  The WT scheme, a piecewise polynomial force interpolation scheme with
time-step dependency, is proposed in this paper for relativistic
particle-in-cell (PIC) simulations. The WT scheme removes the lowest order
numerical Cherenkov instability (NCI) growth rate for arbitrary time steps
allowed by the Courant condition. While NCI from higher order resonances is
still present, the numerical tests show that for smaller time steps, the
numerical instability grows much slower than using the optimal time step found
in previous studies. The WT scheme is efficient for improving the quality and
flexibility of relativistic PIC simulations.
