Does the second picture behaviour happen after the first’s?
The two pictures look like really long particle trails. Have you tried adjusting the particle lifespan? You may be hitting up against the limit on how many particles you can spawn at once. The “wave” then is the emitter briefly halting on spawning new particles until some old particles die off. You could try turning down the particle lifespan to see if the wave disappears. Or increase the maximum particle count.