High Brightness Electron Beam Diagnostics and their ... - CASA
High Brightness Electron Beam Diagnostics and their ... - CASA
High Brightness Electron Beam Diagnostics and their ... - CASA
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harmonicwithproperchoiceoftheKvaluewhichcanbesetbychangingtheundulatorgap5. emissionassociatedwiththethirdharmoniccanbealmostaspowerfulastheemissionatrst Suchfeatureisveryinterestingforproducingshorterwavelengthlight.IntheIRFELoperationat thethird(=1=3)<strong>and</strong>fth(=1=5)harmonichasbeenachieved. fortheIRFELoperation(K=1:00<strong>and</strong>optionally1:39).Inthisgureoneseesthatspontaneous<br />
Figure2.9:Normalizedpoweroftheon-axisundulatorradiationforthetwodierentvalueofK consideredfortheIRFEL.<br />
oftheorderofthewavelength.Thespacingbetweenthetwomirrorsischosensothatthepulse OncearadiationpulseatthewavelengthgiveninEqn.(2.22)hasbeenestablishedviatheinteractionofanelectronbunchwiththemagneticeldoftheundulator,itisrecirculatedinaresonator cavitythatconsistsintwosphericaldielectricmirrors.Oneofthemisatotalreectorwhilethe otherisapartiallyreector<strong>and</strong>out-coupleradiationthroughasmallaperturewithadiameter 2.5.2AmplicationoftheSpontaneousUndulatorRadiation<br />
willcopropagatewiththenextincomingelectronbunch<strong>and</strong>thereforethelengthofthecavityis beasub-multipleof8:003minthecaseoftheIRFEL.Forelectronsinjectedattheresonantenergy L=c=(2)(whereisthetemporalspacingbetweentwoconsecutiveelectronbunches)<strong>and</strong>should<br />
phase,eachelectroninthebunchcan(i)giveenergytotheeld<strong>and</strong>decelerate,thatis\stimulated emission";(ii)takeenergyfromtheradiationeld<strong>and</strong>accelerate,thatis,\absorption".Thusifwe considerabunchofelectronwhosecenterenergyisresonantenergy,wecouldeasilyimaginethat ofenergybetweentheelectron<strong>and</strong>theradiation.Hence,dependingonthevalueoftherelative radiationelectriceld(!v:!E)isnon-zero<strong>and</strong>slowlyvaryingsothattherecanbeanetexchange ponentparalleltotheopticalpulseelectroneld,thescalarproductofanelectronvelocity<strong>and</strong>pulsewill,inprinciple,remainconstant.Sincetheelectronbeamvelocityhasanonzerocom- r=12qus(1+K2),therelativephasebetweentheelectrons<strong>and</strong>thecopropagatingradiation<br />
5TheKvaluedependenceonthegapdisoftheformK/exp(d=u)<br />
Intensity (a.u)<br />
0.5<br />
0.4<br />
0.3<br />
0.2<br />
0.1<br />
0<br />
0.4<br />
0.3<br />
0.2<br />
0.1<br />
0<br />
0 2 4 6 8 10<br />
Harmonic Number<br />
K=1.00<br />
K=1.39
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