  A target composition scheme to optimize the combined proton acceleration
regime is presented and verified by two-dimensional particle-in-cell (2D PIC)
simulations by using an ultra-intense circularly-polarized (CP) laser pulse
irradiating an overdense hydrocarbon (CH) target, instead of a pure hydrogen
(H) one. The combined acceleration regime is a two-stage proton acceleration
scheme combining the radiation pressure dominated acceleration (RPDA) stage and
the laser wakefield acceleration (LWFA) stage sequentially together. With an
ultra-intense CP laser pulse irradiating an overdense CH target, followed by an
underdense tritium plasma gas, protons with higher energies (from about $20$
GeV up to about $30$ GeV) and lower energy spreads (from about $18\%$ down to
about $5\%$ in full-width at half-maximum, or FWHM) are generated, as compared
to the use of a pure H target. It is because protons can be more stably
pre-accelerated in the first RPDA stage when using CH targets. With the
increase of the carbon-to-hydrogen density ratio, the energy spread is lower
and the maximum proton energy is higher. It also shows that for the same laser
intensity around $10^{22}$ $Wcm^{-2}$, using the CH target will lead to a
higher proton energy, as compared to the use of a pure H target. Additionally,
proton energy can be further increased by employing a longitudinally negative
gradient of a background plasma density.
