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DOE OSTI2019

Plasmoid instability in the semi-collisional regime

We investigate analytically and numerically the semi-collisional regime of the plasmoid instability, defined by the inequality δSP ≫ ρs ≫ δin, where δSP is the width of a Sweet-Parker current sheet, ρs is the ion sound Larmor radius, and δin is width of boundary layer that arises in the plasmoid instability analysis. Theoretically, this regime is predicted to exist if the Lundquist number S and the length of the current sheet L are such that (L/ρs ) 14/9 < S < (L/ρs ) 2 (for a sinusoidal-like magnetic configuration; for a Harris-type sheet the lower bound is replaced with (L/ρs ) 8/5 ). These bounds are validated numerically by means of simulations using a reduced gyrokinetic model (Zocco & Schekochihin, Physics of Plasmas 18, 2011) conducted with the code Viriato. Importantly, this regime is conjectured to allow for plasmoid formation at relatively low, experimentally accessible, values of the Lundquist number. Our simulations obtain plasmoid instability at values of S as low as ∼ 250. The simulations do not prescribe a Sweet-Parker sheet; rather, one is formed self-consistenly during the nonlinear evolution of the initial tearing mode configuration. This proves that this regime of the plasmoid instability is realizable, at least at the relatively low values of the Lundquist number that are accessible to current dedicated experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1990

Expanding force-free magnetized plasmoid

Some properties of a plasmoid in which magnetic field dominates are discussed. Linear expansion, which have been proposed, provides a simple model describing slow and topologically self-similar expansion of a low-beta plasmoid. An initially force-free magnetized plasmoid expanding linearly may evolve toward consecutive force-free states. The magnetic field energy of such an expansion is studied by applying the virial equation. The result indicates that the decrease of the magnetic energy of the plasmoid is exactly equal to work done expelling its external pressure. This means that there is no residue of magnetic energy if a force-free magnetized plasmoid expands linearly.

Yang, W.-H.↗

NASA NTRS1991

Three-dimensional kinematic reconnection of plasmoids

The kinematic reconnection model of Lau and Finn (1990) is applied in a theoretical investigation of three-dimensional plasmoid morphology, as seen in the solar corona and earth magnetotail. The derivation of the governing equations is outlined; long, short, and periodic plasmoid models are developed; and the evolution of the stable and unstable manifolds in these models is presented graphically. It is inferred that sheet currents and tangential discontinuities can form on surfaces topologically identical to those where Delta(phi) about equal to Delta(z) singularities occur in the kinematic reconnection model, and can be broadened in a similar way by nonideal effects. Two such surfaces exist in long plasmoids, and also in short plasmoids in the presence of finite resistivity; the intertwined surfaces characteristic of the periodic plasmoid form a fractal set but merge in the presence of finite resistivity, producing structures similar to those proposed by the sheet-current theory of Parker (1983).

Lau, Yun-Tung↗

NASA NTRS1992

On the formation and evolution of plasmoids - A survey of ISEE 3 Geotail data

The magnetic and plasma properties of plasmoids, their evolution with distance downtail, and the effect of the direction of the IMF on the plasmoid magnetic configuration were investigated by examining the ISEE 3 magnetometer and electron plasma measurements of the 1983 ISEE 3 Geotail Mission. Both data sets were systematically examined for the presence of bipolar magnetic signatures that occur while ISEE 3 was in the plasma sheet. Results revealed 366 events consistent with this signature while ISEE was in the plasma sheet. It was found that plasmoids are characterized by high-speed plasma flow and that many of them have a well-defined magnetic core field characterized by a field strength maximum at the center of the pass through the structure. Once completely formed, plasmoids are relatively stable. It was found that the size, velocity, magnetic core strength, and Bz field amplitude of plasmoids do not depend on the distance downtail beyond -100 R(E).

Moldwin, Mark B.↗

NASA NTRS1994

Evolution of the plasmoid-lobe interaction with downtail distance

This study examines the interaction between plasmoids moving anti-sunward at high speeds and the tail lobes which bound them to the north and south. Attention is focused on the influence of changing lobe conditions with downtail distance. It is shown using International Sun Earth Explorer 3 (ISEE 3) measurements that the gradual filling of the lobes with mantle plasma and the decrease in magnetic field intensity reduces the average lobe MHD fast mode speed from 1200 km/s at X = -80 R(sub E) to 400 km/s at X = -220 R(sub E). This results in the ratio of the plasmoid speed to the fast mode speed increasing with downtail distance, from 0.3 at X = -80 R(sub E) to approx. 1 at X = -220 R(sub E). It is argued that the 'standard' traveling compression region (TCR) signature observed closer to the Earth will be distorted at large distances, where the fast mode transit time between the plasmoid and magnetopause becomes long compared to the time for the plasmoid to move past a given point in the tail. This change in the nature of the plasmoid-lobe interaction with downtail distance is offered as an explanation for why the reported rate of TCR occurrence peaks at X = -60 to -130 R(sub E) and decreases in the more distant fail.

Slavin, J. A.↗

NASA NTRS1995

Plasmoid formation and evolution in a numerical simulation of a substorm

Plasmoids are thought to occur as a consequence of the formation of a near-Earth neutral line during the evolution of a geomagnetic substorm. Using a 3D, global MHD simulation of the interaction of the Earth's magnetosphere with the solar wind, we initiate a substorm by a southward turning of the Interplanetary Magnetic Field (IMF) after a long period of steady northward field. A large plasmoid is formed and ejected. We show field line maps of its shape and relate its formation time to the progress of the substorm as indicated by the cross polar potential. Because of the large region of closed field in the magnetotail at the time of the substorm, this plasmoid is longer in axial dimension than is typically observed. We compare the simulation results with the type of satellite observations which have been used to argue for the existence of plasmoids or of traveling compression regions (TCRs) in the lobes or magnetosheath. The simulation predicts that plasmoid passage would result in a strong signal in the cross tail electric field.

Slinker, S. P.↗

NASA NTRS2004

Magnetic and Langmuir Probe Measurements on the Plasmoid Thruster Experiment (PTX)

The Plasmoid Thruster Experiment (PTX) operates by inductively producing plasmoids in a conical theta-pinch coil and ejecting them at high velocity. A plasmoid is a plasma with an imbedded closed magnetic field structure. The shape and magnetic field structure of the translating plasmoids have been measured with of an array of magnetic field probes. Six sets of two B-dot probes were constructed for measuring B(sub z) and B(sub theta), the axial and azimuthal components of the magnetic field. The probes are wound on a square G10 form, and have an average (calibrated) NA of 9.37 x l0(exp -5) square meters, where N is the number of turns and A is the cross-sectional area. The probes were calibrated with a Helmholtz coil, driven by a high-voltage pulser to measure NA, and by a signal generator to determine the probe's frequency response. The plasmoid electron number density n(sub e) electron temperature T(sub e), and velocity ratio v/c(sub m), (where v is the bulk plasma flow velocity and c(sub m), is the ion thermal speed) have also been measured with a quadruple Langmuir probe. The Langmuir probe tips are 10 mm long, 20-mil diameter stainless steel wire, housed in a 6-inch long 4-bore aluminum rod. Measurements on PTX with argon and hydrogen from the magnetic field probes and quadruple Langmuir probe will be presented in this paper.

Koelfgen, Syri J.↗

NASA NTRS2009

Characterization of a Plasmoid in the Afterglow of a Supersonic Flowing Microwave Discharge

We performed a detailed characterization a plasmoid in the afterglow region of an Ar supersonic microwave cavity discharge. The supersonic flow was generated using a convergent-divergent nozzle upstream of the discharge region. A cylindrical cavity was used to sustain a discharge in the pressure range of 100-600 Pa. Optical emission spectroscopy was used to observe populations of excited and ionic species in the plasmoid region. Plasmoid formation in the supersonic flowing afterglow located downstream from the primary microwave cavity discharge was characterized by measuring the radial and axial distributions of Argon excited states and Argon ions. More experiments are being carried out on the plasmoid to understand the discharge parameters within the region, i.e. rotational temperature, vibrational temperature, electron density, and how the electrodynamic and aerodynamic effects combine to form this plasmoid.

Drake, D. J.↗

DOE OSTI2013

Magnetic reconnection mediated by hyper-resistive plasmoid instability

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{sub H}{sup 1/6} with respect to the hyper-resistive Lundquist number S{sub H}≡L{sup 3}V{sub A}/η{sub H}, where L is the system size, V{sub A} is the Alfvén velocity, and η{sub H} is the hyper-resistivity. In the nonlinear regime, reconnection rate becomes nearly independent of S{sub H}, the number of plasmoids scales as S{sub H}{sup 1/2}, and the secondary current sheet length and width both scale as S{sub H}{sup −1/2}. These scalings are consistent with a heuristic argument assuming secondary current sheets are close to marginal stability. The distribution of plasmoids as a function of the enclosed flux ψ is found to obey a ψ{sup −1} power law over an extended range, followed by a rapid fall off for large plasmoids. These results are compared with those from resistive magnetohydrodynamic studies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2015

Optical diagnostic and electrical analysis in dusty RF discharges containing plasmoids

The presence of hydrogenated carbon nitride a-CN{sub x}:H particles confined in an argon dusty discharge induces the appearance of instabilities. Those instabilities, also called plasmoids, are luminous regions which move through the plasma and rotate around the biased electrode circumference. Electrical characteristics of the plasma have been used to evidence the presence of dust particles and to demonstrate that plasmoid appearance is triggered by particles. The light emitted by the plasma is analysed by optical emission spectroscopy. This paper presents the spatial distribution of excited species, such as CN, Ar I… between electrodes both inside plasmoids and in the surrounding dusty plasma. Obtained results allow to get information for the electron energy distribution function. Moreover, the interplay between plasmoid behaviour and particle presence in the plasma is shown.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

FAST MAGNETIC RECONNECTION IN THE SOLAR CHROMOSPHERE MEDIATED BY THE PLASMOID INSTABILITY

Magnetic reconnection in the partially ionized solar chromosphere is studied in 2.5 dimensional magnetohydrodynamic simulations including radiative cooling and ambipolar diffusion. A Harris current sheet with and without a guide field is considered. Characteristic values of the parameters in the middle chromosphere imply a high magnetic Reynolds number of ∼10{sup 6}-10{sup 7} in the present simulations. Fast magnetic reconnection then develops as a consequence of the plasmoid instability without the need to invoke anomalous resistivity enhancements. Multiple levels of the instability are followed as it cascades to smaller scales, which approach the ion inertial length. The reconnection rate, normalized to the asymptotic values of magnetic field and Alfvén velocity in the inflow region, reaches values in the range ∼0.01-0.03 throughout the cascading plasmoid formation and for zero as well as for strong guide field. The outflow velocity reaches ≈40 km s{sup –1}. Slow-mode shocks extend from the X-points, heating the plasmoids up to ∼8 × 10{sup 4} K. In the case of zero guide field, the inclusion of both ambipolar diffusion and radiative cooling causes a rapid thinning of the current sheet (down to ∼30 m) and early formation of secondary islands. Both of these processes have very little effect on the plasmoid instability for a strong guide field. The reconnection rates, temperature enhancements, and upward outflow velocities from the vertical current sheet correspond well to their characteristic values in chromospheric jets.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Thermal quench induced by a composite pellet-produced plasmoid

Injecting shattered pellets is the critical concept of the envisaged ITER disruption mitigation system (DMS). Rapid deposition of large amounts of material should presumably result in controlled cooling of the entire plasma. A considerable transfer of thermal energy from the electrons of the background plasma to the ions accompanies a localized material injection due to the ambipolar expansion along the magnetic field line of the cold and dense plasmoid produced by the ablated pellet. Radiation initially plays the dominant role in the energy balance of a composite plasmoid containing high-Z impurities. A competition between the ambipolar expansion and the radiative losses defines the Thermal Quench scenario, including the amount of pre-quench thermal energy radiated on a short collisional timescale—possibly detrimental for the plasma-facing components. The present work quantifies plasmoid energy balance for disruption mitigation parameters. For pure hydrogen injection, up to 90% of the pre-pellet electron thermal energy may go to the newly injected ions. We also demonstrate that a moderate high-Z impurity content within the plasmoid can reduce highly localized radiation at the beginning of the expansion. The thermal energy will then dissipate on the much longer ion collisional timescale, which would be attractive for ITER DMS.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2018

Aneutronic Fusion in Collision of Oppositely Directed Plasmoids

Tri-Alpha and Helion energy companies have proposed an approach as the near future fusion reactor. The method used in this kind of reactor for attaining high fusion yield is based on the formation and throwing of two plasmoids toward each other. In this study, the optimized reaction rate for interpenetration of two head on colliding plasmoids is investigated. Calculations are performed by supposing the velocity of plasmoids ions as Maxwellian distribution function. Fusion output-to-input power ratio (Q factor) was computed by evaluation of the velocity-averaged cross sections and also ion−electron and ion−ion Coulomb power loss. A fluid model including a computational code has been used for the precise calculations of fusion power balance. The optimum interpenetration velocity and plasmoids parameters required to reach the ignition are studied for aneutronic fusion fuels, such as p–{sup 11}B and D–{sup 3}He, as well as D−T and D−D fuels. The results of investigation show that the breakeven is attainable in specific collision velocity and plasma temperature for each fuel. Also, the plasma density has to be around 10{sup 20} ions/cm{sup 3}.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2017

The First ALMA Observation of a Solar Plasmoid Ejection from an X-Ray Bright Point

Eruptive phenomena such as plasmoid ejections or jets are important features of solar activity and have the potential to improve our understanding of the dynamics of the solar atmosphere. Such ejections are often thought to be signatures of the outflows expected in regions of fast magnetic reconnection. The 304 Å EUV line of helium, formed at around 10{sup 5} K, is found to be a reliable tracer of such phenomena, but the determination of physical parameters from such observations is not straightforward. We have observed a plasmoid ejection from an X-ray bright point simultaneously at millimeter wavelengths with ALMA, at EUV wavelengths with SDO /AIA, and in soft X-rays with Hinode /XRT. This paper reports the physical parameters of the plasmoid obtained by combining the radio, EUV, and X-ray data. As a result, we conclude that the plasmoid can consist either of (approximately) isothermal ∼10{sup 5} K plasma that is optically thin at 100 GHz, or a ∼10{sup 4} K core with a hot envelope. The analysis demonstrates the value of the additional temperature and density constraints that ALMA provides, and future science observations with ALMA will be able to match the spatial resolution of space-borne and other high-resolution telescopes.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Guide field effects on the distribution of plasmoids in multiple scale reconnection

The effects of a finite guide field on the distribution of plasmoids in high-Lundquist-number current sheets undergoing magnetic reconnection in large plasmas are investigated with statistical models. Merging of plasmoids is taken into account either assuming that guide field flux is conserved resulting in nonforce-free profiles in general, or that magnetic helicity is conserved and Taylor relaxation occurs to convert part of the summed guide field flux into reconnecting field flux toward minimum energy states resulting in force-free profiles. It is found that the plasmoid distribution in terms of reconnecting field flux follows a power law with index 7/4 or 1 depending on whether merger frequencies are independent of or dependent on their relative velocity to the outflow speed, respectively. This result is approximately the same for the force-free and nonforce-free models, with nonforce-free models exhibiting indices of 2 and 1 for the same velocity dependencies. Distributions in terms of guide field flux yield indices of 3/2 for the nonforce-free model regardless of velocity dependence. This is notably distinct from the indices of 11/8 and 1 for the force-free models independent of and dependent on velocity, respectively. At low guide field fluxes, the force-free models exhibit a second power law index of 1/2 due to nonconstant flux growth rates. The velocity-dependent force-free model predicts the production of slightly more rapidly moving large guide field flux plasmoids which are supported by observational evidence of flux ropes with strong core fields. Implications are discussed on particle acceleration via Fermi processes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

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 magnetohydrodynamics (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↗

DOE OSTI2019

Relativistic resistive magnetohydrodynamic reconnection and plasmoid formation in merging flux tubes

Herein we apply the general relativistic resistive magnetohydrodynamics code BHAC to perform a 2D study of the formation and evolution of a reconnection layer in between two merging magnetic flux tubes in Minkowski space–time. Small-scale effects in the regime of low resistivity most relevant for dilute astrophysical plasmas are resolved with very high accuracy due to the extreme resolutions obtained with adaptive mesh refinement. Numerical convergence in the highly non-linear plasmoid-dominated regime is confirmed for a sweep of resolutions. We employ both uniform resistivity and non-uniform resistivity based on the local, instantaneous current density. For uniform resistivity we find Sweet–Parker reconnection, from $η$ = 10-2 down to $η$ = 10 -4 , for a reference case of magnetization $σ$ = 3.33 and plasma-$β$ = 0.1. For uniform resistivity $η$ = 5 × 10 -5 the tearing mode is recovered, resulting in the formation of secondary plasmoids. The plasmoid instability enhances the reconnection rate to $v_{rec}$ ~ 0.03$c$ compared to $v_{rec}$ ~ 0.01$c$ for $η$ = 10 -4 . For non-uniform resistivity with a base level $η_0$ = 10 -4 and an enhanced current-dependent resistivity in the current sheet, we find an increased reconnection rate of $v_{rec}$ ~ 0.1$c$. The influence of the magnetization $σ$ and the plasma-$β$ is analysed for cases with uniform resistivity $η$ = 5 × 10 -5 and $η$ = 10 -4 in a range 0.5 ≤ $σ$ ≤ 10 and 0.01 ≤ $β$ ≤ 1 in regimes that are applicable for black hole accretion discs and jets. The plasmoid instability is triggered for Lundquist numbers larger than a critical value of $S_c$ ≈ 8000.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2017

Plasmoid Instability in Forming Current Sheets

The plasmoid instability has revolutionized our understanding of magnetic reconnection in astrophysical environments. By preventing the formation of highly elongated reconnection layers, it is crucial in enabling the rapid energy conversion rates that are characteristic of many astrophysical phenomena. Most previous studies have focused on Sweet–Parker current sheets, which are unattainable in typical astrophysical systems. Here we derive a general set of scaling laws for the plasmoid instability in resistive and visco-resistive current sheets that evolve over time. Our method relies on a principle of least time that enables us to determine the properties of the reconnecting current sheet (aspect ratio and elapsed time) and the plasmoid instability (growth rate, wavenumber, inner layer width) at the end of the linear phase. After this phase the reconnecting current sheet is disrupted and fast reconnection can occur. The scaling laws of the plasmoid instability are not simple power laws, and they depend on the Lundquist number (S), the magnetic Prandtl number (P m ), the noise of the system (${\psi }_{0}$), the characteristic rate of current sheet evolution ($1/\tau $), and the thinning process. We also demonstrate that previous scalings are inapplicable to the vast majority of astrophysical systems. Furthermore, we explore the implications of the new scaling relations in astrophysical systems such as the solar corona and the interstellar medium. In both of these systems, we show that our scaling laws yield values for the growth rate, wavenumber, and aspect ratio that are much smaller than the Sweet–Parker–based scalings.

Sun: flares↗