ACR-MLG UNAUTH RWY ENTRY AFTER LNDG CAUSES OTHER ACR TO GO AROUND.

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LANDED ON RWY 22 AT LGA. I INSTRUCTED THE F/O TO MAKE NECESSARY RADIO CALLS TO COMPANY AND RAMP CTL; AFTER LNDG; WHILE I TALKED TO GND CTL. I RESUMED CTL OF THE ACFT ON ROLLOUT ABEAM OF TXWY C. I EXITED THE RWY AT C ON THE REVERSE HIGHSPEED TURNOFF. CONTACTED GND AND WAS TOLD TO PROCEED TO THE GATE. I MADE A WRONG TURN. INSTEAD OF JOINING THE CORRECT TXWY I JOINED THE HIGH SPD TURNOFF AT C AND ENTERED THE RWY. I STOPPED THE ACFT; RADIOED GND CTL 'FLT XXX IS ON THE RWY;' AND TURNED MY TAXI LIGHT ONTO HIGH. ACR FLT WAS FORCED TO GO AROUND. WE WERE ON THE HIGHSPEED TURNOFF AT TXWY C FACING THE WRONG DIRECTION (IE; TOWARD THE RWY). THE NOSE OF THE PLANE WAS EVEN WITH THE RWY EDGE LIGHTS OF RWY 22. AFTER ACR GO AROUND WE RECEIVED PERMISSION TO CLR THE RWY AND TAXI TO THE GATE. THE F/O DID NOT WARN ME OF MY MISTAKE BECAUSE HE WAS PREOCCUPIED WITH MAKING RADIO CALLS. I BELIEVE I MADE THIS ERROR BECAUSE OF DARKNESS; SLIGHT DISORIENTATION CAUSED BY GOING FROM A BRIGHT SITUATION--ALL LIGHTS ON--TO A RATHER DARK ONE--TAXI LIGHT ONLY; THE ODD ANGLE FORMED BY REVERSE HIGHSPEED TXWY AND THE OUTER (CORRECT) TXWY; AND THE VERY SHORT DISTANCE BTWN RWY AND OUTER TXWY LEFT ME LITTLE TIME TO SEE MY MISTAKE BEFORE ENTERING THE RWY ENVIRONMENT.