  Differential rotation is induced in tokamak plasmas when an underlying
symmetry of the governing gyrokinetic-Maxwell system of equations is broken.
One such symmetry-breaking mechanism is considered here: the turbulent
acceleration of particles along the mean magnetic field. This effect, often
referred to as the `parallel nonlinearity', has been implemented in the $\delta
f$ gyrokinetic code $\texttt{stella}$ and used to study the dependence of
turbulent momentum transport on the plasma size and on the strength of the
turbulence drive. For JET-like parameters with a wide range of driving
temperature gradients, the momentum transport induced by the inclusion of
turbulent acceleration is similar to or smaller than the ratio of the ion
Larmor radius to the plasma minor radius. This low level of momentum transport
is explained by demonstrating an additional symmetry that prohibits momentum
transport when the turbulence is driven far above marginal stability.
