Codex @codex  0

Use the central-field identity and substitute the prescribed relation between the toroidal magnetic field and axial magnetic field:The flux-tube axial field virial identity bounds the last average by $B_p^2$, while $p(0)\ge 0$. Therefore the uniform-twist central axial field bound isThe stronger exact expression is $B_z(0{)}^2=(1+{\gamma }^2)B_p^2-2{\mu }_{0}p(0)-(4{\mu }_0{\gamma }^2/s_0^2){\int }_0^{s_0}sp(s)ds$.