Characterization and Correction of Multipole Field Effect on Electron Beams from a High-Brightness Continuous-Wave Photocathode Gun

1. Introduction

Photocathode guns are crucial components in various modern electron linear accelerators, including free-electron lasers (FEL) [1,2,3,4,5,6,7], energy-recovery linacs [8,9,10], Compton scattering sources [11,12,13,14], and ultrafast electron diffraction (UED) [15,16,17]. The optimal performance of these applications critically depends on the beam quality of the electron sources. In recent years, driven by emerging demands of frontier research and the development of accelerator facilities with enhanced performance, such as high repetition rate x-ray FELs [18,19], continuous-wave (CW) photocathode guns have been rapidly developed to produce electron beams with megahertz (MHz) repetition rates and sub-micron normalized emittance [20]. However, CW photocathode guns, including DC guns [21,22], superconducting radio-frequency (SRF) guns [23,24,25], and very-high-frequency (VHF) normal-conducting radio-frequency (NC RF) guns [26,27,28], typically exhibit lower accelerating gradients and cathode fields compared to S- or L-band NC RF guns [29,30] operated at low repetition rates. In these CW guns, the electron beam typically has a long bunch length and a large transverse beam size to mitigate the emittance growth induced by space charge forces. Such a beam is more sensitive to optical aberrations such as spherical aberration, chromatic aberration, and multipole field aberration. Consequently, more attention should be paid to its transport so as to achieve a high beam quality.

This study focuses on the aberrations caused by multipole fields. Previous research has theoretically analyzed the coupled-transverse-dynamics aberration induced by a DC quadrupole field in the solenoid or an RF quadrupole field from the RF coupler, leading to an increase in two-dimensional projected emittance [31,32]. Experimental studies on several photocathode guns have confirmed that this aberration can be corrected using a downstream quadrupole corrector with appropriate field strength and rotation angle [31,33,34,35,36]. Additionally, theoretical studies and simulations have been carried out to investigate the emittance growth generated by sextupole aberration in a solenoid as well as the corresponding correction method [37]. A successful experimental demonstration of sextupole correction for low-charge beams has also been achieved using a sextupole corrector on a UED beamline [38].

Since 2021, the second-generation DC-SRF photocathode gun, known as the DC-SRF-II gun, has been installed, commissioned, and brought into stable operation at Peking University [39,40,41]. This gun serves as a high-brightness electron source capable of generating high repetition rate CW electron beams. During the commissioning, we observed that the beam was not only affected by quadrupole aberration in transport but also highly sensitive to sextupole aberration. Moreover, the transverse beam distribution became more intricate at relatively high bunch charges up to 100 pC. Therefore, we analyzed the effects of multipole fields on electron distribution and transverse emittance. Especially, we developed a method for rapid characterization of multipole field effect, based on which correction of multipole field aberrations was performed without extensive parameter scanning.

This paper presents a detailed description of our study on the characterization and correction of multipole field effect on electron beams. The remaining part of the paper is organized as following. Section 2 presents an overview of the DC-SRF-II photocathode gun and the beamline. Especially, we analyze the sources of multipole fields in the beamline. Section 3 discusses the impacts of multipole fields on transverse beam performance, including theoretical analyses ignoring space charge effect and numerical simulations considering space charge effect. Section 4 details the method for rapid characterization and correction of multipole fields. Both simulation results and experimental studies are included. Finally, we give a summary in Section 5.

2. Overview of the DC-SRF-II Photocathode Gun and the Beamline

The overall structure of the DC-SRF-II gun is illustrated in Figure 1. It combines a 100 kV DC gap and a 1.3 GHz 1.5-cell SRF cavity, which are connected by a short drift tube. A K₂CsSb photocathode is located in the DC gap and its surface field is 6 MV/m. For the experimental study presented in this paper, the RF cavity is typically operated at an on-axis peak field between 18 to 23 MV/m, which can boost the electron beam energy to 1.9~2.5 MeV. In the cryomodule of the DC-SRF-II gun, an orbit correction coil is installed at the exit to finely adjust the orbit of the extracted electron beam.

To characterize the beam quality, a dedicated diagnostic beamline has been built downstream of the electron gun, as shown in Figure 2. The first solenoid (Sol1), located at the gun exit, serves for beam focusing and emittance compensation. Multiple YAG:Ce screens (Y1-Y5) are installed along the beamline to measure the transverse beam distribution. The scanning slits (S1/S2) and screens (Y3/Y4) are used to measure the transverse phase space and projected emittance at different positions using the single-slit scanning method [42]. Finally, the second solenoid (Sol2) focuses the beam either into a downstream beam dump or through a 90° deflection magnet for energy measurement.

During the commissioning of DC-SRF-II photocathode gun, a distinct distortion of the transverse beam distribution has been observed. After ruling out beam collimation as a cause, this distortion was primarily attributed to the influence of multipole fields. There are two potential sources of multipole fields in our experiments: the asymmetric structure of the RF cavity, which is a result of the single coaxial RF coupler design for the DC-SRF-II gun, and the field distortions in magnetic elements, such as undesired multipole fields in the solenoid generated by the asymmetry of the iron yoke and coil [31,32,33].

To investigate the impact of the first potential source, the three-dimensional electromagnetic field distribution of the SRF cavity was simulated using CST Microwave Studio [43]. By performing Fourier analysis on the angular magnetic field at the location of the coupler, we determined the relative strength of various multipole fields [32]. The ratio between the quadrupole/sextupole and monopole strengths at a distance of 10 mm to the cavity axis is 2.9%/1.1%. On the other hand, since the RF coupling port is located at 45 mm downstream of the SRF cavity’s exit iris, the angular magnetic field therein is typically below 2 Gs. Consequently, the multipole field strength caused by the coupler is minimal. This has been validated by our particle tracking simulation, which indicates that the impact of RF coupler's multipole fields on the beam can be neglected.

To analyze the second source of multipole fields, a three-dimensional translational Hall probe was employed to measure the field distribution of the magnets/coils. The results indicate strong multipole fields in both the orbit correction coil in the cryomodule and the solenoids. Within the orbit correction coil, while the quadrupole field component is small, there is a noticeable sextupole field. When the magnetic field at the center of the coil is 10 Gs, the integrated field strength for the normal sextupole component reaches 2.43 Gs/cm. Therefore, we finally gave up using this correction coil. For the two solenoids shown in Figure 2, the distributions of multipole fields are quite different, but both of them have distinct quadrupole and sextupole field components at the entrance and exit. Taking Sol1 as an example, when the on-axis peak magnetic field strength reaches 480 Gs, the integrated field strength of the normal quadrupole component at two ends is -2.11 Gs and 0.47 Gs, respectively, while that of the normal sextupole component is -0.63 Gs/cm and -0.22 Gs/cm, respectively, as shown in Figure 3.

3. Beam Aberration due to Multipole Fields

3.1. Emittance Growth and Beam Profile Evolution due to Multipole Fields

Previous research [31] has shown that the effects of the RF quadrupole field in a photocathode gun can be mitigated by applying a weak DC quadrupole field. To simplify the analysis, this study primarily focuses on the impact of DC multipole fields on transverse beam dynamics, particularly investigating the emittance growth and beam profile evolution induced by multipole field aberrations. First, we consider normal multipole fields, whose transverse distribution can be expressed as

$$\{\begin{array}{l}{B}_x=K_{n,normal}{r}^n\sin \left(n\theta \right)\\ B_y=K_{n,normal}{r}^n\cos \left(n\theta \right)\end{array},$$

(1)

where $K_{n,normal}={\displaystyle \frac{1}{n!}}{{\displaystyle \frac{{\partial }^n{B}_y}{\partial x^n}}|}_{x,y=0}$ represents the strength of the normal 2(n+1)-pole field.

A multipole field with an arbitrary rotation angle can be regarded as the result of rotating a normal multipole field counterclockwise by an angle α around the z-axis (the direction of beam propagation). By applying a coordinate transformation to Equation (1), the transverse distribution of the multipole field with a rotation angle α is given by

$$\{\begin{array}{l}{B}_x=K_n{r}^n\sin \left[n\theta -\left(n+1\right)\alpha \right]\\ B_y=K_n{r}^n\cos \left[n\theta -\left(n+1\right)\alpha \right]\end{array}.$$

(2)

The equation of motion for electrons in a multipole field can be expressed as

$$\{\begin{array}{l}{\displaystyle \frac{d{p}_x}{d\mathrm{z}}}=e{B}_y\\ {\displaystyle \frac{d{p}_y}{d\mathrm{z}}}=-e{B}_x\end{array}.$$

(3)

With thin lens approximation, the change in transverse momentum of the electrons after passing through the multipole field can be calculated as

$$\{\begin{array}{l}\mathrm{\Delta }{p}_x=eL{B}_y=eL{K}_n{r}^n\cos \left[n\theta -\left(n+1\right)\alpha \right]\\ \mathrm{\Delta }{p}_y=-eL{B}_x=-eL{K}_n{r}^n\sin \left[n\theta -\left(n+1\right)\alpha \right]\end{array},$$

(4)

where L is the effective length of the multipole field.

To simplify the analysis, we assume a cylindrically uniform electron beam with a radius R, zero initial emittance, and zero energy spread. For an arbitrary electron, the initial phase space coordinates can be expressed as $(r\cos \theta ,0)$ with $r\in [0,R]$ and $\theta \in \left[\mathrm{0,2}\pi \right)$. After traversing the multipole field (neglecting the space charge effect), its coordinates become

$$\{\begin{array}{l}x=r\cos \theta \\ x^{\prime }={\displaystyle \frac{\mathrm{\Delta }{p}_x}{p_z}}={\displaystyle \frac{eL{K}_n}{\beta \gamma m_{e}c}}{r}^n\cos \left[n\theta -\left(n+1\right)\alpha \right]\end{array}.$$

(5)

The second-order moments of $x$ and $x^{\text{'}}$ for the electron beam are

$$\begin{array}{c}\langle x^2\rangle ={\displaystyle \frac{R^2}{4}},\hfill \\ \langle {x^{\prime }}^2\rangle ={\displaystyle \frac{1}{\pi R^2}}{\displaystyle \underset{0}{\overset{2\pi }{\int }}{\displaystyle \underset{0}{\overset{R}{\int }}{\left(\frac{eL{K}_n}{\beta \gamma m_{e}c}\right)}^2{r}^{2n}{\cos }^2\left[n\theta -\left(n+1\right)\alpha \right]}}\cdot rdrd\theta ={\left({\displaystyle \frac{eL{K}_n}{\beta \gamma m_{e}c}}\right)}^2{\displaystyle \frac{R^{2n}}{2n+2}},\hfill \\ \begin{array}{c}\langle x{x}^{\prime }\rangle ={\displaystyle \frac{1}{\pi R^2}}{\displaystyle \underset{0}{\overset{2\pi }{\int }}{\displaystyle \underset{0}{\overset{R}{\int }}\frac{eL{K}_n}{\beta \gamma m_{e}c}{r}^{n+1}\cos \theta \cos \left[n\theta -\left(n+1\right)\alpha \right]}}\cdot rdrd\theta \\ =\{\begin{array}{l}{\displaystyle \frac{eL{K}_n}{\beta \gamma m_{e}c}}{\displaystyle \frac{R^2}{4}}\cos 2\alpha \\ 0\end{array}\begin{array}{c}\\ \end{array}\begin{array}{c}(n=1)\\ (n>1)\end{array}\end{array}.\hfill \end{array}$$

(6)

The multipole field induced normalized emittance growth in the x direction can then be expressed as

$${\epsilon }_{n,multipole}=\{\begin{array}{l}{\displaystyle \frac{eL{K}_n}{m_{e}c}}{\sigma }^2\left|\sin 2\alpha \right|\\ {\displaystyle \frac{eL{K}_n}{m_{e}c}}{\displaystyle \frac{2^n{\sigma }^{n+1}}{\sqrt{2\left(n+1\right)}}}\end{array}\begin{array}{c}\\ \end{array}\begin{array}{c}\left(n=1\right)\\ \left(n>1\right)\end{array}.$$

(7)

where $\sigma ={\displaystyle \frac{1}{2}}R$ represents the initial transverse root mean square (rms) size of the beam. In the y direction, we can get the same expression.

Equation (7) shows that the emittance growth due to a multipole field is closely related to the transverse beam size $\sigma$ and the integrated field strength LK_n. As a crosscheck of the equation, we used GPT code [44] to simulate the multipole field induced emittance for different transverse beam sizes and multipole field rotation angles. The results are plotted in Figure 4 (a) and (b), respectively, together with those calculated using Equation (7). Both results agree very well. Note that in this simulation a 2 MeV electron beam with an initial emittance of zero was assumed and the space charge force was disabled.

Based on Equation (5), the transverse beam profile after a multipole field can be derived. Assuming the electron beam drifts a distance s downstream from the multipole field, the transverse coordinates of the electrons are given by

$$\{\begin{array}{l}x(s)=x_0+x^{\prime }s=r\cos \theta +C_n{r}^n\cos \left[n\theta -\left(n+1\right)\alpha \right]\\ y(s)=y_0+y^{\prime }s=r\sin \theta -C_n{r}^n\sin \left[n\theta -\left(n+1\right)\alpha \right]\end{array},$$

(8)

where $C_n=eL{K}_{n}s/\beta \gamma m_{e}c$. Given the weak focusing strength of the multipole field, the transform of the outermost electrons’ coordinates (i.e., a contour for the electron distribution) can be used to represent the beam profile evolution. By substituting r = R into Equation (8), the parametric equation for the beam profile contour is

$$\{\begin{array}{l}X(s)=R\cos \theta +C_n{R}^n\cos \left[n\theta -\left(n+1\right)\alpha \right]\\ Y(s)=R\sin \theta -C_n{R}^n\sin \left[n\theta -\left(n+1\right)\alpha \right]\end{array}.$$

(9)

Figure 5(a-d) show the x-y plane distribution of the electron beam at the initial state and after 3-m drift under the influence of quadrupole, sextupole, and octupole fields, as simulated by GPT. The black solid lines represent the beam profile contours derived from Equation (9), which indicates the evolution of the transverse beam distribution can be accurately depicted. We also plot the corresponding x-x’ phase space in Figure 5(e-h). Similarly, the evolution can be depicted with the contour whose parametric equation can be derived from Equations (5) and (8). Note that after passing through the multipole field, the electron beam’s phase space area expands, indicating an increase of emittance.

3.2. Simulation with Space-Charge Forces

When the electron gun operates with large bunch charges, space charge forces would significantly intensify the aberrations. For a more accurate analysis, space charge effect should be taken into account in the simulation.

We first investigated the evolution of transverse beam profile along the same beamline as the DC-SRF-II gun using the GPT code. The electron beam has a bunch charge of 100 pC and a kinetic energy of 2 MeV. After being focused by the solenoid, the beam then passed through either a normal quadrupole field with an integrated strength of 3 Gs or a sextupole field with an integrated strength of 5 Gs/cm. The solenoid has a peak axial field of 490 Gs and can focus the beam to a waist at z = 4 m.

To evaluate the influence of space charge forces on the evolution of the transverse beam profile, the GPT simulation with space charge forces was first stopped at z = 2.5 m, i.e., 1.5 m upstream of the waist. Subsequent simulations without and with space charge forces were then started at z = 2.5 m and stopped at z = 5 m, i.e., 1 m downstream of the waist.

For the quadrupole field case, a scatter plot of the transverse distribution upstream of the waist (at z = 2.5 m) is shown in Figure 6(a), where red and blue colors are used to tag the particles in the upper and lower regions, respectively. Figure 6(b)/(c) show the transverse distributions at z = 5 m without/with space charge forces. One can see that the space charge force leads to the formation of water drop shaped profiles and the merging of red and bule particles.

For the sextupole field case, the situation is more complicated. Figure 6(d) shows the transverse distribution at z = 2.5 m, where the particles in the trisected regions are tagged with red, green, and blue colors. Without space charge forces, triangular profiles are formed at z = 5 m, as shown in Figure 6(e). However, when space charge forces are included, the red, green, and red particles evolve into moon-shaped profiles separately and get merged at the same time, as shown in Figure 6(f).

Figure 7 shows the beam aberrations observed in the DC-SRF-II experiments under different operating conditions, which are similar to the simulated transverse distributions in Figure 6(c) and 6(f).

The presence of multipole fields can also affect the emittance compensation process of the electron beam. For an RF photocathode gun, emittance compensation process [45,46] results in the alignment of mismatched slices in phase space, thereby reducing the projected emittance. The presence of multipole fields in the beamline, however, induces asymmetric transverse forces on the beam, which would disrupt the compensation process.

Figure 8 shows the simulated evolution of transverse beam size and emittance when a focused electron beam (after the solenoid) traverses a normal quadrupole or sextupole field. The conditions for the simulation are consistent with those in Figure 6. For the quadrupole field case, the defocusing/focusing in the x/y direction affects the charge density distribution, which in turn alters the emittance compensation conditions, leading to asymmetric emittance evolution and especially a significant increase in the y direction after the waist. For the sextupole field case, the emittance minimums become much larger. However, both the beam size and emittance remain equal in x and y directions.

Finally, we demonstrated the impact of RF field, for which the RF phase in the GPT simulation was set to +15° off crest acceleration. This leads to a large energy chirp within the electron bunch and the higher/lower energy electrons are at the bunch head/tail. Due to the energy chirp, different electron slices within the bunch experience distinct focusing/defocusing when passing through the solenoid and normal quadrupole field. Near the beam waist, the head slices of the beam get defocused/focused in x/y direction while the tail slices get focused/defocused. This leads to elliptical profiles with the major axes along x/y direction at bunch head/tail, as shown in Figure 9(b). Consequently, the profile for the whole beam exhibits a cross-star shape, as shown in Figure 9(a).

4. Multipole Characterization and Correction

4.1. Equivalence of Distributed Multipole Fields

Figure 10(a) illustrates the multipole field error distribution along the diagnostic beamline for the DC-SRF-II gun, in which Q_a, Q_b, Q_c and S_a, S_b, S_c denote the quadrupole and sextupole components of the correction coil in the cryomodule and the entrance and exit ends of the solenoid (Sol1). Considering the relatively weak strength, the multipole fields can be modeled as an equivalent field at position d with combined quadrupole and sextupole components, which are denoted as Q_d and S_d, respectively. By matching the electron beam profile according to the effect of the equivalent fields, we can inversely derive the strength and rotation angle of each component of the equivalent multipole fields.

To simplify the analysis, we still assume a cylindrically uniform electron beam with zero initial emittance and neglect the space charge effect first. The electron beam has a radius of R_d at position d and the solenoid, located at a distance l_d from position d, has a focal length of f. The strength, rotation angle, and effective length of Q_d/S_d are K₁/K₂, α₁/α₂, and L₁/L₂, respectively. By substituting these parameters into Equation (9) and taking into account the focusing effect of the solenoid, the parametric equation describing the profile contour of the electron beam at a distance s downstream from position d can be expressed as

$$\{\begin{array}{l}X(s)=R_d\left(1-{\displaystyle \frac{s}{f-l_d}}\right)\cos \theta +C_1{R}_d\cos \left(\theta -2{\alpha }_1\right)+C_2{R}_d{}^2\cos \left(2\theta -3{\alpha }_2\right)\\ Y(s)=R_d\left(1-{\displaystyle \frac{s}{f-l_d}}\right)\sin \theta -C_1{R}_d\sin \left(\theta -2{\alpha }_1\right)-C_2{R}_d{}^2\sin \left(2\theta -3{\alpha }_2\right)\end{array},$$

(10)

where $C_1=e{L}_1{K}_{1}s/\beta \gamma m_{e}c$,$C_2=e{L}_2{K}_{2}s/\beta \gamma m_{e}c$.

We then simulate the evolution of the electron beam’s transverse distribution and emittance growth, for which we assume an electron kinetic energy of 2 MeV, an initial transverse radius of 8 mm, and a solenoid focal length of 2 m. Figure 10(b) shows the transverse distribution of the electron beam at a distance of 1.5 m downstream from the solenoid, which has passed through positions a, b, and c in Figure 10(a). The outmost electrons are plotted as black hollow points in Figure 10(c), which comprises the beam profile contour. A particle swarm algorithm is used afterwards to fit the points to Equation (10). The strength and rotation angle of the equivalent multipole fields, K₁, α₁, K₂ and α₂ at position d are therefore obtained. As a comparison, the fitted contour is plotted in Figure 10(c) and Figure 10(d) together with the simulated electron distribution. Both results agree very well.

The emittance growth ${\epsilon }_{n,quadrupole}$ and ${\epsilon }_{n,sextupole}$caused by the equivalent quadrupole field and sextupole field can be individually calculated using Equation (7). The total equivalent emittance growth is ${\epsilon }_{n,equivalence}=\sqrt{{\epsilon }_{n,quadrupole}{}^2+{\epsilon }_{n,sextupole}{}^2}=4.17$mm-mrad, closely matching the above simulation result of 4.18 mm-mrad with distributed multipole fields. These indicate the beam profile fitting method effectively captures the combined effect of multiple multipole fields on the beam.

As discussed in Section 3, space charge force would make the situation complicated. To minimize its effect, it is crucial to characterize the multipole fields and make corrections before the beam reaches a waist. On the other hand, to include the contribution from external focusing forces, emittance, and space charge forces into the analysis, the parametric equation in Equation (10) can be modified as

$$\{\begin{array}{l}X(s)=R_2\cos \theta +C_1{R}_1\cos \left(\theta -2{\alpha }_1\right)+C_2{R}_1{}^2\cos \left(2\theta -3{\alpha }_1\right)\\ Y(s)=R_2\sin \theta -C_1{R}_1\sin \left(\theta -2{\alpha }_1\right)-C_2{R}_1{}^2\sin \left(2\theta -3{\alpha }_1\right)\end{array}$$

(11)

where R₁ represents the transverse beam size at the location of the equivalent multipole fields, while R₂ represents the transverse beam size at the position of measurement/characterization without considering multipole fields.

4.2. Simulation of Multipole Characterization and Correction

Simulations were performed under the operating conditions of the DC-SRF-II gun, with a bunch charge of 100 pC and an electron kinetic energy of 2.3 MeV. We assumed the equivalent quadrupole and sextupole fields were located at z = 1.2 m, while the position for characterization was at z = 3.2 m, i.e., the Y2 screen in Figure 2. The simulation was first performed without multipole fields. Then the distributed multipole fields along the beamline were included, resulting in the transverse beam profile (at Y2) shown in Figure 11(a). By fitting the contour of this profile to Equation (11), the integrated field strength of the equivalent quadrupole and sextupole fields were derived to be 2.72 Gs and 2.1 Gs/cm, respectively, while the rotation angles were 179.3° and 64.9°, respectively.

Figure 12(a) displays the evolution of the transverse beam size and emittance along the beamline, both showing evident asymmetry. At z = 5.1 m, where the emittance measurement device (EMD) is located in experiments, the emittance in the x/y direction increases to 1.60/1.39 mm-mrad, while the corresponding transverse beam profile gets significantly distorted, as shown in Figure 11(b).

Based on the above characterization results, correction quadrupole and sextupole fields were introduced at z = 1.2 m, both having reversed integrated field strengths but same rotation angles as the derived equivalent multipole fields. The simulated transverse beam profiles after correction are shown in Figure 11(c) and (d), which show significant improvement. In Figure 12(b), we also present the evolution of the transverse beam size and emittance for the corrected beam. At the EMD position, the emittance in the x/y direction is reduced to 0.56/0.55 mm-mrad.

4.3. Experiments of Multipole Characterization and Correction

In the diagnostic beamline of the DC-SRF-II gun, two sets of correctors are installed near the Sol1 solenoid, as shown in Figure 13. The quadrupole corrector before the solenoid has eight coils, constituting a normal/skew quadrupole pair to produce quadrupole field rotatable around the axis. The sextupole corrector after the solenoid has six coils which are mounted on a rotating frame to produce rotatable sextupole field.

Our experiments herein are mainly performed at a bunch charge of 20 pC (the major parameters are listed in Table 1). In the experiments, we first took the beam profile on the Y2 screen, as shown in Figure 14(a). Then the contour was extracted from the beam profile, for which a threshold equal to 5% of the maximum intensity was applied. By fitting the extracted contour, plotted as black points in Figure 14(b), to Equation (11), the rotation angle of the equivalent quadrupole/sextupole field was determined as 114°/34°, while the integrated field strength was 1.68 Gs/1.4 Gs/cm. The fitting curve is depicted by the solid red line in Figure 14(b).

We finally set the quadrupole and sextupole correctors according to the characterization results. Figure 15 shows the transverse beam profiles on the Y2 screen at different solenoid strength both before and after the corrections. We can see more regular and symmetric electron distributions when the corrections are applied.

The electron beam emittance was also measured before and after corrections. Figure 16 shows the results as a function of solenoid field strength. For each measurement after corrections, the strengths and rotation angles of the multipole field correctors were recalculated and adjusted accordingly. From the figure, we can see the optimized/minimum normalized emittance achieved by scanning the solenoid strength was reduced from 0.40 mm-mrad to 0.28 mm-mrad.

Experimental study has also been carried out at a bunch charge of 100 pC, as reported in [41], which demonstrated a reduction of normalized emittance from 0.73 mm-mrad to 0.54 mm-mrad after multipole field corrections.

5. Conclusions

We have investigated the impact of multipole fields on the transverse performance of electron beam from a CW photocathode gun and revealed the sensitivity of the beam profile and emittance to multipole field errors. We have also developed a method for rapid characterization and correction of multipole field effects, which improve the beam quality significantly while avoiding measuring the distributed multipole field errors in magnets and extensive parameter scanning during correction. This study is expected to benefit the development of high-brightness electron sources.