2 - CERN Accelerator School
2 - CERN Accelerator School
2 - CERN Accelerator School
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The solution of the system is<br />
Scattering through thin foil -<br />
VI<br />
This can be solved exactly, or by assuming that the<br />
relative emittance growth is small, then<br />
emittance growth is now only half<br />
π<br />
Δε<br />
rms = θ 2β<br />
rms 0<br />
4<br />
1, β1<br />
Twiss<br />
⎡<br />
⎤<br />
⎢ π θ 2 ⎥<br />
β = β ⎢1−<br />
rms<br />
1 0<br />
⎥<br />
⎢ 4 ε ⎥<br />
⎢⎣<br />
rms ⎥⎦<br />
NB: NB: the the emittance<br />
growth is now only half<br />
of of the the previous estimate!<br />
Downstream of of the the foil foil the the transfer line<br />
line<br />
should be be matched using the the new new Twiss<br />
parameters α1, α1, β1<br />
Massimo Giovannozzi CAS - 2-14 14 October 2005 11<br />
A<br />
β1<br />
β<br />
0<br />
2<br />
1<br />
2<br />
=<br />
−<br />
A<br />
2<br />
0<br />
A<br />
A<br />
A<br />
2<br />
0<br />
2<br />
0<br />
2<br />
1<br />
2<br />
=<br />
2β<br />
0<br />
θ<br />
2<br />
rms
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