It's broken. See these quick renders.
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The far side of each ring doesn't seem to render, no matter what angle the light is coming from. These are clouds, and brightly coloured just for easy editing as I test this out, each ring could use its own independent fractal for variation, here I just used one fractal.
I'll post the clip file of the planet, too. I can't work out how to render the rings on the opposite side of the planet from the camera, maybe someone can find a remedy quicker.
The secret is in the cloud fractal shader's blending shader node. You can't exceed the limits of the 'spacing' value in the 'Main contour' field of inputs and you must use 'Y for altitude' and match that in relation to the ringed planet's altitude. For testing this out this is a tiny planet of 20m radius, its 'Y' value in the scene is 30m. So, I need a 'base altitude' in the contour shader of 10m to bring the rings into the centre, instead of at the top and bottom of the planet.
The contour shader is set to twice the planet radius. If you breach the 'spacing' of the contours with the 'thickness' of the contour shader, it'll also apply rings at the top and bottom of the planet too. Just use careful adjustments to keep it all in line with the planet's radius.
Just tidying it up, maybe someone can fix the rendering issue. I've tried ray tracing the clouds, it doesn't help it. All the ring layers also use no acceleration and have ray traced shadows checked to get the planet to cast onto them, I can't figure out the missing areas...