  Many high-energy astrophysical systems contain magnetized collisionless
plasmas with relativistic particles, in which turbulence can be driven by an
arbitrary mixture of solenoidal and compressive motions. For example,
turbulence in hot accretion flows may be driven solenoidally by the
magnetorotational instability or compressively by spiral shock waves. It is
important to understand the role of the driving mechanism on kinetic turbulence
and the associated particle energization. In this work, we compare
particle-in-cell simulations of solenoidally driven turbulence with similar
simulations of compressively driven turbulence. We focus on plasma that has an
initial beta of unity, relativistically hot electrons, and varying ion
temperature. Apart from strong large-scale density fluctuations in the
compressive case, the turbulence statistics are similar for both drives, and
the bulk plasma is described reasonably well by an isothermal equation of
state. We find that nonthermal particle acceleration is more efficient when
turbulence is driven compressively. In the case of relativistically hot ions,
both driving mechanisms ultimately lead to similar power-law particle energy
distributions, but over a different duration. In the case of non-relativistic
ions, there is significant nonthermal particle acceleration only for
compressive driving. Additionally, we find that the electron-to-ion heating
ratio is less than unity for both drives, but takes a smaller value for
compressive driving. We demonstrate that this additional ion energization is
associated with the collisionless damping of large-scale compressive modes via
perpendicular electric fields.
