  Classical bremsstrahlung of a massless scalar field $\Phi$ is studied in
gravity mediated ultra-relativistic collisions with impact parameter $b$ of two
massive point particles in the presence of $d$ non-compact or toroidal extra
dimensions. The spectral and angular distribution of the scalar radiation are
analyzed, while the total emitted $\Phi-$energy is found to be strongly
enhanced by a $d-$dependent power of the Lorentz factor $\gamma$. The direct
radiation amplitude from the accelerated particles is shown to interfere
destructively (in the first two leading ultra-relativistic orders) with the one
due to the $\Phi-\Phi-graviton$ interaction in the frequency regime
$\gamma/b\lesssim \omega \lesssim \gamma^2/b$ in all dimensions.
