While performing a crossbleed start during pushback; the pushback crew was unable to control the thrust-induced forward impetus of the MD-90 and the tug jackknifed; striking and damaging the radome.

Narrative

This event occurred during pushback; just prior to setting brakes; while doing a crossbleed start. The push tug and the aircraft came in contact. The event that contributed to this incident was an MEL for APU inoperative. Because of the MEL; a start at the gate followed by a crossbleed start either on pushback or after brakes set would be needed. I actually had a face to face with the tug driver. We talked about the need for a huffer cart for engine start. He said we could only start the right engine at the gate. I asked if I could start the second during pushback. He agreed. I actually thought it would be safer to start with the push crew's eyes clearing behind and monitoring the second engine start. We started the right engine at the gate. With the right engine started and brakes set; we did the 'Performance checklist' while ground personnel removed hoses and electrical power.During push; I asked if I was clear to start the left engine. He agreed. I called for the 'Crossbleed' checklist and I pushed up the right engine to 25 PSI minimum according to the 'Supplementary Procedures' checklist. The copilot was doing the checklist when we heard 'STOP! STOP! STOP!' I stepped on brakes. The tug driver said the aircraft had pushed the tug; [which was] now at a 90 angle to the aircraft; but things looked ok. Approximately 20 seconds later he said the tug was in contact with the radome and he needed to get Maintenance. The copilot later said the right engine was approximately 80% N2. Maintenance came and said the radome looked OK but wanted to open it at the gate. We were tugged back to gate with right engine running - no APU. Inside the radome; Maintenance found delamination approximately 6 to 8 inches. The copilot did a logbook write-up.