This paper studies the special effects of the armature reaction field (ARF) on the SC coils in the field-modulation superconducting (SC) machines (FMSCMs). Through comparing with the conventional SC synchronous machines (SCSMs) with similar structure to the electrically-excited synchronous machine (EESM), some special characteristics of the ARF effect of the FMSCMs are found, namely, the ARF will generate abundant moving harmonics with high amplitudes in the airgap, including the fundamental harmonic, all of which are alternating external magnetic field relative to the SC coils. These alternating harmonics will increase the AC loss, and induce high voltages in the SC coils. In order to weaken the ARF effect, some inhibition methods are proposed from the perspective of electrical machine design. Finally, the proposed combined method of simultaneously adding damper-coils and copper shield layer on the double-stator FMSCM (DS-FMSCM) exhibits an excellent inhibition effect, making the harmonic level of the DS-FMSCM match with that of the SCSM, meanwhile, reducing the induced voltages in the SC coils from several hundred volts to several volts.