The design of the LHC and future colliders aims their operation with high intensity beams, with bunch population, Np, of the order of 10 11. This is dictated by a desire to study very rare processes with maximum data sample. HEP colliders are engineering structures of many kilometers in length, whose transverse compactness is achieved by the application of the superconducting technologies and limitations of cost. However the compactness of the structural elements conceals and potential danger for the stable work of the accelerator. This is because a high intensity beam of positively charged particles (protons, positrons, ions) creates around itself an electric self-field of very high intensity, 105 − 106 V/cm. Being located near the conducting surfaces, at the distances of 1-20 mm away from them, the field of such bunches activates the field emission of electrons from the surface. These electrons, in addition to electrons from the ionization of residual gases, secondary electrons and electrons knocked out by synchrotron radiation, contribute to the development of a dense electron cloud in the transport line. The particles of the bunch, being scattered on the dense electron cloud with Ne ∼ Np, leaves the beam and may cause noticeable damage. The paper presents an analysis of the conditions, under which the field emission in the LHC collimator system may become a serious problem. The analogous analysis of a prototype of the International Linear Collider (ILC) project, USLC, reveals that a noticeable field emission will accompany positron bunches on their entire path during acceleration.