Annu. Rev. Astron. Astrophys. 1988. 36: 539-598
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The spectral and polarization characteristics of jets, from radio to X and gamma rays, are consistent with emission by a power-law distribution of relativistic electrons over the whole frequency range, i.e. gammael up to 107 in some cases. Meisenheimer et al (1996) have combined detailed data on the M87 jet over the whole frequency range from radio to X rays. They showed that the spectral profile is very uniform along the jet, corresponding to a power-law electron distribution N(gamma) propto gamma-2.3 for the synchrotron model in a uniform magnetic field. Similarly, the high-frequency cutoff in the synchrotron spectrum is very nearly constant, and this uniformity applies down to the smallest scale, l ~ 10 pc, that can be resolved. Such frequency corresponds, at equipartition, to an electron upper Lorentz factor gammac = 9 × 105. They concluded that reacceleration must be independent from local parameters, as high brightness knots have the same spectrum of low brightness knots. The favored acceleration mechanism should then be of "universal" type. Acceleration by MHD turbulence and shocks are the best candidates to produce a "universal" particle energy spectrum (Bodo et al 1995, Meisenheimer et al 1996b, Ferrari & Melrose 1997).

In the original twin-jet model, radiation was attributed to relativistic electrons reaccelerated in shocks at the hot spots and working surface. Blandford & Ostriker (1978) showed that shocks under rather general conditions produce power-law spectra with slope ~ 2-3, depending on the shock strength, in agreement with the observed radiation spectral index ~ 0.5-1. In connection with acceleration by turbulent MHD modes, Ferrari et al (1979), Eilek (1979), Lacombe (1977) have calculated the time scales of nonlinear coupling of modes, showing how these modes can guarantee a constant input of energy toward particle acceleration. Benford et al (1980) proposed a scenario in which long wavelength unstable MHD modes start a nonlinear cascade toward short wavelength modes and support a Fermi-like acceleration of electrons. Instead of considering instabilities as events that can destroy jets, they must be examined in their positive aspect. Perturbations can grow to shocks and at the same time can cascade energy down to the level of turbulent modes and also eventually couple to radiative modes.

The main question in accelerating electrons is the need for an injection mechanism of already relativistic electrons. In fact, the condition for resonant interaction of electrons with Alfvèn or fast magnetosonic waves (necessary both for stochastic acceleration by turbulent modes or for scattering/trapping across shock discontinuities) is approximately gammamin,e ~ (vu / c) (mp / me) gtapprox 1, where vu is the upstream flow speed (Eilek & Hughes 1991). Injection mechanisms proposed are runaway DC electric fields, electrodynamic forces in current-carrying flows, magnetic field reconnection, shock drifts, etc. The subject has not been explored self-consistently so far. Stochastic acceleration of thermal protons/ions is instead possible; therefore, a situation should be analyzed in which ions are accelerated to ultra-relativistic energies and drag with them electrons via electrostatic instabilities.

A quasi-loss-free transport of particles from the AGN cores to the extended lobes is a possible alternative to reacceleration. Felten (1968) devised two basic scenarios: 1. Jets contain a component of ultrarelativistic protons/ions responsible for carrying the main fraction of energy and momentum that can then be converted into secondary electrons along the jet (Mastichiadis & Kirk 1995); 2. jets contain ultrarelativistic electron/positron pairs carrying the bulk flow and inertia and at the same time providing synchrotron emission (Kundt & Gopal-Krishna 1980).

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