Theoretical calculations supported by numerical simulations show that utilization of the nonlinear dependence of the index of refraction on intensity makes possible the transmission of picosecond optical pulses without distortion in dielectric fiber waveguides with group velocity dispersion. In the case of anomalous dispersion (∂2ω/∂k2>0) discussed here [the case of normal dispersion (∂2ω/∂k2<0) will be discussed in a succeeding letter], the stationary pulse is a ``bright'' pulse, or envelope soliton. For a typical glass fiber guide, the balancing power required to produce a stationary 1-ps pulse is approximately 1 W. Numerical simulations show that above a certain threshold power level such pulses are stable under the influence of small perturbations, large perturbations, white noise, or absorption.

A new theory of the mirror instability is developed which includes the effects of ∇B and ∇n, finite Larmor radius, and a coexisting cold plasma. It is shown that the instability becomes overstable with a frequency equal to the drift wave frequency, which may be determined by the wave-number that gives the maximum growth rate. The theory is applied to explain the sudden kink in the increase (decrease) of proton flux (magnetic field) and the subsequent oscillations observed during a storm time on 18 April 1965 by detectors on the Explorer 26 satellite.

A theory of long‐period (Pc 3 to Pc 5) magnetic pulsations is presented based on the idea of a steady state oscillation of a resonant local field line that is excited by a monochromatic surface wave at the magnetosphere. A coupled wave equation between the shear Alfvén wave representing the field line oscillation and the surface wave is derived and solved for the dipole coordinates. The theory gives the frequency, the sense of polarizations, orientation angle of the major axis, and the ellipticity as a function of magnetospheric parameters. It also clarifies some of the contradicting ideas and observations in relation to the sense of polarization and excitation mechanism. At lower latitude it is shown that the orientation angle rather than the sense of rotation is a more critical parameter in finding the direction of wave propagation in the azimuthal coordinate and hence in finding the evidence of wave excitation at the magnetospheric surface by the solar wind.

A simple nonlinear equation is derived to describe the pseudo-three-dimensional dynamics of a nonuniform magnetized plasma with Te≫Ti by taking into account the three-dimensional electron, but two-dimensional ion dynamics in the direction perpendicular to B0. The equation bears a close resemblance to the two-dimensional Navier–Stokes equation. A stationary spectrum in the frequency range of drift waves is obtained using this equation by assuming a coexisting large amplitude long wavelength mode. The ω-integrated k spectrum is given by k1.8(1+k2)−2.2, while the width of the frequency spectrum is proportional to k3(1+k2)−1, where k is normalized by cs/ωci. The result compares well with the recently observed spectrum in the ATC tokamak.

No abstract