  The recently discovered twist-bend nematic phase, $\rm N_{tb}$, is a
non-uniform equilibrium nematic phase that presents a spontaneous bend with a
precession of the nematic director, $\textbf{n}$, on a conical helix with a
tilt angle $\theta$ and helical pitch $P$. The stability of the $\rm N_{tb}$
phase has been recently demonstrated from the elastic point of view by
extending the Frank elastic energy density of the nematic phase to include the
symmetry element of helical axis, $\bf t$. In the present communication, we
investigate the influence of an external bulk field (magnetic or electric) on
the pitch of the $\rm N_{tb}$ phase. For a material with positive magnetic
susceptibility anisotropy, when the magnetic field $\bf{H}$ is parallel to the
helical axis, $\bf{t}$, the field modifies the coupling parameter between the
director and the helical axis, thus shifting the interval of values for which
this coupling results in the $\rm N_{tb}$ phase. If $\bf{H}$ is perpendicular
to $\bf{t}$, it is shown that the pitch of the nematic director $\bf n$
precession increases with $\bf{H}$, and at a critical value of $H_c$ it becomes
infinite as in a cholesteric liquid crystal, that is, one gets a uniform
orientation of n. Our results include the behaviour of a cholesteric under
field as a limiting case.
