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

A linear model of synergetic current drive with lower-hybrid wave and electron cyclotron wave