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In the last chapter we mentioned the fact that only the fractional part of the spin tune is measurable. Similar to the fact that a traveler going
around a circle ends at the same spot his fellow does when going around in the other direction, we can't be a priori sure when observing a ``resonant'' frequency that this isn't just the mirror frequency of the resonance. According to the Nyquist Theorem we can only measure how much below or above we are from the halfinteger, but not on which side or in mathematical terms, does the measured frequency correspond to
or
. For example the frequency 500 kHz corresponds to a beam energy of 2.372 GeV but also to the mirror energy at 2.475 GeV; this ambiguity is resolved in the following way:
The energy of the beam can be slightly varied using a different RF main frequency. At SLS the RF main frequency is 500 MHz. Beam energy and RF main frequency are related by the momentum compaction factor :

(52) 
Therefore a change in the RF main frequency will lead to a change in beam energy. If the RF main frequency is changed to a lower value, the beam energy will rise. If the resonant frequency increases as well it is the ``real'' resonance; if however the resonant frequency decreases, it is the mirror resonance and viceversa. Thus this procedure always requires a second measurement of the resonant frequency.
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Simon Leemann
20020315