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Jun 1988

Volume 31, Issue 6, pp. 1311-1827

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Ejection mechanisms in the sublayer of a turbulent channel

Javier Jiménez, P. Moin, R. Moser, and L. Keefe

Phys. Fluids 31, 1311 (1988); http://dx.doi.org/10.1063/1.866721 (3 pages) | Cited 14 times

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The structure of the vorticity field in the viscous wall layer of a turbulent channel is studied by examining the results of a fully resolved direct numerical simulation. It is shown that this region is dominated by intense three‐dimensional shear layers in which the dominant vorticity component is spanwise. The advection and reproduction processes of these structures are examined and shown to be consistent with the classical generation mechanism for two‐dimensional Tollmien–Schlichting waves. This process is fundamentally different from the usually accepted mechanism involving hairpin vortices.
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47.27.N- Wall-bounded shear flow turbulence
47.27.Cn Transition to turbulence
47.60.-i Flow phenomena in quasi-one-dimensional systems

The relationship between Brownian motion and the random motion of small particles in a turbulent flow

M. W. Reeks

Phys. Fluids 31, 1314 (1988); http://dx.doi.org/10.1063/1.866722 (3 pages) | Cited 5 times

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Previous works have used the fluctuation–dissipation theorem to evaluate the diffusion coefficient for particles in a turbulent flow which differs from the commonly accepted value. This calculation is reexamined and it is concluded that fluctuation–dissipation expressing energy equipartition is inappropriate for hydrodynamic turbulence.
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47.27.-i Turbulent flows
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
47.55.Kf Particle-laden flows
05.70.-a Thermodynamics

Evolution and breaking of ion‐acoustic waves

Philip Rosenau

Phys. Fluids 31, 1317 (1988); http://dx.doi.org/10.1063/1.866723 (3 pages) | Cited 3 times

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A new amplitude equation governing the velocity evolution of ion‐acoustic waves in a collisionless plasma is derived: Vtt+(V2)xt=[(1−V2)Vx] x+βVxxtt. From this equation the existence of a critical amplitude threshold is immediately deduced, which leads to a double layer and above which solitary waves cannot exist. Above this threshold shock waves form and density undergoes explosive growth. Multidimensional waves and waves due to the magnetic drift are also considered.
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52.35.Fp Electrostatic waves and oscillations (e.g., ion-acoustic waves)
52.35.Sb Solitons; BGK modes
02.90.+p Other topics in mathematical methods in physics (restricted to new topics in section 02)

The general solution of Stokes flow in a half‐space as an integral of the velocity on the boundary

Kalvis M. Jansons and John R. Lister

Phys. Fluids 31, 1321 (1988); http://dx.doi.org/10.1063/1.866724 (3 pages) | Cited 3 times

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The motion in a half‐space of a viscous fluid governed by the Stokes flow equations and driven by the instantaneous velocity on the boundary is considered. It is demonstrated that the flow field can be represented as an integral of the boundary velocity distribution, and the simple kernel function is derived. Previously it was thought necessary for the flow to be represented as an integral of the force distribution on the boundary; the velocity distribution was then related to the force distribution through an integral equation, which was solved numerically. Expressions for the stress field in terms of the velocity distribution on the boundary are also determined, and some technical difficulties involving the convergence of the integrals are discussed.
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47.15.G- Low-Reynolds-number (creeping) flows
87.19.R- Mechanical and electrical properties of tissues and organs

Elastohydrodynamic collision and rebound of spheres: Experimental verification

Guy Barnocky and Robert H. Davis

Phys. Fluids 31, 1324 (1988); http://dx.doi.org/10.1063/1.866725 (6 pages) | Cited 51 times

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Experiments were performed in order to delineate the conditions under which small metal and plastic spheres rebound, as opposed to stick, when dropped upon a smooth quartz surface overlaid with a thin layer of a viscous fluid. The parameters that were varied include the fluid layer thickness and viscosity, and the ball size, density, and elastic properties. The minimum drop height that allowed the ball to rebound out of the fluid layer was determined. The results are in very good agreement with the recent elastohydrodynamic theory of Davis et al. [J. Fluid Mech. 163, 479 (1986)]. Additional experiments were performed for which the quartz surface was made artificially rough by adhering fine glass spheres to it. For these experiments, the resistance to rebound caused by the fluid layer was significantly reduced, in close agreement with the recent theory for rough surfaces developed by Davis [Phys. Chem. Hydro. 9, 41 (1987)].
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62.20.D- Elasticity
45.05.+x General theory of classical mechanics of discrete systems
68.03.-g Gas-liquid and vacuum-liquid interfaces
68.15.+e Liquid thin films

Simulation of nonlinear viscous fingering in miscible displacement

C. T. Tan and G. M. Homsy

Phys. Fluids 31, 1330 (1988); http://dx.doi.org/10.1063/1.866726 (9 pages) | Cited 96 times

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The nonlinear behavior of viscous fingering in miscible displacements is studied. A Fourier spectral method is used as the basic scheme for numerical simulation. In its simplest formulation, the problem can be reduced to two algebraic equations for flow quantities and a first‐order ordinary differential equation in time for the concentration. There are two parameters, the Peclet number (Pe) and mobility ratio (M), that determine the stability characteristics. The result shows that at short times, both the growth rate and the wavelength of fingers are in good agreement with predictions from our previous linear stability theory. However, as the time goes on, the nonlinear behavior of fingers becomes important. There are always a few dominant fingers that spread and shield the growth of other fingers. The spreading and shielding effects are caused by a spanwise secondary instability, and are aided by the transverse dispersion. It is shown that once a finger becomes large enough, the concentration gradient of its front becomes steep as a result of stretching caused by the cross‐flow, in turn causing the tip of the finger to become unstable and split. The splitting phenomenon in miscible displacement is studied by the authors for the first time. A study of the averaged one‐dimensional axial concentration profile is also presented, which indicates that the mixing length grows linearly in time, and that effective one‐dimensional models cannot describe the nonlinear fingering.
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47.20.-k Flow instabilities
47.56.+r Flows through porous media

A paradox concerning the extended Stokes series solution for the pressure drop in coiled pipes

R. Ramshankar and K. R. Sreenivasan

Phys. Fluids 31, 1339 (1988); http://dx.doi.org/10.1063/1.866727 (9 pages) | Cited 9 times

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While the extended Stokes series (ESS) solution for the laminar pressure drop in coiled pipes predicts that the friction ratio (the ratio of pressure drop in the coiled pipe to that in the straight pipe of the same flow rate) varies asymptotically as one‐fourth power of the Dean number, the existing experimental data largely support a square‐root variation; previous boundary layer analyses also predict a square‐root variation. The subject of this paper is an examination of this paradox. A detailed review shows that the existing set of experimental data can be grouped into various categories depending on the precise flow conditions. It is shown that none of the existing data satisfies the proper experimental conditions required by the ESS method. New experiments reveal that the pressure drop demanded by the ESS solution can actually be observed if they are expressly designed to satisfy the conditions demanded by the ESS solution. The implication is that the domains of initial conditions appropriate to the boundary layer and ESS solutions are quite different.
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47.15.Cb Laminar boundary layers
47.32.Ef Rotating and swirling flows

Oscillatory flows in coiled square ducts

S. Ravi Sankar, K. Nandakumar, and J. H. Masliyah

Phys. Fluids 31, 1348 (1988); http://dx.doi.org/10.1063/1.866728 (12 pages) | Cited 34 times

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The development of complex velocity fields in curved ducts from an initially parabolic profile is studied using a three‐dimensional numerical model of the parabolized Navier–Stokes equations. The velocity profiles are influenced strongly by a geometrical parameter Rc (the radius of curvature) and a dynamic parameter Dn (Dean number, Re/(Rc)1/2). For Rc < 10 and Dn up to 200, the velocity fields develop into the previously observed two‐ and four‐cell solutions that are axially invariant and symmetric about the midplane. For Rc =100 and Dn>125 oscillatory solutions develop which are periodic in the axial direction, but are asymmetric about the midplane. Increasing the Dean number over a narrow range results in a significant increase in the frequency of such oscillations. Grid sensitivity tests indicate that such oscillations are not a numerical artifact. Development of oscillatory solutions is delayed with decreasing radius of curvature. Thus for Rc =10, axially invariant two‐dimensional solutions that retain the symmetry about the midplane could be obtained for Dn as high as 300. This trend is consistent with one of the earliest observations by Taylor [Proc. R. Soc. London Ser. A. 124, 243 (1929)] that steady, symmetric laminar flows can be observed over a larger range of Dean number in tightly coiled tubes. However, when an asymmetric perturbation is imposed at the inlet, oscillatory solutions develop even for low Rc, indicating that symmetric two‐dimensional solutions are not stable to asymmetric perturbations, as indicated by Winters [K. W. Winters and R. C. G. Brindley (private communication)]. Numerical results are also presented for flow through curved ducts with periodic step changes in curvature.
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47.60.-i Flow phenomena in quasi-one-dimensional systems
47.20.-k Flow instabilities

The effects of inertia and interfacial shear on film flow on a rotating disk

Timothy J. Rehg and Brian G. Higgins

Phys. Fluids 31, 1360 (1988); http://dx.doi.org/10.1063/1.867005 (12 pages) | Cited 34 times

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In this paper the issue is addressed of how a liquid film of uniform thickness thins on a rotating disk because of the action of centrifugal force. The Navier–Stokes equations in self‐similar form are solved numerically by a finite‐difference method. The effects of film inertia, disk acceleration protocols, and interfacial shear are studied. The numerical results show that inertia has a marked influence on the rate of thinning when the Reynolds number is large and that existing asymptotic theories are inadequate for predicting the transient film thickness. When the disk has a finite acceleration at start‐up, the effects of local inertia are important even at low Reynolds numbers and the thinning rate is reduced. When the overlying phase is a gas, interfacial shear enhances the rate of thinning at sufficiently long spinning times.
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68.15.+e Liquid thin films
47.32.Ef Rotating and swirling flows
47.15.-x Laminar flows

Passive transport in steady Rayleigh–Bénard convection

T. H. Solomon and J. P. Gollub

Phys. Fluids 31, 1372 (1988); http://dx.doi.org/10.1063/1.866729 (8 pages) | Cited 49 times

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Enhancement of the diffusive transport of impurities by two‐dimensional, time‐independent Rayleigh–Bénard convection is studied experimentally. Two impurities are used: a molecular dye (methylene blue) and a particulate impurity (latex spheres). The convective flow is characterized by laser Doppler velocimetry, and the transport is monitored by optical absorption techniques. It is found that the transport can be modeled as a diffusive process on long space and time scales, with an effective diffusion coefficient D∗ whose absolute magnitude and variation with the velocity amplitude W of the flow are in good agreement with recent theoretical predictions. The enhancement factor D∗/D scales with the Peclet number approximately as Pe1/2≡(Wd/πD)1/2, where D is the diffusion coefficient and d the layer depth. Several subtle problems that complicate the study of transport phenomena in cellular hydrodynamic flows are discussed.
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47.27.T- Turbulent transport processes
92.60.hk Convection, turbulence, and diffusion
51.20.+d Viscosity, diffusion, and thermal conductivity

Onset of convection in variable viscosity fluids: Assessment of approximate viscosity–temperature relations

Yen‐Ming Chen and Arne J. Pearlstein

Phys. Fluids 31, 1380 (1988); http://dx.doi.org/10.1063/1.866730 (6 pages) | Cited 5 times

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The effect of the viscosity–temperature relation, μ(T), on the onset of convection in a horizontal fluid layer is discussed. Linear analysis shows that, for aqueous glycerol solutions, the critical Rayleigh numbers (Racrit) obtained using the Arrhenius approximation, μA(T), are in excellent agreement with those employing the actual μ(T) data. The results for the exponential approximation μe(T) differ to an extent that depends on the glycerol mass fraction and the temperature difference (ΔT) between the plates. The error associated with use of μe(T), while small, is of the same order as, or larger than, the uncertainty in careful experiments. For the broad class of liquids for which μA(T) is an excellent approximation to μ, we have assessed the errors in Racrit associated with the widely used μe(T). As ΔT and the viscosity contrast increase, the values of Racrit deviate increasingly from those predicted using μA(T). Also, the relative error in Racrit is much smaller than the maximum relative error in the coefficients [involving μ(T) and its derivatives with respect to T] of the linear disturbance equations.
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47.20.Ft Instability of shear flows (e.g., Kelvin-Helmholtz)
47.27.T- Turbulent transport processes
47.55.Hd Stratified flows

Taylor–Goertler instability for thin‐film flows

P. M. Eagles

Phys. Fluids 31, 1386 (1988); http://dx.doi.org/10.1063/1.866731 (6 pages) | Cited 6 times

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A theory for steady‐state thin‐film flow on a curved bed is presented and disturbances of Taylor or Goertler type are calculated, with reasonable agreement with experimental work.
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47.20.Ft Instability of shear flows (e.g., Kelvin-Helmholtz)
68.15.+e Liquid thin films

The dynamics of three vortices revisited

John Tavantzis and Lu Ting

Phys. Fluids 31, 1392 (1988); http://dx.doi.org/10.1063/1.866732 (18 pages) | Cited 22 times

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The dynamics of three vortices was studied by Synge using the length of the sides of the triangle formed by three vortices as prime variables. The critical states at which the lengths of the sides remain fixed throughout the motion were found to be either equilateral triangles or collinear configurations. The equilateral configurations were shown to be stable or unstable depending on whether the sum of the products of strengths K was greater or less than zero, respectively. In the case K=0, a one‐parameter family of solutions of contracting and another of expanding similar triangles were found. In this paper, it is shown that for this special case, the family of contracting similar solutions is always unstable while the family of expanding ones is stable. The critical states for collinear configurations in the general case are then studied where K is greater than or less than 0. It is shown that there are either six or four critical states depending on the strengths of the vortices. When there are six collinear critical states, three of them are always stable, one is not while the remaining two are unstable (stable) if the equilateral triangle configuration is stable (unstable). When there are only four collinear critical states, they are all stable while the equilateral triangle configuration is always unstable. Since there are two equilateral triangle configurations, clockwise and counterclockwise arrangements of the three vortices, the sum of the indices of all the critical states is equal to +2 regardless of whether K is greater than or less than 0. An integral invariant in trilinear coordinates is derived. When all the critical points and the integral invariant are known, the global behavior of the trajectories is obtained.
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47.15.km Potential flows
47.20.Ky Nonlinearity, bifurcation, and symmetry breaking

Wave structures in jets of arbitrary shape. III. Triangular jets

Shozo Koshigoe, Ephraim Gutmark, Klaus C. Schadow, and Arnold Tubis

Phys. Fluids 31, 1410 (1988); http://dx.doi.org/10.1063/1.867016 (10 pages) | Cited 13 times

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The generalized shooting method, previously developed for the analysis of spatial instability modes of arbitrary shape jets, is applied to incompressible jets with triangular core regions of constant flow. The instability modes of these jets are classified, and calculations are carried out for spatial growth rates, phase velocities, and velocity fluctuation eigenfunctions of three fundamental and two overtone modes. All of the calculated eigenfunctions show negligible velocity fluctuations at the triangle vertices, in good correlation with experimental findings.
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47.20.-k Flow instabilities
47.27.W- Boundary-free shear flow turbulence
47.10.-g General theory in fluid dynamics

Direct interaction approximation of turbulence in the wave packet representation

Tohru Nakano

Phys. Fluids 31, 1420 (1988); http://dx.doi.org/10.1063/1.866733 (11 pages) | Cited 13 times

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The wave packet representation of the Navier–Stokes equations is developed. In order to show its feasibility, it is applied to turbulence in the framework of the direct interaction approximation (DIA). The theory is free from a spurious divergence encountered in the usual DIA theory. The effect of convection due to large eddies is successfully eliminated without relying on any ad hoc approximation, but the contribution from their velocity gradient is included. The Kolmogorov spectrum with the Kolmogorov constant 1.67 is predicted if the shell width is set equal to 2. The passive scalar field in turbulence can be treated similarly, yielding the counterpart of the Kolmogorov constant 0.84. Both the constants agree with experiment fairly well, implying that the present wave packet representation is reliable.
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47.27.Gs Isotropic turbulence; homogeneous turbulence
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion

The fine‐scale intermittency of turbulence

D. Britz, D. A. Shah, and R. A. Antonia

Phys. Fluids 31, 1431 (1988); http://dx.doi.org/10.1063/1.866734 (8 pages) | Cited 2 times

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The technique of Rao et al. [J. Fluid Mech. 48, 339 (1971)], which consists of identifying pulses or regions of strong activity in a narrow bandpass filtered signal, is reexamined in the context of Sreenivasan’s theory [J. Fluid Mech. 151, 81 (1985)], by applying it to white noise and turbulent signals. For white noise, the dependence of pulse characteristics on the threshold and filter center frequency are in close agreement with the theory. There are, however, important differences between white noise and turbulence results, even when the white noise spectrum is shaped to simulate the turbulent spectrum. For the turbulent signal, the theory is valid only for a range of filter parameters for which the departure of the filtered signal from a Gaussian distribution is small. Using wall shear stress and velocity fluctuations in a fully developed turbulent duct flow, the pulse frequency is found to be closely related to the zero‐crossing frequency. It is concluded that the pulse frequency, which is proportional to the Kolmogorov frequency, cannot scale on outer variables.
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47.27.-i Turbulent flows
47.27.Sd Turbulence generated noise

An analytic theory and formulation of a local magnetohydrodynamic lattice gas model

H. Chen, W. H. Matthaeus, and L. W. Klein

Phys. Fluids 31, 1439 (1988); http://dx.doi.org/10.1063/1.866735 (17 pages) | Cited 14 times

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A theoretical description of the newly developed magnetohydrodynamic lattice gas model [Phys. Rev. Lett. 58, 1845 (1987)] is presented. The model is a direct extension of the lattice gas model for incompressible Navier–Stokes fluids. [Phys. Rev. Lett. 56, 1506 (1986)]. In the present model the magnetic force and the magnetic induction effects are formulated with local microscopic dynamical rules only, using a bidirectional random walk process. The development of the theory strongly emphasizes the symmetries connecting the microscopic and macroscopic physics. A preliminary numerical test is described.
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47.65.-d Magnetohydrodynamics and electrohydrodynamics
51.10.+y Kinetic and transport theory of gases
02.70.-c Computational techniques; simulations

Application of nonlinear dynamical invariants in a single electromagnetic wave to the study of the Alfvén‐ion‐cyclotron instability

Niels F. Otani

Phys. Fluids 31, 1456 (1988); http://dx.doi.org/10.1063/1.866736 (9 pages) | Cited 2 times

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Dynamical invariants are derived for particles moving in a single, circularly polarized electromagnetic wave of arbitrary time dependence propagating parallel to a uniform background magnetic field. The invariant associated with helical symmetry is shown to restrict the particle motion to a very narrow region of velocity space. Features of the slow time‐scale motion of fixed points associated with the existence of a fourth adiabatic invariant are described for the case of a slowly varying wave. Characteristics of the particle motion thus derived are applied to the analysis of 1d–3v simulations of the saturation of the Alfvén‐ion‐cyclotron (AIC) instability for a single wave. In particular, an explanation is offered for the appearance of a sharp edge in the velocity distribution function observed in the simulation.
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52.35.Qz Microinstabilities (ion-acoustic, two-stream, loss-cone, beam-plasma, drift, ion- or electron-cyclotron, etc.)
52.65.-y Plasma simulation

Cavitons are solitons: An integrable ponderomotive system

D. J. Kaup

Phys. Fluids 31, 1465 (1988); http://dx.doi.org/10.1063/1.866737 (6 pages) | Cited 3 times

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A new set of integrable soliton equations is presented. It is demonstrated that these equations describe caviton formation in a plasma. The time evolution of the scattering data is obtained and it is found that, unlike other integrable equations where the magnitude of the reflection coefficient was always a constant of the motion, here it may grow and/or decay in time. One physical manifestation of the growth in the reflection coefficient is the pileup of density ripples in front of a microwave source. Also, only cavitons, which are the solitons, are left when the decay conditions dominate.
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52.35.Sb Solitons; BGK modes
52.35.Ra Plasma turbulence

Self‐consistent modification of a fast‐tail distribution by resonant fields in nonuniform plasmas

G. J. Morales, Merit M. Shoucri, and J. E. Maggs

Phys. Fluids 31, 1471 (1988); http://dx.doi.org/10.1063/1.866738 (10 pages) | Cited 4 times

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An analytic study is made of the second‐order modifications produced on the fast‐tail electron distribution function of a nonuniform plasma subjected to resonant excitation by wave sources. The source models considered can represent excitation by external electromagnetic waves propagating obliquely to the plasma density gradient, mode conversion of electrostatic whistlers, beat of two transparent electromagnetic waves, and direct conversion from ripples in the density profile. The calculation treats the Landau damping provided by fast‐tail electrons self‐consistently and is applicable to plasmas having a long density scale length L, i.e., (kDL)1/3 ≫1, where kD is the Debye wavenumber of the warm background electrons. A threshold condition is found for the formation of a positive slope in the tail distribution by the various excitation mechanisms.
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52.25.Fi Transport properties
52.40.Db Electromagnetic (nonlaser) radiation interactions with plasma
52.35.Hr Electromagnetic waves (e.g., electron-cyclotron, Whistler, Bernstein, upper hybrid, lower hybrid)

Saturation of Kelvin–Helmholtz fluctuations in a sheared magnetic field

Bruce D. Scott, P. W. Terry, and P. H. Diamond

Phys. Fluids 31, 1481 (1988); http://dx.doi.org/10.1063/1.866687 (11 pages) | Cited 17 times

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Kelvin–Helmholtz unstable flows are numerically investigated in the context of a sheared E×B flow profile and a sheared magnetic field in the collisional, electrostatic limit. In the extreme form of this limit, density fluctuations are small and the system is described by the nonlinear E×B vorticity dynamics. In order to focus on the role of magnetic shear localization, the computations are confined to two dimensions. For weak magnetic shear the fluctuations become turbulent and saturate by nonlinear cascade to small (dissipative) scales. In a strong magnetic shear regime near the linear stability boundary, nonlinear spatial broadening allows direct access to resistive shear dissipation, leading to saturation at small amplitude with nearly all the fluctuation energy in the longest‐wavelength mode. This is in accordance with previous investigation using a statistical closure analysis [Phys. Fluids 29, 231 (1986)]. The amount of broadening is proportional to the linear growth rate. The fluctuation amplitude scaling with magnetic shear is found to agree closely with the theory.
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47.27.N- Wall-bounded shear flow turbulence
52.35.Ra Plasma turbulence
52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.65.-y Plasma simulation

Drift vortices in inhomogeneous plasmas: Stationary states and stability criteria

E. W. Laedke and K. H. Spatschek

Phys. Fluids 31, 1492 (1988); http://dx.doi.org/10.1063/1.866688 (7 pages) | Cited 19 times

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This paper contains a theoretical treatment of the dynamical behavior of two‐dimensional nonlinear drift waves in plasmas. A simple model is investigated that allows gradients in temperature as well as in particle number density. The general class of stationary states can be specified and from the general description simplifed states can be (re)derived. A quite general method, resulting in general criteria, is proposed to study the dynamics of drift vortices under perturbations. The results are applied to several cases.
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52.35.Kt Drift waves
52.35.Sb Solitons; BGK modes
52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)

Exact resonance broadening theory of diffusion in random electric fields

A. Salat

Phys. Fluids 31, 1499 (1988); http://dx.doi.org/10.1063/1.866689 (6 pages) | Cited 13 times

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Particle motion in random electric fields is considered on the assumption that orbit stochasticity causes the velocity increments at different times to be independent random events with Gaussian probabilities (Wiener process). The resulting resonance broadening term is substantially different from the one derived by Dupree and others [Phys. Fluids 9, 1773 (1966); 11, 1977 (1968); 15, 1496 (1972); Long Time Prediction in Dynamics (Wiley, New York, 1983), p. 319], and describes the continuous loss of particles from the resonance region. The diffusion coefficient D is time dependent, being quasilinear for t≪td (=diffusion time across resonance region). The validity of D∼(〈E2〉)3/4 in the high‐amplitude case of previous theories is questioned.
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52.25.Fi Transport properties
52.35.Ra Plasma turbulence

Relativistic structure of stochastic wave–particle interaction

K. Akimoto and H. Karimabadi

Phys. Fluids 31, 1505 (1988); http://dx.doi.org/10.1063/1.866690 (10 pages) | Cited 21 times

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Stochastic interactions of charged particles with electrostatic waves propagating at arbitrary angles to an external magnetic field are studied based on a relativistic canonical Hamiltonian formalism. The present theory, however, is valid also for electromagnetic waves after a slight modification. The stochasticity threshold is derived utilizing Chirikov’s criterion. It is found that relativistic effects are important for electrons interacting with relatively high phase velocity waves even at nonrelativistic initial energies. In particular, the relativistic generalization of a previous theory [Phys. Rev. Lett. 34, 1613 (1975); Phys. Fluids 21, 2230 (1978)] moves the degeneracy of primary resonances in nearly perpendicular directions to the angles where the parallel phase speed approximately equals the speed of light. It was also demonstrated for the first time that initially low energy electrons can gain relativistic energies (γ≫1) by means of the stochastic interaction with an electrostatic wave, where γ is the relativistic factor. Moreover, properties of second‐order islands that form within primary islands have been studied. Finally, the nature of the stochastic particle energization by electrostatic waves is compared with that by electromagnetic waves, and the results are applied to the problem of electron acceleration during ionospheric modification experiments.
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52.20.Dq Particle orbits
52.50.Gj Plasma heating by particle beams
52.27.Ny Relativistic plasmas

Theory and simulation of electromagnetic beam modes and whistlers

David L. Newman, Robert M. Winglee, and Martin V. Goldman

Phys. Fluids 31, 1515 (1988); http://dx.doi.org/10.1063/1.866691 (17 pages) | Cited 5 times

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Using particle‐in‐cell simulations and analytical methods, a study of the nonlinear evolution of electromagnetic instabilities driven by an anisotropic electron beam (Tb⊥≫Tb∥) in an external magnetic field is performed. The unstable waves are either whistlerlike or beam‐mode‐like depending on the external field strength and beam velocity. The evolution of the particle distribution differs significantly in the two regimes. Even in the presence of a faster electrostatic instability, the electromagnetic waves grow to a significant amplitude. In certain cases, an energetic tail is formed, resulting in enhanced Čerenkov emission of electrostatic waves. The initial evolution of the particle distribution is explained in terms of the interaction of a given linearly unstable wave with the self‐consistent perturbed distribution.
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52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
52.35.Hr Electromagnetic waves (e.g., electron-cyclotron, Whistler, Bernstein, upper hybrid, lower hybrid)
52.65.-y Plasma simulation
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