On Peculiarities of Betatron Oscillations of Accelerated Electron Bunches in Capillary Waveguides

Figure 1

The maximum in the value of the wakefield potential on the capillary axis, , normalized to the value , as a function of the propagation length of the laser pulse in the capillary, for the dimensionless maximum amplitude of the laser field , laser wavelength , plasma wave gamma factor , exponential width of the Gaussian transverse distribution of the laser field at the capillary entrance , the full width of the laser pulse at half its maximum intensity (at ), ; and a silicon capillary waveguide () has a radius of (the ratio is close to the condition for the best laser energy input into a capillary [26]). The length along the capillary is normalized on the dephasing length . The complete numerical solution (14) (with ) and the simplified analytical solution (18) with 2 and 6 modes are shown by different curves (see figure legend).