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Jan 1988

Volume 31, Issue 1, pp. 1-217

Page 1 of 2 Pages Next Page | Jump to Page

The 1987 François Naftali Frenkiel Award for Fluid Mechanics

Phys. Fluids 31, 1 (1988); http://dx.doi.org/10.1063/1.3480119 (1 page)

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Abstract Unavailable

The anomalous behavior of the runup of cnoidal waves

Costas Emmanuel Synolakis, Manas Kumar Deb, and James Eric Skjelbreia

Phys. Fluids 31, 3 (1988); http://dx.doi.org/10.1063/1.866575 (3 pages) | Cited 13 times

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A new solution to the linearized shallow‐water wave equations is introduced for the case of cnoidal waves climbing up a plane beach. The solution is used to calculate the maximum runup. It is shown that the maximum relative runup of cnoidal waves is significantly larger than the runup of monochromatic waves with the same wave height and wavelength far from the shore. It is also shown that the maximum relative runup of cnoidal waves is not a monotonically varying function of the normalized wavelength.
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68.03.Kn Dynamics (capillary waves)
68.05.-n Liquid-liquid interfaces
91.50.Cw Beach and coastal processes
92.10.Hm Ocean waves and oscillations

Chaotic behavior of interacting elliptical instability modes

Carl S. Hellberg and Steven A. Orszag

Phys. Fluids 31, 6 (1988); http://dx.doi.org/10.1063/1.867010 (3 pages) | Cited 8 times

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A three‐mode projection of the Navier–Stokes equations for nonlinear perturbations to an elliptical vortex is studied numerically. It is found that, as the Reynolds number increases, the perturbations undergo a sequence of period doublings leading to chaos according to the Feigenbaum scenario [J. Statis. Phys. 19, 25 (1978); Phys. Lett. 74 A, 375 (1979)].
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47.27.Cn Transition to turbulence
47.52.+j Chaos in fluid dynamics

The effects of electric field fluctuations on bootstrap current and resistivity in toroidal plasmas

K. C. Shaing

Phys. Fluids 31, 8 (1988); http://dx.doi.org/10.1063/1.866581 (4 pages) | Cited 22 times

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The effects of electric field fluctuations on bootstrap current and resistivity in toroidal plasmas are studied in the plateau regime. A tokamak is discussed as an example. The bootstrap current density is more sensitive to the fluctuations than the plasma resistivity because the bootstrap current density depends on the poloidal mode number of the fluctuations, while plasma resistivity depends on the parallel wave vector.
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52.25.Gj Fluctuation and chaos phenomena
52.55.Fa Tokamaks, spherical tokamaks

Transport scaling in the collisionless‐detrapping regime in stellarators

E. C. Crume, Jr., K. C. Shaing, S. P. Hirshman, and W. I. van Rij

Phys. Fluids 31, 11 (1988); http://dx.doi.org/10.1063/1.866559 (4 pages) | Cited 12 times

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Stellarator transport scalings with electric field, geometry, and collision frequency in the reactor‐relevant collisionless‐detrapping regime are determined from numerical solutions of the drift kinetic equation. A new geometrical scaling, proportional to ϵ3/2t rather than ϵtϵ1/2h, is found, where ϵt is the inverse aspect ratio and ϵh is the helical ripple. With the new scaling, no reduction in energy confinement time is associated with large helical ripple, which provides design flexibility. Integral expressions for the particle and heat fluxes that are useful for transport simulations are given.
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52.25.Fi Transport properties
52.55.Jd Magnetic mirrors, gas dynamic traps

Determination of the macroscopic (partial) slip boundary condition for a viscous flow over a randomly rough surface with a perfect slip microscopic boundary condition

Kalvis M. Jansons

Phys. Fluids 31, 15 (1988); http://dx.doi.org/10.1063/1.866563 (3 pages) | Cited 31 times

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Consider a viscous fluid, at zero Reynolds number, moving over a solid surface flat except for a random array of microscopic defects having a small area fraction c. Assuming a microscopic boundary condition of perfect slip, the macroscopic boundary condition is determined from first principles. The asymptotic structure of the solution for a random surface with finite slope is quite different from those of earlier studies in the limit of an ‘‘almost flat’’ surface. The results of this study show that very small amounts of roughness can well approximate a no‐slip boundary condition macroscopically, for example, one defect of the order of 10−9 m per (10−7 m)2 gives a slip length of only 10−5 m.
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68.08.-p Liquid-solid interfaces
68.43.-h Chemisorption/physisorption: adsorbates on surfaces
47.15.Cb Laminar boundary layers

Bubble motion in a Hele–Shaw cell

Anne R. Kopf‐Sill and G. M. Homsy

Phys. Fluids 31, 18 (1988); http://dx.doi.org/10.1063/1.866566 (9 pages) | Cited 28 times

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The shapes and motion of immiscible bubbles in a Hele–Shaw cell driven by the motion of the surrounding fluid were studied. Six classes of steady shapes, some of which are remarkable, were observed. Multiple steady states exist over some ranges of parameters and the shape as a function of speed may slow hysteresis. The observed translational velocities do not agree with available theory, but some of the shapes are in qualitative agreement with those computed by Tanveer [Phys. Fluids 29, 3537 (1986)].
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47.55.Kf Particle-laden flows
47.15.-x Laminar flows

Solutal convection in the melt during solidification of a binary alloy

D. N. Riahi

Phys. Fluids 31, 27 (1988); http://dx.doi.org/10.1063/1.866573 (6 pages) | Cited 4 times

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Nonlinear solutal convection in the melt under a planar solidifying surface is investigated in the limit of small segregation. Stationary solutions of the nonlinear problem are obtained and the preferred mode of convection is determined by a stability analysis. It is found that down‐hexagons (where motion is downward at the cells’ centers) are stable for sufficiently small amplitude Ε, while both down‐hexagons and squares are stable in a range of larger Ε. The dependence of various flow features on the segregation coefficient and the effective depth of the melt is discussed.
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47.27.T- Turbulent transport processes
47.20.Ky Nonlinearity, bifurcation, and symmetry breaking
47.20.Bp Buoyancy-driven instabilities (e.g., Rayleigh-Benard)

Stability and finite amplitude natural convection in a shallow cavity with insulated top and bottom and heated from a side

Hai Perng Kuo and Seppo A. Korpela

Phys. Fluids 31, 33 (1988); http://dx.doi.org/10.1063/1.866574 (10 pages) | Cited 22 times

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The stability of laminar natural convection in a shallow cavity has been studied theoretically. The flow is driven by a horizontal temperature gradient between isothermal vertical sidewalls of the cavity, the top and bottom of which are insulated. It was found that for a Prandtl number (Pr) less than 0.033, shear instability causes stationary transverse cells to be formed in the flow. For larger values of Prandtl number the instability sets in as oscillating longitudinal rolls in the range 0.033<Pr<0.2; and as stationary longitudinal rolls for larger values of Pr. The importance of three‐dimensional disturbances was investigated for Pr=0.02 and they were found to be less critical than two‐dimensional ones. Finite amplitude motions of the stationary transverse cells were simulated by solving the nonlinear equations numerically with the use of pseudospectral methods. This simulation supports the calculations of the onset of the instability by linear theory, and explains why the Nusselt number decreases when secondary flows are present.
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47.20.Bp Buoyancy-driven instabilities (e.g., Rayleigh-Benard)
47.27.T- Turbulent transport processes
47.15.Rq Laminar flows in cavities, channels, ducts, and conduits

Free‐streamline analysis of deformation and dislodging by wind force of drops on a surface

P. A. Durbin

Phys. Fluids 31, 43 (1988); http://dx.doi.org/10.1063/1.866576 (6 pages) | Cited 3 times

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Free‐streamline theory is used to analyze the deformation and dislodging by wind pressure of drops of liquid adhered by surface tension to a solid surface. The critical Weber number for droplets to be dislodged is determined as a function of advancing and receding contact angle. Graphical results for drop shape are in good agreement with observation.
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68.03.Cd Surface tension and related phenomena

Model functions of Reynolds stress models

Johannes Janicka

Phys. Fluids 31, 49 (1988); http://dx.doi.org/10.1063/1.866577 (7 pages) | Cited 2 times

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A Reynolds stress (Re‐stress) model for the prediction of shear flows is presented. Special attention is paid to the determination of the model functions. First, the general modeling assumptions are discussed and the modeling of the equations is then described in detail. It is shown that by successive analysis of different types of flows a set of model functions with a high level of universality can be deduced. Finally, prediction/measurement comparisons in homogeneous shear flows, round jets, plane jets, and wakes are presented.
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47.27.N- Wall-bounded shear flow turbulence
47.10.-g General theory in fluid dynamics

Three‐dimensional centrifugal‐type instabilities in inviscid two‐dimensional flows

B. J. Bayly

Phys. Fluids 31, 56 (1988); http://dx.doi.org/10.1063/1.867002 (9 pages) | Cited 57 times

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In this paper the classical Rayleigh centrifugal instability theory is extended to general inviscid two‐dimensional flows. Sufficient conditions for centrifugal instability are that the streamlines be convex closed curves in some region of the flow, with the magnitude of the circulation decreasing outward. If these conditions are satisfied, a class of three‐dimensional short‐wave instabilities can be constructed, which are localized near the streamline on which the exponent of a certain matrix Floquet problem is maximized.
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47.20.-k Flow instabilities
47.32.Ef Rotating and swirling flows
47.10.-g General theory in fluid dynamics

Magnetohydrodynamic flow in a curved pipe

F. Issacci, N. M. Ghoniem, and I. Catton

Phys. Fluids 31, 65 (1988); http://dx.doi.org/10.1063/1.866578 (7 pages)

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The flow of conductive fluids in highly conductive curved pipes is studied analytically in this paper. The flow is assumed to be steady state, laminar, and fully developed. Coupled continuity, Navier–Stokes, and appropriate Maxwell equations are solved in toroidal coordinates. The dimensionless parameters of the problem are Dean number K and Hartmann number Ha. For low Hartmann numbers [Ha2∼θ(1)], the solution is expanded in a power series of K and Ha2. For intermediate Hartmann numbers [Ha2∼θ(1000)], the solution is expressed as a power series of K. The axial velocity contours are shown to be shifted towards the outer wall. For low Ha, these contours are nearly circular. The effect of a strong transverse magnetic field is to enhance the compression of fluid towards the outer wall. The secondary flow field comprises a symmetric pair of counter‐rotating vortices. A strong magnetic field is found to confine the secondary flow streamlines to a thin layer near the tube wall. The secondary flow rate in the near‐wall boundary layer is increased by the magnetic field. This increase in flow rate raises the possibility of efficient convective cooling of curved first wall tubes in magnetic confinement fusion reactors (MFCR).
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47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.32.Ef Rotating and swirling flows
52.55.Jd Magnetic mirrors, gas dynamic traps

Stability of Bernstein–Greene–Kruskal plasma equilibria. Numerical experiments over a long time

A. Ghizzo, B. Izrar, P. Bertrand, E. Fijalkow, M. R. Feix, and M. Shoucri

Phys. Fluids 31, 72 (1988); http://dx.doi.org/10.1063/1.866579 (11 pages) | Cited 44 times

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Bernstein–Greene–Kruskal (BGK) equilibria for a Vlasov plasma consisting of a periodic structure exhibiting depressions or ‘‘holes’’ in phase space are under consideration. Marginal stability analysis indicates that such structures are unstable when the system contains at least two holes. An Eulerian numerical code is developed allowing noiseless information on the long time phase space behavior (about 103ω−1p) to be obtained. Starting with equilibria with up to six holes, it is shown that the final state is given by a structure with only one large hole, the initial instability inducing coalescences of the different holes. On the other hand, starting with a homogeneous two‐stream plasma it is shown that, in a first step, a BGK periodic structure appears with a number of holes proportional to the length of the system, followed, in a second step, by a coalescence of the holes to always end up with the above mentioned one large hole structure.
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52.65.-y Plasma simulation
52.55.-s Magnetic confinement and equilibrium
52.35.-g Waves, oscillations, and instabilities in plasmas and intense beams
52.25.Fi Transport properties

Soliton decay of nonlinear Alfvén waves: Numerical studies

Silvina Ponce Dawson and Constantino Ferro Fontán

Phys. Fluids 31, 83 (1988); http://dx.doi.org/10.1063/1.866580 (7 pages) | Cited 12 times

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The derivative nonlinear Schrödinger equation is numerically solved for arbitrary initial conditions by an extension of the Ablowitz–Ladik scheme [Stud. Appl. Math 57, 1 (1977)]. The numerical nonlinear difference code, which takes advantage of the inverse scattering method, simulates the original differential equation reproducing common features, like solitons and an infinite set of constants of motion. The long‐time behavior is analyzed in terms of the sign of one of the constants of motion. The formation of a soliton train is seen whenever the constant has a negative value. This fact is the global expression of the Mj≂lhus local criterion to distinguish between modulationally stable and unstable cases.
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52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)

Ponderomotive force in a nonisothermal plasma

Nam C. Lee and George K. Parks

Phys. Fluids 31, 90 (1988); http://dx.doi.org/10.1063/1.866974 (5 pages) | Cited 4 times

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In this paper a formula is derived for the ponderomotive force of electromagnetic fields in collisionless and inhomogeneous plasma when the temperature varies slowly in space and time. This result, compared to the current formula for the isothermal case, has an additional term that involves the temperature gradient. The new result is valid in anisotropic medium and better suited for application to both laboratory and space plasma situations in which the plasma is anisotropic.
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52.25.Mq Dielectric properties

Generalization of the synchrotron absorption–emission coefficient in plasmas to arbitrary direction of propagation

A. Nassri and M. Heindler

Phys. Fluids 31, 95 (1988); http://dx.doi.org/10.1063/1.866975 (4 pages) | Cited 2 times

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A new analytical formulation of the synchrotron absorption and emission coefficient in plasmas, for wave propagation perpendicular to the magnetic field, has been derived previously [Phys. Fluids 29, 3275 (1986)]. These coefficients were shown to be both accurate and analytically simple. Their generalization to arbitrary directions of propagation with respect to the magnetic field is presented here. Based on the analytical formulas for perpendicular propagation and on the exact sum–integral formulation of the coefficients for arbitrary propagation, this generalization is achieved by empirical data fit. Hereby the exact formulation serves as target function for the fitting procedure and subsequently as reference for determination of the accuracy of the results. The generalized analytical representations for the coefficients are presented here, one for each polarization mode and for the low and high temperature domain (above and below a few tens of kilo‐electron‐volts). 
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52.25.Os Emission, absorption, and scattering of electromagnetic radiation

Synchrotron radiation from dynamically evolving runaway tails

Ebraahim Moghaddam‐Taaheri and Loukas Vlahos

Phys. Fluids 31, 99 (1988); http://dx.doi.org/10.1063/1.866976 (8 pages)

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A quasilinear code (2‐D in velocity and wave vector space) based on the Ritz–Galerkin method and finite elements is used to study the synchrotron emission from a dynamically evolving runaway tail. The evolution of runaway tails was studied recently using the same code [Phys. Fluids 28, 3356 (1985)]. The velocity distribution derived from the above code is used to estimate the synchrotron radiation in different time steps. The applicability of these results to the Princeton Large Torus [Phys. Rev. Lett. 49, 1255 (1982)] and solar microwave bursts is also commented on.
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52.25.Os Emission, absorption, and scattering of electromagnetic radiation
96.60.qe Flares

Weakly relativistic dispersion of Bernstein waves

P. A. Robinson

Phys. Fluids 31, 107 (1988); http://dx.doi.org/10.1063/1.866557 (8 pages) | Cited 14 times

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Weakly relativistic effects on the dispersion of Bernstein waves are investigated for waves propagating nearly perpendicular to a uniform magnetic field in a Maxwellian plasma. Attention is focused on those large‐wave‐vector branches that are either weakly damped or join continuously onto weakly damped branches since these are the modes of most interest in applications. The transition between dispersion at perpendicular and oblique propagation is examined and major weakly relativistic effects on dispersion at perpendicular propagation are found to persist at other angles; these effects can dominate even in low‐temperature plasmas. A number of simple analytic criteria are obtained which delimit the ranges of harmonic number and propagation angle within which various types of weakly damped Bernstein modes can exist.
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52.35.Hr Electromagnetic waves (e.g., electron-cyclotron, Whistler, Bernstein, upper hybrid, lower hybrid)
52.27.Ny Relativistic plasmas

Wave–plasma interaction near the second electron cyclotron harmonic

S. Pešić

Phys. Fluids 31, 115 (1988); http://dx.doi.org/10.1063/1.866558 (8 pages) | Cited 2 times

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The linear wave propagation and spatial damping near the second electron cyclotron harmonic in a weakly relativistic Maxwellian plasma for an arbitrary angle of wave incidence are investigated. It is found that mode interaction with linear conversion of the extraordinary mode into a quasilongitudinal mode occurs over a relatively large range of plasma parameters. The absorption properties of the extraordinary and ordinary modes and their scaling laws are examined. The noninductive current drive by electron cyclotron waves is also discussed. The results obtained indicate quite favorable features of the wave–plasma interaction near the second electron cyclotron harmonic for plasma heating, current drive, and diagnostics applications.
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52.40.Db Electromagnetic (nonlaser) radiation interactions with plasma
52.25.Mq Dielectric properties
52.25.Os Emission, absorption, and scattering of electromagnetic radiation
52.50.Gj Plasma heating by particle beams

Measurement of a potential barrier created by electron cyclotron resonance heating

C. P. Chang, M. A. Lieberman, H. Meuth, and A. J. Lichtenberg

Phys. Fluids 31, 123 (1988); http://dx.doi.org/10.1063/1.866560 (6 pages) | Cited 3 times

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An electrostatic potential well and mirror‐trapped hot electrons are created by high power (250 kW), short pulse (3 μsec) electron cyclotron resonance heating (ECRH) of a plasma in one magnetic mirror cell of a multiple mirror experiment. The creation and subsequent decay of the potential well is measured by an electron beam, time‐of‐flight diagnostic. Typically, the barrier rises to −40 V just after ECRH and decays within 100 μsec. A numerical model of the barrier evolution is developed, and the numerical results along with the experimental observations are presented. Both the numerical results and the experimental observations indicate a correlation between the degree of heating (diamagnetic loop voltage output) and the longevity of the barrier. It is shown that the decay of the barrier is determined mainly by the hot‐electron escape rate and the hot‐electron‐neutral ionization rate, rather than by trapping of the passing ions.
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28.52.Av Theory, design, and computerized simulation
52.55.-s Magnetic confinement and equilibrium
52.50.Gj Plasma heating by particle beams
52.70.Ds Electric and magnetic measurements

Nonlinear coupling of waves in the ion cyclotron range of frequencies to tokamak trapped electron modes

John B. McBride

Phys. Fluids 31, 129 (1988); http://dx.doi.org/10.1063/1.866561 (8 pages) | Cited 5 times

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The results of a theoretical study of nonlinear coupling of waves in the ion cyclotron range of frequencies (ICRF) to tokamak dissipative trapped electron modes (DTEM) via sidebands of the ICRF source wave are presented. These interactions can affect the stability of the DTEM spectrum and thus tokamak energy confinement. Explicit expressions are derived for the nonlinear growth rates of DTEM both for fast magnetosonic and ion Bernstein source waves. Fast wave coupling is found to be destabilizing for frequencies in the ICRF at low plasma ion beta, but can be stabilizing for wave frequencies well above the ion gyrofrequency (ω0≳ωciβ−1/2i). Ion Bernstein coupling can also be stabilizing or destabilizing depending on details of the source wave. Waves with ω0>ωci, k0>k, and k0 ρi≳1 appear better suited for stabilization (k0, k are the wavenumbers of the source wave, DTEM). For example, if these conditions are met and 2k0y<k (k0y is the poloidal source wavenumber), it is shown that the whole DTEM spectrum for kρi <1 can be stabilized. Analytic expressions for the ICRF wave electric field strengths for DTEM stabilization are given.
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52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
52.55.Fa Tokamaks, spherical tokamaks

Dissipative trapped particle modes in tandem mirrors

H. L. Berk and C. Y. Chen

Phys. Fluids 31, 137 (1988); http://dx.doi.org/10.1063/1.866562 (12 pages) | Cited 2 times

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The theory for the dissipative trapped particle modes is developed for a tandem mirror taking into account equilibrium rotational effects, electron temperature gradients, and an axial ambipolar potential, for a broad range of collisional parameters. The electrons are treated as a Maxwellian plasma that occupies the central cell and anchor cell regions. It is assumed that the eigenfunction is piecewise constant with abrupt transitions between the anchor and central cell regions. It is found that when ω/νp≳1, with ω the mode frequency and νp the Pastukhov loss rate, that the energy conservation structure of the collision operator produces important changes to previously developed theories. A solution to the problem is achieved by using the solution for the lifetime of an electron in an ambipolar trap, taking into account the global energy conservation. The energy conservation structure also allows a self‐consistent description of dissipative instabilities when thermal gradient and electric fields are present. At very high collision frequency, a new dispersion relation is obtained, which exhibits an axially rotational shear drive coupled to radial temperature gradients producing instability. Numerical studies are presented for some parameters, with the deviation from previous theory highlighted.
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28.52.Av Theory, design, and computerized simulation
52.55.-s Magnetic confinement and equilibrium
52.25.Dg Plasma kinetic equations
52.35.Kt Drift waves
52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)

Pressure surface distortion by applied ion cyclotron waves and magnetic field asymmetries

J. R. Myra and D. A. D’Ippolito

Phys. Fluids 31, 149 (1988); http://dx.doi.org/10.1063/1.866555 (9 pages) | Cited 1 time

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In magnetic confinement devices the pressure surfaces must obey the parallel current constraint. In a tandem mirror, nonquadrupole magnetic field components or ion cyclotron range of frequencies (ICRF) ponderomotive effects enter the parallel current equation in a nontrivial way. The extra terms cause a shift of the plasma column and/or distortion of the pressure surface shape. These effects are examined for three cases of interest: magnetic error fields due to misaligned coils, axial asymmetries in the quadrupole or solenoidal fields, and azimuthally asymmetric ponderomotive effects associated with applied ICRF waves. The ambipolar potential can compensate for asymmetries and permit lowest order isorrhopic equilibria in some cases, but if the passing density between cells is too small (np/na<rTa/eΦRc) this cannot occur and the flux surfaces of the cells disconnect.
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52.30.Cv Magnetohydrodynamics (including electron magnetohydrodynamics)
28.52.Av Theory, design, and computerized simulation
52.55.-s Magnetic confinement and equilibrium

Effect of large‐amplitude perpendicularly propagating radio frequency waves on the interchange instability

Niels F. Otani and Bruce I. Cohen

Phys. Fluids 31, 158 (1988); http://dx.doi.org/10.1063/1.866556 (19 pages) | Cited 3 times

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Results are presented from hybrid 2‐D quasineutral Darwin simulations of the interchange instability in the presence of a large rf wave in the ion‐cyclotron frequency range. The simulation models the plane perpendicular to the background magnetic field using cold particle ions and a cold E×B electron fluid. Related theory is also discussed. Fluid equations appropriate to the simulation model are derived and their properties demonstrated and compared to simulation. A method for solving for the rf‐modified growth rates from the fluid equations is described. It is generally expected that the current component associated with the mean, rf‐induced ion drift is capable of influencing the stability of the interchange mode; however, no modification of the mean ion drift is observed in simulations in which rf is present. Instead, in both the theory and simulation, an electron rf‐field oscillation current dominates the modification to the gravitational current. As a result, even in the presence of large rf fields (Brf/B0=15%), only modest corrections to the interchange growth rates are observed. The effect is stabilizing for kLn≲0.8–0.9, apparently for both signs of the square‐electric‐field gradient, and is destabilizing for larger values of kLn, although the credibility of the simulation begins to become suspect here. Fractional reduction of the interchange growth rate is observed to be quadratically dependent on the rf wave amplitude, independent of ion‐cyclotron resonant effects, and proportional to ∇B2rf/∇B20, consistent with an eikonal theory developed for the study of stabilizing effects on perpendicularly propagating fast Alfvén waves. The results also suggest that additional gradient‐independent stabilizing effects may be operative when kLn∼1. Finally, it is also observed that, while the rf wave has little effect on the interchange instability, the interchange mode strongly affects the rf wave, damping it significantly as the mode saturates.
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28.52.Av Theory, design, and computerized simulation
52.55.-s Magnetic confinement and equilibrium
52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
52.40.Db Electromagnetic (nonlaser) radiation interactions with plasma
52.65.-y Plasma simulation
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