We propose a model of a optical ''wisps'' of the Crab Nebula, features observed in the nebular synchrotron surface brightness near the central pulsar, as manifestations of the internal structure of the shock terminating the pulsar wind. We assume that this wind is composed of ions and a much denser plasma of electrons and positrons, frozen together to a toroidal magnetic field and flowing relativistically. Hoshino et al. (1992) have shown that shocks in such a wind, where the magnetic field is perpendicular to the flow direction, can account for the acceleration of synchrotron-emitting e(+/-) to the power-law distributions observed in the Nebula. For typical pulsar wind parameters, the ions have such high rigidity that their Larmor radius, the basic length scale of the shock structure, is comparable to the observed spacing between the wisps. The shock structure interpretation also accounts naturally for the observed variability of the wisps on timescales of several months. We construct a form of solitary wave model of the shock structure in which we self-consistently solve for the ion orbits and the dynamics of the relativistically hot, magnetized e(+/-) background flow. We ignore dispersion in the ion energies, and we treat the pairs as an adiabatic fluid. The synchrotron emission enhancements, observed as the wisps, are then explained as the regions where reflection of the ions in the self-consistent magnetic field causes compressions of the e(+/-). The wind geometry is assumed to be a radial outflow concentrated around the rotational equatorial plane of the pulsar, to produce the tilted ring morphology of the Nebula observed in X-rays. The Doppler beaming and boosting effects due to the mildly relativistic bulk motion of the e(+/-) readily account for the brightness contrast between the main wisp and faint counterwisp regions, to the northwest and southeast of the pulsar, respectively. We compute synchrotron brightness profiles for model shock structures, incorporating the above effects. Previous work by Hoshino et al. (1992) has suggested that the pairs' energy distribution can be approximated as a relativistic Maxwellian, at least in the first of the magnetic compressions. Approximating the pairs' energy distribution at each point as relativistic Maxwellians, we obtain good agreement with the observed brightness profiles of the main wisp and counterwisp. From this fit, we infer that the upstream Lorentz factor of the wind is y(1) similar to 4 x 10(6) and the preshock magnetic field is B-1 similar to 5 x 10(-5) G, with an ion Larmor radius based on upstream parameters of similar to 0.15 pc, that the equatorial wind must carry most of the 5 x 10(38) ergs s(-1) rotational energy loss of the pulsar, and that roughly two-thirds of this wind energy flux is carried by the ions. It follows that the total injection rate of ions from the pulsar is ZM(i) similar to 3 x 10(34) S-1, close to the Goldreich-Julian current, as would be expected if the pulsar operates as an open-circuited system with ions carrying the return current. We show that the ions are fully ionized at the radii where they encounter the shock and infer that they have been accelerated through at least 20% of the total voltage available on open field lines. The wisp model yields a pair injection rate of N-+/- similar to 5 x 10(37) particles per second. We show that this injection rate is sufficient to account for the nebular X-ray source, whose emission comes primarily from radii slightly larger than the location of the wisps. Our model suggests that the extreme ultraviolet and X-ray spectra of the main wisp and the counterwisp should be close to that of a single-temperature Maxwellian with the temperature of the pairs similar to y(1)m(+/-)c(2)/k similar to 2 x 10(16) K, corresponding to a critical energy for synchrotron emission based on upstream parameters similar to 20 eV. The fact that the wisps appear as elliptical arcs rather than complete ellipses is explained by pitch-angle anisotropy of the synchrotron-emitting e(+/-), which is a natural consequence of the basic acceleration mechanism in these shocks. We use the observations to derive the opening angle of the loss cone as function of distance from the pulsar required to explain the wisps' structure in 1988. We find the opening of the loss cone must decrease by 0.5 rad pc(-1) in the region between 0.04 pc to 0.12 pc from the pulsar. We briefly discuss the physical processes which may control the anisotropy, as well as their relation to the progressive nonthermal heating of the pair plasma with distance from the pulsar.
