A smoke alarm’s function relies on a small amount of radioactive material placed between two electrically charged metal plates. As it releases radiation, it will cause the air molecules in the chamber to ionize and thus create a current flow in between. But when smoke particles enter the chamber, it disrupts this flow of ionized air molecules, and thus reduces the current, causing the alarm to be set off.
Now, alpha particles are detected and emitted instead of gamma or beta radiation because compared to beta and gamma, alpha particles are not that penetrating. That allows alpha particles to be stopped by smoke particles, and therefore cause a reduction in the current flow. This is not possible for beta and gamma rays, because even smoke particles cannot stop their penetrative power.