Adiabatic plasma lens designs for the final focus of TeV electrons

The successful operation of future e+ e- linear colliders (LC) depends on tightly focused beams around nanometer-scale spot sizes at the interaction point to achieve high luminosity. Traditional beam delivery systems face challenges due to chromatic effects and the requirement of small emittance. To overcome these challenges, the concept of adiabatic plasma lenses has emerged as a potential solution. In an azimuthally symmetric adiabatic plasma lens, the beams experience a linear focusing force of $m\omega_p^2 r/2$ proportional to the plasma density. An adiabatic plasma upramp has previously been proposed to provide an increasing focusing force along the beam propagation. However, the tightly focused beam of LC can induce ion motion, enhancing the focusing strength of the plasma lens and reducing the required plasma density. However, synchrotron radiation limits the minimum achievable spot size. Based on this observation, we investigate the possibility of a plasma lens for final focus of the electron arm of 2 TeV-15 TeV COM LC using QuickPIC with adaptive mesh refinement and QPAD. We analyze ion motion effects and introduce a novel approach utilizing a narrow drive beam to enhance the focusing force slope by pulling more ions toward the axis. This design increases the luminosity by two orders of magnitude and reduces the required plasma density by up to four orders of magnitude, with a redesigned plasma ramp profile to mitigate energy loss.