  The design of the LHC and future colliders aims their operation with high
intensity beams, with bunch population, $N_p$, 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, $10^5 - 10^6$ 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 $N_e\sim N_p$, 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.
