  The motion of simple domain walls and of more complex magnetic textures in
the presence of a transport current is described by the
Landau-Lifshitz-Slonczewski (LLS) equations. Predictions of the LLS equations
depend sensitively on the ratio between the dimensionless material parameter
$\beta$ which characterizes non-adiabatic spin-transfer torques and the Gilbert
damping parameter $\alpha$. This ratio has been variously estimated to be close
to 0, close to 1, and large compared to 1. By identifying $\beta$ as the
influence of a transport current on $\alpha$, we derive a concise, explicit and
relatively simple expression which relates $\beta$ to the band structure and
Bloch state lifetimes of a magnetic metal. Using this expression we demonstrate
that intrinsic spin-orbit interactions lead to intra-band contributions to
$\beta$ which are often dominant and can be (i) estimated with some confidence
and (ii) interpreted using the "breathing Fermi surface" model.
