An Air Carrier First Officer reported a NMAC at 10;000 FT south of PHX with a aircraft maneuvering in the vicinity of the departure corridor. The TCAS went immediately to RA with a commanded climb in excess of 7;000 FPM.

Narrative

We were on climb out from PHX; headed South. As we climbed through about 7;000 FT; the PM (Pilot Monitoring) noticed traffic on TCAS some distance ahead -- perhaps 20 miles -- also climbing. They were above our altitude but not climbing as rapidly as we were. They also appeared to be southbound. We were seemingly faster than they were because as we approached 10;000 FT; we were only about 10 miles from them. At this point our aircraft went into a shallower climb of about only 1;000 FPM because we were accelerating to our climb speed from 250 KTS. With about a 10 mile separation; we began approaching their altitude. We were not concerned at that point because we knew we would out climb them before getting too close to them. [Note that at no point during the flight did ATC point out traffic to us.] All of a sudden the aircraft in front of us turned directly toward us; almost at our altitude. We never received the TA. TCAS went straight to giving us the RA; which was to climb; and to climb like a banshee. We were climbing at 7;200 FPM and had still not reached the green area on the RA indication. The other aircraft showed on TCAS to be directly below us by only 200 FT and still climbing. While both of us looked; we never did see the other aircraft. During our serious climb; the PM notified ATC of our RA. Their only response was 'ok.' We are pretty sure this qualifies as a near-miss. This event seems to have occurred because there appeared to be maneuvering traffic that was unaware of the PHX departures. I am fairly sure that ATC also saw the traffic as no danger or concern to us; as we were plotting to out climb them before reaching them. [At least we hope that ATC did not know what the other aircraft was intending to do and simply neglected to tell us.] It is likely; that no one could have predicted that they would turn directly in our path. I an unaware how the airspace is indicated on VFR charts; having not seen one in many years. Clearly; the other aircraft should not have been maneuvering that high in that area; due to the multiple departures from PHX.