Simulation of the avalanche processes inside a gaseous parallel-plate detector has been carried out to obtain the detector readout signal. The traditional models in the field are based on a time-consuming nondeterministic description of the stochastic processes of the avalanche of electrons. Here, we have used a simpler and faster method in which the solutions of transport equations are used for the description of development of both electrons and ions. The model includes the linear Townsend mechanism for the avalanche development in addition to considering space charge field and photo-ionization as the nonlinear mechanisms in the multiplication process. The simulation was performed for the operational conditions of a trigger Resistive Plate Chamber (RPC). In the calculated induced signal, two different time scales corresponding to the fast and the total signals have been distinguished corresponding to the development of electrons and ions, respectively. By proper choosing the drift velocity of the ions, a good agreement between the simulation and experiment is obtained for the waveform of the readout signal. This result cannot be achieved by the traditional stochastic approaches in which the ions are considered stationary.
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