AN SMA LANDED ON RWY 22R AND WAS TOLD TO CLR AT TXWY B. THE SMA WENT TO THE SIDE OF THE RWY; BUT MISSED THE TXWY. WHEN THE SMA WAS APPROX ONE HALF WAY DOWN THE RWY HE SAW A SAAB ACR PASS OVER THE TOP OF HIM ON TKOF. CTLR THEN HAD THE SMA DO A 180 DEG TURN AND EXIT THE RWY AT THE END.

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I CONDUCTED A XCOUNTRY FLT FROM CHARLESTON; WV; BACK TO MCKINNEY; TX; IN AN SMA. THE SECOND LEG OF THAT TRIP WAS FROM CHATTANOOGA; TN; TO LITTLE ROCK; AR; DEVIATING TO THE N AROUND TSTMS. THE FLT WAS AN IFR FLT AND MOST OF THE INITIAL PORTION WAS IN IMC; UNTIL REACHING THE NASHVILLE AREA. THE ARR IN LITTLE ROCK WAS IN GOOD VFR CONDITIONS. I WAS CLRED FOR A LNDG ON RWY 22R; AND LANDED ABOUT XA20Z TIME; JUST BEHIND A JET LNDG ON RWY 22L. AFTER A NORMAL LNDG I WAS INSTRUCTED BY THE TWR TO EXIT THE RWY AT TXWY B. DURING MY ROLLOUT; I STARTED LOOKING FOR THAT TXWY. I COULD SEE TXWYS ON THE R SIDES; BUT I DID NOT SEE ANY SIGNS FOR TXWY B. NOT WANTING TO TURN ONTO A TXWY THAT I WAS NOT CLRED TO GO ON; I CONTINUED TO TAXI DOWN RWY 22R; KEEPING TO THE R (WESTERN) EDGE OF THE RWY; BECAUSE THAT WAS WHERE I EXPECTED TO SEE A SIGN MARKED TXWY 'B.' ALL OF A SUDDEN; I SAW AN AIRPLANE TAKING OFF FROM THE SAME RWY. WHEN THAT AIRPLANE (I LATER LEARNED IT TO BE A SAAB COMMUTER PLANE) PASSED ME; IT WAS ABOUT 100 FT ABOVE ME; AND TO MY L. IT MUST HAVE BEEN TRACKING THE CTRLINE; WHILE I WAS AT THE VERY WESTERN EDGE OF THE RWY. THE TWR THEN STARTED TO ISSUE INSTRUCTIONS FOR ME TO MAKE A 180 DEG TURN AND RETURN BACK TO THE APCH END OF THE RWY. AT THE APCH END; I WAS INSTRUCTED TO TURN L ONTO TXWY C; FOLLOW IT IN AND HOLD AT RWY 18. WHILE ON TXWY C; I WAS ASKED TO COPY A PHONE NUMBER TO CALL; AND I STOPPED TO COMPLY WITH THAT. HAVING CAPTURED THAT NUMBER; I WAS CLRED ACROSS RWY 18 AND INTO THE PARKING AREA. AFTER SECURING THE AIRPLANE; I CALLED THE TELEPHONE NUMBER FROM THE FBO OFFICE. IT TURNED OUT TO BE ADAMS FIELD TWR; AND I TALKED TO A GENTLEMAN BY THE NAME OF MR X. OVER THE PHONE; WE TRIED TO RECONSTRUCT THE SEQUENCE OF EVENTS; BUT WITHOUT MUCH SUCCESS. MR X ASKED ME WHETHER I COULD STAY IN LITTLE ROCK FOR 15 OR 20 MINS SO THAT HE COULD LOOK INTO THIS MATTER SOME MORE. I AGREED AND CALLED BACK AFTER ABOUT 20 MINS. MR X AND MYSELF WENT OVER THE SEQUENCE OF EVENTS ONE MORE TIME; AND WE WERE ABLE TO RECONSTRUCT IT THE WAY I HAVE RELATED IT ABOVE. DURING THIS SECOND TELEPHONE CONVERSATION; I HAD A DETAILED ARPT DIAGRAM IN FRONT OF ME; AND WE CONCLUDED THAT THE CTLR HAD ASSUMED ME TO HAVE EXITED THE RWY AT TXWY B; AND WAS NOT AWARE OF ME STILL BEING ON RWY 22R. ALSO; MR X DISCUSSED THE POSSIBILITY THAT MY POS WAS MORE THAN HALF WAY DOWN THE RWY WHEN THE SAAB PASSED ME. MR X TOOK DOWN MY FULL N-NUMBER; NAME; ADDRESS; AND PLT CERTIFICATE NUMBER. I WAS VERY CONCERNED TO FIND OUT WHAT I HAD DONE WRONG; BUT ALL MR X SAID WAS THAT I COULD PERHAPS HAVE LET THE CTLR KNOW THAT I WAS UNFAMILIAR WITH THE FIELD. I ASKED HIM WHETHER HE KNEW WHETHER THERE WERE SIGNS WITH TXWY DESIGNATORS; AND AFTER ASKING SOMEBODY ELSE IN THE TWR; HE TOLD ME THAT HE THOUGHT SO. IF THEY EXIST; I DID NOT SEE THEM. PERHAPS THEY ARE NOT LIGHTED? GIVEN THAT I HAD RECEIVED INSTRUCTIONS TO 'TURN R ON TXWY B;' I DID NOT WANT TO MAKE THE WRONG TURN; BUT WANTED TO TURN ONTO THE CORRECT TXWY. WHAT COULD I HAVE DONE DIFFERENTLY? I REALLY DON'T KNOW. WHEN I OPERATE AT UNFAMILIAR FIELDS; I ROUTINELY ASK FOR DETAILED TAXI INSTRUCTIONS; BUT THIS OCCURS AFTER EXITING THE ACTIVE RWY; ON THE GND FREQ. I HAVE NEVER HEARD ANYBODY'S UNFAMILIARITY WITH A FIELD BEING DISCUSSED ON THE TWR FREQ DURING THE LNDG PHASE.