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We present the macroscopic scaling of high harmonics generated by two-color laser pulses interacting with Ne gas in a hollow waveguide. We demonstrate that the divergence of harmonics is inversely proportional to the waveguide radius and harmonic yields are proportional to the square of the waveguide radius when the gas pressure and waveguide length are chosen to meet the phase-matching condition. We also show that harmonic yields are inversely proportional to the ionization level of the optimized two-color waveform with proper gas pressure if waveguide radius and length are fixed. These scaling relations would help experimentalists find phase-matching conditions to efficiently generate tabletop high-flux coherent soft x rays for applications.United States. Air Force Office of Scientific Research (FA9550-14-1-0255

Macroscopic scaling of high-order harmonics generated by two-color optimized waveforms in a hollow waveguide