1994 Ford Probe re alternator

1ST of all I am no expert so I appologise for my lack of knowledge etc
and I would be very gratfull for any help or advice re this matter :)

i have a 94 ford probe 2.5 v6 and have just recently broken down due to my alternator belt coming off and causing my battery to drain and my car to stop working, the mechanic says it would be an easy job to take the wheel off and refit the belt, I have the belt in tact but clearly dont have whatever holds the belt on, it must have fallen off on my journey or prior to the belt coming off, my question is can u tell me what the part is that keeps the alternator belt on its cranks ( or whatever u call the bits the belt sits on ) and is it quite expensive to get this part and to replace it, as I said I have the belt intact and there appears to be no more damage that can be detected, other than a flat battery, I did not notice anything falling off the car or see any parts under the car before I started my journey, all I have been told is that the alternator belt has come off causing my battery to drain making the car not start etc / no electrics / drain battery?

after doing some research am I after a " drive belt tensioner"?

is this whats missing and caused my problem?

many thanks :)