Verb Meaning to Process Energy?

In this instance, I would use the verb channel. It's often heard together with 'energy'.

Lexico gives this definition:

  1. Direct towards a particular end or object.
    ‘the council is to channel public funds into training schemes’

And Collins gives the following examples:

5) If you channel your energies or emotions into something, you concentrate on or do that one thing, rather than a range of things.
Stephen is channelling his energies into a novel called Blue. [VERB noun + into]

Synonyms: direct, guide, conduct, transmit

So your sentence would be:

Joseph channelled the energy he had gathered into something new.