A DA2000 PLT RPTS RESPONDING TO A TCASII RA DURING AN NMAC WITH A SMALL CESSNA AT 900 FT DEPARTING PDK.

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I WAS THE PF ON TKOF FROM PDK RWY 20L. AFTER GEAR RETRACTION AT APPROX 300-400 FT AGL; PDK TWR ISSUED ADVISORY OF 'TFC 11 O'CLOCK MOVING NBOUND.' THE CAPT CALLED 'TFC IN SIGHT.' I SAW A SMALL CESSNA APPROX 11-12 O'CLOCK POS COMING DIRECTLY TOWARD MY ACFT. AT THE SAME MOMENT THE TCASII ALERTED A 'TA' ALERT. (WE HAD BEEN ASSIGNED RWY HDG; MAINTAIN 3000 FT ON THE TKOF CLRNC.) APPROX 4-5 SECONDS ELAPSED AND THE CAPT STATED 'TURN L NOW!' I STARTED A L DSNDING TURN OF APPROX 8 DEGS NOSE DOWN AND 30-40 DEGS L BANK (AS I SAW THE CESSNA PASS L TO R AT A DISTANCE OF 300 FT VERT AND 200 FT HORIZ SEPARATION!). AT THE SAME MOMENT I INITIATED THE EVASIVE MANEUVER; THE TCASII ALERTED AN RA 'DSND NOW' AND A 1500-2000 FPM DSCNT COMMAND; AND THE TWR CTLR ISSUED A L TURN 090 DEGS IN THE MIDST OF THE EVASIVE MANEUVER! I INITIATED THE EVASIVE MANEUVER AT APPROX 900 FT AGL AND RECOVERED BTWN 500-600 FT AGL. I THEN RECOVERED AND PROCEEDED WITH A NORMAL CLBOUT PROC. PDK TWR ISSUED A FREQ CHANGE TO DEP WITH NO COMMENT ABOUT THE INCIDENT. THE CAPT-STATED REPLY WAS; 'WHAT WAS THAT GUY DOING?' PDK TWR REPLIED; 'HE WAS GOING TO THE WRONG RWY.' WE THEN CONTINUED THE FLT UNEVENTFULLY. I WOULD LIKE TO NOTE THAT THE PDK ATC CTLR WAS RUNNING MULTIPLE RADIO FREQS: CLRNC; GND AND TWR FREQS. IT IS MY OPINION THE CTLR LOST SITUATIONAL AWARENESS OF THE TFC PATTERN AND FLOW OF TFC. THE CESSNA PLT ALSO HAD NO SENSE OF SITUATIONAL AWARENESS!