REPORT DOCUMENTATION PAGE)MB1No J1[4-oi!88 la REPORT SECURITY CLASSIFiCATION 1b RESTRICTIVE MARle NGS UNCLASSIFIED

SUBJECT TER aS (Continue on reverse of necessary arld idenrtty Oy b ouk urnner) FIELD GROUP SUB-GROUP- Beam break/-up, Linear accelerators,Electron beam instability Beam-circuit interaction,,' / I # 19 ABSTRACT (Continue on reverse if necessary and identify by block number) The temporal and spatial evolution of the cumulative beam breakup instability (BBU) is analyzed numer-ically using a continuum model. It is found that neither phase mixing nor linear transverse focusing is suffi-cient to render BBU stable in a long pulse machine, when external damping is absent. A sufficiently strong nonlinear octupole focusing field may limit the BBU growth, however.,- Y