  We analyze the annihilation of equally-charged particles based on the
Brownian motion model built by F. Dyson for $N$ particles with charge $q$
interacting via the log-Coulomb potential on the unitary circle at a reduced
inverse temperature $\beta$, defined as $\beta=q^2/(k_B T)$. We derive an
analytical approach in order to describe the large-$t$ asymptotic behaviour for
the number density decay, which can be described as a power law, i.e., $n\sim
t^{-\nu}$. For a sufficiently large $\beta$, the power law exponent $\nu$
behaves as $(\beta +1)^{-1}$, which was corroborated through several
computational simulations. For small $\beta$, in the diffusive regime, we
recover the exponent of 1/2 as predicted by single-species uncharged
annihilation.
