The pilot reported that he was completing an aerial application flight over a cultivated field. During the fourth pass, the airplane encountered a dust devil (also called a whirlwind), lost lift and impacted powerlines. Upon impact with the powerlines the rudder separated from the airplane and the airplane began a left turn. Unable to arrest the turn, the pilot reduced power and made a forced landing to the field that he was spraying. Upon touch down the left main landing gear separated from the fuselage and the airplane slid to a stop. The airplane sustained substantial damage to the left wing, vertical stabilizer and rudder. The operator reported there were no preimpact mechanical malfunctions or failures with the airframe or the engine that would have precluded normal operation. A review of the Federal Aviation Administration Aviation (FAA) Weather Handbook (FAA-H-8083-28) and the FAA Aeronautical Information Manual found no detailed information listed about dust devils or the potential hazards of flying through dust devils.