1 Introduction

Free electron laser (FEL) has served as a useful and promising high power and high brightness light source in experimental studies (in the macroscopic world and at atomic and molecular levels), in static physical systems and ultrafast dynamic processes, and in investigations under simple experimental conditions to complex environments [1, 2]. The Shanghai soft X-ray FEL (SXFEL) was developed in phases. The test facility, named SXFEL test facility (SXFEL-TF), has been constructed in China at the Shanghai Synchrotron Radiation Facility (SSRF) campus and is presently under commissioning. It is a critical development step towards a hard X-ray facility [3, 4] and will be upgraded to the SXFEL user facility (SXFEL-UF) next year. The SXFEL-UF consists of two lines working on different FEL types. Especially, one of the beam lines will function as Self-Amplified Spontaneous Emission (SASE) self-seeding mode [5]. Table 1 shows the main beam parameters of the SXFEL.

The major challenge associated with such ultra-short, ultra-fast, and high-brightness light pulses is the requirement of precise synchronization between the electron bunches and seed laser pulses in three-dimensional spaces [6-9]. This is because the seed FEL power relies on the energy exchange of electrons and photons along the undulator section. Energy exchange can only occur when the electron beam and seed laser are synchronized. Therefore, measuring the electron beam arrival time is a key issue for achieving synchronization in femtosecond resolution. Moreover, because SXFEL will be applied as a user facility, it is essential to exploit the possibility of time-resolved experiments, and such experiments demand high resolution of beam arrival time. In short, it is essential to conduct research on beam arrival time.

Currently, beam arrival time measurement is mainly based on the RF cavity scheme [10-13] and electro-optic sampling scheme [14, 15]. According to the published results, the best resolutions of the arrival time are 13 fs based on the RF cavity scheme and 6 fs [16] electro-optic detection scheme. Considering that the latter scheme requires greater cost and extreme complexity, the highly sensitive RF cavity based phase detection scheme was adopted. This scheme is realized with a specific metallic cavity. When an electron bunch passes through the cavity, the eigenmodes of an internal electromagnetic field of the cavity are excited owing to the wakefield effect [18, 17]. For a simple pill-box cavity, TM010 is radially symmetric and has the maximum value at its center. Its amplitude is proportional to the electron bunch charge and is independent of the beam offset [19].

There are various timing jitters that can influence the measurement of beam arrival time. The main jitter results from an electron beam timing jitter at various locations along the undulator. This is mainly because of the dispersive effects in the magnetic bunch compressor chicanes [21, 20]. The energy-dependent path leads to the conversion of a beam energy jitter to an arrival-time jitter in the undulator. The energy jitter comes from the amplitude fluctuations and phase jitter of the accelerating fields, as well as the time jitter of the electron gun and reference clock. The typical detection scheme requires a highly stable reference signal that usually transmits over a long distance and is easily disturbed by temperature and humidity [22], etc. However, the SXFEL environment outside the tunnel currently is not suitable and the reference signal has larger jitter. In other words, this detection scheme applied at SXFEL may not attain appropriate results.

Therefore, a novel scheme using a dual-beam induced pickup signal mixing to measure the beam arrival time or beam flight time has been proposed. The proposed scheme is shown in Fig. 1. The beam arrival time monitor (BAM)#1 is installed immediately behind the RF gun and its generated RF signal can be observed as the reference signal, because the time lag between the driven laser and RF signal is almost constant. Most importantly, this scheme is especially useful for the SASE self-seeding FEL because this facility focuses mainly on the beam flight time between the chicane’s entrance and exit (T23). As the cavities are inside the tunnel where a stable environment exists, and have similar features (such as temperature sensitivity), this dual-cavities signal mixing scheme is expected to obtain better performance. In order to evaluate the practicability and performance of the new scheme, we designed a BAM equipped with two cavities working on different frequencies. In this research, we measured the beam flight times between BAM01’s two cavities and between two BAMs. The layouts of the two BAMs is shown in Fig. 2.

Fig. 1.Full-screen View

(Color online) New proposed scheme to measure the beam arrival or beam flight time

Fig. 2.Full-screen View

(Color online) Layout of BAMs in SXFEL

The remainder of this paper is organized as follows. Sec. 2 introduces the basic principle of a BAM and presents the theoretical temporal resolution formula. In Sec. 3, the design process and simulation results are presented. Along with the simulated parameters, the theoretical temporal resolution is also calculated in this section. The cold test and beam flight time experiments based on the BAM prototypes are described in Sec. 4.

2 basic principle OF BAM

The BAM utilizes the high sensitivity and high resolution of a pill-box cavity to extract precise timing information. When a relativistic electron beam passes through a cavity, the beam interacts electromagnetically with its surroundings to generate an electromagnetic field, named the wakefield. The wakefield will cause energy loss from a beam to an electromagnetic field. The energy loss, E_loss, satisfies: [23]

Here, q is the electron bunch charge, k_loss is the loss factor, L is the cavity length in the z direction, ω is the angular frequency, v is the velocity of the electron bunch, and W and E denote the stored energy and electric field intensity, respectively. Basically the electromagnetic (EM) field inside the cavity is a superposition of several eigenmodes and the transverse field eigenmodes (TM) are combined with three indices: n(azimuthal), m(radial), and p(longitudinal). For TM010 mode, the longitudinal electric field (E_z,010) is:

Here, J₀ is the 0-order Bessel function, j₀₁ is the 1st root, and a is the cavity diameter. The output signal voltage of TM010 (V_out) can then be expressed as follows:

Here Z is the characteristic impedance, which is designed to be 50 Ω usually, and _z is the electron bunch length. R/Q is the normalized shunt impedance. c is the light speed. Q_ext is the external quality factor that is determined by the cavity structure, especially the coupled structure; it is a constant for a given cavity, which complies with the following function:

Here, Q_L is the loaded quality factor; Q₀ is the internal quality factor; ideally it is determined by the material and structure of the cavity. It can be used to evaluate the cavity surface characteristic and energy storage. R/Q depends only on the cavity shape and is related to the beam offset. It describes the energy exchange between the cavity and electron bunches. If the electron beam passes the cavity in the z direction with an offset x and assuming x 0, E_z = constant, the R/Q of TM010 can be calculated:

Here, α_T is the transit time factor. ϵ₀ is vacuum permittivity. J₁ is the 1-order Bessel function, j₀₁ is its 1st root. It further shows that R/Q of a mono-pole is insensitive to the beam position near the cavity center. Thus, the output signal is only depends on the electron bunch charge.

The above output signal voltage is a theoretical value. In fact, there are various noise components; one such component for the cavity is thermal noise. According to Nyquist’s Theorem, thermal noise amplitude (V_tn) is represented as follows:

Here, k_B is the Boltzmann constant, T is the temperature, NF is the noise figure, Δf represents the bandwidth and can be expressed as follows: Δf = f₀₁₀/Q_L, where f₀₁₀ is the frequency of TM₀₁₀. Incidentally, a higher Q_L gives a narrower bandwidth for a determined frequency.

A more detailed discussion on the above theories can be found in Ref. [24-27]. A signal voltage in the time-domain (V_total) and frequency-domain (F(w)) as well as a detected phase (θ_a) can be expressed as follows:

Here Re and Im represent the real and imaginary parts, respectively. Therefore, the beam arrival time (T_a) can be described as follows:

Hence, the time jitter caused by noises (t_nj) is as follows:

Here, SNR is the ratio of signal to noise. In addition, another time shift resulting from frequency-error (Δω) due to the finite sampling time (t_Qj) is denoted as follows:

Considering the clock jitter (t_cjitter) from ADC sampling system and reference signal, the theoretical temporal resolution (Δt) can be derived as follows:

3 DESIGN AND SIMULATION RESULTS OF BAM

3.1 Physical Design of the BAM

A pillbox cavity is easier to fabricate as compared to a rectangular one. For this pillbox-like cavity, the highest excitation of all modes is the TM010 mode whose amplitude is proportional to the electron bunch charge only for a small beam offset[28]. The first dipole mode is the TM110 mode whose amplitude is proportional to the beam offset when it is close to the center. The second common mode is the TM020 mode which is similar than TM010 mode near the cavity center. Fig. 3 shows the first four modes.

Fig. 3.Full-screen View

(Color online) Excited modes in a cylindrical cavity: (a) TM010 mode, (b) TM110-x mode, (c) TM110-y mode, (d) TM020 mode

In this research, a dual-cavity BAM was designed whose pickups work at different resonance frequencies. The physical model is shown in Fig. 4. Each pickup has a pill-box cavity with two feedthroughs. This symmetrical design will not destroy the symmetry of the EM fields. Moreover, it is helpful in the beam tests, especially while conducting two or more measurements simultaneously. The cavity body is made of oxygen-free copper. Both ends of the BAM are connected to a 16 mm beam pipe. The two-dimensional section view of the BAM has been presented in Fig. 5.

Fig. 4.Full-screen View

(Color online) Physical model of the BAM

Fig. 5.Full-screen View

Two-dimensional section view of the BAM

3.2 Simulation Results

3.2.1 Frequency

Choosing an appropriate frequency is significant to the BAM. The resonant frequency of the TM010-mode should be smaller than the cut-off frequency of the beam pipe to avoid their propagation into the beam pipe. For a circular waveguide, the cut-off frequency (f_c) of TE₁₁-mode can be calculated as follows:

$f_{\text{c}}=\frac{1.841\cdot c}{2\pi r_{\text{p}}}\mathrm{.}$ (15)

Here r_p is the beam pipe radius. Thus, the cut-off frequency of a TE11-mode is 11 GHz for a circular waveguide with a 8 mm radius. Moreover, the choice of f₀₁₀ should not be the integral or half-integral multiplication of an accelerating frequency of 2856 MHz to minimize the negative influence of dark current on measurement. Taking all factors into consideration, f010 of the dual-cavities are designed to be 4.685 GHz (cavity 1) and 4.72 GHz (cavity 2), respectively. The remainder of this section will focus on the cavity 1. For the specified cavity frequency, a cylindrical diameter is then determined. The cavity diameter (a) can be calculated as follows:

$a=\frac{j_{01}}{\pi f_{010}\sqrt{{\mu }_0{ϵ}_0}}\mathrm{.}$ (16)

Here μ₀ and ϵ₀ are the permeability and permittivity of vacuum, respectively. For the cavity 1, a is 49 mm.

3.2.2 Cavity Length

The cavity length has great impact on the energy exchange between th electron beams and cavity. A narrow band cavity requires a high quality factor Q₀ while a high Q₀ greatly depends on the cavity length. Based on the previous experience, a 1 MHz bandwidth can be obtained. Thus, Q₀ sets a lower limit on the cavity length L. For the monopole mode TM010 of a cylindrical cavity, the Q₀ can be calculated as follows:

$Q_0=\frac{2L{j}_{01}^2}{2R_{\text{s}}\omega {ϵ}_0(L+a/2)a}\mathrm{,}$ (17)

where R_s is the surface resistance. In addition, owing to the oscillating nature of the EM fields, the field inside the cavity will change when the electron bunch passes through the cavity. This phenomenon reduces the power coupling efficiency of the electron bunch into the cavity. Transit time factor αT is used to characterize this factor, which is expressed as follows:

${\alpha }_{\text{T}}(\beta )=sinc(\frac{\omega L}{\beta c})\mathrm{,}$ (18)

where β = v/c. If the cavity is very long, transit time factor will reduce the power coupling efficiency. Thus, choosing a suitable cavity length is the trade-off between power coupling and quality factor (Q₀). As shown in Fig. 6 and Eqs. (17) (18), when the cavity length is L=6 mm, Q₀ is about 5000, which enables the bandwidth to reach 1 MHz and α_T is larger than 0.8. Therefore, the cavity length is designed to be 6 mm.

Figure 6:Full-screen View

(Color online) Correlations between quality factor (Q₀), transit factor (αT), and cavity length

3.2.3 Cavity Structure and Parameter

In this design, a re-entrant arrival time cavity is applied instead of an ordinary pillbox cavity. This structure offers convenience for frequency tuning during the manufacture process. According to the theory of coaxial lines, the ratio of the inner and outer radius is preferably 2.3 to balance the output power and signal attenuation[29]. The probe diameter and insertion depth are set to be 1.5 mm and 0.25 mm, respectively. The cavity length can be adapted for each cavity radius to maintain the designed frequency. Moreover, as shown in Fig. 7, an external quality factor of 10⁵ was appropriate to balance the voltage amplitude and TM010 mode bandwidth. When the external quality factor reaches 10⁵, the bandwidth is almost constant while the SNR is keeps decreasing.

Fig. 7.Full-screen View

(Color online) Correlations between output voltage (V_out), bandwidth (BW), and external quality factor (Q_ext)

Furthermore, the cavity distance should be longer to avoid crosstalk between the two cavities. In this design, the distance is required to be larger than 60 mm; thus, the theoretical crosstalk is less than -100 dB.

Once the cavity sizes were determined, their simulated parameters can further be calculated with the post-processing template of the eigenmode solver, as displayed in Table. 2. With the above simulated results and Eq. (14), the theoretical temporal resolution is approximately 3.5 fs when the SNR was assumed to be 80 dB.

TABLE 2.Full-screen View

Simulated parameters of the BAM

Parameters	Value (Cavity 1)	Value (Cavity 2)
Frequency (GHz)	4.685	4.72
Q0	4796	4835
Qext(×105)	1.8	1.9
Qload	4671	4716
R / Q(X)	107.2	107.9
τa (ns)	317.7	318
Bandwidth (MHz)	1.00	1.02

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^a Decay time constant

4 The BAM Test Results

4.2 Beam Flight Time Experiments

The two BAMs have been installed in the injector section of the SXFEL test facility and the distance between the two BAMs is approximately 40 m. A beam flight time detection experiment based on the new proposed scheme (the dual-cavities signals mixing scheme) can be performed. This experiment consists of two parts: the beam flight time between BAM01’s two cavities, the beam flight time between BAM01-A and BAM02-A cavities. As discussed above, the first experiment is mainly used to evaluate the performance of the measurement system. The second part is actually used to measure the two BAMs’ beam flight times. Fig. 8 shows the beam flight time detection setup based on the dual-cavities signals mixing scheme. The system consists of four parts: a BAM capturing the beam induced RF signal, an RF front-end, a signal acquisition processor, and an online/offline signal processing system.

Fig. 8.Full-screen View

Beam flight time detection setup based on dual-cavities signals mixing scheme

The raw RF signals from two BAMs’ four cavities were captured by an oscilloscope with a sampling rate of 20 GHz. Fig. 9 shows the four RF signal in time-domain and frequency-domain. Especially, BAM01-B and BAM02-A signals are used as the local oscillator (LO) signals. As the LO input is an exponentially damped sinusoidal signal, the dynamic range and linearity of the mixer will deteriorate with the attenuation of the LO signal.

Fig. 9.Full-screen View

(Color online) Time-domain signals and frequency spectra of the four output signals from BAM01 and BAM02

Currently, the whole signal processing electronics system is placed outside the tunnel for convenient operation in this preliminary research. Thus, low noise and phase-stable cables are required for the RF front-end realized analog down conversions, bandpass filtering, and amplification of RF signals.

After self-mixing, the two generated IF signals are shown in Fig. 10. Their peak amplitudes are approximately 0.2 V, which is considerably smaller than the full scale of the analog-digital-converter (ADC) i.e., 1 V. The frequencies of IF-1 and IF-2 are 35 MHz and 44 MHz, respectively. IF-1 is the measured beam flight time between BAM01’s two cavities, while IF-2 represents the beam flight time between BAM01 and BAM02.

Fig. 10.Full-screen View

(Color online) Two generated IF signals output waveforms and their frequency spectra

The IF signals are then digitized by a 16-bit ADC with a sampling rate of 119 MHz. This signal acquisition processor works at an external trigger of (10 Hz) and external clock mode of (119 MHz). The obtained digital IF signal is processed and corrected online or offline.

The measured two beam flight times over 40 min are given in Fig. 11. The deviations of IF-1 and IF-2 are 37 fs and 51 fs, respectively. For the beam flight times between BAM01’s two cavities, the limitation mainly comes from the unoptimized electronics and environment noise. For the beam flight time between the two BAMs, the beam jitter is additionally a jitter source apart from the measurement system limitations.

Fig. 11.Full-screen View

(Color online) Two beam flight time deviations

5 Summary

To measure the beam arrival time with the limitations of a poor reference signal, a dual-cavities signals mixing scheme is proposed and it is especially useful for the SASE self-seeding FEL facility that focuses more on the beam flight time. Based on this, a BAM equipped with two cavities working at 4.685 GHz and 4.72 GHz, respectively, is designed and two sets of BAMs were installed at the SXFEL injector section. Moreover, two beam flight time experiments, one between a single BAM’s two cavities, and the other between the two BAMs have been investigated to evaluate the performance of the measurement system and the practicability of the new proposed scheme. The measured beam flight times show a standard deviation of 37 fs and 51 fs, respectively, and they are significantly larger than the theoretical values. This is mainly due to the unoptimized electronics and environmental noise, etc. Therefore, further investigations are ongoing, such as planting the whole system inside the tunnel, optimizing the RF front-end system etc. Moreover, further experiments will be conducted soon to demonstrate how close the real system values may become to these promising theoretical values.