Abstract A quasilinear operator for wave–particle interactions in the electron cyclotron range is derived using the cold plasma dispersion relation. The finite width of the beam implies a broadening of the resonance layer in the velocity space which allows the use of a numerically efficient treatment of the operator. The specific case of a pure heating injected at the outer mid-plane is then treated. It allows to treat the beam propagation and absorption easily, simplifying the implementation of the source term in the gyrokinetic code. This specific case is implemented in the gyrokinetic particle-in-cell code ORB5 using a Langevin approach. The derivation and verification of the source operator are presented.