Steady-state FEL: particle dynamics in the FEL portion of a two-beam accelerator Page: 4 of 37
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beam radius is assumed small compared with the waveguide dimensions. The 1-D
FEL equations for a TE mode are:2
d'I = ~- asawsin , la)
dz c Yj
d_= (kw - 6ks) - _ (1 + aw - 2aw as cos 'j) + (lb)
dz 2cy2 dz
das = 1p, eff aw <sin > - mas , (c)
dz 2 ac Y
d _p,eff aw <coss,,
dz 2 wcas Y
where j is an index denoting a particular particle and <> indicates an
average over particles. These equations are an extension of the KMR
equations for an FEL. In these equations, the dispersion relation for a
waveguide relates w and ks. The factor 6ks results because the phase
velocity of radiation in a waveguide is not equal to c. Specifically for a
ks = [(C2 - (21)2 - (2bfn)2]% , (2a)
c2 a b
ks = - ks ,(2b)
where a and b are respectively the x and y dimensions of the waveguide. It is
also important to note that the plasma frequency in equations (lc) and (ld) is
an effective plasma frequency given by
2 8TeI 3
p,eff = 8 m Ia , (3)
where I is the total beam current and m and e are respectively the electron
mass and charge. The factor a in Eq. (lc) is a loss factor meant to model
the removal of microwave power from the FEL waveguide.
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Sternbach, E. & Sessler, A.M. Steady-state FEL: particle dynamics in the FEL portion of a two-beam accelerator, article, September 1, 1985; [Berkeley,] California. (digital.library.unt.edu/ark:/67531/metadc1111506/m1/4/: accessed January 16, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.