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In the conventional design of RF linacs, the bunched beams are not in thermal equilibrium. The space charge forces couple the particle motions between the transverse and the longitudinal directions. Fur-thermore it will cause the equipartitioning process which leads to emittance growth and halo formation. In the design of the China Spallation Neutron Source (CSNS) linac, three cases are investigated using the Hofmann stability charts. In this paper, we present the equipartitioning beam study of the CSNS Alvarez DTL linac.