In a large bowl, mix the juice with all the salt, sugar and spices until the salt and sugar are dissolved.
Place the duck in a dish and pour in the brine. Turn the duck a couple times to coat it evenly. Cover the dish with plastic wrapand refrigeratethe duck marinate for 4 hours.
Set the pellet smoker to 250°F.
Place the duck breast on the smokerrack.
Smoke the duck for around 2 1/2 to 3 hours or until the internal temperature of the meat reaches 150°F.