SUMMARYThis study group was initiated to consider whether there were any "show-stopper" issues with accelerators for heavy-ion warm-dense matter (WDM) and heavy-ion inertial fusion energy (HIF), and to prioritize them. Showstopper issues would appear as limits to beam current; that is, the beam would be well-behaved below the current limit, and significantly degraded in current or emittance if the current limit were exceeded at some region of an accelerator. We identified 14 issues: 1-6 could be addressed in the near term, 7-10 are potentially attractive solutions to performance and cost issues but are not yet fully characterized, 11-12 involve multibeam effects that cannot be more than partially studied in near-term facilities, and 13-14 involve new issues that are present in some novel driver concepts. Comparing the issues with the new experimental, simulation, and theoretical tools that we have developed, it is apparent that our new capabilities provide an opportunity to re-examine and significantly increase our understanding of the number one issue -halo growth and mitigation.