1 Introduction

The Shanghai soft X-ray free electron laser ^[1](SXFEL) is an official XFEL facility. It will provide a fully coherent light source and serve to verify key FEL schemes and technologies covering two-stage cascaded High-Gain Harmonic Generation (HGHG), with an expected capacity to generate 9 nm X-ray laser by adopting an FEL frequency doubling of ultraviolet band seeded laser of 265 nm^[2]. The SXFEL facility, constructed on basis of the HGHG or EEHG scheme, has a strict beam position resolution requirement, being 1 μm at 0.5 nC, to ensure that the electron beam overlaps the generated photon beam stringently and that both can pass through the entire undulator section. Among the various types of BPMs, the cavity BPM can adopt to a resonant cavity structure and through the use of antisymmetric characteristic modes, coupled from the cavity, to measure beam position and can reach a sub-micrometer even nanometer level position resolution has become a critical beam instrumentation component for FEL^[3,4].

For a CBPM, the quality factor (Q) is an important parameter. A cavity of low Q factor means high efficiency of the coupling structure, featuring broad b andwidth, short duration time and higher temporal resolution; whereas a high Q cavity coupling structure is of low efficiency, narrow bandwidth, long duration time and lower temporal resolution. So, the Q value selection needs to match with the whole CBPM system and meets the working mechanism of the FEL facility.

In European X-ray FEL (EXFEL), a low Q CBPM for a multi-bunch working mechanism with a resonant frequency of 3.3 GHz was developed and combined with relevant electronics, achieving position resolutions of well below 1 μm rms ^[5,6]. For the Swiss-FEL, two types of cavity BPM are used. The low Q CBPM used in the Linac can easily separate two adjacent bunches of a 28-ns bunch spacing, while BPM pickups of the same basic structure, but with higher Q value, are used in the undulators that receive only single bunches and have higher resolution and precision requirements ^[7]. Spring-8 designed a low Q cavity BPM with a resonant frequency of 4.76 GHz, with the position resolution of <0.2 μm at a 0.3 nC bunch charge ^[8,9]. KEK designed a low Q Interaction Point BPM (IP-BPM) and achieved a beam position resolution at a normalized charge (1.6 nC) with three low-Q IP-BPMs at 22 nm^[10]. In SLAC, a new X-band CBPM with a high Q factor was developed for the LCLS-II, and combining with an improved receiver and digitizer, they will provide a single-shot position resolution of 50 nm, rather than 200 nm of the LCLS at bunch charge of 200 pC (no experiment results yet) ^[11,12]. In China, Hefei Light Source (HLS) designed a S-band re-entrant cavity BPM with a high-Q factor, and the cold test results showed a position resolution better than 3 μm (no beam test results yet)^[13].

A low Q cavity was designed and tested by our group^[14,15,16]. It features many of the strengths, but the performance was limited by the electronics due to the short duration time. Considering the single-bunch working mechanism of SXFEL, and for matching the electronics to increase the processing gain to achieve a higher resolution, we redesigned and chose a high Q CBPM as the beam position measurement scheme. In addition, relevant electronic components were developed and, as a preliminary performance test, an array of three adjacent high-Q cavity BPMs was installed at the SDUV-FEL facility.

2 Measurement principle of CBPM

For a cylindrical pill-box cavity, when the beam source runs along the z-axis, the bunch does not lose energy in the transverse electric field of the TE mode. However, because of the longitudinal electric field of the TM mode, the bunch loses energy in the longitudinal electric field excited by itself and effectively induces the excitation mode. Therefore, only the TM modes are excited and the amplitude is determined by the bunch energy that is lost. The axial electric field component of the TM110 mode in cylindrical coordinates can be expressed by Eq. (1):

where E₀ is the amplitude of the electric field and J₁ is the first-order Bessel function of the first kind, χ₁₁ is the first root of J₁(ρ) = 0, r is the cavity radius, Φ is the angle between the field of TM110 mode and axial direction, and ρ is the radial coordinate. Since J₁(ρ) is proportional to ρ when ρ ~ 0. Thus, the excited voltage of the TM110 mode is proportional to the beam offset x and beam charge q:

In order to eliminate the beam charge variation effect, an additional monopole mode cavity shall be employed, and the signal amplitude of the monopole mode is independent to the beam position but proportional to the beam charge only.

Due to limited quality factor of the cavity, the energy of all the electromagnetic field modes excited by the cavity has three tracks. Some is stored inside of the cavity, a small portion is lost on the metal wall, and some is coupled out by the appropriate coupling structure, which can be detected by the following electronics.

However, when a bunch of particle beam transits the cavity close to the z-axis, the TM010 mode obtains much of the lost energy; thus, the amplitude is larger than that of the TM110 mode, with a certain amount of crossover in the bandwidth. Therefore, it is important to design an appropriate coupling structure, which outputs the TM110 mode effectively and damp most of the power from the TM010 mode in the meantime. It affects greatly the measurement of position resolution, too^[17].

3 Cavity pickup

On basis of the defects of low Q cavity by beam test, we redesigned a high Q cavity BPM to strategically address the above considerations. The pre-designed parameters of the high Q CBPM are given in Table 1. The working frequency of 4.70 GHz was chosen due to considering the vacuum pipe radius of 8 mm and avoiding dark current from the accelerating system. Cavity material was changed from stainless steel 304 to oxygen-free copper, which raises theoretically the Q value to 7786 and 3120 for the position and reference cavities, respectively.

The three-dimensional structure of the cavity, which consists of seven parts, is shown in Fig. 1. The total length of the probe is kept at 112 mm but the distance between the two cavities increased from 35 mm to 45 mm so as to reduce the possibility of signal coupling between them. The reference cavity has more ports to facilitate cold testing, and the coupling structure changes from magnetic coupling to weaker electric coupling.

Fig.1.Full-screen View

Three-dimensional structure of the high Q CBPM.

Considering the complexity of setting up a platform to test the cavity, we developed a convenient and effective method to test the resonant frequency and the Q factor of cavity by using the Agilent (Santa Clara, CA, USA) N5230A PNA-L network analyzer. We measured S21 parameters, designated the frequency of peak as the cavity working frequency, and obtained the Q factor by measuring the 3 dB bandwidth. As shown in Fig. 2; the cold test working frequency of the cavity is 4.678 and 4.686 GHz for the position cavity and 4.695 GHz for the reference cavity, which accord well with the designed value of 4.70 GHz. However, the correspondent Q factor differs greatly from the design.

Fig.2.Full-screen View

Cold test results of the cavity.

4 System setup

In order to check the actual performance achieve what are expected with the theoretical design, and to test the whole BPM system we developed, the beam test was conducted on the SDUV facility. The BPM system consists of a cavity BPM, a dedicated RF front end, and a homemade digital BPM processor..

Fig. 3 shows an array of three BPM pickups installed at the SDUV test injector facility. The middle cavity (CBPM2) was mounted on a movable stage to imitate the beam offset.

Fig.3.Full-screen View

The BPM test array installed at the SDUV test injector facility and the arrangement.

Because of limitations of ultra-high speed ADC resolution, precise measurements at sub-micrometer level are difficult to achieve with RF sampling methods. It is essential to adopt RF receiver architecture that converts the RF signal to intermediate frequency (IF) to be digitized by high-resolution ADC. The RF front end is shown schematically in Fig. 4^[18].

Fig.4.Full-screen View

Schematic of the RF front end.

An input band pass filter (BPF) selects the cavity signal components at 4.7 GHz to suppress other harmonics coupling from the cavity or the spatial disturbance into the low-noise amplifier (LNA) that follows. The LNA with 45-dB gain is used to adjust the signal intensity from the BPF and to acquire a broader dynamic range. The down conversion operates with an LO and converts the RF signal to IF, which ranges from DC to hundreds of megahertz. Generally, we convert the RF signal to IF at 500 MHz, depending on performance of the DBPM. An adjustable IF amplifier accomplishes the last gain adjustment to fulfill the input requirement of ADCs and with a BPF having a center frequency of 500 MHz, and bandwidth of 10 MHz as an anti-aliasing filter to suppress other amplified harmonics. Both of them are integrated into the DBPM.

The DBPM was developed by our group several years ago (Fig. 5) ^[19,20,21]. Based on software radio architecture, it adopts band-pass sampling technology as the quantization scheme, which consists of a RF pre-processing module, an ADC module, and a digital board module. It has been in good performances. The basic parameters are: sampling rate, 117 MHz; center frequency, 500 MHz; band- width, 10 MHz; ADC resolution, 16 bit; ENOB, >10 bit; and dynamic gain-range, 60 dB.

Fig.5.Full-screen View

The DBPM.

5 Beam test

The beam test was performed on basis of the cold test. A broadband oscilloscope was used to evaluate the CBPM performance directly; the calibration factor and position resolution was also measured by the entire BPM system.

5.1. Cavity evaluation

The signal data collected by the broadband oscilloscope were processed using MATLAB. The CBPM output signal waveform is shown in Fig. 6. The CBPM spectra of the reference and position cavities are shown in Fig. 7.

Fig.6.Full-screen View

RF signals waveform of CBPM.

Fig.7Full-screen View

CBPM spectra of the reference (a) and position (b) cavities.

According to the figures mentioned above, the RF signal waveform in the time domain is consistent with the theoretical expectations. The signal spectra of the reference and position cavities are well in accordance with those of the cold test. We also find that the resonant frequency of three CBPM position cavities has a good consistency, but they differ greatly from the reference cavity frequency, which is caused by solder melts into the reference cavity in welding.

As shown in Fig. 8, Q values of the reference and position cavities are 2134 and 4261, respectively, which is in accordance with the cold test. The cavity decay time can be calculated in the frequency domain and fit into the time domain. In the frequency domain, the decay time can be calculated by Eq. (3):

Fig.8Full-screen View

Q values of the reference (a) and position (b) cavities.Δ×10⁵

$\tau =Q/\left(2\text{π}{f}_{\text{L}}\right),$ (3)

where f_L is the resonant frequency. Thus, the decay time values of the reference and position cavities are calculated at 73 and 145 ns, respectively.

In the time domain, the data-fitting method can help to obtain the decay time directly. However, some pretreatment is necessary for the original data, such as a digital filter to remove the influence of harmonics. Fig. 9 shows the result of 77 ns for reference cavity (144 ns for the position cavity) processed in the time domain, which is close to the result processed in the frequency domain.

Fig.9Full-screen View

Decay time of the reference cavity processed in the time domain.

The results of cavity evaluation generally agree with the design except for the quality factor. The measured Q factors are significantly smaller than the design value. As the cavity was made by brazing two assembly parts and the faying face had some distance from the locating face, the welding seam could cause the energy loss more seriously. This is the most probable factor for the unloaded Q factor being smaller than expected. However, it also can meet the requirements for the project based on the BPM system.

5.2. IF pulse shape

The RF signal output from the cavity is directed down-converted to a low intermediate frequency by this RF front end and is sampled by a signal processor. Two LO were used to obtain the IF signals about 30 MHz and 500 MHz to verify the RF front end, respectively. Fig. 10 shows the IF waveforms sampled by broadband oscilloscope with an LO of 4665 MHz. A LPF of DC to 32 MHz was also used to suppress the high-frequency component generated by the mixer. The waveform and spectrum are in accordance with the theory.

Fig.10Full-screen View

IF waveforms of reference cavity (a) and vertical position cavity (b) sampled by broadband oscilloscope.

With the RF front end and DBPM, IF signals at 500 MHz were sampled. Because of the Sub-Nyquist sampling method, the frequency of the IF signals was transferred to the first Nyquist zone. The waveforms and spectra are shown in Fig. 11. The IF signal waveforms and corresponding spectrums are in line with expectations that prove the RF front end can be applied in the high Q CBPM system.

Fig.11Full-screen View

IF waveforms of reference cavity (a) and horizontal position cavity (b) sampled by DBPM.

5.3. Calibration

The calibration factor is required to convert the position of beam offset. A two-dimensional motion platform was installed under one of the cavities which can imitate the beam offset from −2 to 2 mm, with a step of 200 μm, in both the horizontal and vertical directions. The calibration system is shown schematically in Fig. 12(a). The data were collected by the DBPM, and processed in the frequency domain with MATLAB. Fig. 12(b) shows the calibration factor of the CBPM in vertical direction.

Fig.12Full-screen View

The calibration system (a) and the calibration factor of the CBPM in vertical direction (b).

5.4. Position resolution

The position resolution was measured on basis of correlating readings of the three cavities, as shown in Fig. 13.

Fig.13Full-screen View

Schematic of the position resolution measurement.

By using the geometric relationships in Eq. (4), the position reading of CBPM2 (U2′) can be estimated by the position reading of CBPM1 and CBPM3 (U1 and U3). Also, a position reading of CBPM2 could be obtained by itself (U2). To calculate the difference between U2 and U2′ (∆U) with the assumption that all BPMs have equal position jitters, the position resolution can be calculated by Eq. (5), where GF is a geometrical factor related to the location of the three cavities and can be calculated by Eq. (6), std_Δd is the standard deviation of ∆d and ∆d is the difference in position converted by the calibration factor and ∆U.

$U2\prime =\left(D12\cdot U3+D23\cdot U1\right)/D13,$ (4) ${\delta }_{\text{CBPM}}=GF\cdot st{d}_{\text{Δd}},$ (5) $GF=\frac{1}{\sqrt{{(\frac{D23}{D13})}^2+{(\frac{D12}{D13})}^2+1}}.$ (6)

In the experiment, 1000 sets of data were sampled by the DBPM and were processed offline, with the bunch charge of 20 pC. The gain setting of the RF front end was chosen to provide a linear measurement range of −2 to 2 mm. By using the reference cavity signals to normalize the position cavity signals and with the position of beam offset converted by calibration factor, the position measured and the expected values of the CBPM2 could be obtained (Fig. 14).

Fig.14Full-screen View

Relationship of the position measured and expected.

The ∆d distributions were calculated (Fig. 15), and the CBPM system’s position resolution in vertical direction is 23 μm.

Fig.15Full-screen View

Histogram of the ∆d with 650 samples.

Because the SDUV facility is a test bed only, most of the time it works at a low-charge state (20–30 pC). The beam jitter is also somewhat significant, so we set the linear measurement range at ±2 mm. However, for the SXFEL facility, the charge will be set at 0.5 nC and the beam jitter will be kept within ±500 μm.

In theory, increasing the bunch charge to 0.5 nC from 20 pC means a gain of 25×. Meanwhile, with the measurement range maintained within ±500 μm, we can achieve an electronics gain by 4×. Considering that the most-ideal conditions and the noise of the whole system have not changed a great deal, we can achieve a position resolution of 0.23 μm. Related experiments will be conducted in subsequent research.

6 Conclusion

We have completed the entire CBPM system and conducted the first test in the SDUV facility. The aim is to evaluate the performance of the newly designed high Q CBPM and of the whole CBPM system in preparation for the construction of the SXFEL. The results show that the cavity performance meets the needs of the project, although the quality factor was less than the design value. We obtained a position resolution of 23 μm when the bunch charge was 20 pC, and the linear measurement range was ±2 mm. By theoretical calculations, we can easily fulfill the resolution requirement of 1 μm at 0.5 nC for the SXFEL if we raise the bunch charge and control the measurement range.