A time-dependent collisional-radiative (CR) model is elaborated in the purpose of modeling the penetration of an atomic carbon beam in the edge plasma of a fusion machine in order to probe it. The excited states population densities of the beam are assumed to be modified by electron-induced processes only. All momentum transfer is neglected: the penetration velocity is assumed constant. In typical conditions for the electron density and temperature gradients (partial derivative n(e)/partial derivative(x) approximate to 10(20) m(-4) and partial derivative T-e/partial derivative(x) approximate to 10(7) K m(-1)), the results illustrate the electrons efficiency to ionize the beam. With a velocity equal to 1 km s(-1), the beam is ionized in 20 mu s in these conditions, which corresponds to a penetration depth of 2 cm. During the conversion in ions, the atomic beam is sufficiently excited to emits spectra whose measurement in coupling with the present CR model can provide information on partial derivative n(e)/partial derivative(x) and partial derivative T-e/partial derivative(x).