“…We think that the mechanism responsible for this behavior is that the MW beam accelerates background electrons to high energies which ionize the gas to form a plasma channel through which it propagates as predicted by Bogomolov et al, 1987 [34]. We developed a simple 1D analytical model [42,43] which explains this process of self-channeling and is the result of the non-monotonic behavior of the electron impact ionization cross-section which for He has a maximum at~150 eV and decreases by more than an order of magnitude for electron energies above 10 keV [54]. If we assume a background electron density n 0 ≤ 10 5 cm −3 , then for a microwave beam of Gaussian distribution around r, we obtain an ionization electron density by ln[n e (r, t)/n 0 ] = n g t 0 v(r, t )σ i [w(r, t )]dt , where n g is the gas number density, v the electron velocity and w the electron energy.…”