Modulation compression for short wavelength harmonic generation Page: 3 of 9
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Beam Modulator ChirperA Bunch Compressor A ChirperB Bunch Compressor B
FIG. 1: A schematic plot of the accelerator lattice for modulation compression.
porting through above ideal accelerator lattice using a one-dimensional model. The beam is as-
sumed to be longitudinal frozen in most part of the lattice except that in the bunch compressors.
The initial longitudinal phase space distribution function before the laser modulator is given as,
fo(zo, 8o) = F(zo, o/a), where zo is the longitudinal bunch length, 8o = AEo/Eo is the relative
energy deviation, a is a constant related to the initial energy spread. After the laser modulator,
the energy deviation becomes, 8i = 8o + A sin(kzo), where A = V1/E1 is the initial laser mod-
ulation amplitude, &i = AE1/E1, El = Eo, and k is the modulation wave number. Now, the
beam is transported through the chirper A that will introduce an energy-bunch length correla-
tion, 82 = D081 + h'z1, where h0 = d82/dz2 is the energy chirp across the bunch length of the
beam, 82 = AE2/E2, and D0 = E1/E2 denotes the ratio of total beam energy before and after the
chirper A. Next, the beam passes through the bunch compressor A. The longitudinal bunch length
becomes, z3 = z2 + R5662, where R56 is the momentum compaction factor of the bunch compressor
A. After the bunch compressor, the phase space distribution becomes
1 8 b3 - h0Cz3 - CD0Asin(k(z3 - R5663))) (1)
f3(z3, b3) = -F(z3 - R'663' CDacx
where C = 1/(1 + R56h0) is the bunch compression factor of the first bunch compressor A. Then
the beam is transported through the chirper B that will introduce another energy-bunch length
correlation, 84 = D663 + hz3, where hV is the energy chirp across the bunch length of the beam
caused by the second chirper, Db = E3/E4 denotes the ratio of total beam energy before and after
the chirper B, and 84 = AE4/E4. The phase space distribution becomes
f4(z4, 84) = F(z4(Db + hbR56)/Db - R56/Db64,
84 - (h + haDbC)z4 - CDbDaAsin(k(z4(Db + R56hb)/Db - R56/Db8))
If the second chirper is set up so that h9 = -haDbC, then the distribution function can be written
1 a R b - CDbDaAsin(kCz4 - kRg6/Db8)
f4(z4, 64) = abF(Cz4 - R56/D 4, D'a ) (3)
Finally the beam is transported through the second bunch compressor B. The longitudinal bunch
length of the beam becomes, z5 = z4 + R6,64, where R6, is the momentum compaction factor of
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Qiang, J. Modulation compression for short wavelength harmonic generation, article, January 11, 2010; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc1014715/m1/3/: accessed January 22, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.