[en] Coherent instabilities for coasting beam are studied for the case of NUMATRON. Threshold current of the longitudinal instability is given by the Keil-Scnell criterion and is found to be more than 1 order higher than the incoherent space charge limit. The threshold of the transverse coherent instability is estimated to be about 1 order lower than the space charge limit. The growth rate of the transverse instability when ions up to the space charge limit are accumulated is calculated at 60 msec. As the cure for this instability, a feed-back damping is being considered. Caculations given here are based on rather idealized beam and chamber-wall shape so as to enable the analytical calculation. Experimental studies about the transverse coherent instability as is planned at TARN are highly needed. (author)