Axial velocity (solid line) and (dashed line) as a function of normalized ion-channel frequency for group I and group II orbits.
Illustration of the effect of axial energy spread on the normalized efficiency at the fundamental and the third harmonic radiation in the presence of ion-channel guiding with . is the efficiency of cold beam.
Variation in the saturation length of third harmonic radiation versus energy spread (solid line) and comparing it with the case of applying ion-channel guiding (dashed line).
Variation in the efficiency of third harmonic radiation with variations in the start taper point and the taper slope; ion-channel frequency is and energy spread is .
Variation of efficiency with axial distance z showing the effect of longitudinal energy spread , ion channel, and wiggler magnetic field tapering. (a) group I orbits with ; (b) group II orbit with and ; (c) group II orbit with and .
Variation of saturated third harmonic efficiency with axial energy spread; (dotted line) untapered wiggler and without ion-channel guiding, (dashed line) untapered wiggler with ion-channel frequency , (solid line) tapered wiggler with decreasing slope and with ion-channel frequency .
The bunching parameter of third harmonic |b3 | as a function of distance for (a) a uniform beam; (b) a pre-bunched beam when and (c) . The efficiency of third harmonic versus distance for (d) a uniform beam; (e) a pre-bunched beam when and (f) .
Variation in the bunching parameter of third harmonic versus (a) bunch width and (b) energy spread.
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