 We can see the mesh across the top which is connected to the negative side of the power supply and the wire underneath which is connected to the high voltage positive side. As the ionizing radiation comes in it causes the sparks to happen. As we zoom in an alpha particle is coming from above and it ionizes one of the air particles between the gap. That's then accelerated upwards and that causes a cascade of ions hitting each other which we see as a spark. Each ionization particle coming in is going to cause a spark of its own.