CRJ-700 FLT CREW HAS TCAS RA ENCOUNTER DURING EXPEDITED DESCENT AT ATC REQUEST.

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ATC STARTED US ON A DSCNT PROFILE FROM FL320 WITH SEVERAL STEP-DOWNS. AFTER A VERY BRIEF LEVELOFF AT FL240 ZID ISSUED A CLRNC DOWN TO FL190 AND REQUESTED EXPEDITED DSCNT THROUGH FL200 FOR TFC. WE COMPLIED WITH THE REQUEST BY SELECTING A 2000 FPM DSCNT TO FL190. VERY SHORTLY AFTER THAT; WHILE PASSING THROUGH FL230; ATC REQUESTED WE BE THROUGH FL200 WITHIN 90 SECONDS TO CLR CLBING COMPANY TFC IN OUR 1-2 O'CLOCK POS -- DON'T RECALL THE DISTANCE CALL. I REPLIED WE WOULD TAKE IT RIGHT ON DOWN FOR HIM. WE INCREASED THE DSCNT RATE TO 3500 FPM. MOMENTS AFTER OUR REPLY ATC SAID HE WANTED US TO LEVEL OFF AT FL220; JUST AS WE DSNDED THROUGH IT. I REPLIED 'TOO LATE -- WE'RE ALREADY THROUGH IT.' AFTER THAT; RADIO COMS WERE CONFUSING. ATC WAS ALSO TALKING TO THE OTHER ACFT (I BELIEVE HE WAS ASKING FOR INCREASED CLB RATE -- THERE ALSO SEEMED TO BE SOME CONFUSION FROM THE OTHER ACFT ABOUT ALT ASSIGNMENT). AS I RECALL; AT OR NEARING FL210; STILL DSNDING; WE RECEIVED A TCAS AMBER 'TFC; TFC' MESSAGE; A TARGET DISPLAYED AHEAD AND TO THE R; FOLLOWED VERY SHORTLY BY A TCAS RA. I SEEM TO RECALL A 'MAINTAIN VERT SPD' AURAL AND LOOKED DOWN AT THE VSI CUES INSIDE AND THE RADIO. ATC TWICE REQUESTED CONFIRMATION WE WERE LEVEL AT FL190 WITH SOME URGENCY. I REPLIED SOMETHING TO THE EFFECT THAT 'NOT YET; FOLLOWING TCAS ALERT.' WE RECOVERED THE DSCNT JUST BELOW FL190 AND CLBED BACK UP TO IT. WE WERE BOTH ON THE CTLS AT THE BOTTOM SINCE THE ACFT WAS OUT OF TRIM. WE LEVELED OFF AT FL190 AND WERE PROMPTLY HANDED TO THE NEXT FREQ WITHOUT FURTHER COMMENT FROM ATC. I HAVE TO EMPHASIZE THAT THE TIME FRAME FOR ALL THIS WAS VERY SHORT; I WOULD GUESS LESS THAN 60 SECONDS FROM WHEN WE RECEIVED THE FIRST TCAS ALERT UNTIL WE RECOVERED AND WERE CLR OF CONFLICT. I HAVE NO RECOLLECTION ON THE CLOSEST VERT AND HORIZ PROX TO THE OTHER ACFT; THOUGH I AM SURE IT WAS CLOSE. FLT ATTENDANTS STATED THEY FELT SOME MANEUVERING; BUT NO EXCESSIVE FORCES AND THAT THE PAX WERE OK. I MADE A SHORT ANNOUNCEMENT TO THE PAX EXPLAINING WE NEEDED TO MANEUVER THE ACFT TO STAY CLR OF NEARBY TFC AND APOLOGIZED FOR ANY DISCOMFORT. PERHAPS AN ATC VECTOR FOR INCREASED HORIZ SEPARATION WOULD HAVE BEEN HELPFUL IN THIS SIT; ALTHOUGH ONCE THE IMPENDING CONFLICT BECAME APPARENT TO THE CTLR THERE WAS NOT MUCH TIME TO CHANGE ANYTHING. ONE THING IS CERTAIN: TCAS WAS INSTRUMENTAL IN GUIDING US AWAY FROM A POTENTIAL MISHAP.