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Applying a bi-local mean field approximation to the fractional quantum Hallstate of $\nu=1/3$, we obtain charged and neutral vortex mean field solutionsnumerically. We calculate the mean field energy and the fluctuationcorrections. The charged vortex has a fractional charge and a fractionalangular momentum. The neutral vortex is a bound state of two charged vorticesand has a zero charge and a zero angular momentum. The creation energy of theneutral vortex is about a half of the pair creation energy of two chargedvortices. The magnetic field dependence of the gap energy agrees with theLaughlin's quasiparticle gap energy.Comment: 22 pages, EPHOU-94-001, 8 figures available as a hard copy via  air-mai

Charged and Neutral Vortex Excitations in a Mean Field Theory for the Fractional Quantum Hall Effect