Author

# J. J. Dorning

Other affiliations: Paul Sabatier University, Brookhaven National Laboratory

Bio: J. J. Dorning is an academic researcher from University of Virginia. The author has contributed to research in topics: Nonlinear system & Vlasov equation. The author has an hindex of 13, co-authored 38 publications receiving 586 citations. Previous affiliations of J. J. Dorning include Paul Sabatier University & Brookhaven National Laboratory.

##### Papers

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TL;DR: A sufficient condition for waves of a given phase velocity to exist arbitrarily close to a given spatially uniform Vlasov equilibrium is developed, and sufficient analytical information for the construction of approximate expressions for the electric potential and distribution functions is derived.

Abstract: This paper describes small-amplitude nonlinear plasma wave solutions to the one-dimensional Vlasov-Maxwell equations. A sufficient condition for waves of a given phase velocity to exist arbitrarily close to a given spatially uniform Vlasov equilibrium is developed, and sufficient analytical information for the construction of approximate expressions for the electric potential and distribution functions is derived, with exact knowledge of the asymptotic behavior of the error terms. These results have a very surprising physical implication: the Landau damping of small-amplitude waves is not inevitable. Instead, there exist plasma waves that trap particles even at arbitrarily small amplitude and do not damp.

109 citations

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TL;DR: In this article, the drift flux model is used to make the set of equations dimensionless to ensure the mutual independence of the dimensionless variables and parameters: the steady-state inlet velocity v, the inlet subcooling number N sub and the phase change number N pch.

Abstract: Linear and nonlinear mathematical stability analyses of parallel channel density wave oscillations are reported. The two phase flow is represented by the drift flux model. A constant characteristic velocity v 0 ∗ is used to make the set of equations dimensionless to ensure the mutual independence of the dimensionless variables and parameters: the steady-state inlet velocity v , the inlet subcooling number N sub and the phase change number N pch . The exact equation for the total channel pressure drop is perturbed about the steady-state for the linear and nonlinear analyses. The surface defining the marginal stability boundary (MSB) is determined in the three-dimensional equilibrium-solution/operating-parameter space v − N sub − N pch . The effects of the void distribution parameter C 0 and the drift velocity V g j on the MSB are examined. The MSB is shown to be sensitive to the value of C 0 and comparison with experimental data shows that the drift flux model with C 0 > 1 predicts the experimental MSB and the neighboring region of stable oscillations (limit cycles) considerably better than do the homogeneous equilibrium model ( C 0 = 1, V g j = 0 ) or a slip flow model. The nonlinear analysis shows that supercritical Hopf bifurcation occurs for the regions of parameter space studied; hence stable oscillatory solutions exist in the linearly unstable region in the vicinity of the MSB. That is, the stable fixed point v becomes unstable and bifurcates to a stable limit cycle as the MSB is crossed by varying N sub and/or N pch .

97 citations

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TL;DR: In this paper, a simple mathematical model is developed to describe the dynamics of the nuclear-coupled thermal-hydraulics in a boiling water reactor (BWR) core, which leads to a simple dynamical system comprised of a set of nonlinear ordinary differential equations (ODEs).

Abstract: A simple mathematical model is developed to describe the dynamics of the nuclear-coupled thermal-hydraulics in a boiling water reactor (BWR) core. The model, which incorporates the essential features of neutron kinetics and single-phase and two-phase thermal-hydraulics, leads to a simple dynamical system comprised of a set of nonlinear ordinary differential equations (ODEs). The stability boundary is determined and plotted in the inlet-subcooling-number (enthalpy)/external-reactivity operating parameter plane. The eigenvalues of the Jacobian matrix of the dynamical system also are calculated at various steady-states (fixed points); the results are consistent with those of the direct stability analysis and indicate that a Hopf bifurcation occurs as the stability boundary in the operating parameter plane is crossed. Numerical simulations of the time-dependent, nonlinear ODEs are carried out for selected points in the operating parameter plane to obtain the actual damped and growing oscillations in the neutron number density, the channel inlet flow velocity, and the other phase variables. These indicate that the Hopf bifurcation is subcritical, hence, density wave oscillations with growing amplitude could result from a finite perturbation of the system even when it is being operated in the parameter region thought to be safe, i.e. where the steady-state is stable. Finally, the power-flow map, frequently used by reactor operators during start-up and shut-down operation of a BWR, is mapped to the inlet-subcooling-number/neutron-density (operating-parameter/phase-variable) plane, and then related to the stability boundaries for different fixed inlet velocities corresponding to selected points on the flow-control line. Also, the stability boundaries for different fixed inlet subcooling numbers corresponding to those selected points, are plotted in the neutron-density/inlet-velocity phase variable plane and then the points on the flow-control line are related to their respective stability boundaries in this plane. The relationship of the operating points on the flow-control line to their respective stability boundaries in these two planes provides insight into the instability observed in BWRs during low-flow/high-power operating conditions. It also shows that the normal operating point of a BWR is very stable in comparison with other possible operating points on the power-flow map.

67 citations

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TL;DR: For collisionless plasmas with initial conditions (ICs) near linearly stable equilibria, there exist critical initial states that mark the transition between the ICs from which the electric field evolves to a nonzero timeasymptotic state and those from which it Landau damps to zero as mentioned in this paper.

Abstract: We show that for collisionless plasmas with initial conditions (ICs) near ``single-humped'' linearly stable equilibria, there exist critical initial states that mark the transition between the ICs from which the electric field evolves to a nonzero time-asymptotic state $A(x,t)$, and those from which it Landau damps to zero We develop an equation for $A(x,t)$ and study it as a bifurcation problem, and we obtain the asymptotic field, at leading order, as a finite superposition of waves whose frequencies obey a Vlasov dispersion relation and whose amplitudes satisfy a set of nonlinear algebraic equations

52 citations

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35 citations

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01 May 1978

TL;DR: In this article, the authors have considered the interests of both scientists and practising engineers, in addition to serving the needs of the academia, in order to avoid lengthy and repetitive discussions, that are available in many standard text books on reactor physics.

Abstract: This is cne of the r-are text books written in the discipline of Nuclear Reactor Analysis, where the author has considered the interests of both scientists and practising engineers, in addition to serving the needs of the academia. The most attractive feature of this book is a balanced treatment of theory and practice of the subject matter. The theoretical foundations of the reactor design methods are explained with simplified definitions and relevant practical illustrations. The author scans through quickly the traditional aspects of the so-called reactor physics and takes the reader through the details of the analytical aspects in a conventional manner. Hcwever, there is a definite departure from the classical method of approach in order to avoid lengthy and repetitive discussions, that are available in many standard text books on reactor physics. The chief departure fran tradition is the priority accorded to the treatment of the energy part of the problems as opposed to the spatial Dart normally devoted to by other authors . A similar unorthodox approach has been applied while dealing with the solution of the various equations by giving priority to computer oriented mrethods as opposed to the classical solutions.

507 citations

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TL;DR: An updated review of two-phase flow instabilities including experimental and analytical results regarding density-wave and pressure-drop oscillations, as well as Ledinegg excursions, is presented in this article.

Abstract: An updated review of two-phase flow instabilities including experimental and analytical results regarding density-wave and pressure-drop oscillations, as well as Ledinegg excursions, is presented. The latest findings about the main mechanisms involved in the occurrence of these phenomena are introduced. This work complements previous reviews, putting all two-phase flow instabilities in the same context and updating the information including coherently the data accumulated in recent years. The review is concluded with a discussion of the current research state and recommendations for future works.

292 citations

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TL;DR: In this paper, the formation and dynamics of electron and ion holes in a collisionless plasma are investigated by means of numerical simulations in which analytical solutions of quasi-stationary electron and Ion holes are used as initial conditions.

Abstract: We present a comprehensive review of recent theoretical and numerical studies of the formation and dynamics of electron and ion holes in a collisionless plasma. The electron hole is characterized by a localized positive potential in which a population of electrons is trapped, and a depletion of the electron number density, while the ion hole is associated with localized negative potential in which a population of ions is trapped and a depletion of both the ion and electron densities occur. We present conditions for the existence of quasi-stationary electron and ion holes in unmagnetized and magnetized electron–ion plasmas, as well as in an unmagnetized pair-ion plasma. An interesting aspect is the dynamic interactions between ion and electron holes and the surrounding plasma. The dynamics is investigated by means of numerical simulations in which analytical solutions of quasi-stationary electron and ion holes are used as initial conditions. Our Vlasov simulations of two colliding ion holes reveal the acceleration of electrons and a modification of the initially Maxwellian electron distribution function by the ion hole potentials, which work as barriers for the electrons. A secondary effect is the excitation of high-frequency plasma waves by the streams of electrons. On the other hand, we find that electron holes show an interesting dynamics in the presence of mobile ions. Since electron holes are associated with a positive electrostatic potential, they repel positively charged ions. Numerical simulations of electron holes in a plasma with mobile ions exhibit that the electron holes are, in general, attracted by ion density maxima and repelled by ion density minima. Therefore, standing electron holes can be accelerated by the self-created ion cavities. In a pair plasma, both the temperatures and masses of the positively and negatively charged particles are assumed equal, and therefore one must treat both species with a kinetic theory on an equal footing. Accordingly, a phase-space hole in one of the species is associated with reflected particles in the opposite species. Here standing solitary large-amplitude holes are not allowed, but they must have a propagation speed close to the thermal speed of the particles. We discuss extensions of the existing non-relativistic theories for the electron and ion holes in two directions. First, we describe a fully nonlinear kinetic theory for relativistic electron holes (REHs) in an unmagnetized plasma, and show that the REHs have amplitudes and widths much larger than their non-relativistic counterparts. Second, we extend the weakly nonlinear theories for the electron and ion holes to include the effects of the external magnetic field and the plasma inhomogeneity. The presence of the external magnetic field gives rise to the electron and ion hole structures which have differential scale sizes along and across the magnetic field direction. Consideration of the density inhomogeneity in a magnetized plasma with non-isothermal electron distribution function provides the possibility of bipolar electrostatic pulses that move with the electron diamagnetic drift across the density inhomogeneity and the magnetic field directions. In a plasma with sheared magnetic field we can have fast reconnection involving phase-space vortices in the lower-hybrid frequency range. We further present theoretical and numerical investigations of the nonlinear interaction between ion and electron holes and large amplitude high-frequency electrostatic and electromagnetic waves in plasmas. Since the ion hole is associated with a depletion of both the electron and ion densities, it can work as a resonance cavity for trapped Langmuir waves whose frequencies are below the electron plasma frequency of the unperturbed plasma. Large-amplitude Langmuir waves can modify the ion hole due to the ponderomotive force which pushes the electrons away from the center of the hole. This process can be modeled by a coupled nonlinear Schrodinger and Poisson system of equations, which exhibit a discrete set of trapped Langmuir eigenmodes in the ion hole in plasmas without and with high-Z charged impurities. In a kinetic description, however, the trapped Langmuir waves are Landau damped due to the relatively small length scale of the ion hole. Intense electromagnetic waves (IEMWs) can also be trapped by the REHs in an unmagnetized plasma. We study the localization of arbitrary large amplitudes IEMWs by incorporating nonlinearities associated with relativistic electron mass increase, relativistic ponderomotive force of the IEMWs, and non-isothermal electron distributions. We find that the combined effects of these three nonlinearities produce extremely large amplitude REHs which traps localized IEMWs. Such a nonlinear structure can accelerate electrons to very high energies. The relevance of our investigation to numerous localized structures observed in laboratory and space plasmas is discussed. We also propose to conduct new experiments that can confirm our new theoretical and simulation models dealing with kinetic nonlinear structures in electron–ion and electron–positron plasmas. Finally, we present our views of possible extensions of theoretical models and computer simulations that have been reviewed in here.

165 citations

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TL;DR: In this article, the intensity scaling of stimulated Raman scattering (SRS) for classically large damping regimes (kλD=0.35) was examined, and compared to classical SRS theory.

Abstract: Single hot spot experiments offer several unique opportunities for developing a quantitative understanding of laser-plasma instabilities. These include the ability to perform direct numerical simulations of the experiment due to the finite interaction volume, isolation of instabilities due to the nearly ideal laser intensity distribution, and observation of fine structure due to the homogeneous plasma initial conditions. Experiments performed at Trident in the single hot spot regime have focused on the following issues. First, the intensity scaling of stimulated Raman scattering (SRS) for classically large damping regimes (kλD=0.35) was examined, and compared to classical SRS theory. SRS onset was observed at intensities much lower than expected (2×1015 W/cm2), from which nonclassical damping is inferred. Second, Thomson scattering was used to probe plasma waves driven by SRS, and structure was observed in the scattered spectra consistent with multiple steps of the Langmuir decay instability. Finally, sca...

132 citations

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TL;DR: In this paper, the spectral properties of the time-independent linear transport operator A are studied in its natural Banach space L 1(D × V), where D is the bounded space domain and V is the velocity domain, and the various cross sections in K and the total cross section are piecewise continuous functions of position and speed.

Abstract: In this paper, spectral properties of the time‐independent linear transport operator A are studied. This operator is defined in its natural Banach space L 1(D × V), where D is the bounded space domain and V is the velocity domain. The collision operator K accounts for elastic and inelastic slowing down, fission, and low energy elastic and inelastic scattering. The various cross sections in K and the total cross section are piecewise continuous functions of position and speed. The two cases ν0>0 and ν0=0 are treated, where ν0 is the minimum neutron speed. For ν0=0, it is shown that σ(A) consists of a full half‐plane plus, in an adjoining strip, point eigenvalues and curves. For ν0>0, σ(A) consists just of point eigenvalues and curves in a certain half‐space. In both cases, the curves are due to purely elastic ``Bragg'' scattering and are absent if this scattering does not occur. Finally the spectral differences between the two cases ν0>0 and ν0=0 are discussed briefly, and it is proved that A is the infinitesimal generator of a strongly continuous semigroup of operators.

115 citations