Pulsars : Problems & Progress ASP Conference Series, Vol. 105, 1996 S. Johnston, M. A. Walker and M. Bailes, eds. Radio emission from polar caps in pulsars Jan Kuijpers Sterrekundig Instituut, P.O. Box 80.000, NL-3508 TA Utrecht, The Netherlands Martin Volwerk Lunar and Planetary Laboratory, Univ. of Arizona, Tucson, AZ 85721, USA 1. Physics of the proposed emission process Radiation from a charge accelerated along its path or Linear Acceleration Emis- sion (LAE) involves a number of subtleties (Pauli 1921; Ginzburg 1970, 1989). Potential interest of the mechanism for astrophysics has been pointed out by Wagoner (1969). Melrose (1978) and Rowe (1995) have studied amplified LAE from time-varying electric fields for radio pulsars. In contrast with the latter work our calculations are for static electric field structures or double layers (DLs) as are thought to occur in magnetospheres of neutron stars. In ordinary stellar atmospheres a LAE maser can operate in non-relativistic DLs (Kuijpers 1990) at a frequency w w k DL v « 2n/t tr , and a wave vector k ± {E DL ,B} with k DL — 2n/L (L is the DL length, v is the particle speed, and t tr is the transit time of the DL by the particle). The emission process can be considered as scattering of the electrostatic electric field on fast electrons into electromagnetic radiation satisfying the resonance condition: u — k-v = u DL — k DL -vm —k DL -v, when the frequency of the radiated mode in the frame of the emitting electron equals the Doppler shifted frequency of the electric field of the DL (DL wave frequency UJ DL « 0). For relativistic DLs, as are applicable to pulsar magneto- spheres, the emission is expected to be beamed under an angle 0 w 7" 1 and the frequency of emission boosted (w w k DL v(l — vcosO/c) -1 w j 2 k DL v). 2. Approximations We model the DL by a static, localized, uniform electric field Eo antiparallel to the magnetic field B. We neglect pair creation and choose an initial one- dimensional electron distribution with positive slope p entering the DL: f(j) = Nj p (p+ l)/(Ti + — To + )> To < 7 < Ti- We treat the electromagnetic wave as a pure vacuum wave, and perturb around the unperturbed particle trajectory (v w c). We assume that \k • ^(t)\ < n/2 and \k • ?{t)\ > \k • ^\ 2 over the integration interval, which, in terms of the initial and, respectively, final Lorentz factors 7i, j{, implies k £ ny?/(Lcos6), k < 47i 4 7f/[7 3 (£)Z,cos0], where 6 is the angle between k and v. Since the acceleration between t = 0 and t = ttr (tt r — L/c is the transit time for an electron) strongly decreases with the Lorentz 181 terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0252921100041403 Downloaded from https://www.cambridge.org/core. IP address: 184.72.86.144, on 17 Aug 2020 at 17:13:17, subject to the Cambridge Core