  A linear model of synergetic current drive (SCD) with lower-hybrid wave (LHW)
and electron cyclotron wave (ECW) is proposed to efficiently calculate the
quantitative SCD efficiency and reveal the conditions for the occurrence of
SCD. In this model, the response function dominated by collisions in the
presence of LHW is derived from the adjoint equations by using perturbation and
Green-Function techniques, where the relativistic effect and the trapped effect
are taken into account. The SCD efficiency is compared with the commonly used
ECW current drive (ECCD) efficiency in the parameter space using our linear
model. The results show two features of the synergy effect, One is that it is
inclined to occurs at smaller $y = 2\omega_{c}/\omega$ with the fixed ECW
parallel refractive index $n_{\parallel}$, and the other is that the threshold
values of $y$, at which the synergy effect becomes sufficiently significant,
shifts towards higher values with a decreasing $n_{\parallel}$. The quasilinear
simulation on ECCD and SCD efficiency with a two-dimensional Fokker-Planck code
are consistent with the results of the linear model in trends. Based on the
linear SCD efficiency, criteria for the occurrence and the sufficient
significance of the synergy effect are suggested, which indicate that the
synergy effect is dependent on the power factor that quantifies the degree of
the overlap of the two waves' quasilinear domains, the LHW power, and synergy
electrons. The present work provides a method of quick matching and calculating
of SCD with LHW and ECW, and may be important for the real-time application of
the SCD in future reactors.
