In linear accelerators the maximum achievable beam current is often limited by the Beam Breakup (BBU) instability. This instability arises from the interaction of a transversely displaced beam with the dipole modes of the acceleration cavities. The modes of interest have non-zero transverse magnetic fields at the center of the cavity. This oscillating field imparts a time varying transverse impulse to the beam as it passes through the accelerating gap. Of the various modes possible only the TM/sub 130/ mode has been observed on the Experimental Test Accelerator (ETA) and it is expected to surface on the Advanced Test Accelerator (ATA). The amplitude of the instability depends sensitively on two cavity parameters; Q and Z/sub perpendicular//Q. Q is the well-known qualtiy factor which characterizes the damping rate of an oscillator. Z/sub perpendicular//Q is a measure of how well the beam couples to the cavity fields of the mode and in turn, how the fields act back on the beam. Lowering the values of both these parameters reduces BBU growth.