Fig. 1. Calculated plasma electron-density profiles as a function of radial position with axis density and matched spot size for a parabolic channel (black line) compared with a channel with an component with at the same (blue line) and a channel at the same (red line), respectively.

Fig. 2. (a) The cylindrical 2D-vector integral transform calculation result of an input plane wave electric field with wavelength diffraction propagation by an ideal scattering boundary in a domain, where the data on the negative side of the radial axis are obtained by mirroring. (b) The normalized transverse profile at from calculation data (black line) and fitting the profile with the theoretical function (blue line) and the approximate Gaussian function (red line) for the channel-guided laser requirement.

Fig. 3. (a) The cylindrical PIC simulation result of a laser with wavelength propagating in plasma with ideal matched spot size and , where the data on the negative side of the radial axis are obtained by mirroring. The simulation domain corresponds to plasma channel radius and length cm. (b) The coupling parameter varying along the z-direction between the fitting to the simulation data via Equation (15) at every position in the solid blue line and the calculation values of Equation (15) based on the initial set simulation parameters in the broken red line. The two show good consistency after laser propagating at 1.2 cm.

Fig. 4. (a) Schematic overview of the experimental setup. Laser pulses propagate from right to left along a capillary as the axis in the z-direction. The capillary is carried by a six-axis mover. Gas is injected from pipes to fill the capillary. Electrodes connected to the incentive source are located at both ends. The imaging system consisting of a single object lens and a CCD is downstream. (b) Typical experimentally measured transverse laser spot intensity distributions at the capillary exit plane during plasma discharge for plasma channels with (the upper subfigure) and (the lower one). (c) Discharge phenomenon of a gas-filled capillary viewed from the side.

Fig. 5. Current waveform measured in the No. 9 experiment shown with a solid red line and fitting results with the waveform based on Equation (19) shown with a broken red line, reconstructed evolution of from experimental data shown with blue triangle marks and an exponential decline tendency of evolution shown with a dotted blue line. Both of the red curves above have the -axis on the right in red. Both of the blue curves have the -axis on the left in blue. Subfigure groups made up of a lower one, a measured profile and an upper one, a reconstructed profile via fitting results, in the same column from left to right, correspond to a laser pulse propagating through plasma channels at 245, 343, 458, 537 and 644 ns, respectively. All subfigures are under the unified ruler and color bar placed in the upper right corner inside.

Fig. 6. (a) Measured (solid lines) and fitting (broken lines) current waveforms of Style 1 in red, Style 2 in blue and Style 3 in black with , and respectively in the No. 9, No. 10 and No. 1 experiments correspondingly. (b) Reconstructed evolutions of density profile coefficient shown with triangle marks and exponential decline tendencies shown with broken lines with various styles of waveforms in No. 9 (red), No. 10 (blue) and No. 1 (black) experiments.

Fig. 7. Reconstructed evolutions of density profile coefficient shown with triangle marks and exponential decline tendencies shown with broken lines (a) with various high voltages , 20, 25 and 28 kV for He plasma in the No. 1 (red), No. 2 (blue), No. 3 (black) and No. 4 (green) experiments, (b) with various high voltages , 20, 25 and 28 kV for Ar plasma in the No. 5 (red), No. 6 (blue), No. 7 (black) and No. 8 (green) experiments. (c) Scaling of the exponential decline rate with high voltages for He plasma shown with the light-blue line and Ar plasma shown with the light-red line. The circle marks are in colors corresponding to those in (a) and (b).

Fig. 8. Reconstructed evolutions of the density profile coefficient shown with triangle marks and exponential decline tendencies shown with broken lines (a) with various capillary diameters , and in the No. 11 (red), No. 9 (blue) and No. 12 (black) experiments, and (b) with various pressures , 90 and 100 Torr in the No. 13 (red), No. 14 (blue) and No. 9 (black) experiments. (c) Scaling of the exponential decline rate with diameters. The circle marks are in colors corresponding to those in (a). (d) Scaling of the exponential decline rate with pressures. The circle marks are in colors corresponding to those in (b).

Fig. 9. Reconstructed profile evolutions shown with triangle marks and exponential decline tendencies shown with broken lines from measurements with laser wavelength nm of the front (red) end and nm of a Q-switched laser (blue), respectively.