  Magnetised plasma turbulence can have a multiscale character: instabilities
driven by mean temperature gradients drive turbulence at the disparate scales
of the ion and the electron gyroradii. Simulations of multiscale turbulence,
using equations valid in the limit of infinite scale separation, reveal novel
cross-scale interaction mechanisms in these plasmas. In the case that both
long-wavelength (ion-gyroradius-scale) and short-wavelength
(electron-gyroradius-scale) linear instabilities are driven far from marginal
stability, we show that the short-wavelength instabilities are suppressed by
interactions with long-wavelength turbulence. The observed suppression is a
result of two effects: parallel-to-the-field-line shearing by the long
wavelength $\mathbf{E} \times \mathbf{B}$ flows, and the modification of the
background density gradient by long-wavelength fluctuations. In contrast,
simulations of multiscale turbulence where instabilities at both scales are
driven near marginal stability demonstrate that when the long-wavelength
turbulence is sufficiently collisional and zonally dominated the effect of
cross-scale interaction can be parameterised solely in terms of the local
modifications to the mean density and temperature gradients. We discuss
physical arguments that qualitatively explain how a change in equilibrium drive
leads to the observed transition in the impact of the cross-scale interactions.
