  In this paper, we explain the fundamental properties of the radiation
processess of untrapped kinks moving on discrete lattices or any spatially
periodic potential. In particular we explain qualitatively and quantitatively
the interesting recent experiments of small discrete periodic dynamical arrays
of Josephson junctions. We obtain and show the resonance condition for a kink
to radiate phonons is the kink frequency or one of its harmonics K_j$\dot{X}$
where $\dot{X}$ is the velocity of the kink and the K_j are vectors of the
reciprocal lattice must equal one of the phonon frequencies, $\omega(k)$, where
k are the lattice vectors determined by the lattice spacing and the periodic
boundary conditions. Then we show the radiation resonance conditions determine
the voltage at line center in the experimental currently voltage (I-V)
diagrams.
