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Thermally induced refractive index gratings in Yb-doped fibers lead to transverse mode instability (TMI) above an average power threshold,which represents a severe problem for many applications.To obtain a deeper understanding of TMI,the evolution of the strength of the thermally induced refractive index grating with the average output power in a fiber amplifier is experimentally investigated for the first time.This investigation is performed by introducing a phase shift between the refractive index grating and modal interference patte,which is obtained by applying a pump power variation to the fiber amplifier.It is demonstrated that the refractive index grating is sufficiently strong to enable modal energy coupling at powers that are significantly below the TMI threshold if the induced phase shift is sufficiently large.The experiments indicate that at higher powers,the refractive index grating becomes more sensitive to such phase shifts,which will ultimately trigger TMI.Furthermore,the experimental results demonstrate beam cleaning above the TMI threshold via the introduction of a positive phase shift.This finding paves the way for the development of a new class of mitigation strategies for TMI that are based on controlling the phase shift between the thermally induced refractive index grating and modal interference patte.