Publications
51 results found
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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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-4π 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 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 B, Chittenden J, 2009, α 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, 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.
Appelbe BD, Rachinskii D, Zhezherun A, 2008, Hopf bifurcation a van der Pol type oscillator with magnetic hysteresis, Physica B-Condensed Matter, Vol: 403, Pages: 301-304, ISSN: 0921-4526
We consider models of electronic oscillators of van der Pot type assuming magnetic hysteresis in inductance element. The Preisach nonlinearity is used to model the hysteresis relation. We study local and global behaviour of the branch of cycles originating from the Hopf bifurcation point.
Appelbe BD, McNamara H, Rasskazov O, 2007, Split-hyperbolicity in studying dynamical systems with hysteresis, 2007 AMERICAN CONTROL CONFERENCE, Pages: 3224-3229, ISSN: 0743-1619
Split-hyperbolicity was offered by A. Pokrovskii as an extension of the notions of "unsual" hyperbolicity for non-smooth maps. The nature of this concept makes it very useful in the study of systems with hysteresis. In this article we would like to survey recent results on split-hyperbolicity theory, and to outline its applications to the stabilisation of unstable orbits.
Appelbe BD, 2006, Existence of multiple cycles in a van der Pol system with hysteresis in the inductance, International Workshop on Multi-Rate Processes and Hysteresis, Pages: 1-11
The van der Pol oscillator has interesting properties central to the study of electrical circuits and nonlinear dynamics. This paper demonstrates the effect of modelling the van der Pol oscillator with hysteresis in the inductance element, a feature often omitted, using the derivative of a Preisach nonlinearity. The system is then solved using a recently developed algorithm and it is shown that multiple limit cycles are present.
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