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The magnetic switchbacks observed recently by the Parker Solar Probe have raised the question about their nature and origin. One of the competing theories of their origin is the interchange reconnection in the solar corona. In this scenario, switchbacks are generated at the reconnection site between open and closed magnetic fields, and are either advected by an upflow or propagate as waves into the solar wind. In this paper we test the wave hypothesis, numerically modeling the propagation of a switchback, modeled as an embedded Alfvén wave packet of constant magnetic field magnitude, through the gravitationally stratified solar corona with different degrees of background magnetic field expansion. While switchbacks propagating in a uniform medium with no gravity are relatively stable, as reported previously, we find that gravitational stratification together with the expansion of the magnetic field act in multiple ways to deform the switchbacks. These include WKB effects, which depend on the degree of magnetic field expansion, and also finite-amplitude effects, such as the symmetry breaking between nonlinear advection and the Lorentz force. In a straight or radially expanding magnetic field the propagating switchbacks unfold into waves that cause minimal magnetic field deflections, while a super-radially expanding magnetic field aids in maintaining strong deflections. Other important effects are the mass uplift the propagating switchbacks induce and the reconnection and drainage of plasmoids contained within the switchbacks. In the Appendix, we examine a series of setups with different switchback configurations and parameters, which broaden the scope of our study. © 2021. The American Astronomical Society. All rights reserved., N.M. was supported by a Newton International Fellowship of the Royal Society. D.U. is thankful for the support received through FWF project P27800. This research has received financial support from the European Unions Horizon 2020 research and innovation program under grant agreement No. 824135 (SOLARNET) enabling D.U. a visit to Sheffield University. R.E. is grateful to Science and Technology Facilities Council (STFC, grant number ST/M000826/1) UK and the Royal Society for enabling this research. R.E. also acknowledges the support received by the CAS Presidents International Fellowship Initiative grant No. 2019VMA052 and the warm hospitality received at USTC of CAS, Hefei, where part of the contribution was made. V.M.N. acknowledges the STFC consolidated grant ST/T000252/1 and the BK21 plus program through the National Research Foundation funded by the Ministry of Education of Korea.In order to keep the main body of this paper more transparent, simulations with different switchback parameters and conditions are presented in this Appendix. These additional simulations are carried out in a nonexpanding uniform magnetic field. The results strengthen our conclusions on the property of switchbacks propagating through a gravitationally stratified corona, namely the significant deformations these undergo, and still display the other effects described in Section 3. With funding from the Spanish government through the Severo Ochoa Centre of Excellence accreditation SEV-2017-0709.

The nonlinear resistive-kink mode in the low resistivity plasma in tokamak is investigated through the three-dimensional, toroidal, and nonlinear Hall-MHD code CLT. It is found that, without the two-fluid effect and the toroidal flow, the system can evolve into a steady-state with the saturated main m/n = 1/1 magnetic island and the co-existing large secondary island. The main m/n = 1/1 magnetic island cannot push the hot core plasma out of the q = 1 surface as it does in Kadomstev’s model, and the reconnection is incomplete. However, with the two-fluid effect or the toroidal flow, the nonlinear behaviors of the resistive-kink mode could be essentially different. The two-fluid effect and the toroidal flow can break the symmetry during the plasmoid formation, which destroys the balance between the main m/n = 1/1 magnetic island and the large secondary island. The large secondary island is then merged into the main m/n = 1/1 island. After that, the main m/n = 1/1 island finally occupies the whole mix region, and all magnetic flux in the mix region is reconnected. A similar simulation study has been done in periodic cylindrical geometry (Günter et al 2015 Plasma Phys. Control. Fusion 57 014017), while our work is done in tokamak toroidal geometry. The toroidal effect has also been investigated, and we find that the widths of the main 1/1 island and the secondary island slightly increase with increasing aspect ratios.

Cryogenic pellet injection is an important means of refuelling and terminating fusion plasmas, with fuel pellets exhibiting a range of phenomena beneficial to confinement and the energy balance between ions and electrons. In this investigation we consider the self-similar expansion along magnetic field lines of the plasmoid produced by a small pellet. In particular, we consider the case when the expansion timescale is comparable to the time taken for the pellet gas cloud to cross a field line. It is shown that plasmoid ions acquire a significant fraction of the energy that is transferred to plasmoid electrons via collisions with the ambient plasma. It is found that the expansion is insensitive to the profile of the gas cloud and details of the ionisation of the gas—the plasma flux emerging from the gas cloud is the only quantity that affects the expansion.

Experimental results on registration of different radiations from a heterogeneous plasmoid (HP) created by pulsed-repetitive discharge in the experimental set up PVR are considered in this work. Intensive cold neutron flux, optical radiation and soft X-radiation (Ed>3.8 kV in the electric discharge for stable generation of intensive cold neutron flux.

Using a small (450 J) Mather-type plasma focus device, this research investigates the effects of cathode rod removal from the cathode array in two steps on hard x-ray emission, both in total and specifically from the plasmoid. The effect on anode rod erosion is also measured. Six hard x-ray detectors were placed around the chamber to measure the emitted hard x-rays. By reducing the number of cathode rods, some features of these hard x-rays such as peak intensity and pulse yield decreased and were deteriorated. Besides, the capability of the device for producing and reproducing the hard x-rays with roughly similar and repeatable characteristics diminished. Moreover, the anode erosion took place during the breakdown phase and by using the detectors around the chamber, similar features were obtained both for the total and the plasmoid hard x-rays, but with different scales. The cathode rod removal could violate the symmetry and uniform formation of the current sheath layer during the breakdown phase and could weaken and change the direction of the Lorentz force vector acting on the current sheath layer during the axial phase. It also causes discharge delay and decreases the axial and radial velocities of the current sheath layer which would result in a weak pinch effect and reduced number of energetic runaway electrons inside the plasma column during the pinch phase. These electrons, by colliding the anode surface, are mainly responsible for producing the great portion of the emitted hard x-ray. On the contrary and based on a different mechanism, the cathode rod removal enhances the number of the runaway electrons during the breakdown phase which increases the anode erosion and enhances the impurities that eventually leads to a weak emission of low intensity hard x-rays.

This review summarizes new trends in studies of magnetic reconnection in solar flares. It is shown that plasmoids play a very important role in this primary flare process. Using the results of magnetohydrodynamic and particle-in-cell simulations, we describe how the plasmoids are formed, how they move and interact, and how a flare current sheet is fragmented into a cascade of plasmoids. Furthermore, it is shown that during the interactions of these plasmoids electrons are not only very efficiently accelerated and heated, but electromagnetic (radio) emission is also produced. We also describe possible mechanisms for the triggering of magnetic reconnection. The relevant X-ray and radio signatures of these processes (such as radio drifting pulsation structures, narrowband dm-spikes, and the loop-top and above-the-loop-top X-ray sources) are then described. It is shown that plasmoids can also be formed in kinked magnetic ropes. A mapping of X-points of the magnetic reconnection on the chromosphere (as e.g. a splitting of flare ribbons) is mentioned. Supporting EUV and white-light observations of plasmoids are added. The significance of all these processes for the fast magnetic reconnection and electron acceleration is outlined. Their role in fusion experiments is briefly mentioned.

The study of the ionized environment in the area surrounding PDFL has showed the presence of visible plasmoids moving in the horizontal plane. The study of traces on the X-ray film made it possible to detect a significant number of traces of an identical shape and size that look like the “birds” which were found earlier in other facilities. A preliminary analysis has been carried out for their identification, which led to a conclusion about the nature of these formations, in particular, their identity with the Dirac monopole (or similar object) having a “tail” and “wings” formed by a flow of electrons from the surroundings.

Collisional merging formation of field-reversed configurations (FRCs) at super Alfvenic velocity have been successfully initiated in the FAT-CM device at Nihon University. It is experimentally evidenced that the quiescent FRC profile is formed in a self-organizational manner after distructive disturbances by the super Alfvenic collision of two translated magnetized plasmoids. A drastic increase of the excluded flux compared to the field-reversed theta-pinch formation section has also been observed. This formation process has an important role in realizing an FRC based high-beta reactor core to capture high-energy beam ions, and it has been clearly observed by magnetic diagnostics of excluded flux and internal probe array. The experimental results are compared with two-dimensional magnetohydrodynamic (MHD) simulation results computed for the typical conditions of the FAT-CM experiments. Collisional merging of the two separately translated FRCs causes a conversion of the kinetic energy to mostly thermal ion energy, which contrasts with the spheromak merging dominated by magnetic energy in an MHD manner, resulting in an increase of the ion pressure and polodal flux that drastically expands the FRC volume.

This work is a continuation of our previous studies [1-10] of physical parameters and properties of a long-lived heterogeneous plasmoid (plasma formation with erosive nanoclusters) created by combined discharge in a high-speed swirl flow. Here interaction of metal nanoclusters with hydrogen atoms is studied in a plasma vortex reactor (PVR) with argon-water steam mixture. Metal nanoclusters were created by nickel cathode's erosion at combined discharge on. Dissociated hydrogen atoms and ions were obtained in water steam by electric discharge. These hydrogen atoms and ions interacted with metal nanoclusters, which resulted in the creation of a stable plasmoid in a swirl gas flow. This plasmoid has been found to create intensive soft X-ray radiation. Plasma parameters of this plasmoid were measured by optical spectroscopy method. It has been obtained that there is a high non-equilibrium plasmoid: Te > TV >> TR. The measured coefficient of energy performance of this plasmoid is about COP = 2÷10. This extra power release in plasmoid is supposed to be connected with internal excited electrons. The obtained experimental results have proved our suggestion.

Gas dynamic modeling approach was applied to "plasmoid" formed in experimental electrical discharge breakdown in a cathode ceramic tube filled by a conductive liquid. Measured parameters were applied to the model in order to improve it. Qualitative agreement observed between behavior of the experimental "plasmoid" and model results. Temperature distribution results also agree with experiment in which temperature of 2000 K was registered.

Carbon clusters with diameters in the range of 10 to 50 nm are produced by injecting pulses of acetylene into an inductively coupled plasma in argon and helium. The injection causes plasma instability, which becomes visible as an oscillation of the emission intensity. The frequency of this oscillation can be uniquely correlated to the particle diameter. Consequently, the measurement of the oscillation frequency represents a method to determine particle diameters in situ. The oscillation corresponds to the rotation of a localized plasmoid and a particle cloud around the symmetry axis of the reactor. It is assumed that this rotation is driven by the ion wind crossing the interface between the plasmoid and the particle cloud.

A single-stage pulsed inductive plasma accelerator is modeled as an inductive mass-driver. The plasma is treated as a rigid slug, which acts as the armature. The system is a transformer, with the drive coil serving as the primary and the slug as the secondary. We derive a set of coupled dynamic-circuit equations, which depend on five dimensionless coefficients, and on the functional form of the mutual inductance profile, M (z). For a given coil geometry, M (z) was determined experimentally and compared to the results of calculations carried out with QuickField. The equations are solved with various coefficient values, in order to determine the conditions that yield high efficiencies. It was found that the coupling efficiency can be quite high and likely scales with power, although this does not preclude operation at lower power with acceptable efficiency. The effect of an imbedded magnetic bias flux, as for the case of a plasmoid thruster, was also included in the calculations.

Central fuelling and pellet enhanced performance modes have been obtained with pellets injected vertically from the high field side on the FTU tokamak. Four phases have been recognized: ablation of the pellets, drifting plasmoids, MHD modes which take the density to the centre of the discharge and finally an anomalous drift which further increases the density peaking. Pellet ablation data have been compared with values from a pellet ablation and deposition code. Comparison between 0.8 and 1.1 MA discharges at a high magnetic field (B-T = 7T) has been carried out: a higher performance has been obtained with the latter due to the higher target density and the larger inversion radius which would increase the effects of m = 1 modes to take the density to the plasma centre.

The field-reversed configuration (FRC) offers an attractive alternative approach to magnetically confined fusion because of its extremely high β, simple linear geometry, and natural divertor for helium ash removal. Multi-hundred eV and high density FRCs have been produced using the standard Field Reversed Theta Pinch (RFTP) method, with a confinement scaling that leads to fusion conditions. These FRCs are, however, limited to only tens of mWb fluxes and sub-msec lifetime. Recent progress has been made in building up the flux and sustaining the FRC current using Rotating Magnetic Fields (RMF) in the Translation, Sustainment, and Confinement (TCS) facility at the University of Washington. TCS has demonstrated formation and steady-state sustainment of standard, flux-confined, prolate FRCs. The RMF also provides stability for the n = 2 rotational mode, which is the dominant global instability observed experimentally. Simple calculations show that a strong radially inward force imposed by the RMF increases proportionally to any local outward deformation of the plasma cross section. Evidence of this has been experimentally demonstrated, and the effects of various RMF antenna geometries studied. High temperature FRCs could also be produced in TCS by translating high energy plasmoids formed in the normal theta pinch manner into the confinement chamber containing the RMF antennas. Extremely interesting results were obtained for this translation and capture process. The plasmoids can survive the violent dynamics of supersonic reflections off magnetic mirror structures, producing a stable high-β, near-FRC state with substantial flux conversion from toroidal to poloidal. This is a tribute not only to the robustness of FRCs, but also to the tendency of an FRC to assume a preferred state for a magnetized plasma. The magnetic helicity, as inferred by a simple interpretive model, is approximately preserved, possibly conforming to a high-β relaxation principle.

We investigate the possibility that the mechanism dynamic trapping can play a role in decoupling dense plasma clouds injected in a thinner ambient plasma, by establishing strong magnetic-field-aligned electric fields in the vicinity or in the edge of the cloud. Dynamic trapping has previously been shown to allow such fields to be established and maintained on the time scale of ion motion, also for arbitrarily low current densities. A model is presented of how such fields could arise and decouple injected plasma clouds, a mechanism which we call dynamic decoupling. A dimensionless parameter, the dynamic decoupling factor FDD, is derived which gives an estimate of the importance of the process. One possible application is the CRRES ionospheric injection experiments where anomalous skidding has recently been reported. However, the dynamic decoupling mechanism might also play a role in naturally occurring situations, e.g. the impulsive penetration of plasmoids from the solar wind into the Earth's magnetosphere.

The propagation of edge localized modes (ELMs) towards the main chamber could lead to potentially serious consequences in ITER (Federici G et al 2001 Nucl. Fusion 41 1967). This effect was studied in JET by examining the interaction of a large sample (>200) of Type-I ELMs with an array of Langmuir probes on the outboard limiter. High clearance discharges were used with a separatrix to wall distance of 8?18?cm. The average ELM duration was measured as ~ 200 ? 50??s, the average radial propagation velocity of the ELM plasmoid in the scrape-off layer as v? ~ 0.45 ? 0.1?km?s?1 or as a fraction of the sound speed, v?/cs ~ 0.2%, and its diffusion coefficient, D?, as 500 ? 100?m2?s?1?a significant increase over inter-ELM levels. The above velocities are in good agreement with the lower (? loss) limit of the sheath-limited model of plasmoid propagation (Krasheninnikov S I 2001 Phys. Lett. A 283 368, Krasheninnikov S I et al 2002 29th EPS Conf. on Controlled Fusion and Plasma Physics (Montreux, Switzerland)).

Injection of cryogenic deuterium pellets has been successfully applied in ASDEX Upgrade for external edge localized mode (ELM) frequency control in type-I ELMy H-mode discharge scenarios. A pellet velocity of 560 m s−1 and a size of about 6 × 1019 D-atoms was selected for technical reasons, although even lower masses were found sufficient to trigger ELMs. A moderate repetition rate close to 20 Hz was chosen to avoid over-fuelling of the core plasma. Pellet sequences of up to 4 s duration were injected into discharges close to the L–H threshold, intrinsically developing large compound ELMs at a rate of 3 Hz. With pellet injection, these large ELMs were completely replaced by smaller type-I ELMs at the much higher pellet frequency, accompanied by a slight increase of density and even of stored energy. This external ELM control could be repeatedly switched on and off by just interrupting the pellet train. ELMs were triggered in less than 200 µs after pellet arrival at the plasma edge, at which time only a fraction of the pellet has been ablated, forming a rather localized, three-dimensional plasmoid, which drives the edge unstable well before the deposited mass is spread toroidally. The pellet controlled case has also been compared with a discharge at a somewhat lower density, but with otherwise rather similar data, developing spontaneous 20 Hz type-I ELMs. Despite the different trigger mechanisms, the general ELM features turn out to be qualitatively similar, possibly because of the similarity of the two cases in terms of ELM relevant parameters. The scaling with background plasma, heating power, pellet launch parameters, etc over a larger range still remains to be investigated.

Start-time of magnetic reconnection under typical interplanetary parameters has been numerically simulated by using the two-dimensional compressible magnetohydrodynamic equations with a third-order compact upwind scheme. Magnetic reconnection would occur near the interplanetary current sheet impacted by a plasmoid. Its initiation is associated with the interplanetary plasma parameter β and the momentum of the plasmoid. The higher the β value is, the faster the reconnection takes place. Meanwhile the reconnection occurs earlier with increasing the plasmoid momentum, and increasing driving velocity is more effective in initializing the reconnection than that of the plasma density when the other factors are kept to be the same. The evolution of the reconnection with the heliocentric distance is also investigated.

The ablated material of a frozen hydrogen isotope pellet which is injected into a hot tokamak plasma forms a high β plasmoid. This diamagnetic plasmoid is accelerated to the magnetic low field side of the torus. The high β plasmoid drift was directly observed by an optical diagnostic with high space and time resolution. Spectroscopic measurements of the emitted light allowed the density and temperature of the ablation cloud, and for the first time also of the drifting plasmoids, to be determined. The experiments give a new insight into the dynamics of the formation of striations during the pellet ablation; these striations cause the separation of the ablated material into a sequence of separated, drifting plasmoids. The influence of the drift on the mass deposition profile for high field side pellet injection is discussed. The plasmoid dynamics even influences the radial pellet motion, most probably owing to a rocket effect. The physical principles of the high β plasmoid drift are discussed and compared with the experimental observations.

The interactions of a compact toroid (CT) plasma with an external magnetic field and a tokamak plasma have been studied experimentally on the FACT and JFT-2M devices. Fast framing camera and soft X ray emission profile measurements indicate shift and/or reflection motions of the CT plasma. New electrostatic probe measurements indicate that the CT plasma reaches at least up to the separatrix for discharges with toroidal field strengths of 1.0-1.4 T and that there exists a trailing plasma behind the CT. A large amplitude fluctuation on the ion saturation current and magnetic coil signals is observed. Power spectrum analysis suggests that this fluctuation is related to magnetic reconnection between the CT plasmoid and the toroidal field. The CT, including much of the trailing plasma, may be able to move across the external magnetic field more easily in the drift region of the injector owing to the Hall effect.

This paper focuses on a single fluid, two-dimensional, axisymmetric, time-dependent, magnetohydrodynamic numerical simulation of the formation and evolution of a coronal streamer in a current sheet. Two types of evolution are described: (a) the disruption of the streamer in a CME and (b) the dissolution of the streamer probably caused by the current sheet dissipation in the solar atmosphere. In the first case, the ejected plasmoid density reaches 21 × 109 cm-3 at 8 solar radii from the Sun; in the second case, the maximum density attained is about 5 × 109 cm-3. The temperature does not exceed 5 × 106 K. These plasma parameters fit well the observations.

The three dimensional dynamics of a spheromak-like compact toroid (SCT) plasmoid, which is injected into a magnetized target plasma region, is investigated by using MHD numerical simulations. It is found that the process of SCT penetration into this region is much more complicated than that which has been analysed so far by using a conducting sphere (CS) model. The injected SCT suffers from a tilting instability, which grows with a similar timescale to that of the SCT penetration. The instability is accompanied by magnetic reconnection between the SCT magnetic field and the target magnetic field, which disrupts the magnetic configuration of the SCT. Magnetic reconnection plays a role in supplying the high density plasma, initially confined in the SCT magnetic field, to the target region. The penetration depth of the SCT high density plasma is also examined. It is shown to be shorter than that estimated from the CS model. The SCT high density plasma is decelerated mainly by the Lorentz force of the target magnetic field, which includes not only the magnetic pressure force but also the magnetic tension force. Furthermore, by comparing the SCT plasmoid injection with the bare plasmoid injection, magnetic reconnection is considered to relax the magnetic tension force, i.e. the deceleration of the SCT plasmoid.

The large-scale dynamic evolution of the magnetotail in relation to substorms is most commonly understood and described in terms of magnetic reconnection, neutral line formation, and plasmoid ejection into the distant tail, as well as current disruption and diversion in the inner tail. Recent magnetohydrodynamic simulations have shown that the two aspects, which are often considered as alternative models, may well be part of one unstable process. We review the most recent update of this model. A new element, which has been strongly emphasized recently by observations as well as simulations, is the formation of a thin current sheet in the inner tail during the late substorm growth phase. This presumably eases the onset of instability, although the actual mechanism has not been clearly identified. The basic concept of a large-scale instability, involving the local breakdown of ideal MHD, has not changed significantly. However, recent MHD simulations as well as test particle investigations have put more emphasis on the role of the near tail region in providing current diversion ("disruption") and particle acceleration.

The most promising concept for deep fuelling a reactor is by the injection of compact toroid (CT) plasmoids. The first results showing CT fuelling of a tokamak plasma, without any adverse perturbation to the tokamak discharge, are reported. The Compact Toroid Fueller (CTF) device was used to inject a CT-spheromak plasmoid into the TdeV tokamak. Following the CT penetration, the tokamak particle inventory increased by 16%, the loop voltage and the plasma current did not change, and there was no increase in magnetohydrodynamic (MHD) activity. The number of injected impurities was low and dominated by non-metallic elements. The plasma diamagnetic energy and the energy confinement time increased by more than 35%

The nonlinear evolution of the m = 0 sausage mode in coronal loops (Gold and Hoyle 1960 Mon. Not. R. Astron. Soc. 120 89) is investigated using numerical simulations. For the ideal line-tied case the growth rate of the linear phase of the instability is successfully reproduced, and it is found that the nonlinear development leads to the formation of a new equilibrium with an embedded, curved, current concentration ( not, however, a current sheet). This new equilibrium is not symmetric about the centre of the loop. For periodic boundary conditions a similar evolution is found, but with the final equilibrium being symmetric in which a straight, radial current concentration (possibly a current sheet) is embedded. In the line-tied resistive case the field lines reconnect, leading to the ejection of a plasmoid and relaxation to a (different) equilibrium.

The computer ab initio simulation and analytical theory, that revealed unexpected non-ergodic properties of a classical Coulomb plasma, is overviewed. The results of a many-charged-particles system simulation predict the possible existence of a real metastable plasma, supercooled with respect to its ionization degree. The three-body recombination at this state is suppressed. The existence of such a plasma state is a consequence of the entropy conservation in isolated Hamiltonian systems free from any stochastic action from the outside (external stochastic disturbance). The occurrence of a metastable supercooled plasma (rather similar to a supercooled vapor or superheated liquid) depends on two conditions: First, all the charged particles should behave exactly according to the laws of classical mechanics (hence, most negatively-charged particles should preferably be heavy ions). Second, the plasma ionization degree should be sufficiently high (> 10−3). It is shown from thermodynamic consideration that a mixture of supercooled plasma with a perfect (ideal) gas might form a plasmoid of the ball-lightning type.

The proposed scheme is based on a moving grating of plasmoids in 3-dimensional HF potential wells (RF traps) which are formed by a two-frequency laser field of cylindrical waves with high indices. The accelerating field of slow waves is excited in this grating by means of a similar additional 2-frequency field. Analytical and computational studies of plasmoid dynamics show that this combined scheme can increase the acceleration rate by a factor ~?2?a??1 (doubled Lorentz factor of the grating) with respect to the case of acceleration through the motionless plasmoids grating. For instance, it can provide the rate ~?1?MV/? instead of ~?100?kV/?, ? being the laser wavelength. Focusing properties of the plasmoids grating are discussed.

A large-volume flux closure during transient coaxial helicity injection (CHI) in NSTX-U is demonstrated through resistive magnetohydrodynamics (MHD) simulations. Several major improvements, including the improved positioning of the divertor poloidal field coils, are projected to improve the CHI start-up phase in NSTX-U. Simulations in the NSTX-U configuration with constant in time coil currents show that with strong flux shaping the injected open field lines (injector flux) rapidly reconnect and form large volume of closed flux surfaces. This is achieved by driving parallel current in the injector flux coil and oppositely directed currents in the flux shaping coils to form a narrow injector flux footprint and push the injector flux into the vessel. As the helicity and plasma are injected into the device, the oppositely directed field lines in the injector region are forced to reconnect through a local Sweet–Parker type reconnection, or to spontaneously reconnect when the elongated current sheet becomes MHD unstable to form plasmoids. In these simulations for the first time, it is found that the closed flux is over 70% of the initial injector flux used to initiate the discharge. These results could work well for the application of transient CHI in devices that employ super conducting coils to generate and sustain the plasma equilibrium.

In this paper, a description is provided of the evolution of the dense spherical-like structures—plasmoids—formed in the pinched column of the dense plasma focus at the current of 1 MA at the final phase of implosion of the deuterium plasma sheath and at the phase of evolution of instabilities both at the time of HXR and neutron production. At the stratification of the plasma column, the plasma injected to the dense structures from the axially neighboring regions forms small turbulences which increase first the toroidal structures, and finally generates a non-chaotic current plasmoidal structure with central maximal density. This spontaneous evolution supports the hypothesis of the spheromak-like model of the plasmoid and its sub-millimeter analogy, high-energy spot. These spots, also called nodules formed in the filamentary structure of the current can be a source of the energy capable of accelerating the fast charged particles.

During pellet injection in the TORE SUPRA tokamak, two distinct phases of electron temperature response, a gradual decrease phase followed by a sudden drop phase, have been observed by means of a fast acquisition ECE Fabry-Perot interferometer system. The time delay of the temperature drop between the plasma edge and centre is less than 20 mu s, corresponding to a propagation velocity of the order of 25 km/s, much larger than both the pellet velocity and the ordinary diffusion velocity. A neutral atom diffusion model, together with a modified plasmoid ablatant description, is proposed to explain such phenomena

Considerations are given in favour of two schemes of laser acceleration. The first scheme uses onward-moving radio-wells carrying charged or neutral accelerated plasmoids in a converging guide. The second scheme uses plasmoids grating in radio-wells in a special resonant cavity. Forced oscillations of plasmoids subjected to some additional field give rise to slow e.m. waves which are capable of accelerating charged particles.

(abridged) Magnetic reconnection is the topological reconfiguration of the magnetic field in a plasma, accompanied by the violent release of energy and particle acceleration. Reconnection is as ubiquitous as plasmas themselves, with solar flares perhaps the most popular example. Over the last few years, the theoretical understanding of magnetic reconnection in large-scale fluid systems has undergone a major paradigm shift. The steady-state model of reconnection described by the famous Sweet-Parker (SP) theory, which dominated the field for ~50 years, has been replaced with an essentially time-dependent, bursty picture of the reconnection layer, dominated by the continuous formation and ejection of multiple secondary islands (plasmoids). Whereas in the SP model reconnection was predicted to be slow, a major implication of this new paradigm is that reconnection in fluid systems is fast (i.e., independent of the Lundquist number), provided that the system is large enough. This conceptual shift hinges on the realization that SP-like current layers are violently unstable to the plasmoid instability - implying, therefore, that such current sheets are super-critically unstable and thus can never form in the first place. This suggests that the formation of a current sheet and the subsequent reconnection process cannot be decoupled, as is commonly assumed. This paper provides an introductory-level overview of the recent developments in reconnection theory and simulations that led to this essentially new framework. We briefly discuss the role played by the plasmoid instability in selected applications, and describe some of the outstanding challenges that remain at the frontier of this subject. Amongst these are the analytical and numerical extension of the plasmoid instability to (i) 3D and (ii) non-MHD regimes. New results are reported in both cases.

As a consequence of the evolutionary conditions [28; 29], shock waves can generate high levels of downstream vortical turbulence. Simulations [32-34] and observations [30; 31] support the idea that downstream magnetic islands (also called plasmoids or flux ropes) result from the interaction of shocks with upstream turbulence. Zank et al. [18] speculated that a combination of diffusive shock acceleration (DSA) and downstream reconnection-related effects associated with the dynamical evolution of a "sea of magnetic islands" would result in the energization of charged particles. Here, we utilize the transport theory [18; 19] for charged particles propagating diffusively in a turbulent region filled with contracting and reconnecting plasmoids and small-scale current sheets to investigate a combined DSA and downstream multiple magnetic island charged particle acceleration mechanism. We consider separately the effects of the anti-reconnection electric field that is a consequence of magnetic island merging [17], and magnetic island contraction [14]. For the merging plasmoid reconnection- induced electric field only, we find i) that the particle spectrum is a power law in particle speed, flatter than that derived from conventional DSA theory, and ii) that the solution is constant downstream of the shock. For downstream plasmoid contraction only, we find that i) the accelerated particle spectrum is a power law in particle speed, flatter than that derived from conventional DSA theory; ii) for a given energy, the particle intensity peaks downstream of the shock, and the peak location occurs further downstream of the shock with increasing particle energy, and iii) the particle intensity amplification for a particular particle energy, f(x, c/c0)/f(0, c/c0), is not 1, as predicted by DSA theory, but increases with increasing particle energy. These predictions can be tested against observations of electrons and ions accelerated at interplanetary shocks and the heliospheric termination shock.

The nonlinear growth of the internal kink mode is studied numerically using reduced magnetohydrodynamic equations in cylinder geometry. For low Lundquist numbers, S < 107, the already well-known results have been reproduced: a m/n = 1/1 magnetic island (m: poloidal, n: toroidal mode number) grows while the original core shrinks until full reconnection is achieved. For higher S values, however, the dynamics is found to be qualitatively different from the well-known Kadomtsev's model (Kadomtsev 1975 Sov. J. Plasma Phys. 1 389). The growth of the 1/1 island causes the development of a very thin current sheet which becomes tearing unstable. The current sheet is thus broken up and secondary islands (plasmoids) form. These plasmoids strongly speed up the reconnection and eventually coalesce into one secondary island. The formation of a large secondary island stops the fast reconnection process, leading even to a partial reversal of this process. The final state of sawtooth reconnection is thus no longer an axis-symmetric equilibrium as in the case of complete reconnection for low S values, but a helical equilibrium with two coexisting magnetic islands.

For investigating the damping effect of low-order rational surfaces on the drift of pellet deposited plasmoids, a safety factor (q) profile scan experiment was performed in Tore Supra, on a series of discharges with identical temperature and density profiles. Fast time-resolved density measurements show that the position of the deposition peak does not move smoothly during the ablation/homogenization phase but changes step by step, each step being located close to an integer or half-integer q value. This behaviour is well reproduced by time-dependent simulations with the pellet ablation/deposition code HPI2, which takes into account the braking of the plasmoid drift by external currents flowing along field lines in the background plasma. The key feature of this damping mechanism is a modulation as a function of the local safety factor, the braking being more effective in the vicinity of simple rational q values. The overall agreement between measurements and code predictions for a significant range of edge safety factors is fully consistent with the fact that the limitation of the plasmoid polarization by parallel currents is the dominant damping process of the ∇B-induced drift in tokamaks. (Some figures may appear in colour only in the online journal)

Recent experiments have observed magnetic reconnection in laser-produced high-energy-density (HED) plasma bubbles. We perform two-dimensional (2-D) particle-in-cell (PIC) simulations to investigate magnetic reconnection between two approaching HED plasma bubbles. It is found that the expanding velocity of the bubbles has a great influence on the process of magnetic reconnection. When the expanding velocity is small, a single X line reconnection is formed. However, when the expanding velocity is sufficiently large, we can observe a plasmoid in the vicinity of the X line. At the same time, the structures of the electromagnetic field in HED plasma reconnection are similar to that in Harris current sheet reconnection.

Plasmoids generated by discharging a high-voltage capacitor through electrodes submerged in a weak aqueous electrolyte have attracted attention because of their resemblance to the natural phenomenon of ball lightning. We describe an extensive series of experimental studies which elucidate the mechanism responsible for the production of water plasmoids. We show that a plasma jet from a cathode spot is responsible for the formation of the main plasmoid, which grows in accordance with a current surge due to increasing contact area of the plasma with the liquid–air surface of the electrolyte. Spectra of optical emissions and scanning electron microscope studies indicate that the plasmoids glow because of a combination of chemiluminescence, atomic and molecular excitation, and possible incandescence from small particulates.

Drift displacement during density homogenization is modelled for hydrogen pellets injected into the Large Helical Device (LHD). The pellet ablation and deposition profiles are simulated for neutral-beam injection heated plasmas and are shown to reproduce well the main characteristics of the observed drift displacement for both low-field side and high-field side (HFS) injected pellets. The model describes the parallel expansion of ionized ablated pellet particle cloudlets (plasmoid) in non-axisymmetric magnetic configurations and the associated evolution of the plasmoid drift acceleration force exerted by the average magnetic field gradient over the plasmoid length. It is shown that, during the ablation and early homogenization phases, plasmoids are strongly accelerated towards the inverse direction of the local magnetic field gradient. In the case of the LHD, its direction and magnitude depend mainly on the pellet launching location with respect to the external helical coils. While such an initial drift—induced near the ablation region—is efficiently damped by plasmoid internal currents as soon as the plasmoid length becomes comparable to a toroidal connection length, a weak drift acceleration force is maintained over the whole homogenization time, whose direction depends on whether the confining magnetic field possesses a magnetic well or hill structure. Simulations show that, in a strong magnetic hill configuration like the LHD, this small but long-term drift becomes significant and results in a radially outward displacement of the mass deposition even for pellets injected from the HFS.

A new device, the Inductive Plasma Accelerator, was employed to simultaneously form and accelerate two oppositely directed field reversed configurations (FRCs) where the relative velocity (600 km s−1) of the plasmoids was much larger than their internal thermal motion. Upon collision all of the FRC directional energy was observed to be rapidly thermalized concurrent with complete magnetic reconnection of the two FRCs. Upon merging, the resulting FRC was compressed to kilovolt ion temperatures exhibiting a configuration lifetime better than predicted by past scaling of in situ formed FRCs. With the improved FRC confinement scaling, a pulsed plasma device based on this approach capable of achieving fusion gain is examined. For an FRC with a poloidal flux 20 mWb or greater, the fusion energy yield per pulse exceeds the plasma energy for compression fields of 10 T or more. The scaling is insensitive to the compression chamber radial scale, providing for the possibility of a very compact fusion neutron source.

In order not only to clarify the difference on the motion of a plasmoid induced by a pellet injection between tokamak and helical plasmas but also to obtain the universal understanding on the motion in torus plasmas, magnetohydrodynamic simulations have been carried out in a tokamak, vacuum toroidal field, reversed field pinch (RFP) like- and Large Helical Device (LHD) configurations. It is found that the plasmoid motion depends on the initial location of the plasmoid in the LHD, whereas the plasmoids drift in the direction opposite to that of the curvature vector in a tokamak, vacuum toroidal field and RFP-like configurations. It is also verified that there are two main forces acting on the plasmoid, and the connection length determines the dominant force.

We study spherically symmetric oscillations of electrons in plasma in the frame of classical electrodynamics. Firstly, we analyze the electromagnetic potentials for the system of radially oscillating charged particles. Secondly, we consider both free and forced spherically symmetric oscillations of electrons. Finally, we discuss the interaction between radially oscillating electrons through the exchange of ion acoustic waves. It is obtained that the effective potential of this interaction can be attractive and can transcend the Debye-Huckel potential. We suggest that oscillating electrons can form bound states at the initial stages of the spherical plasma structure evolution. The possible applications of the obtained results for the theory of natural plasmoids are examined., 9 pages in LaTeX2e, no figures; paper was significantly modified, 2 new references added, some inessential mathematics was removed, many typos were corrected; final variant to be published in Physica Scripta

The simultaneous development of the MHD instabilities of Raylegh-Taylor and Kelvin- Helmholtz types at the interface between high-conducting plasmoid and surrounding non- or low- conducting gas is considered. The linear stage of the RTI development is studied analytically for incompressible and compressible fluids. The nonlinear stage of the individual development of the RTI and the coupled development of both instabilities has been investigated numerically. The time-dependent two-dimensional numerical model based on the solution of the Euler gasdynamic equations with body momentum and energy sources of MHD origin has been developed and used in calculations. A disturbance introducing in the background flow has been periodic with varied assignment type and wave length. Fundamental difference between the results of linear and nonlinear analysis has been revealed. In particular, the increment of the RTI development at nonlinear stage is one-two order of magnitude less than that predicted by linear theory and rather weakly depends on initial disturbance mode. In linear analysis the coupled development of the RTI and the KHI is determined by simple summing of the two effects in the expression of wave increment, whereas in nonlinear case the mutual influence of the instabilities leads to essential alterations in their development, main of which is the intensive "layer-by-layer" destruction of the plasmoid surface.