1 Introduction

Superconducting radio frequency(SRF)guns[1–4]were widely investigated in free electron lasers(FELs),energyrecovery linacs(ERLs),electron cooling,etc.The wave-

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?length of a free electron laser is partially restricted by the emittance of the electron beam.Thus,many efforts were made to reduce the beam emittance.The gradient on the surface of the cathode in an SRF gun is very high,so the space charge effect-induced emittance can be very low.A bialkali photocathode[5]is chosen in many electron guns(DC,NCRF,and SRF guns)as the electron source owing to high QE(4–10%),low intrinsic emittance,weeks of lifetime in a reasonable vacuum(～ 2–5 × 10-8Pa).

In SRF guns,a cathode is inserted into the superconducting cavity,and the electric field on the surface of the cathode is around 20 MV/m.The heat induced by the RF field on the stalk can be as high as hundreds of watts[6],so the stalk must be cooled to protect the cathode from degradation.In BNL’s 704 MHz SRF gun[4]and HZDR’s 1.3 GHz SRF gun[1],the cathodes are both cooled by liquid nitrogen.The final temperature of the cathode is stabilized at 80 K.During the cooling process,the QE of the cathode would drop to 20%of the original value in the 704 MHz SRF gun.The detailed description of the cooling effect of a bialkali photocathode can be found in previous Ref.[6].The incident photon energy(2.32 eV)is very close to the ionization energy of the K2CsSb photocathode(～2.1 eV),and the ionization energy change from the cryo effect is in the range of 0–0.15 eV[6].Therefore,the excess energy of emitted electrons is also near the threshold.An analytical model and a code are built to explain this effect.From the analytical model and the code,we predicted that if an electric field was applied to the cathode,the Schottky effect would lower the surface potential and hence would compensate the QE reduction caused by cooling.An experiment was designed to demonstrate this prediction.

2 Experimental section

There are a deposition chamber and a load lock chamber in the bialkali photocathode deposition system(Fig.1).The load lock chamber is baked every time a new photocathode is fabricated.A substrate is mounted in the transport cart,which is connected to the deposition chamber via the load lock chamber.The transport cart consists of long moving bellows,an ion pump,and a high-vacuum gate valve.The substrate can be inserted into the deposition chamber for the photocathode deposition.A heater is connected to the gas inlet tube at the end of the cart.The substrates are heated by hot flowing nitrogen gas.The gas channel can also be used to cool the substrate with flowing nitrogen gas or liquid nitrogen.Three sources,Cs,K,and Sb are assembled in three separate bellows,which are connected with the main chamber using ultrahigh-vacuum gate valves.During the thin- film deposition process,the valve is open and the source arm can be inserted into the chamber.The vacuum of the main chamber can reach 4×10-8Pa with a sputtering ion pump and a non-evaporative gas(NEG)pump.A quartz crystal monitor is used to record the film thickness during the evaporation process.A residual gas analyzer(RGA)can give the residual gas partial pressure in the main chamber.The cathode is irradiated by a 0.5 mW green laser.An anode is equipped in the main chamber to collect electrons emitted from the cathode surface,and the photocurrent is monitored by a Keithley P6485 picoammeter.

The substrate was then moved out,and the cart was disconnected from the main chamber.The transport cart was moved to the cave and connected to the SRF gun.Before the cathode was inserted into the gun,the alignment of the stalk and cavity needed to be performed first.The alignment accuracy was about 50 μm.During the baking process of the load lock chamber,the cathode was protected with a liquid nitrogen finger to avoid being polluted by the gas released from the valve between the cart and the load lock.The liquid nitrogen finger is a stainless steel part,which is cooled by liquid nitrogen and can be moved in and out of the cathode cart by moving the bellows.An in situ QE measurement system was installed in the transport cart to measure the QE of the cathode during the transport process(Fig.3).

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Fig.1(Color online)Bialkali photocathode deposition chamber for the 704 MHz SRF gun

Here,the photoemission of the cathode is ‘pancake photoemission,’based on Ref.[7].The maximum surface charge Qsatcan be expressed as

where f is the laser repetition rate,Epis the peak electric if eld on the surface of the cathode,P is the laser power,hν is the incident photon energy(here,we used the 532 nm green laser),d is the gap length between the anode and the cathode,and θ is the RF phase.With Eqs.(1–3)and the parameters listed in Table 2,the effective QE can be calculated as shown in Fig.4.

1. The substrate was heated at 350°C for 3 h to release the absorbed gas and then cooled to 90°C.

2. After the degassing procedure,a Sb source was moved to the front of the substrate.The heating current was 67 A,and the thickness of the film was monitored from the quartz crystal monitor.

4. After degassing,the Cs activation process was started.The heating current of the Cs source was approximately 5.5–6 A.During the activation process,the photocurrent kept growing.When the photocurrent reached the plateau,the heating power was reduced and the substrate was cooled by the flowing nitrogen gas.

3. The substrate temperature was then raised to 130°C,and the K deposition process was started.During the deposition process,the cathode was irradiated with the 532 nm green laser,and the photocurrent was monitored with the picoammeter.When the photocurrent reached the plateau,the K evaporation stopped.

The QE of the cathode inside of the gun was around 4%and reduced to 1%after RF conditioning and long beam running.The degradation was mainly caused by the multipacting between the cathode stalk and the high-gradient SRF cavity.During the beam experiment,the QE of the cathode dropped to 0.2%owing to the cooling effect[6].The peak gradient on the cathode was set to 11 MV/m.The laser distribution is truncated Gaussian.With the green laser(the wavelength was 532 nm)illuminating the cathode,emitted electrons were accelerated by a high electric field.The bunch charge was measured by integrating current transformer(ICT).The QE of the cathode was calculated by the bunch charge and the laser pulse energy.Then,we started the RF phase scan process;the QE changed with the RF phase during this experiment.

We use Cu-breezed Cr as the substrate for the cathode deposition.The substrate is polished with diamond pastes,with diameters ranging from 10 to 1 nm.The roughness of the substrate after polishing is measured using an atomic force microscope(AFM)and can be found in Fig.2.Laser cleaning[5]is also introduced in the substrate processing to get higher QE.

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After the cathode was inserted into the gun cavity,flowing liquid nitrogen was conducted in the channel to cool the cathode down to 80 K.The detail of the beam experiment can be found in Ref.[4].The parameters of one beam experiment are shown in Table 1.

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Fig.2(Color online)Surface information of the Cr substrate after being polished with diamond nanoparticles.The four inserts are related to the surface topography of the sample,surface of the sample measured using the de flection mode,roughness of the sample along the line in the first insert measured using a constant force mode,and roughness measured using the de flection mode

Fig.3(Color online)Transport cart connected to the 704 MHz SRF gun

Table 1 Parameters in the beam experiment[4]of the 704 MHz SRF gun

Parameters Values Gun voltage(MV) 1.2 Pulse repetition rate(MHz) 9.38 Duty factor 0.3%Bunch charge(pC) 50

3 Results and discussion

The experimental result is shown in Fig.4.During the phase scan process,we could see that the QE of the cathode increased gradually.After 10°,the QE increased much slower.We assume that the space charge limit caused this phenomenon.

Fig.4(Color online)Experimental results,analytical model,and simulation results of the Schottky scan experiment.The black dots are the experimental results.The gray line is the calculation results of the space charge limit.The blue line is the analytical model calculation of the Schottky effect.The red line is the Monte–Carlo simulation of the Schottky effect on the bialkali photocathode.In both the analytical model and the code,the space charge limit is not included

1. Space charge limit calculation

The deposition process of the bialkali photocathode was as follows:

where σsatis the maximum surface charge density,ε0is the vacuum dielectric permittivity,R is the laser beam size,E is the electric field on the surface of the cathode,and θ is the RF phase.The effective QE,which relates to the photocurrent extracted and the incident photon energy,can be calculated as

图3示，以0加药组为标准，OPC处理组(20～40 μg/mL)LC3-Ⅱ相对蛋白表达量分别为2.58±0.12、3.64±0.60和5.72±0.10，高于0加药组，F=1 688.710，P<0.001；0加药组分别与20、30和40 μg/mL 3组比较，差异有统计学意义，均P<0.001；OPC处理组(20～40 μg/mL)p62相对蛋白表达量分别为0.70±0.08、0.51±0.06和0.42±0.04，低于0加药组，F=73.875，P<0.001，其中0加药组与20、30和40 μg/mL 3组比较，差异有统计学意义，均P<0.001。

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2. Schottky effect calculation

Schottky effect-induced surface potential change ΔW[8]at the RF phase θ can be calculated as

Table 2 Parameters used for the calculation of the space charge limit

Parameters Values Permittivity,ε0(C2/N m2) 8.85 × 10-12 Electron charge,e(C) 1.6×10-19 Peak gradient,Ep(MV/m) 11 Laser beam size,rm(mm) 2 laser pulse length(ps) 10 Laser power,p(W) 0.15

where ε is the relative permittivity of a bialkali material.During the beam experiment,the scanned phase was around π/2,so the surface potential change is calculated to be approximately 0.11 eV.

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3. Analytical model

In order to give a detailed description of the Schottky effect on the QE of the cooled bialkali photocathode,we used the same analytical model built to explain the cryogenic performance[6].The model was based on Spicer’s[9]three-step model.The analytical model successfully explained the cooling effect in the previous literature[8].In this model,only those electrons with energy higher than the ionization energy Eecan be emitted into the vacuum.Ee was expected to increase by 0.15 eV when the cathode was cooled to the temperature of liquid nitrogen based on Ref.[10].Here,the Schottky scan effect would change the surface potential with a sine function,and the maximum change in the surface potential is calculated to be 0.11 eV as shown in the last part.We added this surface potential change ΔW into the analytical model[6],and the QE could be written as

where α（¯hω）is the absorption coefficient of K2CsSb at the photon energy ¯hω,Ee（0）is the ionization energy at room temperature,which equals the sum of the bandgap energy Egand the electron af finity Eaat room temperature.The temperature has an effect on the crystal lattice and its surface properties,and hence,the energy bandgap or the electron af finity[11]is changed.φ(T)is the change in the ionization energy at temperature T,and φ(T)is set to zero at room temperature.σ is the energy spread in the valence band.f(E,σ)is the Maxwell–Boltzmann[12]probability distribution function of electrons in the valence band of the bialkali photocathode.C is a constant,which is determined by the cathode material and is fitted as illustrated in Ref.[6].

With ΔW changing as a sine function of the RF phase,Eq.5 can be used to calculate the QE change at different RF phases.The result is shown in Fig.4.The calculated result shows the same trend with the experimental result beyond the space charge limit.

4. Code simulation

In Ref.[6],a Python code was developed to simulate the photoemission process of the bialkali photocathode.The code starts from the initial distribution[13]of electrons in the valence band;after absorbing the photon energy,the excited electron would diffuse in the conduction band.Electron–electron scattering,electron–phonon scattering,and electron–hole scattering are included in the code.At the third step,the electron can emit into the vacuum if the electron energy after the second step is higher than the electron af finity and the transverse momentum is conserved.

This code is used to explain the Schottky effect of the bialkali photocathode.The Schottky effect is added to the code,and the surface potential is changed as illustrated in Eq.3.The electron af finity of the bialkali photocathode at 77 K is 0.3 eV.The change in the electron af finity is set as a sine function of the RF phase.The maximum of the electron af finity change is calculated to be 0.11 eV.We run the code and get the RF phase dependence of the effective QE of the bialkali photocathode at 532 nm.The effective QE change with the laser phase is shown in Fig.4.

At the beginning of the RF scan,the effective QE is restricted by the space charge effect.The simulation starts from 10°,and no space charge effect was included.The simulation results agree well with the experimental results.

4 Conclusion

A high-QE bialkali photocathode was fabricated with a mature deposition method.A Cr substrate was a laser cleaned before the cathode deposition.The cathode was cooled with liquid nitrogen during the beam experiment.The Schottky scan experiment was performed to explore the in fluence of electric field on the bialkali photocathode.The phase scan of the RF field changed the QE of the cathode dramatically.It could compensate the QE drop of the bialkali photocathode caused by the liquid nitrogen temperature.The analytical model and the code,which explained the cooling effect,is used for the first time in this paper to successfully describe the Schottky scan effect.

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