The evolution of the instability of a thin relativistic electron ring has been investigated numerically. The solution of the exact non-linear equation, considering the interactions of ten harmonics of the coherent radiation is obtained. Both the radiation effects and the negative mass effects have been considered for a ring in free space. It is found out that for short times, of order several linear growth times, the instability saturates at a relatively low level of oscillation energy (W_E approximately=10^-2(mc² nu eR). This saturation is accompanied by an increase in the energy spread of the beam up to the threshold value Delta W_cr approximately square root nu / gamma , and with the distribution of energy among several harmonics.