SMA TWIN WITH INSTRUCTOR AND PVT STUDENT HAS RWY EXCURSION INTO INFIELD AREA.

Narrative

AFTER DOING SOME SINGLE ENG WORK IN AN SMA TWIN WE PROCEEDED BACK TO THE ARPT FOR A FEW TOUCH-AND-GOES. (I AM A MULTI-ENG INSTRUCTOR FLYING WITH A RELATIVELY LOW TIME PRIVATE PLT.) WE ENTERED THE PATTERN WITHOUT INCIDENT AND ON OUR TURN FROM BASE TO FINAL I ASKED THE PRIVATE PLT TO TURN ON THE BOOST PUMPS. HOWEVER; INSTEAD OF TURNING ON THE PUMPS; HE TURNED OFF ALL THE MAGNETO SWITCHES FOR BOTH ENGS. BECAUSE OF THE FACT THAT WE WERE SLIGHTLY HIGH AND FAST THE THROTTLES WERE ALREADY AT IDLE SO I COULD NOT TELL THAT THE MAGNETOS WERE OFF. WHEN WE LANDED I WENT FORWARD WITH THE THROTTLES TO COMMENCE A TOUCH-AND-GO. WHEN THE PLANE HESITATED I SEARCHED FOR THE PROB AND FOUND THE SWITCHES TO BE OFF. VERBALIZING THE PROB TO THE STUDENT WAS MISTAKEN FOR A COMMAND TO TURN THE MAGNETOS BACK ON. INSTANTLY; THE R ENG CAME TO LIFE WITH A VENGEANCE; THE DIFFERENTIAL PWR STARTED US OFF THE RWY TOWARDS THE INFIELD. I CHOPPED THE THROTTLES; BUT BECAUSE OF OUR REMAINING SPD AND THE SURGE TO THE L; WE PROCEEDED TOWARDS THE INFIELD AND THAT IS WHERE THE PLANE CAME TO A REST. IN MY ESTIMATION; I BELIEVE THE CONTRIBUTING FACTORS WERE: 1) LOW TIME STUDENT PLT. 2) LNDG SLIGHTLY L OF CTRLINE; REDUCING TIME TO REACT TO THE PROB. 3) POOR MARKING OF SWITCHES; LOCATION (ALL LOOK THE SAME ON THE FAR L PANEL). 4) MISINTERP OF A VERBALIZED PROB. 5) NOT BEING ABLE TO TELL MAGNETOS WERE OFF BECAUSE THROTTLES WERE AT IDLE ON FINAL. 6) NOT IMMEDIATELY CUTTING THROTTLES WHEN I SAW THE MAGNETOS OFF. 7) NOT DOUBLECHKING THE STUDENTS ACTION'S EVERY TIME. SOME POSITIVE POINTS: 1) KEEPING THE WT OFF THE GEAR BY KEEPING THE YOKE BACK. REDUCING THE POSSIBILITIES OF SNAPPING THE GEAR OFF IN THE SOFT DIRT. 2) IMMEDIATELY CUTTING THROTTLES AFTER PWR SURGE. 3) MOST OF ALL; NOT FLIPPING THE PLANE OVER. 4) THE PLANE PAX COMING OUT OF THE WHOLE 'E' TICKET RIDE UNHARMED.