Alexandria-based Atlantic Research Corp. has received a $13 million, multiyear Army contract to manufacture nearly smokeless rocket motors for the Chaparral air defense missile, the company said yesterday.

Atlantic Research -- which researches, designs and builds a range of solid-fuel rocket motors -- said the initial year of the contract will involve sales of about $4.5 million. The company said that it will expand its East Camden, Ark., facility to produce the motors and will add between 50 and 75 personnel at the plant.

The new deal is Atlantic Research's first contract for minimum-smoke rockets, a new technology which interest the military, because rocket smoke exhausts leave a trail to the launch site and because smoke can interfere with the guidance systems of some guided missiles.

The Chaparral missile is designed for use in clear weather against low-flying aircraft.The heat-seeking missiles are carried by and launched from a specially designed tracked carrier.

Gerald Haml, Atlantic Research's executive vice president for operations, said yesterday that this initial deal could lead to other contracts for minimum-smoke rockets. A spokesman for the Army Missile Command in Huntsville, Ala., said that the Army increasingly will be shifting its missiles to the relatively smoke-free systems over the next few years.

The company's sales last year were $82 million, up from $57 million in 1979.

Meanwhile, Beech Aircraft Corp. has awarded Atlantic Research a half-million-dollar contract to manufacture and deliver rocket booster motors for the MGM107A aerial missile target, which is to be used for training defense forces in Taiwan.