Analysis of slice transverse emittance evolution in a very-high-frequency gun photoinjector

Emittance is a key figure-of-merit for high brightness electron beams that enable the success of a broad range of modern accelerator-based instruments. With the successful implementation of the emittance compensation scheme and beam-shaping techniques to align each temporal beam slice in phase space, slice emittance starts to play a more dominating role in determining the beam quality. In this paper, we develop an approach, combining simulations and analytical calculations, to systematically study the evolution of the slice emittance in a very high frequency gun photoinjector, which is under intense R&D worldwide for driving the next generation continuous-wave accelerators. Our approach is capable of tracing various sources that introduce curvature in the transverse phase space, corresponding to the growth of the slice emittance. It is shown that nonlinear transverse space charge forces in the vicinity of cathodes and the spherical aberration of the focusing solenoid are the main sources of nonlinear forces, while in a long drift section space charge forces can actually compensate for nonlinear transverse position-momentum correlations and hence recover the emittance. We further demonstrate that the sources of nonlinearities can be controlled by tailoring the transverse beam density profile and the design of solenoid lenses.

Figure 1

Sketch of a VHF gun photoinjector designed by Tsinghua University.

Figure 2

The evolution of slice emittance and projected emittance in the VHF gun injector.

Figure 3

The relation between slice emittance, correlated emittance, and projected emittance.

Figure 4

Nonlinearity of transverse SC fields with different transverse Gaussian-cut distributions. $R/{\sigma }_x=0.1$ indicates an approximately uniform distribution, $R/{\sigma }_x=1$ or 2 indicates a Gaussian distribution. (a) cigar-like bunch, $\frac{l}{R}=10$. (b) normal bunch, $\frac{l}{R}=1$. (c) pancake-like bunch, $\frac{l}{R}=0.2$.

Figure 5

Emittance evolution curves of the 21st slice in the gun with (a) initial transverse uniform distribution and (b) initial transverse $1\sigma$ Gaussian-cut distribution. The yellow line indicates the $E_z$ field on the axis of the VHF gun. The inset displays the transverse phase space of the slice at position 3.1 mm, where all particles in the bunch just leave the cathode.

Figure 6

The integral momentum of the particles as a function of the radial position at the gun exit. The integral momentum is calculated from the position where all particles are just emitted to the gun exit based on two independent forces: (1) gun rf force (blue) and (2) SC force (red). The linear terms of the integral momentum are subtracted.

Figure 7

The blue dots: the integral momentum contribution of the high-order terms of the rf field as a function of the radial position of each particle at the gun exit. The red dots: the integral momentum contribution of the high-order terms of the SOL1 field as a function of the particles’ radial position at the end of the SOL1 field. Note that the momentum contribution of the rf field is magnified by 10 times in order to compare with the momentum contribution of the SOL1 field.

Figure 8

Emittance growth as a function of the rms beam size at the solenoid center for SOL1 (red) and SOL2 (green). The points are the simulated data in ASTRA. The lines are the fitting curves of ${\epsilon }_r=k*{\sigma }_r^4$.

Figure 9

The evolution curves of the 21st slice in (a) SOL1 and (b) SOL2. The black dashed lines are the on axis solenoid field. The blue and red solid lines indicate the evolution curves of the emittance and the rms beam size in the solenoids, respectively. As a comparison, the purple dotted lines indicate the emittance evolution curves without the solenoids.

Figure 10

The integral momentum contribution of the magnetic field of (a) SOL1 and (b) SOL2 as a function of the radial position of each particle at the end of the solenoid field. The linear term of the integral momentum is subtracted. The red line is a fitting curve of $\mathrm{\Delta }{P}_r=b{r}^3$.

Figure 11

The emittance growth due to $B_z$ on the cathode and the optimal projected emittance as a function of the FWHM of the SOL1 field.

Figure 12

The blue line indicates the emittance evolution of the 21st slice simulated in Astra. The red line is the slice emittance evolution calculated based on Eq. (11) using the particle information at 0.7 m exported from Astra as initial conditions.

Figure 13

(a): The $r-r^{\prime }$ phase space, (b): The average charge density per unit volume within the radius $r$, (c): $r\rho$ as a function of r. The number 1 to 6 in the figure correspond to the positions marked in Fig. 12.

Figure 14

(a) The high-order integral momentum contributions of the buncher rf force. (b) Slice emittance evolution with and without the buncher.

Figure 15

The slice emittance evolutions with and without the linac boosters.

Figure 16

The evolution of the slice emittance and the projected emittance in a typical S-band gun photoinjector. The green line indicates the thermal emittance.