Abstract
This article discusses a beam length measurement technique based on the ${\mathrm{TM}}_{010}$ modes of two cavities in frequency domain. Since the ${\mathrm{TM}}_{010}$ 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 $3.5\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$ for a beam duration of 0.1 ps when the SNR of the difference signal is as low as 10 dB.
Highlights
With the development of the free-electron laser (FEL), the basic requirement of the bunch length measurement has been upgraded to be competent to handle the beam that is less than 1 ps
There have been some methods to get the length of the beam, which has the pulse duration of the order of only 1 ps or less, in an FEL facility, such as optical transition radiation method [1] and zero phasing method [2,3]
A realistic difficulty is to find an analog-to-digital converter (ADC) with effective number of bits (ENOB) of 21 bits which has both the dynamic range of 112 dB and the sampling speed of 10 MHz simultaneously, so the output signals from the two TM010 modes have to be mixed to the same frequency
Summary
With the development of the free-electron laser (FEL), the basic requirement of the bunch length measurement has been upgraded to be competent to handle the beam that is less than 1 ps. There are already comparisons between the femtosecond streak camera, the interferometer and the polychromator which detect the reflective optics, the coherent transition radiation (CTR) and the spectrum of CTR and coherent diffraction radiation, respectively [4]. All of these methods will either cost a lot of time to process or it is difficult to get the beam length in less than 1 s, and few methods are nondestructive. The beam length of about 10 ps with the resolution of about 1 ps can be obtained by using this technique when the signals from button or stripline beam position monitors (BPM) are used [12], which makes it unwise to adopt this method directly in FEL
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