  Self-consistent equations for intrinsic rotation in tokamaks with small
poloidal magnetic field $B_p$ compared to the total magnetic field $B$ are
derived. The model gives the momentum redistribution due to turbulence,
collisional transport and energy injection. Intrinsic rotation is determined by
the balance between the momentum redistribution and the turbulent diffusion and
convection. Two different turbulence regimes are considered: turbulence with
characteristic perpendicular lengths of the order of the ion gyroradius,
$\rho_i$, and turbulence with characteristic lengths of the order of the
poloidal gyroradius, $(B/B_p) \rho_i$. Intrinsic rotation driven by gyroradius
scale turbulence is mainly due to the effect of neoclassical corrections and of
finite orbit widths on turbulent momentum transport, whereas for the intrinsic
rotation driven by poloidal gyroradius scale turbulence, the slow variation of
turbulence characteristics in the radial and poloidal directions and the
turbulent particle acceleration can be become as important as the neoclassical
and finite orbit width effects. The magnetic drift is shown to be indispensable
for the intrinsic rotation driven by the slow variation of turbulence
characteristics and the turbulent particle acceleration. The equations are
written in a form conducive to implementation in a flux tube code, and the
effect of the radial variation of the turbulence is included in a novel way
that does not require a global gyrokinetic formalism.
