If you agreed to help, this quest will start immediately after completing Fire Support. Check the whole station first for various items and dump them to your workbenches in your settlements if you want. Once ready, talk to Paladin Danse again to start the mission.
Follow him on your way to Arcjet Systems. You may encounter raiders along the way. Don't worry about stopping and looting whatever you find along the way since Danse will not proceed without you. Continue following him and take out any threats that may come along your way.
Once inside ArcJet Systems, it's time to explore the area. There isn't that much loot here so take what you want then follow Danse. Talk to him after stumbling upon the wrecked security bots. Continue following him deeper. Once you reached the lab exterior, operate the terminal in the corner to get the Arcjet Lab password. Now operate the terminal in the middle to use the password. Select the option to open the doors.
Upon opening the door, three synths will attack. Destroy them and loot their weapons. Continue to the next room where more synths will be waiting. Destroy them all. In the upper floor there are weapon, armor, and chem stations. There's also an Expert Terminal and Expert Safe. On the shelf in the room with the Chem station is a Novice Toolbox. Loot the area as necessary.
There's also a Novice Door in that same room. Unlock it and collect any loot you find. Go upstairs and before leaving the room, find the Tesla Science on the table with the CEO's terminal beside the couch. Outside there's an automatic turret which you can disable by hacking the repair terminal inside the room to the left of the turret. However, Danse or you'll have a much easier time destroying it instead. There's another auto-turret along the way so destroy it as well. There are some bobby pins and a mentat in restroom. Continue following Danse downstairs to reach the Engine Core.
Once inside, go downstairs and you'll have to find a way to restore Power. Grab the Junkjet heavy weapon from the table. Go to the backroom and collect the Fusion Core from the generator there. Next, hack the Novice terminal. After successfully cracking it, select the Power Options to activate the auxiliary power.
Shortly more enemies will arrive. Help Danse in repelling them. You also have the option to press the big red button to test fire the engine. This should help destroying most of the synths.
After clearing the area, activate the elevator to go up then proceed to the control room. Kill all the synths and one of them should be carrying the Deep Range Transmitter. Loot it from the synth's body then activate the elevator nearby to reach the surface.
Exit the building and talk to Danse. He'll give you his personal laser rifle, Righteous Authority. He will also offer you to join the Brotherhood of Steel. You can select that you're unsure but you're welcome to join them by talking to Danse in the Cambridge Police Station.