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We analyze the motion of the plasma critical layer by two different processesin the relativistic-electron laser-plasma interaction regime ($a_0>1$). Thedifferences are highlighted when the critical layer ions are stationary incontrast to when they move with it. Controlling the speed of the plasmacritical layer in this regime is essential for creating low-$\beta$ travelingacceleration structures of sufficient laser-excited potential for laser ionaccelerators (LIA). In Relativistically Induced Transparency Acceleration(RITA) scheme the heavy plasma-ions are fixed and only trace-density light-ionsare accelerated. The relativistic critical layer and the acceleration structuremove longitudinally forward by laser inducing transparency through apparentrelativistic increase in electron mass. In the Radiation Pressure Acceleration(RPA) scheme the whole plasma is longitudinally pushed forward under the actionof the laser radiation pressure, possible only when plasma ions co-propagatewith the laser front. In RPA the acceleration structure velocity criticallydepends upon plasma-ion mass in addition to the laser intensity and plasmadensity. In RITA, mass of the heavy immobile plasma-ions does not affect thespeed of the critical layer. Inertia of the bared immobile ions in RITA excitesthe charge separation potential whereas RPA is not possible when ions arestationary.

Motion of the Plasma Critical Layer During Relativistic-electron Laser Interaction with Immobile and Comoving Ion Plasma for Ion Acceleration