The effect of the viscosity ratio (M≡${\mathrm{\mu }}_{\mathit{D}}$/${\mathrm{\mu }}_{\mathit{I}}$) in changing the nature of viscous fingering was studied using a simple, physical model of miscible, dispersionless, two-phase, linear flow in model two-dimensional porous media. For all viscosity ratios, the initial flows had an unstable, fractal character which crossed over to stable, compact flow on a time (or length) scale which increased with the viscosity ratio. An empirical scaling of the data enables an asymptotic characterization of both this time scale τ≊${\mathit{M}}_{\mathit{t}}^{\mathrm{\phi }}$, where ${\mathrm{\phi }}_{\mathit{t}}$=0.17±0.03, as well as the front velocity v≊${\mathit{M}}_{\mathit{t}}^{\mathrm{\epsilon }\mathrm{\phi }}$ where ε${\mathrm{\phi }}_{\mathit{t}}$=0.07±0.02. A comparison with identical simulations of radial flow indicates that the same characteristic length scale applies in both linear and radial geometries l≊${\mathit{M}}_{\mathit{l}}^{\mathrm{\phi }}$ where ${\mathrm{\phi }}_{\mathit{l}}$=0.24±0.06, while the time scales differ because of the different relations between time and size in the two geometries.

We develop a formal method for assigning rules to lattice-based walkers which allows the modeling of irreversible growth in systems governed by non-Laplacian partial differential equations. The method is used to study diffusive growth in finite concentration fields. Good agreement with analytic results is obtained. The method is subsequently applied to study electrochemical deposition and investigate the interplay between the electrostatic and diffusion fields. We examine the effect of a local (nonuniform) flow field on deposition on a substrate.

It is shown that screening greatly diversifies the type of patterns that can grow in an electrostatic field. Screening introduces a new length scale and a nontrivial dependence on the boundary conditions. Growing patterns can either have a fractal character (diffusion-limited-aggregation-like) at scales shorter than the screening length, be similar to the Eden model, or even be dense. A transition from dense to multibranched growth occurs at a point which depends on the potentials at the boundaries, the distance between them, and the screening length. Simulations are carried out in one dimension (growth in a channel) and in two dimensions (with different shapes for the outer electrode). The transition from dense to filamentary growth is also investigated by means of an analytical study of the instability, within a similar scheme to the one proposed by Mullins and Sekerka. The results are qualitatively similar for growth in one and two dimensions. Finally, it is shown that, before the transition (dense growth), the aggregate reproduces the shape of the outer electrode.

Theories of two nonlinear processes of magnetic-moment-field generation in wave-plasma interactions are presented here. These processes are (i) resonant excitation of a moment field (REMF) and (ii) stimulated excitation of a moment field (SEMF). This field generally evolves from the wave-induced bending of the direction of motion of constituents of a plasma. It is important when it has a large value, and when it grows to large values with time, because then it effectively controls the wave-induced features of a plasma. Specifically, this growing field gives rise to a strong anisotropy of the plasma in the region of the common direction of propagation of the involved waves, which leads to enhancement of synchrotron and bremmsstrahlung losses, and filamentation. The REMF is a static field of resonance when the beat frequency of two waves equals the frequency of another wave, all propagating in the same direction. The three possible cases of such interaction, involving waves of only high frequencies, with unmagnetized plasmas, for which the REMF formula has been calculated, are (a) two transverse waves and one longitudinal wave, (b) two longitudinal waves and one transverse wave, and (c) three transverse waves. The SEMF is a parametrically stimulated nonoscillating, exponentially temporally growing field of stimulated Brillouin scattering from a signal Alfven wave, a pump Alfven wave, and a signal sound wave. A second simultaneous resonance occurs only for weak nonlinearity and finite electrical conductivity, when the signal Alfven wave frequency equals the parametric frequency shift. This, being a slow process of transfer of plasma kinetic energy to field energy, can be a strong candidate for evolution of the field in plasma configurations of outer space.

X-ray satellite line emission from targets irradiated by intense-light ion beams can be used to diagnose plasma conditions and beam properties. We present results from our analysis of spectroscopic measurements of x-ray Kα satellites emitted from a target irradiated by an intense-light ion beam. In this experiment, performed on the Particle Beam Fusion Accelerator-II device at Sandia, an Al target was irradiated with a 4–6 MeV proton beam with a peak power density of 1–2 TW/${\mathrm{cm}}^2$. Up to 15% of the beam electrical current was in the form of carbon contaminants. A time-integrated spectrum was obtained with a resolution of λ/Δλ>1200. In our analysis, collisional radiative equilibrium (CRE) calculations were performed to study the dependence of the Al Kα emission spectrum on plasma and beam properties. Good agreement is obtained between calculated satellite spectra and the emission features observed in the experimental spectrum. We find that excited states with M-shell spectator electrons contribute significantly to Kα satellite emission spectra, exhibiting relatively broad lines at wavelengths blueshifted with respect to those originating from ground-state configurations. Because of opacity effects, it is likely that only radiation emitted from the outer skin of the target plasma was seen by the detector in the experiment. It is also shown that resonant self-absorption can skew the spectrum towards apparent higher ionization stage. Our results suggest that emission spectroscopy of x-ray satellite lines from thin tracer layers offers a potentially valuable technique for determining plasma conditions in intense-light-ion-beam experiments.

Experiments on plasma wake fields are presented. Properties of wake fields in a two-component plasma are briefly reviewed and compared with the experiments of Nishida et al. [Phys. Rev. Lett. 66, 2328 (1991)]. Characteristics of wake fields in a three-component plasma that consists of positive ions, negative ions, and electrons are then described. These wake fields are created following the injection of either positive or negative ions into a plasma. The relationship between ion-acoustic fast modes and the wake field are investigated and the excitation mechanism is discussed. Critical negative-ion concentrations and modulation effects are examined. The excitation of the wake fields is interpreted using a fluid model.

We report on pump-probe measurements of reflectivity and transmissivity of a plasma produced in transparent solid materials. The plasma is created by irradiating uncoated transparent planar glass targets with 1.0-ps FWHM laser pulses at a peak intensity of 2.0×${10}^{13}$ ${\mathrm{W}/\mathrm{c}\mathrm{m}}^2$. Time-resolved measurements using a probe light pulse incident from the backside are presented, revealing two competing mechanisms: one is highly absorptive due to a bulk underdense plasma formed behind the target surface, and the other is highly reflective due to an overdense plasma layer at the surface. A simple self-consistent and analytical model, similar to the avalanche model, is proposed, leading to both time-dependent and time-integrated solutions to the evolution of plasma density profiles and characteristics of high-intensity-laser-pulse propagation and absorption in the transparent material. Calculations of the probe light interacting with this plasma show that excellent agreement with experimental measurements can only be obtained by including a contribution from the bulk plasma formed behind the surface. Experimental measurements with Au-coated targets are also shown to illustrate elimination of the bulk plasma.

We report simultaneous time-resolved measurements of second-harmonic and Kα emission from layered, planar targets irradiated by 180 ps, Nd-laser pulses focused to an intensity of (1–3)×${10}^{16}$ W/${\mathrm{cm}}^2$. We observe that pulsations of the second-harmonic emission appear to coincide with pulsations of the x-ray fluorescence with each burst lasting about 20 ps and separated by 30–50 ps. The x-ray pulsations indicate that fast electrons are produced in short bursts which can modulate the effective ‘‘temperature’’ in the quarter critical region thereby affecting emission from the two-plasmon decay instability. We suggest these pulsations appear because the laser intensity reaching the critical surface is modulated by a chaotic time-dependent Brillouin reflection from the underdense plasma. Some implications of such a process are discussed.

The profile and the shift of the ${\mathrm{H}}_{\mathrm{\alpha }}$ line of hydrogen were measured and the shift was calculated at high electron densities in a helium plasma. The plasma was produced in a gas-liner pinch, which was diagnosed by Thomson scattering. Densities were between 1×${10}^{18}$ ${\mathrm{cm}}^{\mathrm{-}3}$ and 1×${10}^{19}$ ${\mathrm{cm}}^{\mathrm{-}3}$ and temperatures varied from 4 up to 12.5 eV. The results show a nonlinear behavior of the shift. Corresponding theoretical calculations have been performed, especially taking into account the dynamic screening of the electron-atom interaction. The agreement is very good for densities below 5×${10}^{18}$ ${\mathrm{cm}}^{\mathrm{-}3}$; above that density it is satisfactory.

This paper deals with the behavior of an electron gas in an expanding plasma jet in argon. From the measurements, obtained using a high-quality Thomson-Rayleigh scattering diagnostic, it is shown that the collisional-radiative recombination of argon is small. However, the three-particle recombination plays a determining role in the heating of the electron gas. From the relation between the electron density and the electron temperature in the first part of the expansion, the three-particle recombination coefficient is calculated, which shows good agreement with previous results reported in the literature.

The heliumlike α resonance line is one of the strongest and most frequently observed transitions in plasma spectroscopy. In optically thick plasmas of moderate density, photons emitted in this line typically undergo many absorptions and reemissions before escaping. In the present investigation the time required for this process to occur in aluminum plasma is calculated by numerical solution of the time-dependent equation of radiative transfer, in which the photon transit time between interactions is taken into account. An analytic model is also developed in which the collisional quenching probability is parametrized in terms of an equivalent two-level atom. This model facilitates interpretation of the numerical results and permits economical estimates of the escape time for different plasma elements and conditions. One practical implication of these results is that a subpicosecond x-ray pulse from a femtosecond laser-produced high-density plasma can be broadened by multiple scattering if it propagates into a moderate-density preformed plasma.

The oscillatory behavior of dc discharges between parallel-plane electrodes (1 cm spacing) at low pressures (0.5–3 Torr) is measured and compared with models. For hydrogen these discharges are unstable for wide ranges of discharge current below 0.2 mA/${\mathrm{cm}}^2$ and external circuit resistances above ≊4000 Ω. Lateral constrictions of the discharge occur over a much more limited range of currents and pressures than do oscillations. Laser-induced photoelectron pulses produce damped oscillations for discharge currents below those at which self-sustained oscillations are observed. The frequency of the oscillations varies approximately as the square root of the discharge current and the damping of the oscillations increases with the discharge current. These results agree with simple models developed in an accompanying paper [this issue, Phelps, Petrović, and Jelenković, Phys. Rev. E 47, 2825 (1993)]. Some data are presented for argon and nitrogen.

Measurements are made of damped oscillations in the current and voltage induced by a voltage pulse applied to the stabilizing resistor of discharges in ${\mathrm{H}}_2$ at pressure times electrode spacing values of 0.3 to 1 Torr cm (40–133 Pa cm) operating at voltages of 300 to 2100 V. The use of pulses ≤1 ms long and repetition rates of 10 Hz results in low ion bombardment of the cathode. For pulse currents of 0.01 to 5 mA (2×${10}^{\mathrm{-}7}$–${10}^{\mathrm{-}4}$ A/${\mathrm{cm}}^2$) and an electrode separation and area of 1 cm and 50 ${\mathrm{cm}}^2$, the frequencies and damping constants are 10–300 kHz and 2×${10}^3$–${10}^5$ ${\mathrm{s}}^{\mathrm{-}1}$, respectively. The current densities are small enough so that space-charge distortion of the electric field is small, but not negligible. At currents below those for oscillation growth, the steady-state discharge voltage decreases as expected for a constant negative differential resistance. Values of 1000 to 4000 Ω are obtained depending on pressure and cathode condition. Transient models, developed in an accompanying paper, relate the frequencies, damping constants, and onset of oscillation growth to ion transit times, electron ionization coefficients, and ion-induced electron yields. The growth of discharge current immediately after the application of the voltage pulse is also used to determine discharge parameters.

Simple models are developed to describe the results of measurements of the oscillatory and negative differential resistance properties of low- to moderate-current discharges in parallel-plane geometry. The time-dependent model assumes that the ion transit time is fixed and is short compared to the times of interest, that electrons are produced at the cathode only by ions, and that space-charge distortion of the electric field is small but not negligible. Illustrative numerical solutions are given for large voltage and current changes and analytic solutions for the time dependence of current and voltage are obtained in the small-signal limit. The small-signal results include the frequency and damping constants for decaying oscillations following a voltage change or following the injection of photoelectrons. The conditions for underdamped, overdamped, and self-sustained or growing oscillations are obtained. A previously developed steady-state, nonequilibrium model for low-pressure hydrogen discharges that includes the effects of space-charge distortion of the electric field on the yield of electrons at the cathode is used to obtain the negative differential resistance. Analytic expressions for the differential resistance and capacitance are developed using the steady-state, local-equilibrium model for electron and ion motion and a first-order perturbation treatment of space-charge electric fields. These models generally show good agreement with data from dc and pulsed discharge experiments presented in the accompanying papers.

A closed, nonlinear set of fluid equations that is based on the electron guiding-center orbits and is generally applicable to the analysis of crossed-field, slow-wave devices, is developed. The equations are used to model the behavior of the crossed-field amplifier. The dielectric response from the spoke charge is self-consistently included. A mean-field approximation is introduced to express the effect of the spoke charge on the rf mode profile. The dielectric modifications are then parametrized by an average amplitude factor Λ^ and an average phase shift ψ^ from the vacuum values. In the synchronous with the rf signal frame of reference the streamlines follow the equipotential surfaces of the transformed fields. In the steady state, the flow is incompressible. A uniform-density, constant-height electron hub feeds the current spokes. The secondary electron production at the cathode is computed self-consistently through the secondary-emission coefficient and the average impact energy. The spoke current is determined by the difference of the E×B drift at the top of the hub from the rf phase velocity. At small space-charge density relative to the Brillouin density, the dielectric corrections enter as a rotation ${\mathit{e}}^{\mathit{i}\mathrm{\psi }\mathrm{^}}$ of the complex growth rate relative to the growth without spoke self-fields. The numerical solutions for arbitrary space charge are compared with previous results without spoke-field effects. An increase in the rf gain and in the anode dc current is observed at any given operation point, despite a small drop in the efficiency. It is concluded that the increase in the rf field strength in the anode-cathode space, caused by the spoke self-field, compensates for the detuning effects from the modifications on the rf mode profile. In reentrant devices, the recycling of the space charge further increases the output power and the level of noise generated by the output-input feedback.

The beamstrahlung spectrum for colliding electron (positron) bunches is calculated by a quasiclassical method. The derived formulas apply to the classical and the quantum domain of parameters. Scaling laws for the total radiation energy loss and for the photon spectrum are derived. Our numerical results are in good agreement with those of a previous, purely quantum-mechanical calculation.

We present here for homogeneous anisotropic chiral media an electromagnetic formalism manifestly covariant under the complex rotation group O(3,openC). The constitutive relations, the electromagnetic field equations, and the boundary conditions are discussed. To display the main features of this formalism, we discuss the propagation of plane waves in a medium that is anisotropic and chiral but simple enough to make calculations tractable.

It has been demonstrated recently that weakly overlapping solitons in the dissipatively perturbed nonlinear Schrödinger (NS) equation may form a set of bound states (BS’s). In this work, it is demonstrated that additional ‘‘skew’’ dissipative terms, which occur in various applications, e.g., a term describing the stimulated Raman scattering in a nonlinear optical fiber, destroy all the BS’s provided the corresponding coefficient exceeds a certain critical value. Next, taking as an example the dissipationless NS equation with the higher linear dispersion, it is demonstrated that two solitons or a whole array of them may form BS’s, interacting with each other via emitted radiation. Then, it is shown that the sine-Gordon (SG) breathers, governed by the standard damped ac-driven equation, may form BS’s quite similarly to the NS solitons. At last, interactions of damped NS or SG solitons supported by a parametric ac drive are analyzed, and it is inferred that they, unlike the directly supported solitons, cannot form BS’s.

Vector statistical distribution functions are derived for correlated Gaussian fields. The results may be used to describe the interesting cases of polarization of multiply scattered optical waves from disordered media. The dependence of the parameters (the elements of the covariant Hermitian matrix), which characterize the statistics on the incident polarization field, on the incident and scattered wave-vector direction and on the medium (with slab geometry) are also given.

The time-interval sequences and the spatiotemporal patterns of the firings of a coupled neuronal network are investigated in this paper. For a single neuron stimulated by an external stimulus I, the time-interval sequences show a low-frequency firing of bursts of spikes and a reversed period-doubling cascade to a high-frequency repetitive firing state as the stimulus I is increased. For two neurons coupled to each other through the firing of the spikes, the complexity of the time-interval sequences becomes simple as the coupling strength increases. A network with a large number of neurons shows a complex spatiotemporal pattern structure. As the coupling strength increases, the number of phase-locked neurons increases and the time-interval diagram shows temporal chaos and a bifurcation in the space. The dynamical behavior is also verified by the behavior of the Lyapunov exponent.