Helicopter instructor reported a near miss with an aircraft while in the traffic pattern at a non-towered airport during a training flight. The instructor took the controls and maneuvered away from the aircraft.

Narrative

On Day 0 around XA:55 hours I was conducting flight instruction for a student pilot in a Schweizer 300 helicopter at ZZZ. I observed an airplane approaching from west to east and at approximately 1200 feet (600 feet above our current altitude). We were making our traffic pattern radios call and had turned onto a right downwind for runway 02. The aircraft approaching was a red biplane. The plane began a right turn toward us and I noticed the altitude on Foreflight to indicate they were in a descent and now on a collision course with us. I took the controls and made a rapid descending left turn and then a turn back to the right while descending to reacquire visual. Still no radio calls were made by this aircraft and then we observed the aircraft release a stream of smoke like you would see at an airshow. I think it is more important to communicate intentions of the CTAF than it is to show off and release smoke causing other aircraft which are established in the traffic pattern to make evasive maneuvers.In my opinion; the priorities of this PIC are out of order. If money can be spent on non-essential equipment such as a smoke system; then it would not be unreasonable to spend money on aviation radios.Also; in my opinion; the FAA needs to rethink allowing aircraft to operate inside the Mode C veil without ADS-b and radios. This has led to and will lead to more accidents if not corrected.