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Modifications to polar-gap models for pulsars are discussed for the case where the surface magnetic field, Bs, of the neutron star is strong. For B~4 X 10 8 T, the curvature ,-quanta emitted tangentially to the curved force lines of the magnetic field are captured near the threshold of bound pair creation and are channelled along the magnetic field as bound electron-positron pairs (positronium). The stability of such bound pairs against ionization by the parallel electric field,. Ell' in the polar cap, and against photoionization is discussed. Unlike free pairs, bound pairs do not screen Ell near the neutron star. As a consequence, the energy flux in highly relativistic particles and high-frequency (X-ray and/or ,-ray) radiation from the polar gaps can be much greater than in the absence of positronium formation. We discuss this enhancement for (a) Arons-type models, in which particles flow freely from the surface, and find any enhancement to be modest, and (b) Ruderman-Sutherland-type models, in which particles are tightly bound to the surface, and find that the enhancement can be substantial. In the latter case we argue for a self-consistent model in which partial screening of Ell maintains it close to the threshold value for field ionization of the bound pairs, and in which a reverse flux of accelerated particles maintains the polar cap at a temperature such that thermionic emission supplies the particles needed for this screening. This model applies only in a restricted range of periods, P2 < P < PI, and it implies an energy flux in high-energy particles that can correspond to a substantial fraction of the spin-down power of the pulsar.Nonthermal, high-frequency radiation has been observed from six radio pulsars and Geminga is usually included as a seventh case. The nonthermal luminosity can be higher than can be explained in terms of conventional polar-gap and outer-gap models. The self-consistent polar-gap model proposed here alleviates this difficulty, provided the magnetic field satisfies B ;G 4 X 10 8 T (which is so for five of these pulsars, and plausibly for the other two if a modest nondipolar component is assumed), and the surface temperature (in the absence of heating by the reverse flux) satisfies T; ;S 0·5 X 10 6 K, so that thermionic emission from the surface is unimportant. It is argued that sufficient power is available to explain the observed high-frequency radiation of most of these pulsars. However, the Crab and PSR 0540-69 have periods P < P2, and we suggest that an outer-gap model is more appropriate for these. Our model implies a death line at P = PI "-J 0·5 s for B ;G 4 X 10 8 T, and we speculate on why, nevertheless, radio pulsars with strong fields are found at P > Pl.

Three known examples of coherent emission in radio astronomical sources are reviewed: plasma emission, electron cyclotron maser emission (ECME) and pulsar radio emission.Plasma emission is a multi-stage mechanism with the first stage being generation of Langmuir waves through a streaming instability, and subsequent stages involving partial conversion of the Langmuir turbulence into escaping radiation at the fundamental (F) and second harmonic (H) of the plasma frequency. The early development and subsequent refinements of the theory, motivated by application to solar radio bursts, are reviewed. The driver of the instability is faster electrons outpacing slower electrons, resulting in a positive gradient (df (v )/dv > 0) at the front of the beam. Despite many successes of the theory, there is no widely accepted explanation for type I bursts and various radio continua.The earliest models for ECME were purely theoretical, and the theory was later adapted and applied to Jupiter (DAM), the Earth (AKR), solar spike bursts and flare stars. ECME strongly favors the x mode, whereas plasma emission favors the o mode. Two drivers for ECME are a ring feature (implying df (v)/dv > 0) and a loss-cone feature. Loss-cone driven ECME was initially favored for all applications. The now favored driver for AKR is the ring-feature in a horseshoe distribution, which results from acceleration by a parallel electric on converging magnetic field lines. The driver in DAM and solar and stellar applications is uncertain.The pulsar radio emission mechanism remains an enigma. Ingredients needed in discussing possible mechanisms are reviewed: general properties of pulsars, pulsar electrodynamics, the properties of pulsar plasma and wave dispersion in such plasma. Four specific emission mechanisms (curvature emission, linear acceleration emission, relativistic plasma emission and anomalous Doppler emission) are discussed and it is argued that all encounter difficulties.

We calculate and compare the temporal growth rate and the number of e-folding growths for the following wave modes due to a loss-cone-driven cyclotron maser: fundamental x, o, and z modes and second harmonic x and o modes. The dominant mode of the maser should be the fastest growing mode for a saturated maser and should be the mode with the greatest number of e-folding growths for an unsaturated maser; this mode is the fundamental x mode for mp/•e < 0.3, the z mode (or perhaps the fundamental o mode) for 0.3 < mp/•e < 1.0, and the z mode (or perhaps t•e second harmonic x mode) for 1.0 < mp/•e < 1.3. We discuss the effect of cyc16tron damping by thermal electrons on the growth. Numerical calculations show that the effect is important only when the ratio of the mean energies of the thermal and maser emitting electrons exceeds 0.1-0.2. An analytic expression for the damping rate is derived and is used to show that some earlier treatments of cyclotron damping greatly overestimate the effect for loss-cone-driven maser emission. These results, when applied to AKR, imply that only either the fundamental x mode (for mp/•e < 0.3) or the z mode (for mp./•e 5 0 3) is produced directly by maser emission. We suggest (1) that an o mode component in AKR might be due to partial reflection of x mode radiation incident onto sharp overdense plasma intrusions of the kind observed in the auroral cavity and (2) that a second harmonic component can be produced by coalescence of two z mode waves. 1. 1984; Benson and Akasofu, 1•84]. We argue here that the latter component, which is restricted to•betwcen •2e ' and the upper hybrid frequency zs z mode radiation generated by the process discussed by Hewitt et al. [1983]. In section 2 we discuss the criterion for the dominant mode of a loss-cone-driven maser, and suggest that this is the x mode for mp/•e < 0.3 and the z mode for 897 898 Melrose et al.: Cyclotron Masers in Different Modes I o -• •

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