Solitons in strongly magnetized electron-positron plasmas and pulsar microstructure

1991

For relativistic amplitudes (‘intense propagation’), modulations of electromagnetic (EM) waves in a cold plasma are strongly coupled to longitudinal modes via the ponderomotive force, even if the unmodulated wave is purely transverse. The effect of longitudinal motions is comparable to that of relativistic nonlinearities. Hence a correct and proper expansion procedure requires solution of all the field equations up the appropriate order, including the longitudinal equations. (The plasma is assumed to be fully ionized and cold, with no net charge. The positive component may consist of either positrons or singularly charged ions. Quasi-neutrality is not imposed, but deviations are shown to be small for slow modulations.) We begin by deriving envelope equations (i.e. a reduced set of partial differential equations) governing modulations of intensely propagating, circularly polarized, plane EM plasma waves. (Here the envelope equations are not merely accurate to the appropriate order, but in fact exact.) We then analyse their modulational instabilities. Since the envelope equations are exact, they include the weakly relativistic case (transverse velocities ≪ c) as a limit. We first verify that, in this limit, the envelope equations yield the nonlinear Schrödinger equation (NLS) complete with the correct coefficients and thus the correct modulational instability conditions. Next, although the NLS does not hold for the general case of fully relativistic systems (transverse velocities comparable to c), we still succeed in deriving the modulational instability properties of intensely propagating EM waves in the fully relativistic case directly from the envelope equations, again, reproducing the weakly relativistic case as a test of the perturbation method used. Finally, we apply the results in special cases. For example, in the ultrarelativistic limit (transverse velocities close to c) of either an electron—positron or ion—electron plasma, waves with frequencies below twice the relativistic plasma frequency ωp, where , are unstable. The time scale for growth is comparable to the time for a wave packet to move past a fixed point. (This time scale is much shorter than in the weakly relativistic case, where the time scale for instability is that of the spreading of the wave packet due to linear dispersion.) Our results have important consequences for observations of pulsar micropulses, possible technological applications, and general implications for applications of Whitham theory.

Section: Introductioncontrasting

confidence: 78%

“…(1984Mofiz el al. ( , 1985 and Mofiz & Podder (1987). As a result of ponderomotive effects, both the densities and the relativistic factors in the dispersion relation vary along the propagation direction on the scale of the modulations.…”

Section: Introductionmentioning

confidence: 99%

Instability of intensely propagating circularly polarized electromagnetic pulses in a two-component plasma

1991

“…Problems of this type have often been discussed in terms of the well-known Karpman-Krushkal formalism (Karpman & Krushkal 1967). Unfortunately, applications of this formalism have led to incorrect results in the literature (Mofiz, DeAngelis & Porlani 1984Mofiz & Podder 1987), as noted in papers I-III. The root cause of these incorrect results is not some technicality peculiar to plasma physics, but rather a mathematical subtlety: If one wishes to discuss modulational stability problems in terms of a nonlinear dispersion relation, one should remember that the phase shift due to nonlinear effects may in general (and often does) have contributions not only from the amplitude dependence of the ' nonlinear dispersion relation' but also from the effects of (possibly slow) derivatives of the amplitude.…”

Section: Introductionmentioning

confidence: 99%

Intense propagation in a magnetized cold plasma: modulational instabilities of fully relativistic electromagnetic waves

1992

This paper studies modulational instabilities of intensely propagating, circularly polarized, plane electromagnetic plasma waves in the presence of an external magnetic field pointing exactly in the direction of propagation. By ‘intense propagation’, we mean that eEo/mw (where Eo is the amplitude of the wave's transverse electric field) is comparable to unity, so that the problem is fully nonlinear and cannot be solved by regular perturbation methods. The positive component may consists of either positrons or singly charged ions. The plasma is assumed to be fully ionized and cold. Modulated intensely propagating electromagnetic waves couple (in general) to longitudinal motions via the ponderomotive force. For given wavenumber, the frequency of the wave depends on the amplitude not only via the obvious mechanism of relativistic mass increase but also via the density inhomogeneities induced by the ponderomotive force. This coupling effectively involves derivatives of the envelope, and the effect of longitudinal motions is comparable to that of relativistic nonlinearities. For this reason, a proper expansion procedure requires verification that one has obtained a self-consistent solution of all the field equations up to the appropriate order, including the longitudinal equations. This is best accomplished using the well-known two-timing approach. Modulational instability arises in the case of an ion-electron plasma with relativistic electrons but non-relativistic ions. However, for parameter values appropriate to pulsar magnetospheres, where the electron-cyclotron frequency is much larger than the frequency of the wave, there is no instability on the time scale of a micropulse.

“…Chian & Kennel (1983) pointed out the possible application to pulsar micropulses and obtained a scalar nonlinear Schrodinger (NLS) equation by applying the method of Karpman & Krushkal (1969) (which is based on Whitham's (1974) averaging method) to this dispersion relation. The problem was again considered by Mofiz and collaborators (Mofiz, DeAngelis & Forlani 1984, 1985Mofiz & Podder 1987). Unfortunately, the resulting NLS coefficients in these papers are incorrect, and the force equations in Chian & Kennel (1983) are violated at leading order.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear modulational stability and propagation of an electromagnetic pulse in a two-component neutral plasma

1989

We study nonlinear effects including possible modulational instability of an intense electromagnetic pulse propagating through a fully ionized unmag-netized plasma. (The pulse is assumed to be sufficiently strong to accelerate particles to weakly, but not fully, relativistic velocities.) The envelope is shown to evolve over long time scales in general according to a vector form of the well-known cubic nonlinear Schrödinger (NLS) equation. Three distinct nonlinear effects contribute terms cubic in the amplitude and thus can be of comparable magnitude: ponderomotive forces, relativistic corrections and harmonic generation. In contrast with previous work, our calculation takes all three effects into account. Integrability and modulational stability of any given system are shown to depend on polarization, frequency, composition and temperature, and these dependences are given. We first carry out the calculation in detail for the case of zero temperature. In the special case of a cold positron-electron plasma, in contrast with the predictions of Chian & Kennel (1983), the model is strictly modulationally stable for both linear and circular polarization. We then generalize our result by giving the dependence of the nonlinear coefficients on temperature. As it turns out, finite-temperature effects are qualitatively important only near a critical frequency (<3/2ωp) just above the plasma frequency for which the group velocity is comparable to either (or both) of the sound velocities. The results have important implications for pulsar micropulse observations and possible technological applications.