William Fox

The Plasma Simulation Code

This work describes the Plasma Simulation Code (psc), an explicit, electromagnetic particle-in-cell code with support for different order particle shape functions. We review the basic components of the particle-in-cell method as well as the computational architecture of the psc code that allows support for modular algorithms and data structure in the code. We then describe and analyze in detail a distinguishing feature of psc: patch-based load balancing using space-filling curves which is shown to lead to major efficiency gains over unbalanced methods and a previously used simpler balancing method.

A dynamic magnetic tension force as the cause of failed solar eruptions

Coronal mass ejections are solar eruptions driven by a sudden release of magnetic energy stored in the Sun’s corona. In many cases, this magnetic energy is stored in long-lived, arched structures called magnetic flux ropes. When a flux rope destabilizes, it can either erupt and produce a coronal mass ejection or fail and collapse back towards the Sun. The prevailing belief is that the outcome of a given event is determined by a magnetohydrodynamic force imbalance called the torus instability. This belief is challenged, however, by observations indicating that torus-unstable flux ropes sometimes fail to erupt. This contradiction has not yet been resolved because of a lack of coronal magnetic field measurements and the limitations of idealized numerical modelling. Here we report the results of a laboratory experiment that reveal a previously unknown eruption criterion below which torus-unstable flux ropes fail to erupt. We find that such ‘failed torus’ events occur when the guide magnetic field (that is, the ambient field that runs toroidally along the flux rope) is strong enough to prevent the flux rope from kinking. Under these conditions, the guide field interacts with electric currents in the flux rope to produce a dynamic toroidal field tension force that halts the eruption. This magnetic tension force is missing from existing eruption models, which is why such models cannot explain or predict failed torus events.

A laboratory study of asymmetric magnetic reconnection in strongly driven plasmas.

Magnetic reconnection, the annihilation and rearrangement of magnetic fields in a plasma, is a universal phenomenon that frequently occurs when plasmas carrying oppositely directed field lines collide. In most natural circumstances, the collision is asymmetric (the two plasmas having different properties), but laboratory research to date has been limited to symmetric configurations. In addition, the regime of strongly driven magnetic reconnection, where the ram pressure of the plasma dominates the magnetic pressure, as in several astrophysical environments, has also received little experimental attention. Thus, we have designed the experiments to probe reconnection in asymmetric, strongly driven, laser-generated plasmas. Here we show that, in this strongly driven system, the rate of magnetic flux annihilation is dictated by the relative flow velocities of the opposing plasmas and is insensitive to initial asymmetries. In addition, out-of-plane magnetic fields that arise from asymmetries in the three-dimensional plasma geometry have minimal impact on the reconnection rate, due to the strong flows.

Ultrafast proton radiography of the magnetic fields generated by a laser-driven coil current

Magnetic fields generated by a current flowing through a U-shaped coil connecting two copper foils were measured using ultrafast proton radiography. Two ∼1.25 kJ, 1-ns laser pulses propagated through laser entrance holes in the front foil and were focused to the back foil with an intensity of ∼3 × 1016 W/cm2. The intense laser-solid interaction induced a high voltage between the copper foils and generated a large current in the connecting coil. The proton data show ∼40–50 T magnetic fields at the center of the coil ∼3–4 ns after laser irradiation. The experiments provide significant insight for future target designs that aim to develop a powerful source of external magnetic fields for various applications in high-energy-density science.

Laboratory observation of resistive electron tearing in a two-fluid reconnecting current sheet

The spontaneous formation of plasmoids via the resistive electron tearing of a reconnecting current sheet is observed in the laboratory. These experiments are performed during driven, antiparallel reconnection in the two-fluid regime within the Magnetic Reconnection Experiment. It is found that plasmoids are present even at a very low Lundquist number, and the number of plasmoids scales with both the current sheet aspect ratio and the Lundquist number. The reconnection electric field increases when plasmoids are formed, leading to an enhanced reconnection rate.

Electron heating and energy inventory during asymmetric reconnection in a laboratory plasma

Electron heating and the energy inventory during asymmetric reconnection are studied in the laboratory plasma with a density ratio of about 8 across the current sheet. Features of asymmetric reconnection such as the large density gradients near the low-density side separatrices, asymmetric in-plane electric field, and bipolar out-of-plane magnetic field are observed. Unlike the symmetric case, electrons are also heated near the low-density side separatrices. The measured parallel electric field may explain the observed electron heating. Although large fluctuations driven by lower hybrid drift instabilities are also observed near the low-density side separatrices, laboratory measurements and numerical simulations reported here suggest that they do not play a major role in electron energization. The average electron temperature increase in the exhaust region is proportional to the incoming magnetic energy per an electron/ion pair but exceeds scalings of the previous space observations. This discrepancy is explained by differences in the boundary condition and system size. The profile of electron energy gain from the electric field shows that there is additional electron energy gain associated with the electron diamagnetic current besides a large energy gain near the X line. This additional energy gain increases electron enthalpy, not the electron temperature. Finally, a quantitative analysis of the energy inventory during asymmetric reconnection is conducted. Unlike the symmetric case where the ion energy gain is about twice more than the electron energy gain, electrons and ions obtain a similar amount of energy during asymmetric reconnection.

Instability-enhanced friction in the presheath of two-ion-species plasmas

The speed at which ions enter a sheath is a fundamental property of a plasma that also provides a useful boundary condition in modeling. A recent theory proposed that this can be significantly influenced by an instability-enhanced friction force arising from two-stream instabilities in the presheath when multiple ion species are present. Although experiments appeared to confirm this theory, recent particle simulations have brought it into question. We reconcile this controversy using direct numerical solutions of the dispersion relation, which show that there is a dependence on the electron-ion temperature ratio that was not considered previously. In addition, particle-in-cell simulations are used to show that ion-ion two-stream instabilities can arise near the sheath edge and generate an enhanced ion-ion friction force. Only by accounting for the instability-enhanced friction force can theory predict the simulated ion speeds at the sheath edge.

Laboratory study of low-β forces in arched, line-tied magnetic flux ropes

The loss-of-equilibrium is a solar eruption mechanism whereby a sudden breakdown of the magnetohydrodynamic force balance in the Suns corona ejects a massive burst of particles and energy into the heliosphere. Predicting a loss-of-equilibrium, which has more recently been formulated as the torus instability, relies on a detailed understanding of the various forces that hold the pre-eruption magnetic flux rope in equilibrium. Traditionally, idealized analytical force expressions are used to derive simplified eruption criteria that can be compared to solar observations and modeling. What is missing, however, is a validation that these idealized analytical force expressions can be applied to the line-tied, low-aspect-ratio conditions of the corona. In this paper, we address this shortcoming by using a laboratory experiment to study the forces that act on long-lived, arched, line-tied magnetic flux ropes. Three key force terms are evaluated over a wide range of experimental conditions: (1) the upward hoop fo...

A simple model for estimating a magnetic field in laser-driven coils

Magnetic field generation by laser-driven coils is a promising way of magnetizing plasma in laboratory high-energy-density plasma experiments. A typical configuration consists of two electrodes—one electrode is irradiated with a high-intensity laser beam and another electrode collects charged particles from the expanding plasma. The two electrodes are separated by a narrow gap forming a capacitor-like configuration and are connected with a conducting wire-coil. The charge-separation in the expanding plasma builds up a potential difference between the electrodes that drives the electrical current in the coil. A magnetic field of tens to hundreds of Teslas generated inside the coil has been reported. This paper presents a simple model that estimates the magnetic field using simple assumptions. The results are compared with the published experimental data.

Quasi-static and dynamic magnetic tension forces in arched, line-tied magnetic flux ropes

Solar eruptions are often driven by magnetohydrodynamic instabilities such as the torus and kink instabilities that act on line-tied magnetic flux ropes. Recent laboratory experiments designed to study these eruptive instabilities have demonstrated the key role of both dynamic (Myers et al 2015 Nature 528 526) and quasi-static (Myers et al 2016 Phys. Plasmas 23 112102) magnetic tension forces in contributing to the equilibrium and stability of line-tied magnetic flux ropes. In this paper, we synthesize these laboratory results and explore the relationship between the dynamic and quasi-static tension forces. While the quasi-static tension force is found to contribute to the flux rope equilibrium in a number of regimes, the dynamic tension force is substantial mostly in the so-called failed torus regime where magnetic self-organization events prevent the flux rope from erupting.