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This article discusses a beam length measurement technique based on the TM_{010} modes of two cavities in frequency domain. Since the TM_{010} pickup monitor has a much better signal-to-noise ratio (SNR) than the other monitors, it can improve the measuring range and resolution limit of the beam length measurement in the frequency domain to achieve the real-time measurement of the pulse duration of the order of 1 ps or less with the resolution of about 10 fs. The root-mean-square length of a beam—which does not necessarily have a Gaussian distribution—can be obtained by choosing the working frequency of the cavity to be much less than the critical frequency of the beam. The modeling and analysis of the above theory were also made simultaneously. The resulting resolution was about 100 fs when the step size was chosen to be 200 fs in this simulation after the higher order mode coupling effect was eliminated and the beam offset was corrected by using the Bessel function. An efficient algorithm was also provided in case the measurement system would achieve the SNR of 112 dB when there could be some issue in signal processing. This algorithm can still provide the length result with the resolution of 3.5  μm for a beam duration of 0.1 ps when the SNR of the difference signal is as low as 10 dB

physical review special topics. accelerators and beams

Subpicosecond beam length measurement study based on the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>TM</mml:mi><mml:mn>010</mml:mn></mml:msub></mml:math>mode

Subpicosecond beam length measurement study based on theTM010mode