  Radio emission, polarization, and Faraday rotation maps of the radio jet of
the galaxy 3C 303 have shown that one knot of this jet carries a {\it
galactic}-scale electric current and that it is magnetically dominated. We
develop the theory of magnetically dominated or Poynting-flux jets by making an
analogy of a Poynting jet with a transmission line or waveguide carrying a net
current and having a potential drop across it (from the jet's axis to its
radius) and a definite impedance which we derive. Time-dependent but not
necessarily small perturbations of a Poynting-flux jet are described by the
"telegrapher's equations." These predict the propagation speed of disturbances
and the effective wave impedance for forward and backward propagating wave
components. A localized disturbance of a Poynting jet gives rise to localized
dissipation in the jet which may explain the enhanced synchrotron radiation in
the knots of the 3C 303 jet, and also in the apparently stationary knot HST-1
in the jet near the nucleus of the nearby galaxy M87. For a relativistic
Poynting jet on parsec scales, the reflected voltage wave from an inductive
termination or load can lead to a backward propagating wave which breaks down
the magnetic insulation of the jet giving $|{\bf E}| /|{\bf B}|\geq 1$. At the
threshold for breakdown, $|{\bf E}|/|{\bf B}|=1$, positive and negative
particles are directly accelerated in the ${\bf E \times B}$ direction which is
approximately along the jet axis. Acceleration can occur up to Lorentz factors
$\sim 10^7$. This particle acceleration mechanism is distinct from that in
shock waves and that in magnetic field reconnection.
