The coupling between transverse waves on a ``no‐space‐charge'' beam model via an rf pump field is investigated. It is found that the pump field should be two‐dimensional in order to couple only two waves together. For high‐frequency pumping only waves of same polarization can couple together, for low‐frequency pumping only two waves of opposite polarization can couple together. For high‐frequency pumping no ``spilling'' of higher‐order noise frequencies will occur. For low‐frequency pumping no ``spilling'' will occur if the pump field is purely circularly polarized. Except for cyclotron‐cyclotron wave coupling the pump wave will always be in synchronism with a beam wave and thus interact actively or passively with the beam. The effect of this coupling is investigated.