Spawn particles from a position

This is an old question, but thought I'd answer here for posterity:

What you want to do is have a particle system, and each frame add some new particles that you create through code to its list of particles. I put a complete demo here which should be pretty clear.

 ParticleSystem yourParts = GameObject.Find("yourParts").GetComponent<ParticleSystem>();
 int partsPerFrame = 20;
 
 void Update() {
   //Get the particles already in the system
   ParticleSystem.Particle[] particles_original = new ParticleSystem.Particle[yourParts.particleCount];
   yourParts.GetParticles (particles_original);
 
   //Make an array of particles to add
   ParticleSystem.Particle[] particles_new = new ParticleSystem.Particle[partsPerFrame];
   Vector3 spawnPos;
   for(int i = 0; i < partsPerFrame; i++) {
     //Here I'm setting their position randomly, but you could pass any position you want here
     spawnPos = new Vector3(Random.Range(-10.0f, 10.0f), Random.Range(-10.0f, 10.0f), Random.Range(-10.0f, 10.0f));
     particles_new[i] = makePart(spawnPos);
   }
 
   //Combine the currently existing particles with the new ones you just created
   ParticleSystem.Particle[] particles_final = new ParticleSystem.Particle[particles_original.Length + particles_new.Length];
   particles_original.CopyTo(particles_final, 0);
   particles_new.CopyTo(particles_final, particles_original.Length);
 
   //And put them into the particle system
   yourParts.SetParticles (particles_final, particles_final.Length);
 }
 
 //This initialises all of the ParticleSystem.Particle attributes whenever you make one.
 //Each attribute is assigned a variable that I store as class variables. I didn't write them in because it would end up too messy looking.
 ParticleSystem.Particle makePart(Vector3 position) {
         ParticleSystem.Particle r = new ParticleSystem.Particle();
         r.angularVelocity = part_angularVelocity;
         r.color = part_color;
         r.lifetime = part_lifetime;
         r.position = position;
         r.rotation = part_rotation;
         r.size = part_size;
         r.startLifetime = part_startLifetime;
         r.velocity = part_velocity;
         
         return r;
     }

@zettam, There is another, more efficient and very easy way:

Make your particle system simulate in World Space, and make special object that only holds your particle system.

Then, every time you want to burst, just move the emitter into the position you want, and burst there.

If you want to burst in two or more places at the same time, make array / list op positions, and in the update() on your script, teleport-emit() in all these positions.

Just don't forget to set the system to simulate in World space, because in local space, particles will be parented to the object :)

Wouldn't this just mean that you instantiate a prefab particle system at the required location that has the required values, but just one single particle?

You can use ParticleSystem.Emit() and provide overrides for the .position property

https://docs.unity3d.com/ScriptReference/ParticleSystem.Emit.html