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International audience; The effect of plasma turbulence on the trajectories of dust particles is investigated for the first time. The dynamics of dust particles is computed using the ad-hoc developed Dust Injection Simulator code, using a 3D turbulent plasma background computed with the TOKAM3X code. As a result, the evolution of the particle trajectories is governed by the ion drag force, and the shape of the trajectory is set by the Stokes number St ∝ a d /n 0 , with a d the dust radius and n 0 the density at the separatrix. The plasma turbulence is observed to scatter the dust particles, exhibiting a hyperdiffusive regime in all cases. The amplitude of the turbulent spread of the trajectories ∆r 2 is shown to depend on the ratio Ku/St, with Ku ∝ u rms the Kubo number and u rms the fluctuation level of the plasma flow. These results are compared with a simple analytical model, predicting ∆r 2 ∝ (Ku/St) 2 t 3 , or ∆r 2 ∝ (u rms n 0 /a d) 2 t 3. As the dust is heated by the plasma fluxes, thermionic emission sets the dust charge, originally negative, to slightly positive values. This results in a substantial reduction of the ion drag force through the suppression of its Coulomb scattering component. The dust grain inertia is then no longer negligible, and drives the transition from a hyperdiffusive regime towards a ballistic one.

Graphite ablation by an electric arc or a laser/solar flux is widely used for the synthesis of carbon nanomaterials. Previously, it was observed in multiple arc experiments that the ablation rate is a strong nonlinear function of the arc current and it drastically increases at some threshold current. We developed an analytical model explaining this transition in the rate of ablation by an electric arc or a laser/solar flux. The model not only explains the observations but can also accurately predict the experimentally observed ablation rates. The model takes into account redeposition of carbon back to the ablated surface, which is the key process responsible for the observed effects.

A novel regime of the saturation of the Pierce-type ion-sound instability in a bounded ion-beam-plasma system is revealed in 1D particle-in-cell simulations. It is found that the saturation of the instability is mediated by the oscillating virtual anode potential structure. The periodically oscillating potential barrier separates the incoming beam ions into two groups. One component forms a supersonic beam, which is accelerated to an energy exceeding the energy of the initial cold ion beam. The other component is organized as a self-consistent phase space structure of trapped ions with a wide energy spread—the ion hole. The effective temperature (energy spread) of the ions trapped in the hole is lower than the initial beam energy. In the final stage, the ion hole expands over the whole system length.

Ion beam charge neutralization by electron injection is a complex kinetic process. Recent experiments show that the resulting self-potential of the ion beam after neutralization by plasma is much lower than the temperature of plasma electrons [Stepanov et al., Phys. Plasmas 23, 043113 (2016)], indicating that kinetic effects are important and may affect the neutralization of the ion beam. We performed a numerical study of the charge neutralization process of an ion beam making use of a two-dimensional electrostatic particle-in-cell code. The results show that the process of charge neutralization by electron injection is composed of two stages. During the first stage, the self-potential of the beam is higher than the temperature of injected electrons (Te/e) and all injected electrons are captured by the ion beam. During the second stage, hot electrons escape from the ion beam and the beam self-potential (φ) decreases because cold electrons slowly accumulate resulting in the beam self-potential φ to become much lower than Te/e in agreement with previous experimental observations at Princeton Advanced Teststand. We also determined that the resulting φ scales as φ ∼ T e, in agreement with previous experimental observations from Gabovich's group. In addition, the results show that the transverse position of the electron source has a great impact on ion beam neutralization. A slight shift of the electron source as relevant to the ion thrusters leads to a large increase in the beam self-potential because of an increase in potential energy of injected electrons.

The Electron Cyclotron Drift Instability (ECDI) driven by the electron $E\times B$ drift in partially magnetized plasmas is investigated with highly resolved particle-in-cell simulations. The emphasis is on two-dimensional effects involving the parallel dynamics along the magnetic field in a finite length plasma with dielectric walls. It is found that the instability develops as a sequence of growing cyclotron harmonics demonstrating wave breaking and complex nonlinear interactions, being particularly pronounced in ion density fluctuations at short wavelengths. At the same time, nonlinear evolution of fluctuations of the ion and electron density, as well as the anomalous electron current, shows cascade toward long wavelengths. Tendency to generate long wavelength components is most clearly observed in the spectra of the electron density and the anomalous current fluctuations. An intense but slowly growing mode with a distinct eigen-mode structure along the magnetic field develops at a later nonlinear stage enhancing the tendency toward long wavelength condensation. The latter mode having a finite wavelength along the magnetic field is identified as the Modified Two-Stream Instability (MTSI). It is shown that the MTSI mode results in strong parallel heating of electrons., 14 pages, 19 figures, 2 tables

Atmospheric pressure arcs have recently found application in the production of nanoparticles. Distinguishing features of such arcs are small length and hot ablating anode characterized by intensive electron emission and radiation from its surface. We performed one-dimensional modeling of argon arc, which shows that near-electrode effects of thermal and ionization non-equilibrium play important role in operation of a short arc, because the non-equilibrium regions are up to several millimeters long and are comparable with the arc length. The near-anode region is typically longer than the near-cathode region and its length depends more strongly on the current density. The model was extensively verified and validated against previous simulation results and experimental data. Volt-Ampere characteristic (VAC) of the near-anode region depends on the anode cooling mechanism. The anode voltage is negative. In case of strong anode cooling (water-cooled anode) when anode is cold, temperature and plasma density gradients increase with current density resulting in decrease of the anode voltage (absolute value increases). Falling VAC of the near-anode region suggests the arc constriction near the anode. Without anode cooling, the anode temperature increases significantly with current density, leading to drastic increase in the thermionic emission current from the anode. Correspondingly, the anode voltage increases to suppress the emission - and the opposite trend in the VAC is observed. The results of simulations were found to be independent of sheath model used: collisional (fluid) or collisionless model gave the same plasma profiles for both near-anode and near-cathode regions., 29 pages, 16 figures

Cross-field anomalous transport is an important element of the operation and performance of E × B discharges. The anomalous electron current is driven by instabilities which may be excited in such plasmas due to presence of the strong E × B electron current. Using 1D particle-in-cell simulations we study the development of the the E × B drift cyclotron instability 1 driven exclusively by the E × B flow, in absence of density and magnetic field gradients. In this case, the instability occurs due to the resonance between the ballistic $kv _{E} \times _{B}$ modes and electron cyclotron harmonics $m\omega _{ce}$. Initially, in the linear stage we observe the growth of the most unstable $m^{th}$ harmonic, consistent with the linear theory. At a later stage, the intense electron heating is observed due to phase-space mixing of the electron distribution function and the mode robustly reorganizes into the fundamental mode that propagates with the acoustic speed in the ion frame 2, 3, with a sub-dominant spectrum of higher order cyclotron side-bands. A progressive inverse cascade to a larger scale structure (with a size larger than the the length scale of the fundamental mode) in the anomalous current is also observed in the non-linear stage.

Long-time evolution of the two-stream instability of an ion beam pulse propagating through a background plasma is investigated using a large-scale, one-dimensional kinetic simulation. After initial saturation of the two-stream instability due to particle trapping in the plasma wave, significant portion of the initially trapped in the wave field electrons become detrapped and move ahead of the ion beam. It is found that particles can be accelerated in front of the ion beam at a potential amplitude lower than predicted because the cold background electrons are moderately heated as they travel through the plasma wave generated due to the initial two-stream instability. The potential wells in the plasma wave is non-sinusoidal because of the modulations in both ion and electron densities. The detrapped electron population forms an electron beam that propagates faster than the ion beam and starts to interact with the background plasma ahead of the beam pulse. Secondary two-stream instability between the streaming electrons and background plasma electrons develops ahead of the ion beam pulse leading to heating of the background electrons. The heating of plasma electrons and beam ions eventually extinguish the instability.

The left branch of the Paschen curve for helium gas is studied both experimentally and by means of particle-in-cell/Monte Carlo collisions (PIC/MCC) simulations. The physical model incorporates electron, ion, and fast atom species whose energy-dependent anisotropic scattering on background neutrals, as well as backscattering at the electrodes, is properly accounted for. For the range of breakdown voltage 15 kV ≤ V br ≤ 130 kV, a good agreement is observed between simulations and available experimental results for the discharge gap d = 1.4 cm. The PIC/MCC model is then used to estimate the Paschen curve at higher voltages up to 1 MV, based on the availability of input atomic data. We find that the pd similarity scaling does hold, and that above 300 kV the value of pd at breakdown begins to increase with increasing voltage.

Results are presented from two-dimensional (radial-azimuthal), electrostatic Particle-In-Cell simulations of a Penning discharge, where an electron beam is injected along the axis, parallel to the magnetic field, into a cylindrical plasma radially bounded by grounded metal. In preliminary, one-dimensional (radial) simulations, the anomalous electron transport is solely due to the instability of the pure lower-hybrid mode. With also the azimuthal direction numerically resolved, the Simon-Hoh mode becomes active and the lower-hybrid mode is destabilized by density-gradient effects. In the more realistic, twodimensional simulations, the lower-hybrid and Simon-Hoh modes both contribute to the anomalous transport. These latter simulations demonstrate the excitation of an azimuthally asymmetric, spoke-like structure rotating in the direction of ExB and electron diamagnetic drifts and persisting throughout the remainder of this simulation. The spokes are characterized by an increase in plasma density and are shown to channel most of the radial leakage current. The spoke appears similar to the one seen in experiments and it exhibits the same scaling with ion mass. The Hall parameter in the simulations is also in good agreement with experiment.

Propagation of charged particle beams in background plasma as a method of space charge neutralization has been shown to achieve high degrees of charge and current neutralization and therefore can enable nearly ballistic propagation and focusing of charged particle beams. Correspondingly, use of plasmas for propagation of charged particle beams has important applications for transport and focusing of intense particle beams in electric propulsion, inertial fusion and high energy density laboratory plasma physics. However, the streaming of beam ions through a background plasma can lead to development of the two-stream instability between the beam ions and the plasma electrons [1, 2]. The electric and magnetic self-fields enhanced by the two-stream instability can lead to defocusing of the ion beam and fast scattering of an electron beam. Using particle-in-cell (PIC) simulations, we study the scaling of the instability-driven selfelectromagnetic fields and consequent defocusing forces with the background plasma density and beam ion mass. We identify plasma parameters where the defocusing forces can be reduced.

Propagation of charged particle beams in background plasma as a method of space charge neutralization has been shown to achieve a high degree of charge and current neutralization and therefore enables nearly ballistic propagation and focusing of charged particle beams. Correspondingly, use of plasmas for propagation of charged particle beams has important applications for transport and focusing of intense particle beams in inertial fusion and high energy density laboratory plasma physics. However, the streaming of beam ions through a background plasma can lead to development of the two-stream instability between the beam ions and the plasma electrons. The beam electric and magnetic fields enhanced by the two-stream instability can lead to defocusing of the ion beam. Using particle-in-cell (PIC) simulations, we study the scaling of the instability-driven self-electromagnetic fields and consequent defocusing forces with the background plasma density and beam ion mass. We identify plasma parameters where the defocusing forces can be reduced., Comment: 28 pages, submitted to Phys. Plasmas

The optimal pitch angle which maximizes the penetration distance, along the magnetic field, of relativistic charged particles injected from the midplane of an axisymmetric field is investigated analytically and numerically. Higher-order terms of the magnetic moment invariant are necessary to correctly determine the mirror point of trapped energetic particles, and therefore the loss cone. The modified loss cone resulting from the inclusion of higher-order terms is no longer entirely defined by the pitch angle but also by the phase angle of the particle at the point of injection. The optimal orientation of the injection has a nonzero component perpendicular to the magnetic field line, and is in the plane tangential to the flux surface. Numerical integration of particle orbits were carried out for a relativistic electron in a dipole field, showing agreement with analytic expressions. The results are relevant to experiments, which are concerned with injection of relativistic beams into the atmosphere from aboard a spacecraft in the magnetosphere.

A barium titanate ferroelectric cylindrical plasma source has been developed, tested and delivered for the Neutralized Drift Compression Experiment NDCX-II at Lawrence Berkeley National Laboratory (LBNL). The plasma source design is based on the successful design of the NDCX-I plasma source. A 7 kV pulse applied across the 3.8 mm-thick ceramic cylinder wall produces a large polarization surface charge density that leads to breakdown and plasma formation. The plasma that fills the NDCX-II drift section upstream of the final-focusing solenoid has a plasma number density exceeding 10 10 cm −3 and an electron temperature of several eV. The operating principle of the ferroelectric plasma source are reviewed and a detailed description of the installation plans is presented. The criteria for plasma sources with larger number density will be given, and concepts will be presented for plasma sources for driver applications. Plasma sources for drivers will need to be highly reliable, and operate at several Hz for millions of shots.

The streaming of an intense ion beam relative to background plasma can cause the development of fast electrostatic collective instabilities. The plasma waves produced by the two-stream instability modify the ion beam current neutralization and produce non-linear average forces which can lead to defocusing of the ion beam. Recently, a theoretical model describing the average de-focusing forces acting on the beam ions has been developed, and the scalings of the forces with beam-plasma parameters have been identified (Startsev et al. in press [1] ). These scalings can be used in the development of realistic ion beam compression scenarios in present and next-generation ion-beam-driven high energy density physics and heavy ion fusion experiments. In this paper the results of particle-in-cell simulations of ion beam propagation through neutralizing background plasma for NDCX-II parameters are presented. The simulation results show that the two-stream instability can play a significant role in the ion beam dynamics. The effects of velocity tilt on the development of the instability and ion beam compressibility for typical NDCX-II parameters are also simulated. It is shown that the two-stream instability may be an important factor in limiting the maximum longitudinal compression of the ion beam.

We study formation of the Vibrational Distribution Function (VDF) in a molecular gas at low pressure, when vibrational levels are excited by electron impact and deactivated in collisions with walls and show that this problem has a convenient analytical solution that can be used to obtain VDF and its dependence on external parameters. The VDF is determined by excitation of vibrational levels by an external source and deactivation in collisions with the wall. Deactivation in wall collisions is little known process. However, we found that the VDF is weakly dependent on the functional form of the actual form of probability gamma_v'->v for a vibrational number v' to transfer into a lower level v at the wall. Because for a given excitation source of vibrational states, the problem is linear the solution for VDF involves solving linear matrix equation. The matrix equation can be easily solved if we approximate probability, in the form: gamma_v'->v=(1/v')theta(v'->v). In this case, the steady-state solution for VDF(v) simply involves a sum of source rates for levels above , with a factor of 1/(v+1). As an example of application, we study the vibrational kinetics in a hydrogen gas and verify the analytical solution by comparing with a full model., 11 pages, 6 figures, letter

The excitation and propagation of electrostatic solitary waves(ESWs) are observed in two-dimensional particle-in-cell simulations of ion beam neutralization by electron injection by a filament. Electrons from the filament are attracted by positive ions and bounce inside ion beam pulse. Bouncing back and forth electron streams then starts to mix, creating the two-stream instability. The instability saturates with the formation of ESWs. These ESWs reach several centimeters in longitudinal size and are stable for a long time. The excitation of large-amplitude ESWs reduces the degree of neutralization of the ion beam pulse. In addition, the dissipation of ESWs causes heating of neutralizing electrons and their escape from the ion beam, leading to further reduction of neutralization degree., 9 pages, 5 figures

Hall plasma devices operate in the regimes when the electrons are magnetized and ions are not. In these conditions standard drift waves due to the plasma density gradient do not exist however another mode appears as a result of the combined response of the inertia of un-magnetized ions and electron drift. This mode is destabilized by the ExB electron drift due to the equilibrium electric field: this is the collisionless Simon-Hoh instability. The local theory predicts that the condition 4ω∗ωE > k⊥2Cs2 is required for the instability, ω∗ and ωE are the electron drift frequency and frequency of the equilibrium ExB drift, respectively; k⊥ is the wave-vector perpendicular to the magnetic field, and Cs is the ion sound velocity. We investigate stability of this mode in general case with spatial profiles of ω∗ and ωE when the local theory is not applicable. The stability of nonlocal modes in slab and cylindrical geometry are investigated numerically with Chebyshev spectral method. The results of theoretical analysis are compared with experimental results from Penning and Hall thruster experiments in an attempt to identify the source of large scale structures in these discharges.

The plasma inside a Hall thruster is a complex environment full of instabilities and interesting physical phenomena such as anomalous transport. To better understand this complex plasma dynamics, a nonlinear fluid model has been developed. The model contains the effect of electron inertia, electron collisions, electron temperature and density gradients as well as nonlinearities in the ion velocity and the electron advection term that arises from the ExB drift. The model is simulated using BOUT++, a framework for plasma simulations developed at the Lawrence Livermore National Laboratory. The linear limits of the model correspond to the lower hybrid mode rendered unstable by collisions and to the density gradient drift instabilities.

This paper reviews and discusses recent experimental, theoretical, and numerical studies of plasma-wall interaction in a weakly collisional magnetized plasma bounded with channel walls made from different materials. A low-pressure E ×B plasma discharge of the Hall thruster was used to characterize the electron current across the magnetic field and its dependence on the applied voltage and the electron-induced secondary electron emission (SEE) from the channel wall. The presence of a depleted anisotropic electron energy distribution function with beams of secondary electrons was predicted to explain the enhancement of the electron cross-field current observed in experiments. Without the SEE, the electron cross-field transport can be reduced from anomalously high to nearly classical collisional level. The suppression of the SEE was achieved using an engineered carbon-velvet material for the channel walls. Both theoretically and experimentally, it is shown that the electron emission from the walls can limit the maximum achievable electric field in the magnetized plasma. With nonemitting walls, the maximum electric field in the thruster can approach a fundamental limit for a quasi-neutral plasma.

An quasi-analytical model has been developed to map out the low-pressure (left-hand) branch of the Paschen curve at very high voltage when electrons are in the runaway regime and charge exchange/ionization avalanche by ions and fast neutral atoms becomes important. The model has been applied to helium gas between parallel-plate electrodes, at potentials ranging in magnitude between 10 and 1000 kilovolt. The respective value of reduced electric field E/n varies in the range of 50-6000kTd, with reduced density nd (where n is the gas density and d is the inter-electrode distance) on the order of 10^20 m^-2. Three regimes of the breakdown have been identified according to relative share of impact ionization by electrons, by ions, and by fast neutrals. The analytical Paschen curve is compared to those obtained with a detailed Particle-In-Cell/Monte Carlo (PIC/MCC) simulation, and also to experimental measurements [11]. The model provides accurate predictions for up to ~1000kTd , constrained by availability and quality of required input data.

A rotating plasma spoke is shown to develop in two-dimensional full-sized kinetic simulations of a Penning discharge cross-section. Electron cross-field transport within the discharge is highly anomalous and correlates strongly with the spoke phase. Similarity between collisional and collisionless simulations demonstrates that ionization is not necessary for spoke formation. Parameter scans with discharge current $I_d$, applied magnetic field strength $B$ and ion mass $m_i$ show that spoke frequency scales with $\sqrt{e E_r L_n / m_i}$, where $E_r$ is the radial electric field, $L_n$ is the gradient length scale and $e$ is the fundamental charge. This scaling suggests that the spoke may develop as a non-linear phase of the collisionless Simon-Hoh instability.

Electrostatic particle-in-cell simulations of a Penning discharge are performed in order to investigate azimuthally asymmetric, spoke-like structures previously observed in experiments. Two-dimensional simulations show that for Penning-discharge conditions, a persistent nonlinear spoke-like structure forms readily and rotates in the direction of ExB and electron diamagnetic drifts. The azimuthal velocity is within about a factor of two of the ion acoustic speed. The spoke frequency follows the experimentally observed scaling with ion mass, which indicates the importance of ion inertia in spoke formation. The spoke provides enhanced (anomalous) radial electron transport, and the effective cross-field conductivity is several times larger than the classical (collisional) value. The level of anomalous current obtained in the simulations is in good agreement with the experimental data. The rotating spoke channels most of the radial current, observable by an edge probe as short pulses., Submitted to PoP, revised version

Hall thruster operation is characterized by strong breathing oscillations of the discharge current, the plasma density, the temperature, and the electric field. Probe- and laser-induced fluorescence (LIF) diagnostics were used to measure temporal variations of plasma parameters and the xenon ion velocity distribution function (IVDF) in the near-field plasma plume in regimes with moderate (

The long-time evolution of the two-stream instability of a cold ion beam pulse propagating though the background plasma is investigated using a large-scale one-dimensional electrostatic kinetic simulation. The three stages of the instability are identified and investigated in detail. After the initial linear growth and saturation by the electron trapping, a portion of the initially trapped electrons becomes detrapped and moves ahead of the ion beam pulse forming a {forerunner} electron beam, which causes a secondary two-stream instability that preheats the upstream plasma electrons. Consequently, the self-consistent nonlinear-driven turbulent state is set up at the head of the ion beam pulse with the saturated plasma wave sustained by the influx of the cold electrons from the upstream of the beam that lasts until the final stage when the beam ions become trapped by the plasma wave. The beam ion trapping leads to the nonlinear heating of the beam ions that eventually extinguishes the instability.

Interaction of an intense electron beam with a finite-length, inhomogeneous plasma is investigated numerically. The plasma density profile is maximal in the middle and decays towards the plasma edges. Two regimes of the two-stream instability are observed. In one regime, the frequency of the instability is the plasma frequency at the density maximum and plasma waves are excited in the middle of the plasma. In the other regime, the frequency of the instability matches the local plasma frequency near the edges of the plasma and the intense plasma oscillations occur near plasma boundaries. The latter regime appears sporadically and only for strong electron beam currents. This instability generates copious amount of suprathermal electrons. The energy transfer to suprathermal electrons is the saturation mechanism of the instability.

Evaluation of ion–atom charge-changing cross-sections is needed for many accelerator applications. A Classical Trajectory Monte Carlo (CTMC) simulation has been used to calculate ionization and charge-exchange cross-sections. For benchmarking purposes, an extensive study has been performed for the simple case of hydrogen and helium targets in collisions with various ions. Despite the fact that the simulation only accounts for classical mechanics, the calculations are comparable to experimental results for projectile velocities in the region corresponding to the vicinity of the maximum cross-section. The shortcomings of the CTMC method for multielectron target atoms are discussed.

This paper presents a survey of the present theoretical understanding based on advanced analytical and numerical studies of collective processes and beam–plasma interactions in intense heavy ion beams for applications to ion-beam-driven high energy density physics and heavy ion fusion. The topics include: discussion of the conditions for quiescent beam propagation over long distances; and the electrostatic Harris instability and the transverse electromagnetic Weibel instability in highly anisotropic, intense one-component ion beams. In the longitudinal drift compression and transverse compression regions, collective processes associated with the interaction of the intense ion beam with a charge-neutralizing background plasma are described, including the electrostatic electron–ion two-stream instability, the multispecies electromagnetic Weibel instability, and collective excitations in the presence of a solenoidal magnetic field. The effects of a velocity tilt on reducing two-stream instability growth rates are also discussed. Operating regimes are identified where the possible deleterious effects of collective processes on beam quality are minimized.

Over the past two years noteworthy experimental and theoretical progress has been made towards the top-level scientific question for the US programme on heavy-ion-fusion-science and high energy density physics: ‘How can heavy-ion beams be compressed to the high intensity required to create high energy density matter and fusion conditions?’ New results in transverse and longitudinal beam compression, high-brightness transport and beam acceleration will be reported. Central to this campaign is final beam compression. With a neutralizing plasma, we demonstrated transverse beam compression by an areal factor of over 100 and longitudinal compression by a factor of >50. We also report on the first demonstration of simultaneous transverse and longitudinal beam compression in plasma. High beam brightness is key to high intensity on target, and detailed experimental and theoretical studies on the effect of secondary electrons on beam brightness degradation are reported. A new accelerator concept for nearterm low-cost target heating experiments was invented, and the predicted beam dynamics validated experimentally. We show how these scientific campaigns have created new opportunities for interesting target experiments in the warm dense matter regime. Finally, we summarize progress towards heavy-ion fusion, including the demonstration of a compact driver-size high-brightness ion injector. For all components of our high intensity campaign, the new results have been obtained via tightly coupled efforts in experiments, simulations and theory.

Longitudinal compression factors in excess of 50 of a 300-keV, 20-mA K + ion beam have been demonstrated in the Neutralized Drift Compression Experiment (NDCX) in agreement with LSP particle-in-cell simulations using the experimental tilt voltage waveform. Here, pre-formed plasma provides beam neutralization for a 1–2-m drift length. To achieve simultaneous transverse and longitudinal compression, we must understand and account for the impact of the applied velocity tilt on the transverse phase space of the beam. Of equal importance to achieving warm dense matter and heavy ion fusion conditions, is quantifying the effect of beam plasma interactions, including stability and neutralization, on the beam transport throughout the drift section up to the target. Critical new issues relate to transverse focusing of the axially compressing ion beam in a high-field (3–15 T) solenoid that is filled with plasma. Integrated LSP simulations that include modeling of the diode, magnetic transport, induction bunching module, plasma neutralized transport, solenoidal focusing and beam target interaction, are assisting in the design of a near-term warm dense matter experiment. We discuss the simulation algorithms and present calculations of designs for such an experiment that will heat an aluminum target up to roughly 1-eV temperature.

We present simulations and analysis of the heating of warm dense matter foils by ion beams with ion energy less than one MeV per nucleon to target temperatures of order one eV. Simulations were carried out using the multi-physics radiation hydrodynamics code HYDRA and comparisons are made with analysis and the code DPC. We simulate possible targets for a proposed experiment at LBNL (the so-called Neutralized Drift Compression Experiment, NDCXII) for studies of warm dense matter. We compare the dynamics of ideally heated targets, under several assumed equation of states, exploring dynamics in the two-phase (fluid-vapor) regime.

Properties of the multi-species electromagnetic Weibel instability are investigated for an intense ion beam propagating through background plasma. Assuming that the background plasma electrons provide complete charge and current neutralization, detailed linear stability properties are calculated within the framework of a macroscopic cold-fluid model for a wide range of system parameters.

This paper presents plans for neutralized drift compression experiments, precursors to future target heating experiments. The target-physics objective is to study warm dense matter (WDM) using short-duration (∼1 ns) ion beams that enter the targets at energies just above that at which dE/dx is maximal. High intensity on target is to be achieved by a combination of longitudinal compression and transverse focusing. This work will build upon recent success in longitudinal compression, where the ion beam was compressed lengthwise by a factor of more than 50 by first applying a linear head-to-tail velocity tilt to the beam, and then allowing the beam to drift through a dense, neutralizing background plasma. Studies on a novel pulse line ion accelerator were also carried out. It is planned to demonstrate simultaneous transverse focusing and longitudinal compression in a series of future experiments, thereby achieving conditions suitable for future WDM target experiments. Future experiments may use solenoids for transverse focusing of un-neutralized ion beams during acceleration. Recent results are reported in the transport of a high-perveance heavy ion beam in a solenoid transport channel. The principal objectives of this solenoid transport experiment are to match and transport a space-charge-dominated ion beam, and to study associated electron-cloud and gas effects that may limit the beam quality in a solenoid transport system. Ideally, the beam will establish a Brillouin-flow condition (rotation at one-half the cyclotron frequency). Other mechanisms that potentially degrade beam quality are being studied, such as focusing-field aberrations, beam halo, and separation of lattice focusing elements.

This paper presents a survey of the present theoretical understanding of plasma neutralization of intense heavy ion beams. Particular emphasis is placed on determining the degree of charge and current neutralization. We previously developed a reduced analytical model of beam charge and current neutralization for an ion beam pulse propagating in a cold background plasma. The model made use of the conservation of generalized fluid vorticity. The predictions of the analytical model agree very well with numerical simulation results. The model predicts very good charge neutralization during quasi-steady-state propagation, provided the beam pulse duration is much longer than the electron plasma period. In the opposite limit, the beam pulse excites large-amplitude plasma waves. If the beam density is larger than the background plasma density, the plasma waves break, which leads to electron heating. The reduced-fluid description provides an important benchmark for numerical codes and yields useful scaling relations for different beam and plasma parameters. This model has been extended to include the additional effects of a solenoidal magnetic field, gas ionization and the transition regions during beam pulse entry and exit from the plasma. Analytical studies show that a sufficiently large solenoidal magnetic field can increase the degree of current neutralization of the ion beam pulse. However, simulations also show that the self-magnetic field structure of the ion beam pulse propagating through background plasma can be complex and non-stationary. Plasma waves generated by the beam head are greatly modified, and whistler waves propagating ahead of the beam pulse are excited during beam entry into the plasma. Accounting for plasma production by gas ionization yields a larger self-magnetic field of the ion beam compared to the case without ionization, and a wake of the current density and self-magnetic field are generated behind the beam pulse. Beam propagation in a dipole magnetic field configuration and background plasma has also been studied.

To create high-energy density matter and fusion conditions, high-power drivers, such as lasers, ion beams, and X-ray drivers, may be employed to heat targets with short pulses compared to hydro-motion. Both high-energy density physics and ion-driven inertial fusion require the simultaneous transverse and longitudinal compression of an ion beam to achieve high intensities. We have previously studied the effects of plasma neutralization for transverse beam compression. The scaled experiment, the Neutralized Transport Experiment (NTX), demonstrated that an initially un-neutralized beam can be compressed transversely to � 1 mm radius when charge neutralization by background plasma electrons is provided. Here, we report longitudinal compression of a velocity-tailored, intense, neutralized 25 mA K + beam at 300 keV. The compression takes place in a 1–2 m drift section filled with plasma to provide space-charge neutralization. An induction cell produces a head-to-tail velocity ramp that longitudinally compresses the neutralized beam, enhances the beam peak current by a factor of 50 and produces a pulse duration of about 3 ns. The physics of longitudinal compression, experimental procedure, and the results of the compression experiments are presented. r 2007 Elsevier B.V. All rights reserved.

Electron energy probability functions (eepfs) have been measured along the axis of a low pressure plasma expanding in a magnetic nozzle. The eepf at the maximum magnetic field of the nozzle shows a depleted tail commencing at an energy corresponding to the measured potential drop in the magnetic nozzle. The eepfs measured along the axis demonstrate that the sum of potential and kinetic energies of the electrons is conserved thus confirming the validity of non-local approach to kinetics of the electron dynamics of a low-pressure plasma expanding in a magnetic nozzle.

We have commenced experiments with intense short pulses of ion beams on the Neutralized Drift Compression Experiment-II at Lawrence Berkeley National Laboratory, by generating beam spots size with radius r < 1 mm within 2 ns FWHM and approximately 10^10 ions/pulse. To enable the short pulse durations and mm-scale focal spot radii, the 1.2 MeV Li+ ion beam is neutralized in a 1.6-meter drift compression section located after the last accelerator magnet. An 8-Tesla short focal length solenoid compresses the beam in the presence of the large volume plasma near the end of this section before the target. The scientific topics to be explored are warm dense matter, the dynamics of radiation damage in materials, and intense beam and beam-plasma physics including selected topics of relevance to the development of heavy-ion drivers for inertial fusion energy. Here we describe the accelerator commissioning and time-resolved ionoluminescence measurements of yttrium aluminium perovskite using the fully integrated accelerator and neutralized drift compression components., 7 pages, 9 figures

Generation of anomalously energetic suprathermal electrons was observed in simulation of a high- voltage dc discharge with electron emission from the cathode. An electron beam produced by the emission interacts with the nonuniform plasma in the discharge via a two-stream instability. Efficient energy transfer from the beam to the plasma electrons is ensured by the plasma nonuniformity. The electron beam excites plasma waves whose wavelength and phase speed gradually decrease towards anode. The short waves near the anode accelerate plasma bulk electrons to suprathermal energies. The sheath near the anode reflects some of the accelerated electrons back into the plasma. These electrons travel through the plasma, reflect near the cathode, and enter the accelerating area again but with a higher energy than before. Such particles are accelerated to energies much higher than after the first acceleration. This mechanism plays a role in explaining earlier experimental observations of energetic suprathermal electrons in similar discharges., Comment: 5 pages

A particle-in-cell code has been developed for simulations of plasmas of Hall thruster discharges. The simulated system is a plasma slab bounded by dielectric walls with secondary electron emission. An external, accelerating electric field directed parallel to the walls and an external magnetic field directed normal to the walls are applied. The strongly anisotropic non-Maxwellian electron velocity distribution function is obtained in simulations. The average energy of electron motion parallel to the walls is defined by collisional heating in the accelerating electric field. This energy is much higher than the average energy of electron motion normal to the walls, which is determined by the energy of electrons produced in ionization and by scattering of electrons by neutral atoms. The electron distribution function for velocity components normal to the walls is depleted for energies above the near-wall plasma potential. The effects of Coulomb collisions on the electron velocity distribution function and electron wall losses are studied

In low-pressure radio-frequency (RF) discharges, the electron-energy distribution function (EEDF) is typically non-Maxwellian for low plasma density. The nonlocal plasma conductivity, plasma density profiles, and EEDF are all nonlinear and nonlocally coupled. For accurate calculation of the discharge characteristics, the EEDF needs to be computed self-consistently. The method of fast self-consistent one-dimensional of planar inductively coupled discharges driven by a RF electromagnetic field is presented. The effects of a non-Maxwellian EEDF, plasma nonuniformity, and finite size, as well as the influence of the external magnetic field on the plasma properties are considered and discussed

Experimental details on providing active neutralization of high brightness ion beam have been demonstrated for Heavy Ion Fusion program. A K + beam was extracted from a variable–perveance injector and transported through 2.4 m long quadrupole lattice for final focusing. Neutralization was provided by a localized cathode arc plasma plug and a RF volume plasma system. Effects of beam perveance, emittance, convergence focusing angle, and axial focusing position on neutralization have been investigated. Good agreement has been observed with theory and experiment throughout the study. r 2005 Elsevier B.V. All rights reserved. PACS: 52.59.Bi,Fn; 29.27.� a; 52.40.Mj; 41.75.Fr,Ht; 29.27.� a

Knowledge of ion–atom ionization cross-sections is of great importance for many accelerator applications. We have recently investigated theoretically and experimentally the stripping of more than 18 different pairs of projectile and target particles in the range of 3–38 MeV/amu to study the range of validity of both the Born approximation and the classical trajectory calculation. In most cases, both approximations give similar results. However, for fast projectile velocities and low-ionization potentials, the classical approach is not valid and can overestimate the stripping cross-sections by neutral atoms by an order-of-magnitude. Therefore, a hybrid approach that automatically chooses between the Born approximation and the classical mechanics approximation depending on the parameters of the collision has been developed. When experimental data and theoretical calculations are not available, approximate formulas are frequently used. Based on experimental data and theoretical predictions, a new fit formula for ionization cross-sections by fully stripped ions is proposed. The resulting plots of the scaled ionization cross-sections of hydrogen by fully stripped ions are presented. The new fit formula has also been applied to the ionization cross-sections of helium. Again, the experimental and theoretical results merge close together on the scaled plot.

Ion beam pulse propagation through a background plasma in a solenoidal magnetic field has been studied analytically. The neutralization of the ion beam current by the plasma has been calculated using a fluid description for the electrons. This study is an extension of our previous studies of beam neutralization without an applied magnetic field. The high solenoidal magnetic field inhibits radial electron transport, and the electrons move primarily along the magnetic field lines. For high-intensity ion beam pulses propagating through a background plasma with pulse duration much longer than the electron plasma period, the quasi-neutrality condition holds, n e = n b + n p , where n e is the electron density, n b is the density of the ion beam pulse, and n p is the density of the background plasma ions (assumed unperturbed by the beam). For one-dimensional electron motion, the charge density continuity equation ∂ ρ / ∂ t + ∇ · j = 0 combined with the quasi-neutrality condition [ ρ = e ( n b + n p - n e ) = 0 ] yields j = 0 . Therefore, in the limit of a strong solenoidal magnetic field, the beam current is completely neutralized. Analytical studies show that the solenoidal magnetic field starts to influence the radial electron motion if ω ce ⩾ ω pe β (where ω ce = eB / mc is the electron gyrofrequency, ω pe is the electron plasma frequency, and β = V b / c is the ion beam velocity relative to the speed of light). This condition holds for relatively small magnetic fields. For example, for a 100 MeV, 1 kA Ne + ion beam ( β = 0.1 ) and a plasma density of 10 11 cm - 3 , B corresponds to a magnetic field of 100 G.

Plasma neutralization of an intense ion pulse is of interest for many applications, including plasma lenses, heavy ion fusion, cosmic ray propagation, etc. An analytical electron fluid model has been developed to describe the plasma response to a propagating ion beam. The model predicts very good charge neutralization during quasi-steady-state propagation, provided the beam pulse duration {tau}{sub b} is much longer than the electron plasma period 2{pi}/{omega}{sub p}, where {omega}{sub p} = (4{pi}e{sup 2}n{sub p}/m){sup 1/2} is the electron plasma frequency and n{sub p} is the background plasma density. In the opposite limit, the beam pulse excites large-amplitude plasma waves. If the beam density is larger than the background plasma density, the plasma waves break. Theoretical predictions are compared with the results of calculations utilizing a particle-in-cell (PIC) code. The cold electron fluid results agree well with the PIC simulations for ion beam propagation through a background plasma. The reduced fluid description derived in this paper can provide an important benchmark for numerical codes and yield scaling relations for different beam and plasma parameters. The visualization of numerical simulation data shows complex collective phenomena during beam entry and exit from the plasma.

In low-pressure discharges, where the electron mean free path is larger or comparable with the discharge length, the electron dynamics is essentially nonlocal. Moreover, the electron energy distribution function (EEDF) deviates considerably from a Maxwellian. Therefore, an accurate kinetic description of the low-pressure discharges requires knowledge of the nonlocal conductivity operator and calculation of the non-Maxwellian EEDF. The previous treatments made use of simplifying assumptions: a uniform density profile and a Maxwellian EEDF. In the present study a self-consistent system of equations for the kinetic description of nonlocal, nonuniform, nearly collisionless plasmas of low-pressure discharges is reported. It consists of the nonlocal conductivity operator and the averaged kinetic equation for calculation of the non-Maxwellian EEDF. This system was applied to the calculation of collisionless heating in capacitively and inductively coupled plasmas. In particular, the importance of accounting for t...

Knowledge of ion-atom ionization cross sections is of great importance for many applications. When experimental data and theoretical calculations are not available, approximate formulas are frequently used. Based on experimental data and theoretical predictions, a new fit for ionization cross sections by fully stripped ions is proposed.

One approach being explored as a route to practical fusion energy uses heavy ion beams focused on an indirect drive target. Such beams will lose electrons while passing through background gas in the target chamber, and therefore it is necessary to assess the rate at which the charge state of the incident beam evolves on the way to the target. Accelerators designed primarily for nuclear physics or high energy physics experiments utilize ion sources that generate highly stripped ions in order to achieve high energies economically. As a result, accelerators capable of producing heavy ion beams of 10 to 40 MeV/amu with charge state 1 currently do not exist. Hence, the stripping cross sections used to model the performance of heavy ion fusion driver beams have, up to now, been based on theoretical calculations. We have investigated experimentally the stripping of 3.4 MeV/amu Kr+7 and Xe+11 in N2; 10.2 MeV/amu Ar+6 in He, N2, Ar, and Xe; 19 MeV/amu Ar+8 in He, N2, Ar, and Xe; 30 MeV He+1 in He, N2, Ar, and Xe; and 38 MeV/amu N+6 in He, N2, Ar, and Xe. The results of these measurements are compared with the theoretical calculations to assess their applicability over a wide range of parameters.

This article presents analytical and simulation studies of intense heavy ion beam propagation, including the injection, acceleration, transport and compression phases, and beam transport and focusing in background plasma in the target chamber. Analytical theory and simulations that support the High Current Experiment (HCX), the Neutralized Transport Experiment (NTX), and the advanced injector development program, are being used to provide a basic understanding of the nonlinear beam dynamics and collective processes, and to develop design concepts for the next-step Integrated Beam Experiment (IBX), an Integrated Research Experiment (IRE), and a heavy ion fusion driver. Three-dimensional nonlinear perturbative simulations have been applied to collective instabilities driven by beam temperature anisotropy, and to two-stream interactions between the beam ions and any unwanted background electrons; three-dimensional particle-in-cell simulations of the 2-MV electrostatic quadrupole (ESQ) injector have clarified the influence of pulse rise time; analytical studies and simulations of the drift compression process have been carried out; syntheses of a four-dimensional particle distribution function from phase-space projections have been developed; and studies of the generation and trapping of stray electrons in the beam self-fields have been performed. Particle-in-cell simulations, involving preformed plasma, are being used to study the influence of charge and current neutralization on the focusing of the ion beam in NTX and in a fusion chamber.

The propagation of a high-current finite-length ion charge bunch through a background plasma is of interest for many applications, including heavy ion fusion, plasma lenses, cosmic ray propagation, and so forth. Charge neutralization has been studied both analytically and numerically during ion beam entry, propagation, and exit from the plasma. A suite of codes has been developed for calculating the degree of charge and current neutralization of the ion beam pulse by the background plasma. The code suite consists of two different codes: a fully electromagnetic, relativistic particle-in-cell code, and a relativistic Darwin model for long beams. As a result of a number of simplifications, the second code is hundreds of times faster than the first one and can be used for most cases of practical interest, while the first code provides important benchmarking for the second. An analytical theory has been developed using the assumption of long charge bunches and conservation of generalized vorticity. The model predicts nearly complete charge neutralization during quasi-steady-state propagation provided the beam pulse duration τb is much longer than the inverse electron plasma frequency ωp−1, where ωp = (4πnpe2/me)1/2 and np is the background plasma density. In the opposite limit, the beam head excites large-amplitude plasma waves. Similarly, the beam current is well neutralized provided ωpτb >> 1 and the beam radius is much larger than plasma skin depth δp = c/ωp. Equivalently, the condition for current neutralization can be expressed in terms of the beam current as Ib >> 4.25Zb βb(nb /np)kA, where nb is the beam density, Zb is the ion charge, and Vb = βbc is the beam velocity; and the condition for charge neutralization can be expressed as Ib >> 4.25βb3(nb /np)(rb /lb)2kA, where lb and rb are the beam length and radius, respectively. For long charge bunches, the analytical results agree well with the results of numerical simulations. The visualization of the data obtained in the numerical simulations shows complex collective phenomena during beam entry into and exit from the plasma.

The left branch of the Paschen curve for helium gas is studied both experimentally and by means of particle-in-cell/Monte Carlo collision (PIC/MCC) simulations. The physical model incorporates electron, ion, and fast atom species whose energy-dependent anisotropic scattering on background neutrals, as well as backscattering at the electrodes, is properly accounted for. For the range of breakdown voltage 15 kV≤Vbr≤130 kV, a good agreement is observed between simulations and available experimental results for the discharge gap d = 1.4 cm. The PIC/MCC model is used to predict the Paschen curve at higher voltages up to 1 MV, based on the availability of input atomic data. We find that the pd similarity scaling does hold and that above 300 kV, the value of pd at breakdown begins to increase with increasing voltage. To achieve good agreement between PIC/MCC predictions and experimental data for the Paschen curve, it is essential to account for impact ionization by fast atoms (produced in charge exchange) and ions and for anisotropic scattering of all species on background atoms. With the increase of the applied voltage, energetic fast atoms progressively dominate in the overall ionization rate. The model makes this clear by predicting that breakdown would occur even without electron- and ion-induced ionization of the background gas, due to ionization by fast atoms backscattered at the cathode, and their high production rate in charge exchange collisions. Multiple fast neutrals per ion are produced when the free path is small compared to the electrode gap.