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A dense plasma focus (DPF) is a relatively compact coaxial plasma gun, which completes its discharge as a Z-pinch. These devices are designed to operate at a variety of scales to produce short (

Optimization of neutron yields from dense plasma focus devices is a complex multi-faceted challenge that necessitates the prudent selection of mechanical constraints such as the electrode and insulator geometries. Here, the neutron yield is found to significantly depend on the insulator length. As the length of the insulator increases, the exposed anode length traveled by the sheath during the run-down phase decreases. This suggests an increase in the optimal fill pressure with increasing insulator length to maintain the pinch time near peak current. However, in the present study, the opposite trend is observed—the optimal fill pressure for neutron production decreases with increasing insulator length. Optical probing of the sheath from run-down to the pinch reveals significant plasma filamentation with increasing pressure and a dependence of insulator length on filamentation onset. A direct consequence of increased filamentation is a reduction in mass sweeping efficiency, directly quantified as a function of fill pressure for the first time.

In situ monitoring is required to improve the understanding and increase the reliability of additive manufacturing methods such as laser powder bed fusion (LPBF). Current diagnostic methods for LPBF capture optical images, X-ray radiographs, or measure the emission of thermal or acoustic signals from the component. Herein, a methodology based on the thermal emission of electrons - thermionic emission - from the metal surface during LPBF is proposed which can resolve laser-material interaction dynamics. The high sensitivity of thermionic emission to surface temperature and surface morphology is revealed to enable precise determination of the transition between conduction and keyhole mode melting regimes. Increases in thermionic emission are correlated to laser scanning conditions that give rise to pore formation and regions where surface defects are pronounced. The information presented here is a critical step in furthering our understanding and validation of laser-based metal additive manufacturing. In situ monitoring during additive manufacturing is an emerging approach for validating the quality of built parts. Here, thermal emission of electrons from the metal surface during laser processing is shown to be an effective indicator of conduction or keyhole melting regimes.

The dense plasma focus (DPF) can be an intense source of x rays, wherein the insulator sleeve strongly dictates the electrical breakdown, which subsequently affects the formation of a plasma sheath and a collapse phase. Experiments on a 25 kJ DPF (operated at 4.4 kJ) are carried out to demonstrate the influence of insulator surface morphology on the pinch structure, dynamics, and x-ray yield using a Ne fill. Two borosilicate insulators are directly compared, one with a smooth finish and the other machined with four circumferential grooves traversing the perimeter of the exterior insulator surface. Comparisons are made through same-shot imaging diagnostics of the evolving plasma sheath during breakdown, rundown, and at the pinch in addition to the time-resolved measurements of emitted x rays via filtered photodiodes. The presence of structures on the insulator sleeve reduces x-ray production across all fill pressures by a factor of 2.8 ± 2.4 on average and reduces the highest x ray producing shots by a factor of 5.5 ± 1.8. Observations of sheath asymmetry and inhomogeneity at lift-off are observed and correlated with subsequent observations of off-axis radial collapse. Taken together, this suggests that local variations in the insulator surface decrease the spatial uniformity of the sheath, leading to an azimuthally asymmetric focus, reduced electron densities, and, ultimately, degraded x-ray production.

Axisymmetric (m = 0) gyrokinetic and extended-MHD simulations of a sheared-flow Z-pinch plasma are performed with the high-order finite volume code COGENT. The present gyrokinetic model solves the long-wavelength limit of the gyrokinetic equation for both ion and electron species coupled to the electrostatic gyro-Poisson equation for the electrostatic potential. The extended-MHD model is electromagnetic and includes the effects of the gyro-viscous pressure tensor, diamagnetic electron and ion heat fluxes, and generalized Ohm's law. A prominent feature of this work is that the radial profiles for the plasma density and temperature are taken from the fusion Z-pinch experiment (FuZE), and the magnetic field profile is obtained as a solution of the MHD force balance equation. Such an approach allows to address realistic plasma parameters and provide insights into the current and planned experiments. In particular, it is demonstrated that the radial profiles play an important role in stabilization, as the embedded guiding center ( E × B) drift has a strong radial shear, which can contribute to the Z-pinch stabilization even in the absence of the fluid flow shear. The results of simulations for the FuZE plasma parameters show a decrease in the linear growth rate with an increase in the flow shear; however, full stabilization in the linear regime is not observed even for large (comparable to the Alfven velocity) radial variations of the axial flow. Nonlinear stability properties of the FuZE plasmas are also studied, and it is found that profile broadening can have a pronounced stabilizing effect in the nonlinear regime.

The pinch-formation stage of a deuterium dense plasma focus, and associated “shock-flash” neutron yield, is studied using 1D kinetic simulations considering a plasma column with initial pressure P, initial radius R, and the compression to be driven by a constant current I. The relative behavior of the compression is shown to be similar for fixed ratios of the characteristic ion mean free path to the radius of the plasma column at stagnation, λ s t / R s t. This dimensionless parameter is shown to scale like I 4 / ( P 3 R 5 ). The compression ratio, R / R s t, is found to be a minimum when λ s t / R s t ≈ 1 and is the largest in the collisionless limit where λ s t ≫ R s t. This behavior is in contrast to the analogous planar pinch where R / R s t decreases from one constant for λ s t / R s t ≪ 1 to a smaller constant for λ s t / R s t ≫ 1. The yield in the collisionless regime is shown to fall between the two well-known I4 scaling laws. Furthermore, this regime exhibits qualities that potentially make it appealing for radiography applications, such as increased localization in time and space of the neutron formation.

Experiments have demonstrated that a Z-pinch can persist for thousands of times longer than the growth time of global magnetohydrodynamic (MHD) instabilities such as the m = 0 sausage and m = 1 kink modes. These modes have growth times on the order of t a = a / v i, where vi is the ion thermal speed and a is the pinch radius. Axial flows with d u z / d r ≲ v i / a have been measured during the stable period, and the commonly accepted theory is that this amount of shear is sufficient to stabilize these modes as predicted by numerical studies using the ideal MHD equations. However, these studies only consider specific equilibrium profiles that typically have a modest magnitude for the logarithmic pressure gradient, q P ≡ d ln P / d ln r, and may not represent experimental conditions. Linear stability of the sheared-flow Z-pinch is studied here via a direct eigen-decomposition of the matrix operator obtained from the linear ideal MHD equations. Several equilibrium profiles with a large variation of qP are examined. Considering a practical range of k, 1 / 3 ≲ ka ≲ 10, it is shown that the shear required to stabilize m = 0 modes can be expressed as d u z / d r ≥ C γ 0 / ( k a ) α. Here, γ 0 = γ 0 ( k a ) is the profile-specific growth rate in the absence of shear, which scales approximately with | q P |. Both C and α are profile-specific constants, but C is order unity and α ≈ 1. It is further demonstrated that even a large value of shear, d u z / d r = 3 v i / a, is not sufficient to provide linear stabilization of the m = 1 kink mode for all profiles considered. This result is in contrast to the currently accepted theory predicting stabilization at much lower shear, d u z / d r = 0.1 v i / a, and suggests that the experimentally observed stability cannot be explained within the linear ideal-MHD model.

The dynamical formation of a Z-pinch in the strong-shock limit is studied in this paper using one-dimensional (1D) simulations of a two-temperature magnetohydrodynamic model. The classic 1D picture consists of three stages: run-in, reflected-shock, and expansion. The special case of a constant current I and uniform gas fill, which are approximate conditions of the pinch-formation stage in a dense plasma focus, is examined in detail. Time-profiles for the shock-front and piston positions during the run-in stage are compared with some of the commonly used 0D models from the literature. Some practical improvements to these models are presented here and it is shown that this model gives the best agreement with results from the simulations. Maximum compression of the plasma is achieved when the reflected shock from the axis meets the incoming current layer. The ratio of the plasma radius at this time with respect to its initial radius is found from the simulations to be r p / R ≈ 1 / 8 using 5/3 for the adiabatic coefficient γ. The pressure and temperature of the compressed plasma are found to peak a short time after maximum compression due to the inability of the reflected shock to completely stagnate the incoming plasma driven by the converging current layer. The variation of the results with a finite dI/dt and for different values of γ is presented.

A number of experimental and theoretical studies suggest that the presence of a modest radial shear in the axial plasma flow velocity can provide stabilization of Z-pinch plasmas against the most destructive kink and sausage ideal MHD instabilities, thereby making the flow stabilized Z-pinch (FSZP) systems attractive for magnetic fusion energy applications [1]. While radial variations in the plasma flow velocity that occur on the pinch-size scale $a$ can indeed generate sufficient phase-mixing for the stabilization of large-scale (k~ 1/a) MHD modes, weaker short-scale drift-wave instabilities that occur on a much smaller ion gyroradius scale are less affected by the large-scale velocity shear. Left behind, the drift microturbulence can substantially enhance classical (collisional) transport coefficient including plasma viscosity and can act over time to reduce the velocity shear and degrade the confinement. In this paper we present the initial results from gyrokintic simulations aimed to assess the influence of the ion gyro-scale drift microturbulence on the stability and transport properties of FSZP systems. The simulations are performed with the high-order finite-volume Eulerian gyrokinetic code COGENT and the results are analyzed for the parameters characteristic of the current and planned FSZP experiments.

Both microscopic and macroscopic impacts of the electromagnetic effects on blob dynamics are considered. Linear stability analysis and nonlinear BOUT++ simulations demonstrate that electromagnetic effects in high temperature or high beta plasmas suppress the resistive drift wave turbulence in the blob when resistivity drops below a certain value. In the course of blob’s motion in the SOL its temperature is reduced, which leads to enhancement of resistive effects, so the blob can switch from electromagnetic to electrostatic regime, where resistive drift wave turbulence become important. It is found that inhomogeneity of magnetic curvature or plasma pressure along the filament length leads to bending of the high-beta blob filaments. This is caused by the increase of the propagation time of plasma current (Alfven time) in higher-density plasma. The effects of sheath boundary conditions on the part of the blob away from the boundary are also diminished by the increased Alfven time.

A dense plasma focus (DPF) device is a type of plasma gun that drives current through a set of gas/plasma-filled coaxiallike electrodes that JxB pushes the ambient gas downstream and causes it to implode on axis to form a Z-pinch. This implosion drives hydrodynamic and kinetic instabilities that generate strong electric fields, which produces a short intense pulse of x-rays, high-energy $( \gt;100$ keV) electrons and ions, and (in deuterium and helium gases) neutrons. Practically all simulation efforts to date ignore the breakdown stage and assume that the entire gas-filled device turns into a fully ionized plasma instantaneously. However, simulations have shown that the pinch performance can be sensitive to the structure of the plasma sheath during rundown, which, in turn, can be sensitive to breakdown physics. In this work, we present results of an effort to model the breakdown stage and sheath formation using the particle-in-cell (PIC) code LSP. Helium and deuterium gases with pressures in the 1–10Torr range and peak-applied voltages of 20–36kV are considered. Breakdown is observed to occur in the experiments over times scales on the order of 10–100ns. In these parameter regimes, field emission from the cathode, possibly aided by insulator physics, seems to be what causes the gas to break down. Using different field-emission models, the sensitivity of things such as whether or not breakdown occurs, the time scale for breakdown to occur, and the nature of the sheath formation are studied.

Dense plasma focus (DPF) devices use co-axial electrodes to drive kA to MA of current through a Z-pinch plasma implosion. As the plasma implodes, kinetic instabilities [1] in the pinch create MV/cm electric fields that accelerate particles to high-energy (>100 keV). By using deuterium or tritium as a fill gas, a short (few ns), high-intensity neutron source is generated. The goal of our group a LLNL is to simulate and understand the core physics of these devices so that we can optimize them for a variety of applications. For instance, some devices are constrained based on their size and power usage, e.g., to fit into an oil-logging well, while still producing a sizeable neutron yield. Other devices must to be optimized to produce the highest possible neutron yield (up to 1014 per pulse) when power constraints are of little concern. In order to meet such requirements, we investigate a variety of techniques using high-fidelity simulations with the kinetic code LSP: – Shaping the interior anode in a way to promote instability growth and reduce asymmetries. – Adding a periodic gas jet to increase the neutron yield and reliability of ion acceleration. – Increasing the density of the fill gas to produce a higherdensity pinch, thus creating a better “target” for the accelerated ions. – Reversing the electrode polarity to investigate its role in electric field generation and subsequent ion generation.

The effects of m = 0 modes on equilibrium Z-pinch plasmas are studied in this paper using a drift-ideal magnetohydrodynamic (MHD) model. The model equations are an extension of ideal MHD to include finite-ion-inertial-length/cyclotron-frequency (Ωi) effects in Ohm's law and in the electron and ion heat transport equations. The linear modes contained in this model include the ideal interchange (sausage) mode and in the magnetized limit, Ωiτi≫1 with τi the ion collision time, nonideal entropy modes. It is well known that these two modes are decoupled in the kρs≪1 limit, where k is the axial mode number and ρs=cs/Ωi is the gyro-Bohm scale with cs the sound speed [B. Kadomtsev, Sov. Phys. JETP-USSR 10, 780 (1960)]. For Bennett equilibrium profiles, it is shown that the regions of stability for both modes are completely governed by the adiabatic coefficient γ in these limits. Equilibria with Bennett profiles are stable to entropy modes for γ 2. However, these modes are no longer decoupled when kρs≳1. The simulation results of the fully nonlinear set of equations in the magnetized limit show that seeded modes with kρs≳1 and γ = 5/3 display the characteristics of both ideal and entropy modes. The general heat flux for both ions and electrons as a function of the species magnetization is retained in the model. Both the linear and nonlinear behaviors of seeded modes for kρs≳1 display a strong dependence on the magnetization of the ions. The growth rate increases linearly with k at large kρs when the ions are magnetized but decreases with increasing k when Ωiτi≲1.The effects of m = 0 modes on equilibrium Z-pinch plasmas are studied in this paper using a drift-ideal magnetohydrodynamic (MHD) model. The model equations are an extension of ideal MHD to include finite-ion-inertial-length/cyclotron-frequency (Ωi) effects in Ohm's law and in the electron and ion heat transport equations. The linear modes contained in this model include the ideal interchange (sausage) mode and in the magnetized limit, Ωiτi≫1 with τi the ion collision time, nonideal entropy modes. It is well known that these two modes are decoupled in the kρs≪1 limit, where k is the axial mode number and ρs=cs/Ωi is the gyro-Bohm scale with cs the sound speed [B. Kadomtsev, Sov. Phys. JETP-USSR 10, 780 (1960)]. For Bennett equilibrium profiles, it is shown that the regions of stability for both modes are completely governed by the adiabatic coefficient γ in these limits. Equilibria with Bennett profiles are stable to entropy modes for γ 2. However,...

Axisymmetric stability properties of sheared flow Z-pinch plasmas are studied by making use of the gyrokinetic approximation in the long-wavelength limit. Numerical simulations are carried out with the high-order finite-volume code COntinuum Gyrokinetic Edge New Technology (COGENT) and are analyzed for the parameters characteristic of the FuZE experiment. Reduction of the linear growth rate with increasing shear is observed, and the results are elucidated by making use of a local dispersion relation analysis. In addition, COGENT simulations are compared with fully kinetic particle-in-cell simulations, and with an ideal magnetohydrodynamics (MHD) model. Good agreement between the gyrokinetic and fully kinetic results for the linear stability is found, with the gyrokinetic model requiring much less computational time due to its ability to step over particle gyroperiod. The ideal MHD model is found to be consistent with the kinetic models in the long-wavelength part of the spectra (kρi), while failing to adequately predict short-scale (kρi) stability. Here, k is the axial wavelength vector and ρi is the ion gyroradius.

Recent 3D studies on plasma blobs (coherent structures found in the edge region of magnetic confinement devices) have demonstrated that the drift wave instability can strongly limit the blob’s coherency and cross field convective nature that is predicted by 2D theory. However, the dominant unstable drift wave modes that effect plasma blobs were found to exist in parameter regimes that only marginally satisfied several of the major assumptions considered for the validity of the reduced collisional fluid equations used in the study. Namely, the neglect of electron heat flow, finite electron mean free path effects, and thermal ions. A follow up study demonstrated how the drift wave instability might change if a set of equations that does not suffer from the limitations mentioned above were considered. In the present paper, the results of this later work are used to discuss the limitations on using the collisional fluid equations for 3D studies of plasma blobs.

Direct irradiation of materials by electron beams (e-beams) has been used to study material response.2,3 The desire to utilize high-power (∼ TW) generators to achieve higher specific energy deposition over larger areas has led to several approaches. One approach utilizes a monolithic e-beam diode with an external magnetic field (B field). The external B field allows the diode to operate in the bipolar, space-charge-limited regime without the current being magnetically limited to a lower value. The field also is used to guide the e-beam through the gas-filled region between the vacuum diode and the object to be irradiated. An alternate approach, discussed in this presentation, utilizes multiple diodes electrically in parallel, with each diode running below the critical current to obtain a high current. The e-beams are then scattered in foils and combined in the gas-transport region to achieve the desired irradiation uniformity and area. We report on experiments that have been performed on the Gamble II generator at NRL (∼ 1 MV, ∼ 800 kA, ∼ 60 ns) designed to study this second approach. Diagnostics include diode voltage and current, a net-current monitor, interferometry, spectroscopy, an axial array of Ta-strip x-ray witness plates, and a segmented calorimeter. Experiments have been performed with a single ring diode and two nested ring diodes. Where possible, the measurements are compared with results from ITS and from the recently-developed ABC model4 for the interaction of the e-beam with the gas. Results show that the beam is very nearly charge and current neutralized as it propagates ∼ 20 cm in 1-Torrr N2 gas. Beam scattering from both the anode and a Ti scattering foil in the gas results in a relatively uniform radial beam profile.

The Gamble II generator at the Naval Research Laboratory produces ∼100 ns pulse duration, relativistic-electron beams with peak energies on the order of 1MV and peak currents of about 800 kA with annular beam areas between 40–80 cm2. This gives peak current densities ∼10 kA/cm2. For many different applications, a nitrogen gas in the 1 Torr range is used as a charge- and current-neutralizing background to achieve beam transport. For these parameter regimes, the gas transitions from a weakly-ionized molecular state to a strongly-ionized atomic state on the time scale of the beam pulse. A detailed gas-chemistry model is presented for a dynamical description of the nitrogen plasmas produced in such experiments. The model is coupled to a 0D circuit model representative of annular beams, and results for 1Torr nitrogen are in good agreement with experimental measurements of the line-integrated electron density and the net current. It is found that the species are mostly in the ground and metastable states during the atomic phase, but that ionization proceeds predominantly through thermal ionization of the higher-lying optically-allowed states with excitation energies close to the ionization limit. The model also predicts the time-dependence of line intensities from both molecular and atomic species.

In this study, COGENT is a continuum gyrokinetic code for edge plasmas being developed by the Edge Simulation Laboratory collaboration. The code is distinguished by application of the fourth order conservative discretization, and mapped multiblock grid technology to handle the geometric complexity of the tokamak edge. It is written in v∥-μ (parallel velocity – magnetic moment) velocity coordinates, and making use of the gyrokinetic Poisson equation for the calculation of a self-consistent electric potential. In the present manuscript we report on the implementation and initial testing of a succession of increasingly detailed collision operator options, including a simple drag-diffusion operator in the parallel velocity space, Lorentz collisions, and a linearized model Fokker-Planck collision operator conserving momentum and energy (© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Plasma blobs found in the edge region of tokamaks are important to understand because they contribute to a large amount of the plasma particle transport in the SOL (scrape off layer). Most of the work to date is limited to 2D theory and simulations by ignoring the variation of blob parameters along the magnetic field line. 3D effects are examined in the electrostatic limit in this paper using the code BOUT++ by allowing for the variation of blob density and potential along the field line. It is demonstrated that the 3D variation of these parameters can lead to a Boltzmann potential relation that will cause the blob to spin and induce turbulent motion via unstable drift waves (© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Experiments were performed to maximize the neutron yield from a 2 kJ dense plasma focus (DPF) and characterize the amount of copper sputtered from the surface of an anode by varying the diameter of the anodes’ on-axis hollow. The hollow is a void in the copper material along the longitudinal axis of the anode. All the anodes had an outer diameter of 1.2 in. and the diameter of the hollow varied from 0 in. (no hollow) to 1 in. The anodes with a hollow produced a greater number of neutrons per discharge than the anode without a hollow. Over 40 discharges, the hollow anode that yielded the most neutrons (9.1 ±0.4 ×10 6 neutrons per discharge produced with the 0.75 in. hollow) produced >6 times more neutrons than the anode with no hollow. A qualitative observation of the anodes after 130 discharges showed less surface damage on anodes with a larger hollow. Quantitative sputter measurements were performed by characterizing the amount of copper sputtered onto on-axis quartz targets for three newly machined anodes, each with a particular hollow diameter. The quantitative results matched the qualitative observations: the copper sputter was reduced using larger hollows. The largest hollow sputtered 17 ±1.0 nm/sr/discharge of copper, a reduction of 69 % compared to the anode with the most damage.Experiments were performed to maximize the neutron yield from a 2 kJ dense plasma focus (DPF) and characterize the amount of copper sputtered from the surface of an anode by varying the diameter of the anodes’ on-axis hollow. The hollow is a void in the copper material along the longitudinal axis of the anode. All the anodes had an outer diameter of 1.2 in. and the diameter of the hollow varied from 0 in. (no hollow) to 1 in. The anodes with a hollow produced a greater number of neutrons per discharge than the anode without a hollow. Over 40 discharges, the hollow anode that yielded the most neutrons (9.1 ±0.4 ×10 6 neutrons per discharge produced with the 0.75 in. hollow) produced >6 times more neutrons than the anode with no hollow. A qualitative observation of the anodes after 130 discharges showed less surface damage on anodes with a larger hollow. Quantitative sputter measurements were performed by characterizing the amount of copper sputtered onto on-axis quartz targets for three newly machined ano...

Magnetic field penetration in current-carrying plasmas is being studied in a plasma opening switch geometry. Several Marshall guns1 are used to inject single or multi-species plasmas between coaxial conductors connected to the output of NRL's Hawk pulsed-power generator. Following injection of the plasma, the generator is used to apply an electrical pulse with a peak current of 700 kA, a peak voltage of 640 kV, and a rise time of 1.2 µs. Initially the plasma acts as a short, conducting all of the current. Over time, the resulting magnetic field interacts with the plasma through a combination of magnetohydrodynamic (MHD) plasma translation and field penetration that is not well understood2–4. Eventually a quasi-neutral gap forms in the plasma5,6, allowing electrical power to flow downstream. The quality of this switching is affected by the manner in which the gap is formed. This process is monitored using magnetic probes and a ribbon-beam interferometer running parallel to the axis of the accelerator and spanning the inter-electrode plasma region. Particle-in-cell (PIC) modeling shows that the relative importance of MHD translation and field penetration in the gap formation process is dependent upon the radial density gradient and composition of the plasma7. These parameters of the initial injected plasma are adjusted experimentally using the Marshall guns for light (hydrogen), heavy (argon), and mixed light and heavy components. The experimentally-observed behavior of the resulting opening switch plasmas in the presence of the interacting magnetic field is compared with results from PIC modeling.

The behavior of intense electron beams (those with current densities on the order of hundreds of kA/cm2 and beam rise times on the order of 100 ns) traveling through gaseous media depends strongly on the transport properties of the media. For example, the conductivity of a gas, which depends sensitively on its ionization state and temperature, has a strong influence on the beam behavior through the plasma return current. Because the beam is responsible for ionizing and heating the gas, self-consistently solving for the gas transport properties and the beam propagation is essential for an accurate description of the system. An advanced gas chemistry model to describe the transport properties of a strongly disturbed air system is presented in this work. The model includes rate equations for the different gas states that include molecular and atomic states as well as excited and multiply ionized states. Furthermore, the model includes an energy equation for the heavy species. For validation purposes, the model is used in the simulation of an intense electron beam generated by a ring diode experiments on Gamble II [1] and injected into a gas cell. The LSP code is used for the simulations [2]. The results are compared with the previously used “swarm model” in LSP, which is only valid for very weakly ionized systems.

The Monte-Carlo electron code, MCSwarm [1], is being developed as a test bed for algorithms to be included in particle-in-cell codes like Quicksilver [2] and EMPHASIS [3] to self-consistently model the transport of intense beams through a background gas. In this paper, the MCSwarm code is used to study the electron kinetics as the secondary electron distribution approaches equilibrium. Electron runaway is observed in MCSwarm for moderately high electric fields. The runaway condition is strongly dependent on the angular scattering law as well as on the secondary electron energy distribution created by beam impact. The scattering model in MCSwarm is based on a doubly-differential cross section calculated from the first-Born approximation which is sampled so that sampled distributions preserve the total cross-section and the momentum-transfer cross section.[4] The method of preserving low-order moments statistically hides the underlying distribution and sampling method but is sufficiently accurate provided there are a large number of collisions over the scale-length of interest. The secondary electron energies are sampled using the results of Opal.[5] The MCSwarm code is used to study the sensitivity of the angular distribution and the secondary electron energy distribution from beam impact on the runaway condition.

Magnetic field penetration in electron-magnetohydrodynamics (EMHD) can be driven by density gradients through the Hall term [Kingsep et al., Sov. J. Plasma Phys. 10, 495 (1984)]. Particle-in-cell simulations have shown that a magnetic front can go unstable and break into vortices in the Hall-driven EMHD regime. In order to understand these results, a new fluid model had been derived from the Ly/Ln≪1 limit of EMHD, where Ly is the length scale along the front and Ln is the density gradient length scale. This model is periodic in the direction along the magnetic front, which allows the dynamics of the front to be studied independently of electrode boundary effects that could otherwise dominate the dynamics. Numerical solutions of this fluid model are presented that show for the first time the relation between Hall-driven EMHD, electron inertia, the Kelvin-Helmholtz (KH) instability, and the formation of magnetic vortices. These solutions show that a propagating magnetic front is unstable to the same KH mode...

Most of the work to date on plasma blobs found in the edge region of magnetic confinement devices is limited to 2D theory and simulations which ignore the variation of blob parameters along the magnetic field line. However, if the 2D convective rate of blobs is on the order of the growth rate of unstable drift waves, then drift wave turbulence can drastically alter the dynamics of blobs from that predicted by 2D theory. The density gradients in the drift plane that characterize the blob are mostly depleted during the nonlinear stage of drift waves resulting in a much more diffuse blob with a greatly reduced radial velocity. Sheath connected plasma blobs driven by effective gravity forces are considered in this Letter and it is found that the effects of resistive drift waves occur at earlier stages in the 2D motion for smaller blobs and in systems with a smaller effective gravity force. These conclusions are supported numerically by a direct comparison of 2D and 3D seeded blob simulations.

Magnetic pushing of plasmas is an important fundamental phenomena in plasma physics. In the presence of strong plasma-density gradients, Hall-magnetohydrodynamics forces can lead to penetration of the magnetic field into the plasma. For multicomponent plasmas, simulations show that the magnetic field can penetrate the heavy-ion component of the plasma while simultaneously pushing the light ions. Images are presented of the simulated plasma densities showing the resulting species separation.

The impacts of the electromagnetic effects on resistive and collisionless drift waves are studied. A local linear analysis on an electromagnetic drift-kinetic equation with Bhatnagar-Gross-Krook-like collision operator demonstrates that the model is valid for describing linear growth rates of drift wave instabilities in a wide range of plasma parameters showing convergence to reference models for limiting cases. The wave-particle interactions drive collisionless drift-Alfven wave instability in low collisionality and high beta plasma regime. The Landau resonance effects not only excite collisionless drift wave modes but also suppress high frequency electron inertia modes observed from an electromagnetic fluid model in collisionless and low beta regime. Considering ion temperature effects, it is found that the impact of finite Larmor radius effects significantly reduces the growth rate of the drift-Alfven wave instability with synergistic effects of high beta stabilization and Landau resonance.

A passive method for controlling the trajectory of an intense, hollow electron beam is proposed using a vacuum structure that inductively splits the beam's return current. A central post carries a portion of the return current (I1), while the outer conductor carries the remainder (I2). An envelope equation appropriate for a hollow electron beam is derived and applied to the current divider. The force on the beam trajectory is shown to be proportional to (I2-I1), while the average force on the envelope (the beam width) is proportional to the beam current Ib = (I2 + I1). The values of I1 and I2 depend on the inductances in the return-current path geometries. Proper choice of the return-current geometries determines these inductances and offers control over the beam trajectory. Solutions using realistic beam parameters show that, for appropriate choices of the return-current-path geometry, the inductive current divider can produce a beam that is both pinched and straightened so that it approaches a target at...

The impacts of the electromagnetic effects on blob dynamics are considered. Electromagnetic BOUT++ simulations on seeded high-beta blobs demonstrate that inhomogeneity of magnetic curvature or plasma pressure along the filament leads to bending of the blob filaments and the magnetic field lines due to increased propagation time of plasma current (Alfven time). The bending motion can enhance heat exchange between the plasma facing materials and the inner scrape-off layer (SOL) region. The effects of sheath boundary conditions on the part of the blob away from the boundary are also diminished by the increased Alfven time. Using linear analysis and BOUT++ simulations, it is found that electromagnetic effects in high temperature and high density plasmas reduce the growth rate of resistive drift wave instability when resistivity drops below a certain value. The blobs temperature decreases in the course of its motion through the SOL and so the blob can switch from the electromagnetic to the electrostatic regime where resistive drift waves become important again.

Electron vortices are observed in the numerical simulation of current carrying plasmas on fast time scales where the ion motion can be ignored. In plasmas with nonuniform density n, vortices drift in the B × ∇n direction with a speed that is on the order of the Hall speed. This provides a mechanism for magnetic field penetration into a plasma. Here, we consider strong vortices with rotation speeds Vϕ close to the speed of light c where the vortex size δ is on the order of the magnetic Debye length λB=|B|/4πen and the vortex is thus nonquasineutral. Drifting vortices are typically studied using the electron magnetohydrodynamic model (EMHD), which ignores the displacement current and assumes quasineutrality. However, these assumptions are not strictly valid for drifting vortices when δ ≈ λB. In this paper, 2D electron vortices in nonuniform plasmas are studied for the first time using a fully electromagnetic, collisionless fluid code. Relatively large amplitude oscillations with periods that correspond to h...

The inviscid evolution of localized density stratifications under the influence of a uniform gravity field in a homogeneous, ambient background is studied. The fluid is assumed to be incompressible, and the stratification, or filament, is assumed to be initially isotropic and at rest. It is shown that the center of mass energy can be related to the center of mass position in a form analogous to that of a solid object in a gravity field g by introducing an effective gravity field geff, which is less than g due to energy that goes into the background and into non-center of mass motion of the filament. During the early stages of the evolution, geff is constant in time and can be determined from the solution of a 1D differential equation that depends on the initial, radially varying density profile of the filament. For small amplitude filaments such that ρ0 ≪ 1, where ρ0 is the relative amplitude of the filament to the background, the early stage geff scales linearly with ρ0, but as ρ0→∞, geff→g and is thus i...

Fluctuations in fusion boundary and similar plasmas often have the form of filamentary structures, or blobs, that convectively propagate radially. This may lead to the degradation of plasma facing components as well as plasma confinement. Theoretical analysis of plasma blobs usually takes advantage of the so-called Boussinesq approximation of the potential vorticity equation, which greatly simplifies the treatment analytically and numerically. This approximation is only strictly justified when the blob density amplitude is small with respect to that of the background plasma. However, this is not the case for typical plasma blobs in the far scrape-off layer region, where the background density is small compared to that of the blob, and results obtained based on the Boussinesq approximation are questionable. In this report, the solution of the full vorticity equation, without the usual Boussinesq approximation, is proposed via a novel numerical approach. The method is used to solve for the evolution of 2D and 3D plasma blobs in a regime where the Boussinesq approximation is not valid. The Boussinesq solution under predicts the cross field transport in 2D. However, in 3D, for parameters typical of current tokamaks, the disparity between the radial cross field transport from the Boussinesq approximation and full solution is virtually non-existent due to the effects of the drift wave instability.

Vortex formation and propagation are observed in kinetic particle-in-cell (PIC) simulations of magnetic pushing in the plasma opening switch. These vortices are studied here within the electron-magnetohydrodynamic (EMHD) approximation using detailed analytical modeling. PIC simulations of these vortices have also been performed. Strong v×B forces in the vortices give rise to significant charge separation, which necessitates the use of the EMHD approximation in which ions are fixed and the electrons are treated as a fluid. A semi-analytic model of the vortex structure is derived, and then used as an initial condition for PIC simulations. Density-gradient-dependent vortex propagation is then examined using a series of PIC simulations. It is found that the vortex propagation speed is proportional to the Hall speed vHall≡cB0/4πneeLn. When ions are allowed to move, PIC simulations show that the electric field in the vortex can accelerate plasma ions, which leads to dissipation of the vortex. This electric fiel...

The 3D effects on sheath connected plasma blobs that result from parallel electron dynamics are studied by allowing for the variation of blob density and potential along the magnetic field line and using collisional Ohm’s law to model the parallel current density. The parallel current density from linear sheath theory, typically used in the 2D model, is implemented as parallel boundary conditions. This model includes electrostatic 3D effects, such as resistive drift waves and blob spinning, while retaining all of the fundamental 2D physics of sheath connected plasma blobs. If the growth time of unstable drift waves is comparable to the 2D advection time scale of the blob, then the blob’s density gradient will be depleted resulting in a much more diffusive blob with little radial motion. Furthermore, blob profiles that are initially varying along the field line drive the potential to a Boltzmann relation that spins the blob and thereby acts as an addition sink of the 2D potential. Basic dimensionless param...

The standard local linear analysis of drift waves in a plasma slab is generalized to be valid for arbitrarily collisional electrons by considering the electrons to be governed by the drift-kinetic equation with a BGK-like (Bhatnagar-Gross-Krook) collision operator. The obtained dispersion relation reduces to that found from collisionless kinetic theory when the collision frequency is zero. Electron temperature fluctuations must be retained in the standard fluid analysis in order to obtain good quantitative agreement with our general solution in the highly collisional limit. Any discrepancies between the fluid solution and our general solution in this limit are attributed to the limitations of the BGK collision operator. The maximum growth rates in both the collisional and collisionless limits are comparable and are both on the order of the fundamental drift wave frequency. The main role of the destabilizing mechanism is found to be in determining the parallel wave number at which the maximum growth rate w...

The interactions of a relativistic free electron with a pulsed electromagnetic (EM) plane wave in the presence of constant magnetic fields are studied using the well-known constants of motion. The goal is to determine the energy gained by the electron after the wave has passed. For a constant magnetic field along the axis of the wave, a general solution for the energy gain as a function of the vector potential describing the EM plane wave is obtained. Solutions for magnetic fields transverse to the axis of the wave are sought in the limit where the cyclotron frequency is much less than the wave frequency and are examined using several different profiles for the wave amplitude. For this case, an adiabatic invariant is found that shows that there is no energy gain when an EM plane wave comes and goes with a profile that is slowly varying in time with respect to the cyclotron motion.