private airplane; private jet
Refers to an aircraft owned and used by an individual or company, not for commercial passenger service. Often used in contrast to commercial airliners.
See also: ビジネスジェット
He travels around the world in his private jet.
The tycoon owns two private airplanes.
ビジネスジェット specifically refers to a business jet, often smaller and used for corporate travel, while 自家用機 is a broader term for any privately owned aircraft.
Compound of 自家用 (private use) + 機 (aircraft).