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We have analyzed the electromagnetic-mode structure inside a bounded-wave electromagnetic pulse (EMP) simulator. This has been done by the application of the singular value decomposition method to time-domain data generated by self-consistent, three-dimensional finite-difference time-domain simulations. This combination of two powerful techniques yields a wealth of information about the internal mode structure which cannot be otherwise obtained. To our knowledge, this is the first time such a comprehensive study has been done. In the absence of a test object, the transverse electromagnetic (TEM) mode is dominant throughout the simulator length. TM1 dominates over other transverse electromagnetic (TM) modes over most of the length. Close to the termination, the TEM mode weakens marginally, while higher order TM modes become stronger. The enhancement of TM2, and the weakening of TEM near the termination, have been explained in physical terms. Placement of a perfectly conducting test object in the parallel-plate section increases the strength of higher order TM modes, at the cost of TEM. Hence, the object is subjected to electromagnetic fields that deviate significantly from the desired TEM form. A physical interpretation has been provided for this phenomenon. The enhancement of electromagnetic fields near the top and bottom faces of the object are explained in terms of the Poynting flux distribution.