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The problem of kinematic effects in the gluon and color dipole cascades isaddressed in the large N_c limit of SU(N_c) Yang--Mills theory. We investigatethe tree level multi-gluon components of the gluon light cone wave functions inthe light cone gauge keeping the exact kinematics of the gluon emissions. Wefocus on the components with all helicities identical to the helicity of theincoming gluon. The recurrence relations for the gluon wave functions arederived. In the case when the virtuality of the incoming gluon is neglected theexact form of the multi-gluon wave function is obtained. Furthermore, wepropose an approximate scheme to treat the kinematic effects in the colordipole evolution kernel. The new kernel entangles longitudinal and transversedegrees of freedom and leads to a reduced diffusion in the impact parameter.When evaluated in the next-to-leading logarithmic (NLL) accuracy, the kernelreproduces the correct form of the double logarithmic terms of the dipole sizeratios present in the exact NLL dipole kernel. Finally, we analyze thescattering of the incoming gluon light cone components off a gluon target andthe fragmentation of the scattered state into the final state. The equivalenceof the resulting amplitudes and the maximally-helicity-violating amplitudes isdemonstrated in the special case when the target gluon is far in rapidity fromthe evolved gluon wave function.

Exact kinematics in the small x evolution of the color dipole and gluon cascade