mode - CERN Accelerator School
mode - CERN Accelerator School
mode - CERN Accelerator School
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Stabilization of long chains:<br />
the π/2 <strong>mode</strong><br />
Solution:<br />
Long chains of linac cells are operated in the π/2 <strong>mode</strong> <strong>mode</strong>, which is<br />
intrinsically insensitive to differences in the cell frequencies.<br />
Perturbing<br />
<strong>mode</strong><br />
ω<br />
0 6.67 13.34 20.01 26.68 33.35<br />
0<br />
π/2<br />
π<br />
k<br />
Operating<br />
<strong>mode</strong><br />
Perturbing<br />
<strong>mode</strong><br />
<strong>mode</strong> π/2<br />
2 2<br />
Contribution from adjacent <strong>mode</strong>s proportional to f − f with the sign !!!<br />
Contribution from equally spaced <strong>mode</strong>s in the dispersion curve will cancel<br />
each other.<br />
1<br />
0<br />
46
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