Nuclear Waste is a byproduct of running the Fission Reactor, it is Radioactive and if it is released it will contaminate the environment.
A Small amount is stored in the Reactor itself but should be piped into other blocks for storage or use. Note that only designated storage blocks (Currently only the Radioactive Waste Barrel), pipes and machines that use it for recipes (The Solar Neuron Activator and the Pressurized Reaction Chamber) will accept it. It can not be inserted into other blocks. The Gauge Dropper similarly can not extract or delete it.
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