The longitudinal and radial wakefields produced by a single laser pulse in a plasma are calculated. The limits on the laser wakefield acceleration because of diffraction, optical guiding, and energy loss due to radiation are examined. In particular for a bi-Gaussian laser beam, the energy gain about 4.6 GeV/cm s is estimated. A general constraint on the plasma density is presented. All the limits are compared and a localized density channel of width 4.6 x 10(-5) cm is proposed. (C) 1999 American Institute of Physics. [S0034-6748(99)03304-3].