For the dome, just add an IcoSphere and add a Wireframe Modifier and a Bevel Modifier. For the Wireframe modifier, increase the wire size, uncheck "Replace Original" (this will leave the original object visible in addition to the wireframe), and set the Material Offset to 1 (we will be using 2 materials - one for the beams and one for the "zap" glass - material offset picks one for the wires and the other for the main object):

For the shader, the "wire beams" part is rather simple, just use a Principled BSDF and increase the metallic and lower the roughness (not shown). For the "zap" glass, start with the glass setup highlighted below. If you're using EEVEE, make sure the material's blend mode is set to "Alpha-Blend" or "Alpha-Hashed"

For the "Zapping light", use the shader setup below - I warped the vectors of a Wave Texture with a Noise Texture so it can still be rather straight while still having funky (electric) edges. I use this texture as a mix factor between the glass, and a Blue emission.

Lastly, for the "animation", I used a Value Node - in the field are of this node (pink) I entered the word #frame - this is a driver that will make the number of the value equal to the frame number at any given time. I connected it to a Modulo (Math) node to make the pulses intermittent, and then a Divide (also Math) node, to make the pulses "linger" for a bit longer. I used this as a final mix factor between my emission glass, and just "regular" glass, so the "light" pulses.
I also used this value to change the W component of the Noise Texture (make sure to switch it to 4D for the W to be available) to make the noise "animate" as well.

Final result looks something like this. Don't forget to enable "Bloom" in the render properties.
