How to change the mesh of a particle system at runtime C#

There is no single instance of the Mesh class for a particle system. Rather, it is a collection of meshes where each particle is a 2-triangle plane that is essentially a textured billboard. You can't access these in the same sense you access the .mesh property of a MeshFilter component.

But, depending on what you want to do with it, you have some options. MonoBehavior exposes a property called particleEmitter that allows you to access the ParticleEmitter component. It in turn exposes an array which contains instances of the Particle class. These contain the data you would typically associate with a single particle, such as its velocity, color, position, etc. You may then change these properties as you see fit, and assign the changed array of particles back to the emitter when done, like so:

     Particle[] particles = particleEmitter.particles;
     particles[0].position = new Vector3(0, 0, 0);
     particleEmitter.particles = particles;

This is somewhat akin to how you would modify the individual vertices of a Mesh and then assign the changed vertex array back to the mesh to see your changes take effect. Have a look at the particleEmitter (and, possibly, the particleSystem) property in scripts, and see if they satisfy your needs. If you use an editor that doesn't offer code completion (Intellisense), you can see the available properties of class ParticleEmitter here:

http://docs.unity3d.com/Documentation/ScriptReference/ParticleEmitter.html

And class Particle here:

http://docs.unity3d.com/Documentation/ScriptReference/Particle.html

You can access the mesh of Particle Fx via ParticleSystemRenderer.mesh

For example:

 GetComponent<ParticleSystemRenderer>().mesh = 
 Resources.GetBuiltinResource("Capsule.fbx");