The effects of weakly felativistic trapped electrons on whistler instability in the magnetic-mirror configuration are studied. Using the simplified box model(1) the eigen equation is solved with perturbative approach including the weakly relativistic trapped effects. It is found that whistler instability can be driven by the anisotropic hot electrons, while relativisity increases the threshold value of instability and descreases the growth rate as well as makes the unstable modes shifting to low frequency.
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