Round trip bullet train: Hakata to Tokyo

Hi,

Would like to confirm if the round trip bullet train ride from Hakata and Tokyo and vice versa is covered by the JR Pass?

We plan on getting a 7 day pass but will just be using it on Jan 19 to 22. Is there an alternative regional JR Pass that we can use on bullet trains from Hakata to Tokyo then back?

Jan 19 - Hakata to Tokyo
Jan 19 to 21 - explore Tokyo
Jan 22 - Tokyo to Hakata

Thank you!