The stability of an electronic plasma in a large-amplitude dipolar fie
ld is analyzed. In such a wave the relativistic electron mass variatio
n must be taken into account and in an overdense plasma an instability
arises. The corresponding weakly relativistic theory of Tsintsadze [S
ov. Phys. JETP 32, 684 (1971)] is extended to the fully relativistic r
egime. The growth rate of the instability can attain a significant fra
ction of the dipolar field frequency. The relevance of this instabilit
y to the fast ignitor concept is discussed. (C) 1998 American Institut
e of Physics.