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We analyze the propagation of a short intense laser pulse in underdense cold plasma. When no electron cavitation is present, a global invariant H is obtained, and its relation with self-focusing is studied. For relativistic self-focusing, H0 is a sufficient and necessary condition. For relativistic and ponderomotive self-focusing, H0 is sufficient but not necessary. Numerical simulations are performed to confirm the above points.
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Chen et al. (1993) studied this question.
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