The bridge

From the Swap Machine, turn left and start following the path. You'll soon come to an odd bridge.

You can cross the first arm of the bridge, but the second arm is hanging out in midair. Drop down the stairs on the back/left side of the bridge.

Turn the wheel you find here to activate the bridge mechanism. Climb back into the bridge and use the lever in front of you. Push it to the right to swing the bridge around.

Once you step off the bridge, turn around and interact with the silver bar with the red handle. This is a sort of lock preventing the bridge from swinging farther. This doesn't matter right now, but it'll come up soon.

Turn back around and start heading down the path. There are a few twists and turns along the way, but this path doesn't branch off at all.

Temple

Eventually, you'll arrive at a temple with a familiar red beam nearby. Just like in Hunrath, there are a few steps you'll have to take to get everything in Kaptar straightened out — disable the red beam, turn the power back on and water the Tree.

Head about halfway up the temple steps and keep walking toward the red beam. You'll be able to see a path down to a sphere (complete with wood paneling) that looks a lot like it was cut out of Hunrath.

Inside, you'll find a map of Kaptar and another Swap Machine. There's a window you can look through to see the red beam emitter, but there's no way to get to it and, besides, there's no blue beam to destroy it with.

Back to Hunrath

Use the Swap Machine to travel back to Hunrath. You'll be transported to one of the buildings in Downtown Hunrath. There's a minecart track next door that runs right behind the Swap Machine. How convenient.

Go retrieve your mine cart. If you've been following this guide, it's probably still up the canyon where you used it to access the dome wall the first time. If you haven't been following this guide and don't know where your cart is, we'd suggest you start following the tracks and maybe try to keep better track of your toys .

Drive the cart back to the building in Downtown Hunrath. You'll have to throw a couple switches along the way, but you're mostly just backtracking the first time you moved the cart.

Once you and the cart are behind the Swap Machine, you can access it through the window. Use it to travel back to Kaptar.

Back up as far as you can and switch to the laser controls. Point the laser at the beam to destroy it.

Use the Swap Machine to hop back to Hunrath and move the cart out of the tunnel, then go back inside the building and use the Swap Machine to travel back to Kaptar one more time.