High voltage anode electron gun

In the image it can be seen that the anode voltage of a SEM field emission electron gun is up to 30kV.
I think that at that voltage an electric arc can occur between the electrons and the anode, or am I wrong?

Or is the distance between the electron beam and the anode large enough that the arc does not occur?

Or is the exit velocity of the first anode (due to field emission) high enough not to hit the anode?