Multiple space and time scales arise in plasma turbulence in magnetic confinement fusion devices because of the smallness of the square root of the electron-to-ion mass ratio (m e /m i ) 1/2 and the consequent disparity of the ion and electron thermal gyroradii and thermal speeds. Direct simulations of this turbulence that include both ion and electron space-time scales indicate that there can be significant interactions between the two scales. The extreme computational expense and complexity of these direct simulations motivates the desire for reduced treatment. By exploiting the scale separation between ion and electron scales, and expanding the gyrokinetic equations for the turbulence in (m e /m i ) 1/2 , we derive such a reduced system of gyrokinetic equations that describes cross-scale interactions. The coupled gyrokinetic equations contain novel terms which provide candidate mechanisms for the observed cross-scale interaction. The electron scale turbulence experiences a modified drive due to gradients in the ion scale distribution function, and is advected by the ion scale E ×B drift, which varies in the direction parallel to the magnetic field line. The largest possible crossscale term in the ion scale equations is sub-dominant in our (m e /m i ) 1/2 expansion.Hence, in our model the ion scale turbulence evolves independently of the electron scale turbulence. To complete the scale-separated approach, we provide and justify a parallel boundary condition for the coupled gyrokinetic equations in axisymmetric equilibria based on the standard "twist-and-shift" boundary condition. This approach allows one to simulate multi-scale turbulence using electron scale flux tubes nested within an ion scale flux tube.Scale-Separated Turbulence otherwise questionable. Examples may be found in [11][12][13][14][15][16][17]. Nonetheless, it is known that electron scale turbulence can drive experimentally relevant levels of transport in some cases [13]. Electron scale transport has been observed on NSTX [18], and is a candidate for anomalous transport on MAST [14,17].Without directly simulating or observing the full multi-scale turbulence, it is difficult to assess to what extent there are cross scale interactions in the turbulence, and whether or not all scales will contribute significantly to the transport. Unfortunately, studying multi-scale turbulence through direct simulation is made very challenging by the size of (m e /m i ) 1/2 for a realistic deuterium plasma, (m e /m i ) 1/2 ∼ 1/60, which determines the separation of ρ th,e /ρ th,i ∼ (m e /m i ) 1/2 and v th,i /v th,e ∼ (m e /m i ) 1/2 . For example, if one wanted to extend the resolution of a well-resolved ion scale simulation to capture both the a/v th,i and a/v th,e time scales then one must increase the resolution in time by approximately v th,e /v th,i ∼ (m i /m e ) 1/2 . To resolve length scales perpendicular to the magnetic field line comparable to both ρ th,i and ρ th,e one must increase the resolution in both the perpendicular directions by ρ th,i /ρ th,e ∼ ...