  Energy-frontier accelerators provide powerful tools performing high precision
measurements confirming the fundamental of the physics and broadening new
research horizons. Such machines are either driven by circular or linear
accelerators. The circular machines, having the center-mass (CM) energy values
reaching 200 GeV (for leptons) and above, experience beam energy loss and
quality dilution, for example, due to synchrotron radiation, limiting the
overall CM energy achievable and requiring a constant energy top-up to
compensate the loss and the beam quality dilution. Linear colliders overcome
these limitations, while the finite capabilities of generating high average
current beams limits the luminosity. This is partially compensated by the
quality of the colliding beams. In this work, we suggest a novel design of
circular-linear accelerator based on the merging of the "non-emitting",
low-energy storage rings and energy recovery linear accelerators. We suggest
using the recently considered dual-axis asymmetric cavities to enable the
operation of such a system, and in particular the energy recovery from spent,
high-intensity beams. The machine considered, under the scope of the
SNOWMASS-2021 initiative, can be potentially used to reach ultimate energy
frontiers in high-energy physics as well as to drive next generation light
sources. The merging of circular and linear systems, and applications of dual
axes cavities, should allow the maintaining of high beam quality, high
luminosity, and high energy efficiency - "The Best of Both Words". It also
offers a flexible energy management, opening clear opportunity for reducing the
running cost. We note that the numbers shown in the paper are for illustration
purpose and can be improved further.
