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We study in this paper the dynamics of the field and plasma in the discharge column created by the Bessel (axicon-focused) laser beam in homogeneous gas. The investigation is based on the model of the axially symmetric discharge in the field of a rotating cylindrical wave converging at a given angle to the axis of symmetry. The transverse component of electric field is circular-polarized at the axis; its undisturbed radial profile (in the absence of plasma) is the zero order Bessel function. We focus on the effect of the natural plasma waves generation considered previously for other types of the optical and microwave discharges. The spatiotemporal evolution of the plasma density and electric field is calculated numerically based on the vector wave equation for the slow time envelope of the field, constitutive equation of plasma as a medium with a spatial dispersion, and known expressions for the impact, tunnel and multiphoton ionization rates. It has been found that the scenario of the breakdown process depends greatly on the convergence angle of the wave. If this angle is less than some critical value (/spl sim/25/spl deg/), the maximum plasma density approximately corresponds to the condition of the total internal reflection. However, at the angle exceeding the critical one, the plasma density at the axis increases in the sharpening regime and passes the critical point, after that the fast ionization wave containing the plasma, resonance point at the leading front propagates in the radial direction. This process is accompanied by the sharp growth of the incident wave absorption and the resonance excitation of high intensity Langmuir wave in the plasma The following increase of the plasma density in the discharge volume results in the adiabatic frequency up-conversion of the excited Langmuir oscillations and the resonant excitation of the surface plasmon ("geometrical" resonance) of the produced plasma. The resonance effects considered change sharply the value an- spatial distribution of ionization rate and give rise to appearance of the upshifted frequencies in the spectrum of radiation reflected by plasma column.