Mushroom arch wire is used in
Mushroom-shaped lingual arch forms
Natural variations in facial–lingual tooth dimensions are significant enough on the lingual  aspects to require routine first-order bends. Distal to the cuspids, mesial to the molars and  sometimes at the maxillary laterals.
Fujita introduced the concept of ‘mushroom-shaped  archwire’ in conjunction with the lingual appliance.
Beggs appliance
Lingual appliance
Straight wire appliance
Edgewise appliance