We propose a three dimensional pulsar magnetosphere model in which the vertical size of the outer gap is first determined by a self-consistent model in which the outer gap is limited by the pair production from collisions of thermal photons produced by polar cap heating of backflow outer gap current and the curvature photons emitted by the gap accelerated charged particles. The transverse size of the outer gap is determined by local pair production condition. In principle, there are two topologically disconnected outer gaps existing in the magnetosphere of a pulsar and both incoming and outgoing particle flows are allowed. And yet double-peak light curves with strong bridges are most common. Using this model and its local properties, we compare the model results with phase-resolved spectra of the Crab pulsar and Geminga.

Within the framework of a single polar cap model we calculate the energy dependence of phase separation between two peaks in the gamma-ray lightcurve of the Vela pulsar. Results are confronted with EGRET data (Kanbach 1999).

Comptonisation may play an important role in determining beam patterns and hence pulse profiles in X-ray pulsars. We describe a Monte Carlo simulation used to investigate the spectra and pulse profiles emitted by two semi-infinite homogeneous cyclindrical accretion columns diametrically located on the surface of a ‘canonical’ neutron star.

In the relativistic plasma surrounding a pulsar, a subluminal ordinary-mode electromagnetic wave will propagate along a magnetic field line. After some distance, it can break free of the field line and escape the magnetosphere to reach an observer. We apply a simple model of pulsar radio emission based on this scenario to the case of the Vela pulsar and find it reproduces some qualitative characteristics of the observed Vela pulse profile.

A current sheet separates, beyond the closed part of the pulsar magnetosphere, two half-spaces with oppositely directed magnetic fields. It is shown that reconnection in this sheet may provide a source for high-energy emission.

The non-spherical symmetric and exact thermal evolution model is used to calculate the transient thermal response to pulsar glitches. The three ways of energy release originated from glitches, namely the ‘shell’, ‘ring’ and ‘spot’ cases are compared. The ‘ring’ case is always the middle one in terms of the response time, the response duration and the intensity of the response. Taking the relativistic light bending effect and the rotational effect into consideration, the X-ray light curves resulting from the thermal response to the glitches are calculated. Only the ‘spot’ case produces modulative X-rays. Different sets of parameters result in different evolution patterns of light curves. This is thus a good method to determine the equations of state for pulsars.

We have simulated the development of the pair cascade in a range of magnetic field strengths. We determined the efficiencies of lepton and secondary photon production, as well as the distribution functions of the pair plasma and of the escaping photons. We find the magnetic field has the most important effect on the cascade; primary beam energies and seed photon emissivities are of less importance.

I summarize the theory of acceleration of non-neutral particle beams by starvation electric fields along the polar magnetic field lines of rotation powered pulsars, including the effect of dragging of inertial frames which dominates the acceleration of a space charge limited beam. I apply these results to a new calculation of the radio pulsar death line, under the hypotheses that pulsar “death” corresponds to cessation of pair creation over the magnetic poles and that the magnetic field has a locally dipolar topology. The frame dragging effect in star centered dipole geometry does improve comparison of the theory with observation, but an unacceptably large conflict between obsrvation and theory still persists. Offsetting the dipole improves the comparison, but a fully satisfactory theory requires incorporating magnetic conversion of inverse Compton gamma rays, created by scattering thermal photons from the surface of old neutron stars (t > 108 years) kept warm (T ≥ 105 K) by friction between the rotating core and the crust. The result is a “death valley” for pulsars; offsets of the dipole center from the stellar center in the oldest stars ~ (0.7 − 0.8)R* suffice. The resulting theory predicted the existence of rotation powered pulsars with these advanced ages, a prediction confirmed by the recent discovery that PSR J2144-3933 actually has a rotation period of 8.5 seconds.

The anisotropic and relativistic features of the pulsar pair plasma are adequately modelled using relativistic one-dimensional Jűttner-Synge distribution functions. The dispersion relation for wave propagation in such a plasma involves coefficients that specifically depend on the distribution function of its particles. An analytical determination of these coefficients allows us to obtain characteristics of quasi-longitudinal waves together with the conditions for the unstable interaction of ultrarelativistic beam and plasma. Similar derivations concern electromagnetic waves.

The plasma motion in pulsar magnetospheres is no longer classical, but quasi-classical, following stochastic trajectories, when random curvature radiation of high energetic gamma-ray photons takes place. This implies an extension to the relativistic kinetic theory of plasmas. But with high energies involved other quantum radiative processes become important, in the context of vacuum (quantum) electrodynamics. The consequences for pulsar radiation mechanisms will be outlined.

We propose that the violent breakdown of the Ruderman-Sutherland type vacuum gap above the pulsar polar cap region may produce copious primary particles and make the charge density above the gap in excess of the Goldreich-Julian density. Such an excess residue of charge density may arise some re-acceleration regions above the gap due to the space-charge-limited flow mechanism. Such re-acceleration regions, if exist, may accelerate particles to carry away more spin-down energy, and may have some implications for pulsar γ-ray emission.

A simplified model provided the framework for our investigation into the distribution of energy and charge densities above the polar caps of a rotating neutron star. We assumed a neutron star with m = 1.4M⊙, r = 10km, dipolar field |B0| = 1012G, B||Ω and Ω = 2Π · (0.5s)−1. The effects of general relativity were disregarded. The induced accelerating electric field E|| reaches E0 = 2.5 · 1013 V m−1 at the surface near the magnetic poles. The current density along the field lines has an upper limit nGJ, when the electric field of the charged particle flow cancels the induced electric field: At the poles nGJ(r = rns, θ = 0) = 1.4 · 1017m−3. The work function (surface potential barrier) EW is approximated by the Fermi energy EF of magnetised matter. Following Abrahams and Shapiro (1992) one needs to revise the surface density from the canonical 1.4 · 108kg m−3 down to ρFe = 2.9 · 107kg m−3. With we obtain a value of EF = Ew = 417eV. There are two relevant particle emission processes: Field (cold cathode) emission by quantum-mechanical tunneling of charges through the surface potential and thermal emission which is a purely classical process. In strong electric fields it is enhanced by the lowering of the potential barrier due to the Schottky effect. The combined Dushman-Schottky equation with tells us, that at temperatures > 2 · 105K the the Goldreich-Julian current can be supplied thermal emission alone. The surface temperature however has a lower limit in the order of 105 K due to the rotational braking. Therefore, in most cases a sufficient supply of charges for the Goldreich-Julian current is available and the electrical field accelerating the particles will be quenched as a result of their abundance. Otherwise a residual equilibrium electric field Eeq remains with: and hence the equilibrium density is: n = nfieid(Eeq, EW) + nDS(Eeq, EW, T) For a temperature just below the onset of thermal emission (T = 1.85 · 105K) the charge density is found to vary almost linearly with the work function EW for values of EW between 0.3 and 2 keV. At the chosen value for EW of 417 eV the residual electric field amounts to only 8.5% of the vacuum value. Even in the residual electric field the particles are rapidly accelerated to relativistic energies balanced by inverse Compton and curvature radiation losses.

Some aspects of relativistic electron-positron plasma dynamics in the pulsar magnetosphere are discussed. Namely it is shown that if we take into account the influence of centrifugal force, this gives rise to the new dynamical effect of plasma particle radial braking in the pulsar magnetosphere. Also the possibility of aperiodic instability development in the pulsar magnetosphere is demonstrated. The mechanism for the toroidal magnetic field generation is proposed. Besides, the possible changes of the pulsar magnetosphere structure caused by above mentioned processes is considered.

Based on the polar cap model, we investigated in the energy loss of accelerated electrons in a neutron star magnetosphere by inverse Compton scattering of thermal photospheric radiation. An analytical treatment is presented, which turns out ranges in the magnetic field strength and thermal temperature where ultrarelativistic electrons can not survive.

We study emission of particles and photons from a pulsar polar cap. The Goldreich-Julian model for the regime of free emission of charged particles from the neutron star surface is used. In this case the electric field is generated due to the general relativistic effect of dragging of inertial frames. The spectra and shapes of gamma-ray pulses, the parameters of the electron-positron plasma and the intensity of X-ray emission from hot spots in the polar region of radio pulsars are discussed. The effect of non-dipole magnetic field on X-ray emission of polar caps is considered. It is shown that the increase of magnetic line curvature leads to much smaller temperatures and X-ray luminosities of the polar caps as compared with the purely dipole field.

Similar to the terrestrial collision accelerators of e±, another kind of accelerator is above a positively or negatively charged pulsar polar cap. In the case of pulsars with magnetic axis parallel (anti-parallel) to rotational axis, relativistic e+ (e−) with Lorentz factor γ ~ 106 hit the electrons in the polar caps. These scenarios are investigated both for pulsars being BSSs (bare strange stars) and for pulsars being NSs (neutron stars). Such a study may be valuable to differentiate NSs and BSSs observationally.

We propose a full polar cap cascade model which includes the curvature and inverse Compton emission of the primary particles, and both synchrotron radiation and inverse Compton of the higher generation pairs. Such a full cascade model can reproduce both the Lγ ∝ (Lsd)1/2 and the Lx ~ 10−3Lsd dependences observed from the known spin-powered pulsars.

The evidence for associations between neutron stars and supernova remnants is reviewed. After summarizing the situation for young radio pulsars, I consider the evidence from associations that young neutron stars can have properties very different from those of radio pulsars. This, though still controversial, shakes our simple perception of the Crab pulsar as prototypical of the young neutron star population.

The fact that the majority of the youngest radio pulsars are surrounded by expanding supernova remnants is strong evidence that neutron stars are produced in the supernovae of massive stars. In many cases, the pulsar appears significantly offset from the geometric centre of the supernova remnant, indicating that the neutron star has moved away from the site of the explosion with a substantial space velocity since birth. Here we show that the these offsets show an overwhelming preference for one sign in terms of Galactic longitude, a result that has important implications for the number of genuine associations. The origin of this statistically significant effect may lie in a differential Galactic rotational velocity between stars and gas in the interstellar medium.

In October 1997 daily monitoring observations of the Crab pulsar at 327 MHz and 610 MHz with an 85ft telescope in Green Bank, WV showed a jump in the dispersion by 0.12 cm −3 pc. Pulses were seen simultaneously at both old and new dispersions for a period of days. In the months before this event faint ghost emission, a replica of the pulse, was detected with a nearly frequency independent delay that quadratically diminished to zero. There was also a curious shift in the phase, a slowdown, at all frequencies at the time of the dispersion jump. I attribute most of these phenomena to the perturbing optics of a plasma prism that is located in the filamentary interface between the synchrotron nebula and the supernova ejecta and which crosses the line of sight over a period of months. The required density, scale length and velocity are reasonable given detailed HST and previous observations of these filaments.