ATTEMPTING TO FIND SMOOTH AIR FOR A TRAINING FLT; ENCOUNTERED SMT IN DESCENT; RESULT IN STEEP CLIMBING TURN TO AVOID TRAFFIC AND ENDED UP IN THE TCA.

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I WAS MAKING MY FIRST FLT OF THE DAY WITH A NEW STUDENT. THE WIND WAS VERY STRONG; 20-30 KTS. WE DEPARTED AND CLBED TO THE S IN VERY TURB AIR. MY STUDENT WAS DOING AN EXCELLENT JOB REQUIRING ONLY MY COACHING. NORMALLY I CONDUCT LESSONS AT 3000' MSL; BUT THE AIR WAS STILL VERY ROUGH SO I DECIDED TO CLB TO FIND SMOOTHER AIR AND SEE HOW MY STUDENT COULD DO IN MORE REASONABLE CONDITIONS. THE AIR DID SMOOTH OUT AROUND 4000'; YET THERMALS WERE STILL PRESENT BENEATH SCATTERED CUMULUS. WE BEGAN OUR LEVEL OFF AT 4500'; YET DID NOT STOP OUR ASCENT UNTIL 4800'; STILL SIMPLY COACHING MY STUDENT. AT THAT INSTANT I CAUGHT A TWIN OUT OF THE CORNER OF MY EYE; APPROX 11 O'CLOCK; ONCOMING AND DSNDING. I THEN TOOK THE AIRPLANE AND MADE A HARD; CLBING RIGHT TURN TO AVOID; AND CONTINUED UNTIL I HAD THE TWIN BELOW AND TO MY RIGHT. I WAS NOW AT 5300'; VERY NEAR THE EDGE OF THE TCA AND I BEGAN A STEEP DSNDING SPIRAL DOWN TO 2500'. WE WENT BACK TO MEACHAM; WHERE THE TWR ASKED IF WAS HAD BEEN S OF DOWNTOWN AT 5500'. THEY THEN TOLD ME TO CALL TRACON AND GAVE ME THE PHONE NUMBER. I FEEL MY INCIDENT WAS INADVERTENT; AND ALSO AVOIDABLE. I DO FEEL THAT THERE SHOULD BE PROCS STANDARDIZED AND TESTED FOR ON THE AIRMAN WRITTEN TEST. THESE PROCS WOULD PROMOTE A PLT'S RPT W/O FEAR OF REPERCUSSIONS. THESE RPTS WOULD ENABLE ATC TO SAFELY HANDLE EACH OCCURRENCE. I SHOULD HAVE CALLED APCH CTL AS SOON AS I REALIZED I MIGHT BE IN THE TCA. I KNOW THAT I WAS VERY NEAR THE LAT LIMITS. HAD I CALLED APCH; THEY COULD HAVE TOLD ME FOR SURE AND DIRECTED ME THE QUICKEST WAY OUT. AS IT WAS I DID WHAT I THOUGHT BEST.