NMAC IN THE TFC PATTERN BTWN SMA AND SMT; OPPOSITE DIRECTION TFC.

Narrative

ON SUNDAY; AUGUST; AT APPROX PM00 LCL; 1 OF MY STUDENTS AND I HAD TAKEN OFF ON RWY 5 AND ENTERED THE DOWNWIND FOR L TFC. WHILE APCHING THE MIDFIELD DOWNWIND I NOTICED THE HEADLIGHTS OF AN ACFT FLYING DIRECTLY TOWARD US. TAKING CTL OF THE ACFT FROM THE STUDENT; I CLOSED THE THROTTLE AND BEGAN A DIVING R TURN. WE HAD BEEN AT THE CORRECT PATTERN ALT OF 1500 FT MSL. WHEN THE PLANE PASSED OVERHEAD AND TO THE L WE HAD LOST APPROX 300 FT. OUR PATTERN GND TRACK WAS OVER THE APCH END FOR RWY 14 WHICH IS ABOUT 1500 FT FROM THE RWY WE WERE USING. AS I BEGAN THE EVASIVE MANEUVER THE TWR TRANSMITTED AN ODD TFC ADVISORY. 'SMA X DO YOU HAVE THE TFC.' SINCE I WAS UNAWARE THAT THERE WAS EXPECTED TO BE TFC FLYING DIRECTLY AT US WHILE ON THE DOWNWIND LEG; THIS CALL SEEMS RATHER ODD. 'I HAVE A JET OR A LARGE TWIN FLYING STRAIGHT AT ME;' I RESPONDED. 'WE AREN'T TALKING TO THEM.' THE TWR CALLED BACK. AFTER WE DOVE AWAY TO THE R; I ASKED THE STUDENT TO REGAIN CTL AND RESUME THE L HAND PATTERN. THE TWR ASKED US TO THEN EXTEND THE DOWNWIND LEG AND THEN REQUESTED WE LEAVE THE ATA AND DEPART TO THE W. THE TWR WAS RECEIVING A LOT OF INCOMING TFC AND I ASSUMED THEY ALSO WANTED US TO CALM OURSELVES. I DIDN'T FOLLOW THE COMS AFTER OUR NEAR MISS VERY CLOSELY; BUT I HAD SOUNDED LIKE THE TWR WAS IN TOUCH WITH THIS TWIN; AN SMT Y; WHO HAD NOT IDENTED THE ARPT DURING HIS APCH AND HAD GIVEN POOR POS RPTS. THE TWR WAS WORKING WITH THE OTHER ACFT PRIOR TO ITS INCURSION INTO OUR PATTERN AND LATER CLRED THEM TO LAND. WHY WE WERE SENT OUT OF THE ATA; AND NOT BROUGHT BACK IN FOR 10 MIN; I'M NOT SURE.