Bernstein, Ira B.Overview
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Most widely held works by
Ira B Bernstein
Linear stability of selfsimilar flow
by D. L Book
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Book
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4 editions published in 1978 in English and held by 50 WorldCat member libraries worldwide A soluble model of the development of the RayleighTaylor instability in perturbations about a timevarying state of a compressible medium is presented. A Lagrangian description is employed to rederive the equations for the selfsimilar motion of an ideal fluid and to obtain the linearized equations of motion for perturbations about a general timevarying basic state. The resulting formalism is applied in cylindrical geometry to calculate the growth of flutelike RayleighTaylor modes associated with a similarity solution modeling the implosion and expansion of a liquid liner. A complete solution is obtained for the perturbed motion. The only modes for which the perturbation amplitudes grow faster than the unperturbed linear radius are divergence and curlfree. Numerical and analytical results are obtained for these and shown to reduce in the short wavelength limit to those previously for incompressible timeindependent basic states. (Author)
An energy principle for hydromagnetic stability problems
by Ira B Bernstein
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Book
)
2 editions published in 1957 in English and held by 6 WorldCat member libraries worldwide
A rapid numerical procedure for determining axisymmetric transverse electric electromagnetic fields via boundary integrals
by Ira B Bernstein
(
Book
)
2 editions published in 1988 in English and held by 5 WorldCat member libraries worldwide An important engineering problem is the determination of the electromagnetic fields in microwave systems, for example tapered waveguides, horns, scatterers, close cavities, and open resonators. Consider the case of axisymmetric transverse electric modes. Such problems for monochromatic radiation can be reduced to consideration of an elliptic partial differential equation similar to the Helmholtz equation. Methods have been developed for the direct numerical solution of the partial differential equation. Variational principles have been used to optimally determine approximate values of object of interest like reflection and transmission coefficients. An alternative approach is the reduction of the problem to consideration of an integral equation defined on the metallic walls defining the object (the boundary integral method). These have been solved for the case of scalar fields described by the Helmholtz equation. The boundary integral equation method is feasible when the Greens function is known in a computationaly convenient form, and is very often much more computationaly efficient than its competitors, particularly when the geometry is complex. The theory and effective numerical implementation are described of such a boundary integral equation approach for the case of an axisymmetric transverse electric electromagnetic field. The technique is readily generalizable to arbitrary axisymmetric fields. (JHD)
Waves in a plasma in a magnetic field
by Ira B Bernstein
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Book
)
1 edition published in 1957 in English and held by 3 WorldCat member libraries worldwide
Exact nonlinear plasma oscillations
by Ira B Bernstein
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Book
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1 edition published in 1957 in English and held by 3 WorldCat member libraries worldwide
WaveParticle Interactions on Relativistic Electron Beams
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Book
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3 editions published between 1980 and 1983 in English and held by 3 WorldCat member libraries worldwide Summaries are provided on the following topics: Linearized Theory including Axial Magnetic Field; NonLinear Theory; QuasiLinear Theory; and Single Particle Theory for Free Electron Laser with a strong Axial Field
Plasma oscillations with diffusion in velocity space
by Andrew Lenard
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Book
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1 edition published in 1958 in English and held by 2 WorldCat member libraries worldwide A model of plasma oscillations in the presence of small angle collisions is presented which admits of exact analytic solution. Certain features of the true collsion terms are preserved. Namely, the effect of collisions is represented by a diffusion in velocity space, which makes the distribution function tend to the Maxwell distribution, and which conserves the number of particles. In the limit of infrequent collisions the results of Landau are recovered
Ion wave instabilities
by Ira B Bernstein
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Book
)
2 editions published between 1959 and 1960 in English and held by 2 WorldCat member libraries worldwide
Stability of SelfSimilar Flow. 6. Uniform Implosion of an Ablatively Driven Shell
by D. L Book
(
Book
)
2 editions published in 1979 in English and held by 2 WorldCat member libraries worldwide The linear stability of a uniformly imploding shell, modeled as an ideal polytropic fluid, is investigated. Two types of unstable modes are found: incompressible irrotational perturbations localized at the outer surface, ascribable to RayleighTaylor instability, and compressible modes, associated with convective instability. KIDDER'S (1976) result for the RayleighTaylor modes is shown to hold independently of the form of the shell density profile. By means of a variational principle it is shown that the criterion for convective instability is the existence of a region within which the differential of p times rho to the negative gamma power in respect to r>0. Analytic solutions for both spatial and temporal dependence of the perturbations are presented, and the results applied to pellets imploded by the action of a laser or chargedparticle beam. (Author)
Theory of Electrostatic Probes in a Low Density Plasma
by Ira B Bernstein
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Book
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2 editions published between 1958 and 1959 in English and held by 2 WorldCat member libraries worldwide
A multiple bounce theory for the expansion and retardation of a cold plasma explosion bubble
by Ira B Bernstein
(
Book
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1 edition published in 1964 in English and held by 1 WorldCat member library worldwide
On the explosion of a supernova into the interstellar magnetic field  Part II
by Ira B Bernstein
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Book
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1 edition published in 1965 in English and held by 1 WorldCat member library worldwide
Linear Stability of SelfSimilar Flow. 8. Imploding Cylindrical and Spherical Shocks in the CCW Approximation
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Book
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1 edition published in 1980 in English and held by 1 WorldCat member library worldwide Analytical and computational techniques are developed to investigate the stability of converging shock waves in cylindrical and spherical geometry. The linearized ChesterChisnellWhitham (CCW) equations describing the evolution of an arbitrary perturbation about an imploding shock wave in an ideal fluid are solved exactly in the strongshock limit for a density profile rho(r) approx (r to the q power). All modes are found to be relatively unstable (i.e., the ratio of perturbation amplitude to shock radius diverges as the latter goes to zero), provided that q is not too large. The nonlinear CCW equations are solved numerically for both moderate and strong shocks. The smallamplitude limit agrees with the analytical results, but some forms of perturbation which are stable at small amplitude become unstable in the nonlinear regime. The results are related to the problem of pellet compression in experiments on inertial confinement fusion. (Author)
The effect of charge exchange on the critical current for the onset of ion wave instabilities
by Ira B Bernstein
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Book
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1 edition published in 1961 in English and held by 1 WorldCat member library worldwide
Parallel Concepts in the Derivation of the Classical and Quantum Boltzmann Equations
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Book
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1 edition published in 1974 in English and held by 1 WorldCat member library worldwide The kinetic equation describing a spacially inhomogeneous dilute gas is derived from the appropriate hierarchy equations according to both classical and quantum mechanics. In the former case one obtains the Boltzmann equation, in the latter the UehlingUhlenbeck equation. The derivations in the two cases are completely parallel and assume only that twoparticle correlation functions factor into products of oneparticle functions when the two particles are separated by distances greater than the range lambda of the interaction potential, and that terms of order n(lambda cubed) <<1, where n is the particle density, may be dropped compared with terms of order unity in equations of motion. (Author)
Runaway electrons in an ideal Lorentz plasma
by Ira B Bernstein
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Book
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1 edition published in 1963 in English and held by 1 WorldCat member library worldwide
Electron Distribution Functions in Weakly Ionized Plasma
by Ira B Bernstein
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Book
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1 edition published in 1968 in English and held by 1 WorldCat member library worldwide
A note on the stability of a currentcarrying plasma
by Ira B Bernstein
(
Book
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1 edition published in 1961 in English and held by 1 WorldCat member library worldwide
Plasma oscillations I
by Ira B Bernstein
(
Book
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1 edition published in 1960 in English and held by 1 WorldCat member library worldwide
Numerical simulation of tokamak electron dynamics
by W. H Miner
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Book
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1 edition published in 1981 in English and held by 1 WorldCat member library worldwide In a tokamak, the electron distribution deviates from a Maxwellian. This is because the magnetically untrapped electrons moving parallel to the applied electric field tend to run away. Because of the presence of trapped electrons, the distribution also departs from the ChapmanEnskog solution of the weak electric field problem. Previous analytic and numerical methods have treated this distortion in the limit of vanishingly small electric fields, a vanishing small number of trapped electrons, or both. We present a numerical method which relaxes these limitations, and illustrate the distribution functions which result from it. (Author) more
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Boundary element methods Differential equations Diffusion Electrodynamics Electromagnetic fields Electron distribution Ionization Ionization of gases Isothermal transformation diagrams Magnetic fields Numerical analysis Oscillations Plasma (Ionized gases) Plasma oscillations Similarity (Physics) Smallangle scattering Trappedparticle instabilities Waves

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