## Publications

33 results found

Sio H, Moody JD, Ho DD,
et al., 2021, Diagnosing plasma magnetization in inertial confinement fusion implosions using secondary deuterium-tritium reactions, *Review of Scientific Instruments*, Vol: 92, Pages: 1-5, ISSN: 0034-6748

Diagnosing plasma magnetization in inertial confinement fusion implosions is important for understanding how magnetic fields affect implosion dynamics and to assess plasma conditions in magnetized implosion experiments. Secondary deuterium–tritium (DT) reactions provide two diagnostic signatures to infer neutron-averaged magnetization. Magnetically confining fusion tritons from deuterium–deuterium (DD) reactions in the hot spot increases their path lengths and energy loss, leading to an increase in the secondary DT reaction yield. In addition, the distribution of magnetically confined DD-triton is anisotropic, and this drives anisotropy in the secondary DT neutron spectra along different lines of sight. Implosion parameter space as well as sensitivity to the applied B-field, fuel ρR, temperature, and hot-spot shape will be examined using Monte Carlo and 2D radiation-magnetohydrodynamic simulations.

Meaney KD, Hoffman NM, Kim Y,
et al., 2021, Time resolved ablator areal density during peak fusion burn on inertial confinement fusion implosions, *PHYSICS OF PLASMAS*, Vol: 28, ISSN: 1070-664X

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Appelbe B, Velikovich AL, Sherlock M,
et al., 2021, Magnetic field transport in propagating thermonuclear burn, *Physics of Plasmas*, Vol: 28, Pages: 1-9, ISSN: 1070-664X

High energy gain in inertial fusion schemes requires the propagation of a thermonuclear burn wave from hot to cold fuel. We consider the problem of burn propagation when a magnetic field is orthogonal to the burn wave. Using an extended-MHD model with a magnetized α energy transport equation, we find that the magnetic field can reduce the rate of burn propagation by suppressing electron thermal conduction and α particle flux. Magnetic field transport during burn propagation is subject to competing effects: the field can be advected from cold to hot regions by ablation of cold fuel, while the Nernst and α particle flux effects transport the field from hot to cold fuel. These effects, combined with the temperature increase due to burn, can cause the electron Hall parameter to grow rapidly at the burn front. This results in the formation of a self-insulating layer between hot and cold fuel, which reduces electron thermal conductivity and α transport, increases the temperature gradient, and reduces the rate of burn propagation.

Crilly AJ, Appelbe BD, Mannion OM,
et al., 2021, The effect of areal density asymmetries on scattered neutron spectra in ICF implosions, *Physics of Plasmas*, Vol: 28, Pages: 1-9, ISSN: 1070-664X

Scattered neutron spectroscopy is a diagnostic technique commonly used to measure areal density in inertial confinement fusion experiments. Deleterious areal density asymmetries modify the shape of the scattered neutron spectrum. In this work, a novel analysis is developed, which can be used to fit the shape change. This will allow experimental scattered neutron spectroscopy to directly infer the amplitude and mode of the areal density asymmetries, with little sensitivity to confounding factors that affect other diagnostics for areal density. The model is tested on spectra produced by a neutron transport calculation with both isotropic and anisotropic primary fusion neutron sources. Multiple lines of sight are required to infer the areal density distribution over the whole sphere—we investigate the error propagation and optimal detector arrangement associated with the inference of mode 1 asymmetries.

Crilly AJ, Appelbe BD, Mannion OM,
et al., 2020, Neutron backscatter edge: A measure of the hydrodynamic properties of the dense DT fuel at stagnation in ICF experiments, *Physics of Plasmas*, Vol: 27, Pages: 012701-1-012701-11, ISSN: 1070-664X

The kinematic lower bound for the single scattering of neutrons produced in deuterium-tritium (DT) fusion reactions produces a backscatter edge in the measured neutron spectrum. The energy spectrum of backscattered neutrons is dependent on the scattering ion velocity distribution. As the neutrons preferentially scatter in the densest regions of the capsule, the neutron backscatter edge presents a unique measurement of the hydrodynamic conditions in the dense DT fuel. It is shown that the spectral shape of the edge is determined by the scattering rate weighted fluid velocity and temperature of the dense DT fuel layer during neutron production. In order to fit the neutron spectrum, a model for the various backgrounds around the backscatter edge is developed and tested on synthetic data produced from hydrodynamic simulations of OMEGA implosions. It is determined that the analysis could be utilized on current inertial confinement fusion experiments in order to measure the dense fuel properties.

Appelbe B, Sherlock M, El-Amiri O,
et al., 2019, Modification of classical electron transport due to collisions between electrons and fast ions, *Physics of Plasmas*, Vol: 26, Pages: 102704-1-102704-12, ISSN: 1070-664X

A Fokker-Planck model for the interaction of fast ions with the thermal electrons in a quasineutral plasma is developed. When the fast ion population has a net flux (i.e., the distribution of fast ions is anisotropic in velocity space), the electron distribution function is perturbed from Maxwellian by collisions with the fast ions, even if the fast ion density is orders of magnitude smaller than the electron density. The Fokker-Planck model is used to derive classical electron transport equations (a generalized Ohm's law and a heat flow equation) that include the effects of the electron-fast ion collisions. It is found that these collisions result in a collisionally induced current term in the transport equations which can be significant. The new transport equations are analyzed in the context of a number of scenarios including α particle heating in inertial confinement fusion and magnetoinertial fusion plasmas as well as ion beam heating of dense plasmas.

Tong JK, McGlinchey K, Appelbe BD,
et al., 2019, Burn regimes in the hydrodynamic scaling of perturbed inertial confinement fusion hotspots, *Nuclear Fusion*, Vol: 59, Pages: 1-16, ISSN: 0029-5515

We present simulations of ignition and burn based on the Highfoot and high-density carbon indirect drive designs of the National Ignition Facility for three regimes of alpha-heating—self-heating, robust ignition and propagating burn—exploring hotspot power balance, perturbations and hydrodynamic scaling. A Monte-Carlo particle-in-cell charged particle transport package for the radiation-magnetohydrodynamics code Chimera was developed for this purpose, using a linked-list type data structure.The hotspot power balance between alpha-heating, electron thermal conduction and radiation was investigated in 1D for the three burn regimes. Stronger alpha-heating levels alter the hydrodynamics: sharper temperature and density gradients at hotspot edge; and increased hotspot pressures which further compress the shell, increase hotspot size and induce faster re-expansion. The impact of perturbations on this power balance is explored in 3D using a single Rayleigh–Taylor spike. Heat flow into the perturbation from thermal conduction and alpha-heating increases by factors of , due to sharper temperature gradients and increased proximity of the cold, dense material to the main fusion regions respectively. The radiative contribution remains largely unaffected in magnitude.Hydrodynamic scaling with capsule size and laser energy of different perturbation scenarios (a short-wavelength multi-mode and a long-wavelength radiation asymmetry) is explored in 3D, demonstrating the differing hydrodynamic evolution of the three alpha-heating regimes. The multi-mode yield increases faster with scale factor due to more synchronous compression producing higher temperatures and densities, and therefore stronger bootstrapping of alpha-heating. The perturbed implosions exhibit differences in hydrodynamic evolution due to alpha-heating in addition to the 1D effects, including: reduced perturbation growth due to ablation from both fire-polishing and stronger thermal conduction; and fa

Walsh CA, McGlinchey K, Tong JK,
et al., 2019, Perturbation modifications by pre-magnetisation of inertial confinement fusion implosions, *Physics of Plasmas*, Vol: 26, ISSN: 1070-664X

Pre-magnetisation of inertial confinement fusion implosions on the National Ignition Facility has the potential to raise current high-performing targets into the ignition regime [Perkins et al. "The potential of imposed magnetic fields for enhancing ignition probability and fusion energy yield in indirect-drive inertial confinement fusion," Phys. Plasmas 24, 062708 (2017)]. A key concern with this method is that the application of a magnetic field inherently increases asymmetry. This paper uses 3-D extended-magnetohydrodynamics Gorgon simulations to investigate how thermal conduction suppression, the Lorentz force, and α-particle magnetisation affect three hot-spot perturbation scenarios: a cold fuel spike, a time-dependent radiation drive asymmetry, and a multi-mode perturbation. For moderate magnetisations (B0 = 5 T), the single spike penetrates deeper into the hot-spot, as thermal ablative stabilisation is reduced. However, at higher magnetisations (B0 = 50 T), magnetic tension acts to stabilise the spike. While magnetisation of α-particle orbits increases the peak hot-spot temperature, no impact on the perturbation penetration depth is observed. The P4-dominated radiation drive asymmetry demonstrates the anisotropic nature of the thermal ablative stabilisation modifications, with perturbations perpendicular to the magnetic field penetrating deeper and perturbations parallel to the field being preferentially stabilised by increased heat-flows. Moderate magnetisations also increase the prevalence of high modes, while magnetic tension reduces vorticity at the hot-spot edge for larger magnetisations. For a simulated high-foot experiment, the yield doubles through the application of a 50 T magnetic field-an amplification which is expected to be larger for higher-performing configurations.

Johnson MG, Appelbe BD, Chittenden JP,
et al., 2019, Impact of imposed mode 2 laser drive asymmetry on inertial confinement fusion implosions, *Physics of Plasmas*, Vol: 26, ISSN: 1070-664X

Low-mode asymmetries have emerged as one of the primary challenges to achieving high-performing inertial confinement fusion implosions. These asymmetries seed flows in the implosions, which will manifest as modifications to the measured ion temperature (Tion) as inferred from the broadening of primary neutron spectra. The effects are important to understand (i) to learn to control and mitigate low-mode asymmetries and (ii) to experimentally more closely capture thermal Tion used as input in implosion performance metric calculations. In this paper, results from and simulations of a set of experiments with a seeded mode 2 in the laser drive are described. The goal of this intentionally asymmetrically driven experiment was to test our capability to predict and measure the signatures of flows seeded by the low-mode asymmetry. The results from these experiments [first discussed in M. Gatu Johnson et al., Phys. Rev. E 98, 051201(R) (2018)] demonstrate the importance of interplay of flows seeded by various asymmetry seeds. In particular, measured Tion and self-emission x-ray asymmetries are expected to be well captured by interplay between flows seeded by the imposed mode 2 and the capsule stalk mount. Measurements of areal density asymmetry also indicate the importance of the stalk mount as an asymmetry seed in these implosions. The simulations brought to bear on the problem (1D LILAC, 2D xRAGE, 3D ASTER, and 3D Chimera) show how thermal Tion is expected to be significantly lower than Tion as inferred from the broadening of measured neutron spectra. They also show that the electron temperature is not expected to be the same as Tion for these implosions.

McGlinchey K, Appelbe BD, Crilly AJ,
et al., 2018, Diagnostic signatures of performance degrading perturbations in inertial confinement fusion implosions, *Physics of Plasmas*, Vol: 25, ISSN: 1070-664X

We present 3D radiation-hydrodynamics simulations of indirect-drive inertial confinement fusion experiments performed at the National Ignition Facility (NIF). The simulations are carried out on two shots from different NIF experimental campaigns: N130927 from the high foot series and N161023 from the ongoing high density carbon series. Applying representative perturbation sources from each implosion, synthetic nuclear diagnostics are used to post-process the simulations to infer the stagnation parameters. The underlying physical mechanisms that produce the observed signatures are then explored. We find that the radiation asymmetry and tent scar perturbations extend the nuclear burn width; this is due to an asymmetric stagnation of the shell that causes the delivery of mechanical PdV work to be extended compared to an idealised implosion. Radiation asymmetries seed directed flow patterns that can result in a difference in the inferred ion temperature ranging from 80 eV to 230 eV depending on the magnitude and orientation of the asymmetry considered in the simulation; the tent scar shows no such temperature difference. For N130927, radiation asymmetries dominate the yield and inferred ion temperature and the tent scar has the largest influence on the neutron burnwidth. For N161023, the fill tube decreases the burn width by injecting mix into the hot spot, leading to a smaller hot spot and increased energy losses. Both the radiation asymmetry and the fill tube generate directed flows that lead to an anisotropic inferred temperature distribution. Through existing and novel synthetic neutron imaging techniques, we can observe the hot spot and shell shape to a degree that accurately captures the perturbations present.

Crilly AJ, Appelbe BD, McGlinchey K,
et al., 2018, Synthetic nuclear diagnostics for inferring plasma properties of inertial confinement fusion implosions, *Physics of Plasmas*, Vol: 25, ISSN: 1070-664X

A suite of synthetic nuclear diagnostics has been developed to post-process radiation hydrodynamics simulations performed with the code Chimera. These provide experimental observables based on simulated capsule properties and are used to assess alternative experimental and data analysis techniques. These diagnostics include neutron spectroscopy, primary and scattered neutron imaging, neutron activation, γ-ray time histories and carbon γ-ray imaging. Novel features of the neutron spectrum have been analysed to infer plasma parameters. The nT and nD backscatter edges have been shown to provide a shell velocity measurement. Areal density asymmetries created by low mode perturbations have been inferred from the slope of the downscatter spectrum down to 10 MeV. Neutron activation diagnostics showed significant aliasing of high mode areal density asymmetries when observing a capsule implosion with 3D multimode perturbations applied. Carbon γ-ray imaging could be used to image the ablator at a high convergence ratio. Time histories of both the fusion and carbon γ signals showed a greater time difference between peak intensities for the perturbed case when compared to a symmetric simulation.

Gatu Johnson M, Appelbe BD, Chittenden JP,
et al., 2018, Impact of asymmetries on fuel performance in inertial confinement fusion, *Physical Review E*, Vol: 98, ISSN: 2470-0045

Low-mode asymmetries prevent effective compression, confinement, and heating of the fuel in inertial confinement fusion (ICF) implosions, and their control is essential to achieving ignition. Ion temperatures (Tion) in ICF experiments are inferred from the broadening of primary neutron spectra. Directional motion (flow) of the fuel at burn also impacts broadening and will lead to artificially inflated "Tion" values. Flow due to low-mode asymmetries is expected to give rise to line-of-sight variations in measured Tion. We report on intentionally asymmetrically driven experiments at the OMEGA laser facility designed to test the ability to accurately predict and measure line-of-sight differences in apparent Tion due to low-mode asymmetry-seeded flows. Contrasted to chimera and xrage simulations, the measurements demonstrate how all asymmetry seeds have to be considered to fully capture the flow field in an implosion. In particular, flow induced by the stalk that holds the target is found to interfere with the seeded asymmetry. A substantial stalk-seeded asymmetry in the areal density of the implosion is also observed.

Walsh C, Chittenden JP, McGlinchey K,
et al., 2017, Self-Generated magnetic fields in the stagnation phase of indirect-drive implosions on the national ignition facility, *Physical Review Letters*, Vol: 118, ISSN: 1079-7114

Three-dimensional extended-magnetohydrodynamic simulations of the stagnation phase of inertial confinement fusion implosion experiments at the National Ignition Facility are presented, showing self-generated magnetic fields over 10^4 T. Angular high mode-number perturbations develop large magnetic fields, but are localized to the cold, dense hot-spot surface, which is hard to magnetize. When low-mode perturbations are also present, the magnetic fields are injected into the hot core, reaching significant magnetizations, with peak local thermal conductivity reductions greater than 90%. However, Righi-Leduc heat transport effectively cools the hot spot and lowers the neutron spectra-inferred ion temperatures compared to the unmagnetized case. The Nernst effect qualitatively changes the results by demagnetizing the hot-spot core, while increasing magnetizations at the edge and near regions of large heat loss.

Appelbe B, Pecover J, Chittenden J, 2017, The effects of magnetic field topology on secondary neutron spectra in magnetized liner inertial fusion, *High Energy Density Physics*, Vol: 22, Pages: 27-36, ISSN: 1878-0563

The Magnetized Liner Inertial Fusion (MagLIF) concept involves the compression of a magnetized fuel such that the stagnated fuel contains a magnetic field that can suppress heat flow losses and confine α particles. Magnetic confinement of α particles reduces the fuel ρR required for ignition. Recent work [1,2] has demonstrated that the magnitude of the magnetic field in deuterium fuel can be inferred from the yields and spectra of secondary DT neutrons. In this work we investigate the potential for using the shape of the secondary neutron spectra to diagnose the magnetic field topology in the stagnated fuel. Three different field topologies that could possibly occur in MagLIF experiments are studied: (1) a cylindrical fuel column containing axial and azimuthal magnetic field components, (2) a fuel column which is pinched at the ends to form a magnetic mirror and (3) a fuel column that has a helical tube shape with magnetic field lines following the helical path of the tube’s axis. Each topology is motivated by observations from experimental or simulated MagLIF data. For each topology we use a multi-physics model to investigate the shapes of the secondary neutron spectra emitted from a steady-state stagnated fuel column. It is found that the azimuthal and helical topologies are more suitable than the mirror topology for reproducing an asymmetry in the axial spectra that was observed in experiments. Gorgon MHD simulations of the MagLIF implosion in 1D are also carried out. These show that sufficient azimuthal magnetic field can penetrate from the liner into the fuel to qualitatively reproduce the observed spectral asymmetry.

Appelbe BD, 2016, Rotating Leaks in the Stadium Billiard, *Chaos*, Vol: 26, ISSN: 1089-7682

The open stadium billiard has a survival probability,P(t), that depends on the rate ofescape of particles through the leak. It is known that the decay ofP(t) is exponentialearly in time while for long times the decay follows a power law. In this work weinvestigate an open stadium billiard in which the leak is free to rotate around theboundary of the stadium at a constant velocity,ω. It is found thatP(t) is verysensitive toω. For certainωvaluesP(t) is purely exponential while for other valuesthe power law behaviour at long times persists. We identify three ranges ofωvaluescorresponding to three different responses ofP(t). It is shown that these variations inP(t) are due to the interaction of the moving leak with Marginally Unstable PeriodicOrbits (MUPOs).

Chittenden JP, Appelbe BD, Manke F,
et al., 2016, Signatures of asymmetry in neutron spectra and images predicted by three-dimensional radiation hydrodynamics simulations of indirect drive implosions, *Physics of Plasmas*, Vol: 23, ISSN: 1089-7674

We present the results of 3D simulations of indirect drive inertial confinement fusion capsules driven by the “high-foot” radiation pulse on the National Ignition Facility. The results are post-processed using a semi-deterministic ray tracing model to generate synthetic deuterium-tritium (DT) and deuterium-deuterium (DD) neutronspectra as well as primary and down scatteredneutronimages. Results with low-mode asymmetries are used to estimate the magnitude of anisotropy in the neutronspectra shift, width, and shape. Comparisons of primary and down scatteredimages highlight the lack of alignment between the neutron sources,scatter sites, and detector plane, which limits the ability to infer the ρr of the fuel from a down scattered ratio. Further calculations use high bandwidth multi-mode perturbations to induce multiple short scale length flows in the hotspot. The results indicate that the effect of fluid velocity is to produce a DT neutronspectrum with an apparently higher temperature than that inferred from the DD spectrum and which is also higher than the temperature implied by the DT to DD yield ratio.

Appelbe B, Chittenden J, 2016, The effects of ion temperature on the energy spectra of T + T → 2n + α reaction products, *High Energy Density Physics*, Vol: 19, Pages: 29-37, ISSN: 1574-1818

The effects of ion temperature on the energy spectra of products of the T + T → 2n + α reaction are modelled and analysed. A model is derived by assuming that the spectra in the centre of mass (CM) frame for a given reaction energy are known. The model is then applied to two different sets of data for the energy spectra in the CM frame. In both cases, it is shown that varying the ion temperature causes significant changes in the shapes of the n and α spectra. For the n spectrum, the apparent intensity of sequential decay through the ground state of 5He decreases with increasing temperature. For the α spectrum, the sharp edge in the CM frame spectrum near 3.75 MeV caused by the dineutron reaction channel results in a thermally broadened spectrum with a high-energy tail at energies > 4 MeV. Knowledge of such features may help to interpret data from experiments designed to investigate the T + T reaction at low reaction energies.

Appelbe B, Chittenden J, 2015, Neutron spectra from beam-target reactions in dense Z-pinches, *Physics of Plasmas*, Vol: 22, ISSN: 1089-7674

The energy spectrum of neutrons emitted by a range of deuterium and deuterium-tritium Z-pinch devices is investigated computationally using a hybrid kinetic-MHD model. 3D MHD simulations are used to model the implosion, stagnation, and break-up of dense plasma focus devices at currents of 70 kA, 500 kA, and 2 MA and also a 15 MA gas puff. Instabilities in the MHD simulations generate large electric and magnetic fields, which accelerate ions during the stagnation and break-up phases. A kinetic model is used to calculate the trajectories of these ions and the neutron spectra produced due to the interaction of these ions with the background plasma. It is found that these beam-target neutron spectra are sensitive to the electric and magnetic fields at stagnation resulting in significant differences in the spectra emitted by each device. Most notably, magnetization of the accelerated ions causes the beam-target spectra to be isotropic for the gas puff simulations. It is also shown that beam-target spectra can have a peak intensity located at a lower energy than the peak intensity of a thermonuclear spectrum. A number of other differences in the shapes of beam-target and thermonuclear spectra are also observed for each device. Finally, significant differences between the shapes of beam-target DD and DT neutron spectra, due to differences in the reaction cross-sections, are illustrated.

Ampleford DJ, Hansen SB, Jennings CA, et al., 2015, Scaling and enhancement of non-thermal line emission on z to hν ∼ 22 kev

Appelbe B, Chittenden J, 2014, Relativistically correct DD and DT neutron spectra, *HIGH ENERGY DENSITY PHYSICS*, Vol: 11, Pages: 30-35, ISSN: 1574-1818

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- Citations: 24

Appelbe B, Chittenden J, 2014, Understanding neutron production in the deuterium dense plasma focus, *AIP Conference Proceedings*, Vol: 1639, Pages: 9-14

Taylor S, Appelbe B, Niasse NP,
et al., 2013, Effect of perturbations on yield in ICF targets-4 pi 3D hydro simulations, *IFSA 2011 - SEVENTH INTERNATIONAL CONFERENCE ON INERTIAL FUSION SCIENCES AND APPLICATIONS*, Vol: 59, ISSN: 2100-014X

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Appelbe BD, Chittenden J, 2012, Quasi-monoenergetic spectra from reactions in a beam-target plasma, *Physics of Plasmas*, Vol: 19, ISSN: 1070-664X

We investigate the kinematics of two-body (m(1) + m(2) -> m(3) + m(4)) fusion reactions occurring when a beam interacts with a plasma target. An exact expression for the energy spectrum of the product particles is derived. The derivation shows that there is an anisotropic lower limit on the energy of one of the product species. There is a range of beam energies for which this limit acts to suppress thermal broadening of the energy spectra of the particles emitted in the beam direction. The beam energy at which maximum suppression occurs is identified. At this beam energy, the width of the spectrum can be up to a couple of orders of magnitude narrower than the spectrum produced by a thermal plasma. The results indicate that the highly monoenergetic beams of fusion product particles may be produced from hot plasma targets.

Appelbe BD, 2011, Nuclear Fusion Reaction Kinetics and Ignition Processes in Z Pinches

This thesis presents work on two topics related to nuclear fusion in plasmas.The first topic is the energy spectrum of products of fusion reactions in plasmas,called the production spectrum. The second is an investigation of the fusion reactionprocesses in high energy density Z pinch plasmas and the feasibility of ignition ofsuch plasmas.A method is presented for the derivation of production spectra for plasmas withvarious distributions of ion velocities. The method is exact, requiring the solution ofa 5 dimensional integral and is suitable for both isotropic and anisotropic distributions.It is shown that many of the integrals can be solved analytically. The solutionsare used to study the spectra of neutron energies produced by deuterium-deuteriumand deuterium-tritium reactions. It is found that for maxwellian distributions of ionsthe neutron spectrum is asymmetric with a longer high energy tail when comparedwith gaussian approximations of the spectrum.Deuterium and deuterium-tritium Z pinch plasmas are studied computationallyusing a hybrid code in which the fuel is modelled as a magnetohydrodynamic (MHD)fluid and fast ions are modelled as discrete particle-in-cell (PIC) particles. Usinga Z pinch model in which the magnetic and thermal pressures are in equilibriumit is found that significant energy gain can be achieved for currents greater than50MA. Deuterium gas puff experiments with a 15MA current are also analysedcomputationally in order to determine the reaction mechanism. The results of MHDsimulations in 3 dimensions are post-processed with a PIC code to model reactionsoccurring due to the acceleration of deuterium ions by large electric fields. It isfound that reactions due to this beam-target mechanism represent a small fraction(0.0001) of the number of thermonuclear reactions.

Appelbe BD, Chittenden J, 2011, The production spectrum in fusion plasmas, *Plasma Physics and Controlled Fusion*, Vol: 53, ISSN: 0741-3335

Significant broadening of the energy spectrum of the products of nuclear reactions occurs in fusion plasmas. We provide a method for calculating the shape of this production spectrum for arbitrary plasma distribution functions. The method is exact and can be used for both isotropic and anisotropic distributions. We derive expressions for Maxwellian ( both stationary and moving with a bulk fluid velocity), bi-Maxwellian and beam-target plasmas. The neutron spectrum produced by the D+D -> He(3) +n reaction is studied as an example. It is shown that the neutron spectrum produced from a Maxwellian plasma becomes asymmetric at high plasma temperatures with a long high-energy tail. The effect of bulk fluid velocity on the neutron spectrum is shown to be significant in some cases. In particular, the spectrum produced by an imploding shell has a much greater FWHM than the spectrum obtained from a stationary plasma. The spectrum produced by a beam-target interaction shows significant anisotropy in the high-energy tail as the viewing angle varies from perpendicular to parallel to the beam direction.

Appelbe B, Chittenden J, 2010, Ignition in deuterium-tritium z-pinches, 2010 IEEE 37th International Conference on Plasma Sciences (ICOPS), Publisher: IEEE

Appelbe BD, Flynn D, McNamara H,
et al., 2009, Rate-Independent Hysteresis in Terrestrial Hydrology A VEGETATED SOIL MODEL WITH PREISACH HYSTERESIS, *IEEE Control Systems Magazine*, Vol: 29, ISSN: 1066-033X

The goal of this article is twofold. The first objective is to demonstrate the role of hysteresis in hydrology. The second objective is to describe a class of simple and convenient mathematical models of hydrological systems with hysteresis and to briefly discuss methods for the quantitative and qualitative analysis of such models. This article is organized as follows. In the first section we discuss the role of the Preisach model. We then present an explicit expression for analogues of wetting and drying curves in the Preisach model context. The central role in this section is occupied by special one-parameter classes of Preisach operators which are useful as models of soil-water hysteresis for particular soils. Fitting is discussed in the context of the GRIZZLY database of hysteretic soil-water characteristics. The second section introduces a simple but instructive example of a differential equation coupled with a Preisach nonlinearity. This equation serves as a basis for modeling vegetated soil in terrestrial hydrology. The third section is dedicated to the FEST model, where FEST stands for "fully vegetated slab of soil with transpiring plants". This model describes drainage, transpiration, and infiltration flows in a fully vegetated slab of soil. We demonstrate that hysteresis effects are critical, both on qualitative and quantitative levels, for modeling hydrological systems and flows in soil, while theoretical analysis and numerical implementation of the models raise interesting mathematical questions. To demonstrate the application of this model we use rainfall data gathered in the Feale region in County Kerry, Ireland, covering a period of 19 months between July 2002 and February 2004. The FEST model includes a quantitative description of the dynamics of the plant biomass, which depends on the amount and regularity of precipitation and soil type, including details of soil-water hysteresis. Hence, the FEST model can be used as a component of ecologi

Appelbe B, Chittenden J, 2009, alpha Heating in a Stagnated Z-pinch, 7th International Conference on Dense Z-Pinches, Publisher: AMER INST PHYSICS, Pages: 21-24, ISSN: 0094-243X

Appelbe BD, Chittenden J, 2009, α Heating in a Stagnated Z-pinch, 7th International Conference on Dense Z-Pinches, Pages: 21-24, ISSN: 0094-243X

A computational investigation of a scheme for magneto-inertial confinement fusion in a Z-pinch is carried out. In the scheme implosion of a deuterium-tritium fuel mass is preceded by formation of a hotspot containing warm, dense plasma on axis. The presence of the hotspot increases energy yield. Compression of the hotspot by the main fuel mass initiates thermonuclear burn. There is significant heating of the plasma by thermonuclear a particles which are confined by the strong magnetic field of the Z-pinch.

Appelbe BD, Pokrovskii A, 2008, ODEs involving the derivative of a Preisach operator with a degenerated density, *Physica B-Condensed Matter*, Vol: 403, Pages: 443-447, ISSN: 0921-4526

This paper examines a class of operator-differential equations that contain derivatives of the Preisach operator. We offer a solution for situations where the density function of the Preisach operator is zero in a region bounded by the Preisach plane bi-sector. This solution is relevant for systems in which output remains constant following a change in direction of input. We apply the solution to problems in terrestrial hydrology.

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