Hybrid Plasma Simulation Research Articles

HPIC2: A hardware-accelerated, hybrid particle-in-cell code for dynamic plasma-material interactions

The exascale era of high performance computing promises to bring the field of computational plasma physics ever closer to the goal of accurate multiscale modeling. Such computers will rely on hardware acceleration to offload work to dedicated components, notably general-purpose graphics processing units (GPUs). However, devices from different manufacturers require software to be written with different parallel programming models, greatly increasing the code maintenance burden of applications designed to perform on more than one such device. hPIC2 is a hybrid plasma simulation code developed with the Kokkos performance portability framework to target the architectures that will drive exascale computing for the foreseeable future. As a hybrid simulation code, hPIC2 investigates the simultaneous use of various plasma models on the same domain, at the same time. hPIC2 also optionally couples to RustBCA, which accurately models ion-material interactions using the binary collision approximation (BCA) method [1]. hPIC2 therefore achieves scalable performance on a variety of computing architectures when simulating complex and diverse plasmas, particularly near plasma-material interfaces.

Hybrid plasma simulations of a magnetically shielded Hall thruster

Numerical simulations of a magnetically shielded Hall effect thruster with a centrally mounted cathode are performed with an axisymmetric hybrid particle-in-cell/fluid code and are partially validated with experimental data. A full description of the plasma discharge inside the thruster chamber and in the near plume is presented and discussed, with the aim of highlighting those features most dependent on the magnetic configuration and the central cathode. Compared to traditional magnetic configurations, the acceleration region is mainly outside the thruster, whereas high plasma densities and low temperatures are found inside the thruster. Thus, magnetic shielding does not decrease plasma currents to the walls, but reduces significantly the energy fluxes, yielding low heat loads and practically no wall erosion. The injection of neutrals at the central cathode generates a secondary plasma plume that merges with the main one and facilitates much the drift of electrons toward the chamber. Once inside, the magnetic topology is efficient in channeling electron current away from lateral walls. Current and power balances are analyzed to assess performances in detail.

Remote sensing of cometary bow shocks: modelled asymmetric outgassing and pickup ion observations

ABSTRACT Despite the long escort by the ESA Rosetta mission, direct observations of a fully developed bow shock around 67P/Churyumov–Gerasimenko have not been reported. Expanding on our previous work on indirect observations of a shock, we model the large-scale features in cometary pickup ions, and compare the results with the ESA Rosetta Plasma Consortium Ion Composition Analyser ion spectrometer measurements over the pre-perihelion portion of the escort phase. Using our hybrid plasma simulation, an empirical, asymmetric outgassing model for 67P, and varied interplanetary magnetic field (IMF) clock angles, we model the evolution of the large-scale plasma environment. We find that the subsolar bow shock standoff distance is enhanced by asymmetric outgassing with a factor of 2 to 3, reaching up to $18\,000\, \rm {km}$ approaching perihelion. We find that distinct spectral features in simulated pickup ion distributions are present for simulations with shock-like structures, with the details of the spectral features depending on shock standoff distance, heliocentric distance, and IMF configuration. Asymmetric outgassing along with IMF clock angle is found to have a strong effect on the location of the spectral features, while the IMF clock angle causes no significant effect on the bow shock standoff distance. These dependences further complicate the interpretation of the ion observations made by Rosetta. Our data-model comparison shows that the large-scale cometary plasma environment can be probed by remote sensing the pickup ions, at least when the comet’s activity is comparable to that of 67P, and the solar wind parameters are known.

Hybrid Plasma Simulations of Farley‐Buneman Instabilities in the Auroral E‐Region

AbstractWe implemented a hybrid continuous solver for fluid electrons and kinetic ions. Because the simulation is continuous, numerical noise is not an issue as it is for particle‐in‐cell approaches. Moreover, given that the ion kinetic equation is solved using a characteristic based method, no particle pushes have to be done. Our main goals are to reduce the computational cost of the simulations proposed by Kovalev (Kovalev et al., 2008, https://doi.org/10.5194/angeo2628532008) and reproduce the main experimental features of Farley‐Buneman instabilities measured by radars and rockets. The equations were derived from first principles using the approximations that are satisfied in the auroral E‐region. Various tests will be presented to assess numerical accuracy. With the proposed numerical framework, we are able to recover important nonlinear features associated with Farley‐Buneman instabilities: wave turning of dominant modes, and saturation of density irregularities at values consistent with experiments.

Three-dimensional hybrid simulation of single cathode spot vacuum arc plasma jet under axial magnetic field

Vacuum arc is a special metal vapor discharge phenomenon, because its discharge medium totally comes from the evaporation and ionization of electrode materials. In the case of low current, the vacuum arc is completely composed of plasma jets emitted from discrete cathode spots on the cathode surface and the current carried by each spot depends on the cathode material. When the arc current exceeds a certain value, a certain number of cathode spot plasma jets will appear. Vacuum arcs play a very important role in some industrial applications such as vacuum circuit breakers, vacuum coatings and electric thrusters. As an important plasma control method, the external axial magnetic field (AMF) has an important influence on the macroscopic morphology and microscopic parameter distribution of the vacuum arc. Various studies of vacuum arc under AMF have been carried out and some progress has been made. However, the existing literature about the simulation research of vacuum arc is mostly concentrated in the case of large current, and less attention is paid to the case of small current. The reason is that the traditional methods, magneto-hydrodynamics or particle-in-cell, are limited by either accuracy or efficiency, and cannot be effectively applied to the low current vacuum arc plasma jet simulations. In this paper, we develop a fully three-dimensional hybrid plasma simulation algorithm to study the single cathode spot vacuum arc plasma jet under AMF. In this model, ions are modelled as particles while electrons are treated as massless fluid, and the self-generated magnetic field is also considered. To simplify the condition, the cathode spot in our model only exists as a plasma jet source, thus the detailed mechanism of producing plasmas is neglected. And the movement of the cathode spot is not considered either. The results show that the single cathode spot plasma jet diffuses into the interelectrode in a cone shape after leaving the cathode spot, and the ion density drops rapidly from cathode to anode. Under the simulation conditions in this paper (<i>I</i> ≤ 150 A), the self-generated magnetic field will not have a significant influence on the plasma jet itself in the case of low current. The external AMF has a compressive effect on the diffusion of the vacuum arc plasma jet. Under the AMF, the radial movement of the ions is suppressed, and the decrease of the ion radial velocity leads to a smaller diffusion radius of the jet. This compression effect of the AMF on the plasma jet is related to both the intensity of the external AMF and the magnitude of the arc current. In the case of a constant arc current magnitude, the compression effect gradually increases as the value of the AMF intensity gradually increases; in the case of a constant value of the external AMF, the compression effect gradually decreases as the current gradually becomes larger.

3D hybrid modelling of the extinction of multiple cathode spots in vacuum

Plasma transport during continuous extinction processes from high-current arcs to full extinction is an important issue in the study of vacuum arcs. However, to describe this transition, the traditional methods, magneto hydrodynamics or particle-in-cell, are limited by either accuracy or efficiency. In this paper, we developed a fully 3D hybrid plasma simulation algorithm to study the extinction process of multiple cathode spots in a vacuum environment. Cathode spots are modelled as independent plasma sources rather than treating the whole cathode surface as an indivisible source. For a better balance between efficiency and accuracy, ions are modelled as particles and electrons are treated as a massless fluid. Using this model, the effects of cut-off time and the locations of cathode spots on the extinction process are studied. The results show that during an extinction process, the total number of ions between the electrodes gradually decreases and the mean velocity of the ions gradually increases. When the current approaches zero, two regions can be observed in the gap: the separated jet region, and the common plasma channel region. The last three surviving cathode spots have significant impacts on the ion distribution at current zero, whose values depend on the distances to them. The closer together the three cathode spots are, the higher the value that the local ion density will reach. In addition, at current zero, the maximum ion density appears near the last extinguished cathode spot.

Hybrid Simulations of Magnetodisc Transport Driven by the Rayleigh‐Taylor Instability

AbstractPlasma transport in the rapidly rotating giant magnetospheres is thought to involve a centrifugally driven flux tube interchange instability, similar to the Rayleigh‐Taylor (RT) instability. In three dimensions, the convective flow patterns associated with the RT instability can produce strong guide field reconnection, allowing plasma mass to move radially outward while conserving magnetic flux (Ma et al., 2016, https://doi.org/10.1002/2015JA022122). We present a set of hybrid (kinetic ion/fluid electron) plasma simulations of the RT instability using high plasma beta conditions appropriate for the inner and middle magnetosphere at Jupiter and Saturn. A density gradient, combined with a centrifugal force, provide appropriate RT onset conditions. Pressure balance requires only a temperature gradient as the magnetic pressure is constant. Pressure balance is achieved with a temperature gradient in a fixed magnetic field. The three‐dimensional simulation domain represents a local volume of the magnetodisc resonant cavity. Simulated RT growth rates compare favorably with linear theory, where the fundamental mode of the resonant cavity determines the largest (stabilizing) parallel wavelength. We suggest that the perpendicular scale of RT structures is determined by the fundamental mode, which limits growth due to magnetic tension. Finally, we investigated strong guide field magnetic reconnection and diffusive processes as plausible mechanisms to facilitate kinetic‐scale radial transport.

The Lunar Paleo‐Magnetosphere: Implications for the Accumulation of Polar Volatile Deposits

AbstractAnalyses of lunar samples suggest the Moon once possessed a dynamo from ~4.25 Ga until perhaps as recently as 1 Ga, with surface field strengths between ~5 and 100 μT. While the exact timing, strength, and structure of these paleomagnetic fields are not precisely known, such relatively strong fields imply that the Moon also likely possessed a magnetosphere. Here, we present hybrid plasma simulations of the structure and morphology of the putative lunar “paleo‐magnetosphere” for varying surface field strengths and orientations, using ambient solar wind conditions representative of the early Sun. The presence of the paleo‐magnetosphere reduces total solar wind fluxes to the lunar surface overall yet, for a spin‐aligned dynamo, increases the relative solar wind flux to the lunar polar regions. In turn, the paleo‐magnetosphere may have altered the rate of volatile accretion to the Moon over its history.

A generalized quasi-neutral fluid-particle hybrid plasma model and its application to energetic-particle-magnetohydrodynamics hybrid simulation

A generalized fluid-particle hybrid model for collisionless plasmas under the assumption of quasi-neutrality is presented. The system consists of fluid ions and electrons as well as arbitrary numbers of species whose dynamics is governed by the Vlasov equation. The proposed model is thus a generalized version of the well-known standard hybrid plasma simulation model, in which the ions are fully kinetic whereas the electrons are assumed to be a fluid. Since the proposed model employs the exact form of the generalized Ohm's law, the mass and energy densities, as well as the charge-to-mass ratio of the kinetic species, are taken to be arbitrary. In the absence of the kinetic species, it reduces to the quasi-neutral two-fluid model [1]. In the opposite situation where the mass and energy densities of the kinetic species are much larger than the fluid ions, it is nothing more than the standard hybrid model with finite electron inertia effect. If the kinetic species is an energetic particle (EP) population having negligible mass density but substantial energy density and the scale size is much larger than the ion and electron inertial lengths, it describes the self-consistent coupling between the magnetohydrodynamics (MHD) and the EP dynamics. The energetic-particle-magnetohydrodynamics (EP-MHD) hybrid model is thus a special case of the more general model described in this paper. Advantages of this approach over the existing models are discussed. A three-dimensional simulation code solving the proposed set of equations is described. The code combines the Particle-in-Cell scheme for solving the kinetic species and a Riemann-solver-based code for the two-fluid equations. Several benchmark simulation results are shown to confirm that the code successfully captures the dynamics of the EP population interacting self-consistently with the MHD fluid.

On the role of ion-scale whistler waves in space and astrophysical plasma turbulence

Abstract. Competition of linear mode waves is studied numerically to understand the energy cascade mechanism in plasma turbulence on ion-kinetic scales. Hybrid plasma simulations are performed in a 3-D simulation box by pumping large-scale Alfvén waves on the fluid scale. The result is compared with that from our earlier 2-D simulations. We find that the whistler mode is persistently present both in the 2-D and 3-D simulations irrespective of the initial setup, e.g., the amplitude of the initial pumping waves, while all the other modes are excited and damped such that the energy is efficiently transported to thermal energy over non-whistler mode. The simulation results suggest that the whistler mode could transfer the fluctuation energy smoothly from the fluid scale down to the electron-kinetic scale, and justifies the notion of whistler turbulence.

THE IBEX RIBBON AND THE PICKUP ION RING STABILITY IN THE OUTER HELIOSHEATH. I. THEORY AND HYBRID SIMULATIONS

ABSTRACT The nearly circular band of energetic neutral atom emission dominating the field of view of the Interplanetary Boundary Explorer (IBEX ) satellite, is most commonly attributed to the effect of charge exchange of secondary pickup ions (PUIs) gyrating about the magnetic field in the outer heliosheath and the interstellar space beyond. Several models for the PUI dynamics of this mechanism have been proposed, each requiring either strong or weak scattering of the initial pitch angle. Conventional wisdom states that ring distributions tend to generate waves and scatter onto a shell on timescales too short for charge exchange to occur. We performed a careful study of ring and thin shell proton distribution stability using theoretical tools and hybrid plasma simulations. We show that the kinetic behavior of a freshly injected proton ring is a far more complicated process than previously thought. In the presence of a warm Maxwellian core, narrower rings could be more stable than broader toroidal distributions. The scattered rings possess a fine structure that can only be revealed using very large numbers of macroparticles in a simulation. It is demonstrated that a “stability gap” in ring temperature exists where the protons could retain large gyrating anisotropies for years, and the wave activity could remain below the level of the ambient magnetic fluctuations in interstellar space. In the directions away from the ribbon, however, a partial shell distribution is more likely to be unstable, leading to significant scattering into one hemisphere in velocity space. The process is accompanied by turbulence production, which is puzzling given the very low level of magnetic fluctuations measured in the outer heliosheath by Voyager 1.

Modeling of the energetic ion observations in the vicinity of Rhea and Dione

During several flybys of the Cassini spacecraft by the saturnian moons Rhea and Dione the energetic particle detector MIMI/LEMMS measured a significant reduction of energetic ion fluxes (20–300keV) in their vicinity, which is caused by the absorption of those ions at the moon surfaces.In order to simulate the observed depletion profiles we developed an energetic particle tracer, which can be used to simulate the charged particle trajectories considering different models of the saturnian magnetosphere. This particle tracer is using an adaptive fourth order Gauss Runge–Kutta calculation method and its background magnetospheric model can be varied from that of a simple dipole, to a more complex one that includes also non-dipolar perturbations. The electromagnetic environment of each local, moon–magnetosphere interaction region is modeled through a hybrid plasma simulation code. Using this energetic particle tracer we explore which of these magnetospheric characteristics are more important in shaping the MIMI/LEMMS ion profiles. We also examine if MIMI/LEMMS responds primarily to protons (as typically assumed in many studies) or also to heavier ions, using calibration information, observations of the energy flux spectrum by the MIMI/CHEMS instrument (on board of Cassini as well) and different simulation results.Our results show that MIMI/LEMMS indeed measures heavier ions as well. Also we discovered that wrapping of magnetic field lines, even if it caused local perturbations only about few percent of the background magnetic field, can cause measurable changes in the spatial and energy distribution of fluxes measured by MIMI/LEMMS. These results are important for correct interpretation of MIMI/LEMMS data, and offer capabilities for a precise in-flight instruments’ cross-calibration. Besides that, our simulation approach can be employed in similar environments (Titan, Enceladus, jovian moons, etc.) for constraining the magnetic topology of their interaction region and for identifying the composition and charge-states of ions at high energies, where capabilities of the available or future instruments can be limited.

ARTEMIS observations of extreme diamagnetic fields in the lunar wake

We present two Acceleration, Reconnection, Turbulence, and Electrodynamics of the Moon's Interaction with the Sun (ARTEMIS) observations of diamagnetic fields in the lunar wake at strengths exceeding twice the ambient magnetic field during high plasma beta conditions. The first observation was 350 km from the lunar surface while the Moon was located in the terrestrial magnetosheath with elevated particle temperatures. The second observation was in the solar wind ranging from 500 to 2000 km downstream, with a relatively low magnetic field strength of approximately 1.6 nT. In both cases, the plasma beta exceeded 10. We discuss the observations and compare the data to hybrid plasma simulations in order to validate the model under such extreme conditions and to elucidate the global structure of the lunar wake during these observations. The extreme nature of the diamagnetic field in the lunar wake provides an important end-member test case for theoretical and modeling studies of the various plasma processes operating in the lunar wake.

H-VLPL: A three-dimensional relativistic PIC/fluid hybrid code

The novel PIC/fluid hybrid plasma simulation code H-VLPL3D is introduced. In addition to the particle-in-cell algorithm, it uses a new numerical fluid scheme for wake field simulations. Specially designed for the accurate simulation of very long wake fields, this scheme is capable of simulating ∼1000 plasma oscillations of the wake. A comprehensive description of the discretization schemes is given, and we demonstrate the code's correctness and its order of accuracy. Also, its superior efficiency in the plasma wake field acceleration (PWFA) regime is shown.

Spectral evolution of two-dimensional kinetic plasma turbulence in the wavenumber-frequency domain

We present a method for studying the evolution of plasma turbulence by tracking dispersion relations in the energy spectrum in the wavenumber-frequency domain. We apply hybrid plasma simulations in a simplified two-dimensional geometry to demonstrate our method and its applicability to plasma turbulence in the ion kinetic regime. We identify four dispersion relations: ion-Bernstein waves, oblique whistler waves, oblique Alfvén/ion-cyclotron waves, and a zero-frequency mode. The energy partition and frequency broadening are evaluated for these modes. The method allows us to determine the evolution of decaying plasma turbulence in our restricted geometry and shows that it cascades along the dispersion relations during the early phase with an increasing broadening around the dispersion relations.

Current flow and pair creation at low altitude in rotation-powered pulsars’ force-free magnetospheres: space charge limited flow

We report the results of an investigation of particle acceleration and electron–positron plasma generation at low altitude in the polar magnetic flux tubes of rotation-powered pulsars, when the stellar surface is free to emit whatever charges and currents are demanded by the force-free magnetosphere. We apply a new 1D hybrid plasma simulation code to the dynamical problem, using Particle-in-Cell methods for the dynamics of the charged particles, including a determination of the collective electrostatic fluctuations in the plasma, combined with a Monte Carlo treatment of the high-energy gamma-rays that mediate the formation of the electron–positron pairs. We assume the electric current flowing through the pair creation zone is fixed by the much higher inductance magnetosphere, and adopt the results of force-free magnetosphere models to provide the currents which must be carried by the accelerator. The models are spatially one dimensional, and designed to explore the physics, although of practical relevance to young, high-voltage pulsars. We observe novel behaviour (a) When the current density j is less than the Goldreich–Julian value (0 < j/jGJ < 1), space charge limited acceleration of the current carrying beam is mild, with the full Goldreich–Julian charge density comprising the charge densities of the beam and a cloud of electrically trapped particles with the same sign of charge as the beam. The voltage drops are of the order of mc2/e, and pair creation is absent. (b) When the current density exceeds the Goldreich–Julian value (j/jGJ > 1), the system develops high voltage drops (TV or greater), causing emission of curvature gamma-rays and intense bursts of pair creation. The bursts exhibit limit cycle behaviour, with characteristic time-scales somewhat longer than the relativistic fly-by time over distances comparable to the polar cap diameter (microseconds). (c) In return current regions, where j/jGJ < 0, the system develops similar bursts of pair creation. These discharges are similar to those encountered in previous calculations by Timokhin of pair creation when the surface has a high work function and cannot freely emit charge. In cases (b) and (c), the intermittently generated pairs allow the system to simultaneously carry the magnetospherically prescribed currents and adjust the charge density and average electric field to force-free conditions. We also elucidate the conditions for pair creating beam flow to be steady (stationary with small fluctuations in the rotating frame), finding that such steady flows can occupy only a small fraction of the current density parameter space exhibited by the force-free magnetospheric model. The generic polar flow dynamics and pair creation are strongly time dependent. The model has an essential difference from almost all previous quantitative studies, in that we sought the accelerating voltage (with pair creation, when the voltage drops are sufficiently large; without, when they are small) as a function of the applied current. The 1D results described here characterize the dependence of acceleration and pair creation on the magnitude and sign of current. The dependence on the spatial distribution of the current is a multi-dimensional problem, possibly exhibiting more chaotic behaviour. We briefly outline possible relations of the electric field fluctuations observed in the polar flows (both with and without pair creation discharges) to direct emission of radio waves, as well as revive the possible relation of the observed limit cycle behaviour to microstructure in the radio emission. Actually modelling these effects requires the multi-dimensional treatment, to be reported in a later paper.

Energetic electron observations of Rhea’s magnetospheric interaction

Saturn’s moon Rhea is thought to be a simple plasma absorber, however, energetic particle observations in its vicinity show a variety of unexpected and complex interaction features that do not conform with our current understanding about plasma absorbing interactions. Energetic electron data are especially interesting, as they contain a series of broad and narrow flux depletions on either side of the moon’s wake. The association of these dropouts with absorption by dust and boulders orbiting within Rhea’s Hill sphere was suggested but subsequently not confirmed, so in this study we review data from all four Cassini flybys of Rhea to date seeking evidence for alternative processes operating within the moon’s interaction region. We focus on energetic electron observations, which we put in context with magnetometer, cold plasma density and energetic ion data. All flybys have unique features, but here we only focus on several structures that are consistently observed. The most interesting common feature is that of narrow dropouts in energetic electron fluxes, visible near the wake flanks. These are typically seen together with narrow flux enhancements inside the wake. A phase-space-density analysis for these structures from the first Rhea flyby (R1) shows that Liouville’s theorem holds, suggesting that they may be forming due to rapid transport of energetic electrons from the magnetosphere to the wake, through narrow channels. A series of possibilities are considered to explain this transport process. We examined whether complex energetic electron drifts in the interaction region of a plasma absorbing moon (modeled through a hybrid simulation code) may allow such a transport. With the exception of several features (e.g. broadening of the central wake with increasing electron energy), most of the commonly observed interaction signatures in energetic electrons (including the narrow structures) were not reproduced. Additional dynamical processes, not simulated by the hybrid code, should be considered in order to explain the data. For the small scale features, the possibility that a flute (interchange) instability acts on the electrons is discussed. This instability is probably driven by strong gradients in the plasma pressure and the magnetic field magnitude: magnetometer observations show clearly signatures consistent with the (expected) plasma pressure loss due to ion absorption at Rhea. Another potential driver of the instability could have been gradients in the cold plasma density, which are, however, surprisingly absent from most crossings of Rhea’s plasma wake. The lack of a density depletion in Rhea’s wake suggests the presence of a local cold plasma source region. Hybrid plasma simulations show that this source cannot be the ionized component of Rhea’s weak exosphere. It is probably related to accelerated photoelectrons from the moon’s negatively charged surface, indicating that surface charging may play a very important role in shaping Rhea’s magnetospheric interaction region.

Plasma Dynamics in Low-Pressure Capacitively Coupled Oxygen Plasma Using PIC–MCC/Fluid Hybrid Model

Low-pressure ( <; 20 mT) capacitively coupled plasmas are now widely used for plasma processing in the semiconductor industry. In particular, O2 plasmas are being used for etching, photoresist ashing, and chamber cleaning. At low pressure, the electron mean free path increases, making kinetic effects more important. To consider kinetic effects, a hybrid plasma simulation tool has been developed that couples the particle-in-cell/Monte Carlo collision model for charged species with a fluid model for neutral species. Oxygen plasma has been modeled using this hybrid model for a range of pressures. It is observed that the electrons primarily absorb power at the sheath edge during sheath expansion. These energetic beam electrons are responsible for plasma production and sustenance through collisions. The beam electrons are stronger at lower pressure and retain their beam characters for a longer distance. For a constant RF voltage, the electron density increases with pressure.

Two dimensional simulation of ion beam-plasm interaction

Hybrid plasma simulation is a model in which different components of the plasma are treated differently. In this work the ions are treated as particles while the electrons are treated as a neutralizing background fluid through which electric signals may propagate. Deuterium ion beams incident on the tritium plasma interact with the plasma through the wake electric and magnetic fields of the beam currents. The model is described by the Vlasov-Maxwell-fluid equations with displacement currents omitted in the Ampere's equation. Euler scheme advances the ion positions and velocities while finite difference scheme approximates the spatial derivatives of field quantities. Bilinear interpolation is used in interpolating field quantities from the grid points to push particles in their respective positions. The beam parameters that determine the response of the plasma are the beam velocity Vb, the density nb and the radius rb. It was found that the sharpness of the characteristic frequencies for power absorption increased with increasing beam density while increasing the beam radius destroyed the characteristic frequencies and spread the frequency band of the continuous lines. The Joule heating of the plasma fluctuated in time and could be localized. Increasing nb delocalized the heating. The magnetic field profile did not respond sharply to beam parameters but the respond was sufficient enough to cause inhomogeneity in the direction of applied magnetic field B&#963. Journal of the Nigerian Association of Mathematical Physics Vol. 9 2005: pp. 561-572

Energy deposition models for short-pulse laser-solid interaction experiments

Reliable models for the transport and deposition of energy in solid targets during short-pulse laser matter interactions are vital for designing and interpreting material properties experiments, and of clear relevance to the fast igniter. We conduct hybrid plasma simulations using LSP, considering relatively modest intensities to facilitate comparisons with radiation hydrodynamic models. The relative effects of thermal wave heating, direct collisional heating by fast electrons and Ohmic heating are discussed. Target heating depends strongly on the form of the hot electron distribution produced by the absorption of the incident laser pulse at the vacuum-matter interface. Where the hot electron population is assumed to be a discrete beam, we find good agreement with our models. For the case of a thermalised hot electron population, target heating by hot electrons is reduced. Under these conditions, the interplay between fast-electron and thermal wave heating is unclear, which has implications for target heating experiments.