding of magnetic reconnection in resistive magnetohydrodynamics has gone through a f... more Our understanding of magnetic reconnection in resistive magnetohydrodynamics has gone through a fundamental change in recent years. The conventional wisdom is that magnetic reconnection mediated by resistivity is slow in laminar high Lundquist (S) plasmas, constrained by the scaling of the reconnection rate predicted by Sweet-Parker theory. However, recent studies have shown that when S exceeds a critical value 104,theSweet−Parkercurrentsheetisunstabletoasuper−Alfvenicplasmoidinstability,withalineargrowthratethatscalesasS1=4.Inthefullydevelopedstatisticalsteadystateoftwo−dimensionalresistivemagnetohydrodynamicsimulations,thenormalizedaveragereconnectionrateisapproximately0.01,nearlyindependentofS,andthedistributionfunctionfðwÞofplasmoidmagneticfluxwfollowsapowerlawfðwÞ10 4 , the Sweet-Parker current sheet is unstable to a super-Alfv enic plasmoid instability, with a linear growth rate that scales as S 1=4 . In the fully developed statistical steady state of two-dimensional resistive magnetohydrodynamic simulations, the normalized average reconnection rate is approximately 0.01, nearly independent of S, and the distribution function f ðwÞ of plasmoid magnetic flux w follows a power law f ðwÞ 104,theSweet−Parkercurrentsheetisunstabletoasuper−Alfvenicplasmoidinstability,withalineargrowthratethatscalesasS1=4.Inthefullydevelopedstatisticalsteadystateoftwo−dimensionalresistivemagnetohydrodynamicsimulations,thenormalizedaveragereconnectionrateisapproximately0.01,nearlyindependentofS,andthedistributionfunctionfðwÞofplasmoidmagneticfluxwfollowsapowerlawfðwÞ w À1 . When Hall effects are included, the plasmoid instability may trigger onset of Hall reconnection even when the conventional criterion for onset is not satisfied. The rich variety of possible reconnection dynamics is organized in the framework of a phase diagram. V C 2013 AIP Publishing LLC. [http://dx.

Physical review. E, 2016

Recently a variational integrator for ideal magnetohydrodynamics in Lagrangian labeling has been ... more Recently a variational integrator for ideal magnetohydrodynamics in Lagrangian labeling has been developed. Its built-in frozen-in equation makes it optimal for studying current sheet formation. We use this scheme to study the Hahm-Kulsrud-Taylor problem, which considers the response of a 2D plasma magnetized by a sheared field under sinusoidal boundary forcing. We obtain an equilibrium solution that preserves the magnetic topology of the initial field exactly, with a fluid mapping that is non-differentiable. Unlike previous studies that examine the current density output, we identify a singular current sheet from the fluid mapping. These results are benchmarked with a constrained Grad-Shafranov solver. The same signature of current singularity can be found in other cases with more complex magnetic topologies.

Strong unipolar core magnetic fields and density compression are observed in the plasmoids which ... more Strong unipolar core magnetic fields and density compression are observed in the plasmoids which produce suprathermal electrons during magnetotail reconnection with a weak guide field (< 3% B0, where B0 is the reconnecting field strength)[1]. The in-plane electric fields in these plasmoids are localized near the plasmoid core and point toward the core. Hall MHD and PIC simulations show that these features are consistent with plasmoids generated in the reconnection electron current sheet. In particular, the strong density compression and unipolar core field can be generated under sufficiently low upstream beta (<=0.4) with a weak ambient guide field. The beta-dependence of the core-field generation allows us to infer the upstream condition of the observed magnetotail reconnection based on the observed plasmoid internal structures. [4pt] [1] Phys. Plasmas, 16, 056501 (2009)

Supra-arcade downflows (hereafter referred to as SADs) are low-emission, elongated, finger-like f... more Supra-arcade downflows (hereafter referred to as SADs) are low-emission, elongated, finger-like features observed in active region coronae above post-eruption flare arcades. Observations exhibit downward moving SADs intertwined with bright upward growing spikes. Whereas SADs are dark voids, spikes are brighter, denser structures. Although SADs have been observed for more than a decade, the mechanism of the formation of SADs remains an open issue. Using three-dimensional resistive magnetohydrodynamic simulations, we demonstrate that Rayleigh-Taylortype instabilities develop in the downstream region of a reconnecting current sheet. The instabilities result in the formation of low-density coherent structures that resemble SADs, and high-density structures that appear to be spike-like. Comparison between the simulation results and observations suggests that Rayleigh-Taylor-type instabilities in the exhaust of reconnecting current sheets provide a plausible mechanism for observed SADs.

ABSTRACT Magnetic reconnection, a ubiquitous phenomenon in astrophysics, space science and magnet... more ABSTRACT Magnetic reconnection, a ubiquitous phenomenon in astrophysics, space science and magnetic confinement research, frequently proceeds much faster than predicted by simple resistive MHD theory. Acceleration can result from the break-up of the thin Sweet–Parker current sheet into plasmoids, or from two-fluid effects decoupling mass and magnetic flux transport over the ion inertial length or the drift scale depending on the absence or presence of a strong magnetic guide field. We describe new results on the modelling of sawtooth reconnection in a simple tokamak geometry (circular cylindrical equilibrium) pushed to realistic Lundquist numbers for present day tokamaks. For the resistive MHD case, the onset criteria and the influence of plasmoids on the reconnection process agree well with earlier results found in the case of vanishing magnetic guide fields. While plasmoids are also observed in two-fluid calculations, they do not dominate the reconnection process for the range of plasma parameters considered in this study. In the two-fluid case they form as a transient phenomenon only. The reconnection times become weakly dependent on the S-value and for the most complete model—including two-fluid effects and equilibrium temperature and density gradients—agree well with those experimentally found on ASDEX Upgrade

Supra-arcade fans are bright, irregular regions of emission that develop during eruptive flares a... more Supra-arcade fans are bright, irregular regions of emission that develop during eruptive flares above flare arcades. The underlying flare arcades are thought to be a consequence of magnetic reconnection along a current sheet in the corona. At the same time, theory predicts plasma jets from the reconnection sites which are extremely difficult to observe directly because of their low densities. It has been suggested that the dark supra-arcade downflows (SADs) seen falling through supra-arcade fans may be low-density jet plasma. The head of a low-density jet directed toward higher-density plasma would be Rayleigh-Taylor unstable, and lead to the development of rapidly growing low-and high-density fingers along the interface. Using Solar Dynamics Observatory/Atmospheric Imaging Assembly 131 Å images, we show details of SADs seen from three different orientations with respect to the flare arcade and current sheet, and highlight features that have been previously unexplained, such as the splitting of SADs at their heads, but are a natural consequence of instabilities above the arcade. Comparison with three-dimensional magnetohydrodynamic simulations suggests that SADs are the result of secondary instabilities of the Rayleigh-Taylor type in the exhaust of reconnection jets.

The Astrophysical Journal, 2014

Magnetic fields without a direction of continuous symmetry have the generic feature that neighbor... more Magnetic fields without a direction of continuous symmetry have the generic feature that neighboring field lines exponentiate away from each other and become stochastic, hence the ideal constraint of preserving magnetic field line connectivity becomes exponentially sensitive to small deviations from ideal Ohm's law. The idea of breaking field line connectivity by stochasticity as a mechanism for fast reconnection is tested with numerical simulations based on reduced magnetohydrodynamics equations with a strong guide field line-tied to two perfectly conducting end plates. Starting from an ideally stable force-free equilibrium, the system is allowed to undergo resistive relaxation. Two distinct phases are found in the process of resistive relaxation. During the quasi-static phase, rapid change of field line connectivity and strong induced flow are found in regions of high field line exponentiation. However, although the field line connectivity of individual field lines can change rapidly, the overall pattern of field line mapping appears to deform gradually. From this perspective, field line exponentiation appears to cause enhanced diffusion rather than reconnection. In some cases, resistive quasi-static evolution can cause the ideally stable initial equilibrium to cross a stability threshold, leading to formation of intense current filaments and rapid change of field line mapping into a qualitatively different pattern. It is in this onset phase that the change of field line connectivity is more appropriately designated as magnetic reconnection. Our results show that rapid change of field line connectivity appears to be a necessary, but not a sufficient condition for fast reconnection.

Physics of Plasmas, 2010

An overview of some recent progress on magnetohydrodynamic stability and current sheet formation ... more An overview of some recent progress on magnetohydrodynamic stability and current sheet formation in a line-tied system is given. Key results on the linear stability of the ideal internal kink mode and resistive tearing mode are summarized. For nonlinear problems, a counterexample to the recent demonstration of current sheet formation by Low and Janse ͓Astrophys. J. 696, 821 ͑2009͔͒ is presented, and the governing equations for quasistatic evolution of a boundary driven, line-tied magnetic field are derived. Some open questions and possible strategies to resolve them are discussed.

The Astrophysical Journal, 2008

We present numerical simulations of the growth and saturation of the Kelvin-Helmholtz instability... more We present numerical simulations of the growth and saturation of the Kelvin-Helmholtz instability in a compressible fluid layer with and without a weak magnetic field. In the absence of a magnetic field, the instability generates a single eddy which flattens the velocity profile, stabilizing it against further perturbations. Adding a weak magnetic field -weak in the sense that it has almost no effect on the linear instability -leads to a complex flow morphology driven by MHD forces and to enhanced broadening of the layer, due to Maxwell stresses. We corroborate earlier studies which showed that magnetic fields destroy the large scale eddy structure through periodic cycles of windup and resistive decay, but we show that the rate of decay decreases with decreasing plasma resistivity η, at least within the range of η accessible to our simulations. Magnetization increases the efficiency of momentum transport, and the transport increases with decreasing η.

The Astrophysical Journal, 2012

The compression or expansion of a magnetic field that is initially potential is considered. It wa... more The compression or expansion of a magnetic field that is initially potential is considered. It was recently suggested by Janse & Low that, following the volumetric deformation, the relevant lowest energy state for the magnetic field is another potential magnetic field that in general contains tangential discontinuities (current sheets). Here, we examine this scenario directly using a numerical relaxation method that exactly preserves the topology of the magnetic field. It is found that, of the magnetic fields discussed by Janse & Low, only those containing magnetic null points develop current singularities during an ideal relaxation, while the magnetic fields without null points relax toward smooth force-free equilibria with finite nonzero current.

Physics of Plasmas, 2005

The ideal magnetohydrodynamic equations are usually derived under the assumption V A Ӷ c, where V... more The ideal magnetohydrodynamic equations are usually derived under the assumption V A Ӷ c, where V A is the Alfvén speed and c is the speed of light. This system of equations is extended to low density plasmas wherein V A can be comparable to or greater than c. This involves relaxation of the usual charge quasineutrality assumption and the inclusion of electromagnetic momentum on par with plasma momentum. The extended system is applied to interchange instabilities in "line-tied" slab geometry as well as to centrifugally confined plasmas. It is found that interchange growth rates are reduced by a factor of 1 + V A 2 / c 2 , corresponding to a larger effective mass resulting from the extra electromagnetic momentum. Line tying is unaffected.

Physics of Plasmas, 2004

Particle sources and resulting density profiles are shown to play an important role in the magnet... more Particle sources and resulting density profiles are shown to play an important role in the magnetohydrodynamic ͑MHD͒ stability of azimuthally rotating axially magnetized plasmas. In the absence of particle sources, density profiles relax under resistive diffusion to pile up to the outside of the system consistent with the outward centrifugal forces. In particular, particle sources would have to be placed appropriately to maintain desired density profiles for fusion applications of centrifugally confined systems. Tailoring of the density profiles could, however, be used to achieve control over MHD stability. Long wavelength Kelvin-Helmholtz modes as well as short wavelength interchange modes are studied in relation to profile tailoring and efficacy of velocity shear. It is concluded that judiciously placed particle sources could be used to enhance stability.

Physics of Plasmas, 2006

It is well known that the radial displacement of the m = 1 internal kink mode in a periodic screw... more It is well known that the radial displacement of the m = 1 internal kink mode in a periodic screw pinch has a steep jump at the resonant surface where k · B =0 ͓Rosenbluth, Dagazian, and Rutherford, Phys. Fluids 16, 1894 ͑1973͔͒. In a line-tied system, relevant to solar and astrophysical plasmas, the resonant surface is no longer a valid concept. It is then of interest to see how line-tying alters the aforementioned result for a periodic system. If the line-tied kink also produces a steep gradient, corresponding to a thin current layer, it may lead to strong resistive effects even with weak dissipation. Numerical solution of the eigenmode equations shows that the fastest growing kink mode in a line-tied system still possesses a jump in the radial displacement at the location coincident with the resonant surface of the fastest growing mode in the periodic counterpart. However, line-tying thickens the inner layer and slows down the growth rate. As the system length L approaches infinity, both the inner layer thickness and the growth rate approach the periodic values. In the limit of small ⑀ ϳ B / B z , the critical length for instability L c ϳ ⑀ −3 . The relative increase in the inner layer thickness due to line-tying scales as ⑀ −1 ͑L c / L͒ 2.5 .

Physics of Plasmas, 2003

The ideal magnetohydrodynamics stability of a Dean flow plasma supported against centrifugal forc... more The ideal magnetohydrodynamics stability of a Dean flow plasma supported against centrifugal forces by an axial magnetic field is studied. Only axisymmetric perturbations are allowed for simplicity. Two distinct but coupled destabilization mechanisms are present: flow shear ͑magnetorotational instability͒ and magnetic buoyancy ͑Parker instability͒. It is shown that the flow shear alone is likely insufficient to destabilize the plasma, but the magnetic buoyancy instability could occur. For a high Mach number (M S ), high Alfvén Mach number (M A ) system with M S M A տR/a (R/a is the aspect ratio͒, the Parker instability is unstable for long axial wavelength modes. Implications for the centrifugal confinement approach to magnetic fusion are also discussed.

Physics of Plasmas, 2013

Magnetic reconnection mediated by the hyper-resistive plasmoid instability is studied with both l... more Magnetic reconnection mediated by the hyper-resistive plasmoid instability is studied with both linear analysis and nonlinear simulations. The linear growth rate is found to scale as S 1/6 H with respect to the hyper-resistive Lundquist number S H ≡ L 3 V A /η H , where L is the system size, V A is the Alfvén velocity, and η H is the hyper-resistivity. In the nonlinear regime, reconnection rate becomes nearly independent of S H , the number of plasmoids scales as S * yiminh@princeton.edu

Physics of Plasmas, 2012

The effects of the initial upstream plasma b on the plasmoid instability are studied via twodimen... more The effects of the initial upstream plasma b on the plasmoid instability are studied via twodimensional resistive magnetohydrodynamic simulations. For cases with nonuniform b dependent initial plasma mass density and uniform temperature, our numerical results indicate that the critical Lundquist number for onset of the plasmoid instability depends on the initial plasma b. The critical Lundquist number is approximately 2000 À 3000 for b ¼ 50 and is 8000 À 10 000 for b ¼ 0:2. The higher the b, the smaller the critical Lundquist number is. Similar to previous studies of high-b systems, the average reconnection rate in low b systems is found to become weakly dependent on the Lundquist number in the plasmoid-unstable regime. However, the average reconnection rate, normalized to the asymptotic value of upstream BV A , is lower in a low b system than that in a high b system. The magnetic energy spectral index, which characterizes fragmentation of the reconnection layer, is approximately two and is insensitive to b in the high-Lunquist number regime. It is also found that the magnetic reconnection rate becomes similar for different b cases, if the initial forcebalance is provided by temperature gradient instead of density gradient. Therefore, it is concluded that the b-dependence mentioned above may be largely attributed to the density variation. V C 2012 American Institute of Physics. [http://dx.

Physics of Plasmas, 2013

ABSTRACT The results from guide field studies on the Magnetic Reconnection Experiment (MRX) are c... more ABSTRACT The results from guide field studies on the Magnetic Reconnection Experiment (MRX) are compared with results from Hall magnetohydrodynamic (HMHD) reconnection simulation with guide field. The quadrupole field, a signature of two-fluid reconnection at zero guide field, is modified by the presence of a finite guide field in a manner consistent with HMHD simulation. The modified Hall current profile contains reduced electron flows in the reconnection plane, which quantitatively explains the observed reduction of the reconnection rate. The present results are consistent with the hypothesis that the local reconnection dynamics is dominated by Hall effects in the collisionless regime of the MRX plasmas. While very good agreement is seen between experiment and simulations, we note that an important global feature of the experiments, a compression of the guide field by the reconnecting plasma, is not represented in the simulations. V C 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4805244]

Physics of Plasmas, 2013

Our understanding of magnetic reconnection in resistive magnetohydrodynamics has gone through a f... more Our understanding of magnetic reconnection in resistive magnetohydrodynamics has gone through a fundamental change in recent years. The conventional wisdom is that magnetic reconnection mediated by resistivity is slow in laminar high Lundquist (S) plasmas, constrained by the scaling of the reconnection rate predicted by Sweet-Parker theory. However, recent studies have shown that when S exceeds a critical value 104,theSweet−Parkercurrentsheetisunstabletoasuper−Alfvenicplasmoidinstability,withalineargrowthratethatscalesasS1=4.Inthefullydevelopedstatisticalsteadystateoftwo−dimensionalresistivemagnetohydrodynamicsimulations,thenormalizedaveragereconnectionrateisapproximately0.01,nearlyindependentofS,andthedistributionfunctionfðwÞofplasmoidmagneticfluxwfollowsapowerlawfðwÞ10 4 , the Sweet-Parker current sheet is unstable to a super-Alfv enic plasmoid instability, with a linear growth rate that scales as S 1=4 . In the fully developed statistical steady state of two-dimensional resistive magnetohydrodynamic simulations, the normalized average reconnection rate is approximately 0.01, nearly independent of S, and the distribution function f ðwÞ of plasmoid magnetic flux w follows a power law f ðwÞ 104,theSweet−Parkercurrentsheetisunstabletoasuper−Alfvenicplasmoidinstability,withalineargrowthratethatscalesasS1=4.Inthefullydevelopedstatisticalsteadystateoftwo−dimensionalresistivemagnetohydrodynamicsimulations,thenormalizedaveragereconnectionrateisapproximately0.01,nearlyindependentofS,andthedistributionfunctionfðwÞofplasmoidmagneticfluxwfollowsapowerlawfðwÞ w À1 . When Hall effects are included, the plasmoid instability may trigger onset of Hall reconnection even when the conventional criterion for onset is not satisfied. The rich variety of possible reconnection dynamics is organized in the framework of a phase diagram. V C 2013 AIP Publishing LLC. [http://dx.