A new general purpose computer code call EBQ, has been written to simulate the beam dynamics of the ETA, find its beam emittance and evaluate effects of changes in the electrode positions and external magnetic fields. The original calculations of the ETA were made with EGUN and yielded considerable insight into the operation of the device in the non-relativistic regime. The EBQ code was written specifically to attend to the special problems associated with high current relativistic beam propagation in axially symmetric machines possessing external 2-dimensional electric and magnetic fields. The coherent electric and magnetic self-fields of the beam must be calculated accurately. Special care has been used in the relativistic regime where a high degree of cancellation occurs between the self-magnetic and self electric forces of the beam. Additionally, EBQ can handle equally well non-relativistic problems involving multiple ion species where the space charge from each must be included in its mutual effect on the others. Such problems arise in the design of ion sources where different charge and mass states are present.