Multifunctional longitudinal beam manipulation based on double emittance exchange

The black curve indicates the final bottom length, which is estimated using Eq. Because the quadrupole scan results are used to estimateεx,3 in Eq. 5.6), the black curve includes a limited error region, which is shown as the blue shaded area. The red dashed line indicates the bottom length (σz,1) at the entrance to the DEEX beamline.

Figure 1: Schematic of PAL-XFEL beamline [6]. . . . . . . . . . . . . . . . . . . . .

High quality X-ray for free electron laser facility

After the bottom compression, the beam has a large residual chirp, which will increase the X-ray pulse bandwidth in the spectrum. To suppress the energy dissipation, the rf cavity and corrugated tubes [7, 8] were used after the bottom compressor.

High temporal and spatial resolutions for ultrafast electron diffraction

Although, the MeV beam energy has the weak space charge force, it still increases the length of the bunch through the nonlinear time-energy correlation at the head and tail of the bunch. Because the length of the swarm was limited by the time–energy correlation at the head and tail, the collision reduced the length of the swarm by several tens of fs.

High gradient and energy efficiency for advanced accelerator concept

When the ray propagates free space with lengthD, then the. where γ is Lorentz's relativistic factor. 2.2) where the effective length of the quadrupole is the field gradient and the magnetic stiffness of the beam.

Figure 4: Longitudinal dielectric structure wakefield driven (blue line) by 1 nC Gaussian beam (orange line).

Principle of EEX

Horizontal divergence and fractional energy deviation at the TDC output can be expressed explicitly using. The TDC creates a horizontal kick depending on the longitudinal position and energy change depending on the horizontal position [see Eq.

Figure 7: Electric and magnetic fields inside the TDC [22].

Limiting factors in EEX

Ideal DEEX beamline

Among the two EEXs, the first EEX beamline transfer matrix can be given using Eq. This means that the matrix for the second EEX can be obtained using η → −η together with the setting κ → −κ (to ensure the EEX condition). Therefore, the transfer matrix for the entire DEEX beamline can be expressed as. 3.3), we note that if the initial beam is decoupled before EEX, the last beam after EEX remains decoupled in a linear order.

Consequently, the LPS can be effectively manipulated using transverse optics, which is significantly simpler and more flexible.

Thick-cavity effects in DEEX beamline

3.3), we note that if the initial beam is disconnected before the EEX, the last beam after the EEX remains disconnected in a linear order. In particular, we emphasize that the matrix elements R55, R56, R65 and R66, which determine the final phase space of the longitudinal beam, contain the optical parameters for the transverse beam, such as C, S, C' and S'. The initial bunch length and chirp are recorded at the first entry of the EEX beamline, while the transverse properties are controllable using quadrupoles.

Therefore, we can set the appropriate σz,3 and C3of−1/ξ to reduce the effect of the thick cavity from the second EEX beamline.

Theoretical analysis for multifunctional LPS manipulation

Theoretical analysis of tunable bunch compression

Theoretical analysis of flexible chirp control

Theoretical analysis of nonlinear LPS manipulation

This equation allows to estimate the controllable range of chirps in the fixed length of the final group. where 1, s2 and s3 are the first, second and third order coefficients of the horizontal phase space. Although, the phase space has nonlinearities, the initial horizontal phase space and the final LPS must follow Liouville's theorem. The blue bars are the histogram result and the orange line is the equalization result. Figure 8 shows the comparison between a numerical particle tracking and an analytical equation.

When = 6 3 then the third order coefficient disappears in the horizontal phase space and the peaks disappear.

Table 1: Initial horizontal beam parameters and second EEX transfer matrix elements for Fig

Argonne Wakefield Accelerator facility

AWA laser
AWA photoinjector
AWA experimental beamline
AWA homemade octupole magnet

The procedure for manufacturing the eight-pole is as follows: 1. Determine the location and find the required maximum strength of the eight-pole. For these reasons and physical size issues, the best position of the octapole is between the first and second quadrupoles in the center section. The octapole also uses a field strength parameter Baoct3, where Boct is the magnetic field on the pole surface and the drill radius.

After deciding the maximum strength of the octupole, we performed the physical design of the octupole magnet.

Figure 10: 100 pC beam AWA photoinjector simulation results using Impact-T code [46]. (a) is LPS when the laser temporal distribution is flattop

Beam diagnostic methods

YAG screen

In this situation, OTR can be useful because it has a low photon flux production than the YAG. Beyond the YAG, a 45◦ mirror is installed to reflect the emitted light from the beam lines.

Quadrupole scan

Here d is the length between the quadrupole and the screen, is the effective length of the quadrupole, Bρis the magnetic rigidity of the beam, and is the gradient of the quadrupole. Therefore, we need to consider the analytical beam sizes at the screen, based on the transport equation. For example, if we scanned the quadrupole gradient from a T/m tobT/m with points and measured both horizontal and vertical beam sizes at each point, initial beam sizes, slopes, and emittances are unknown factors in the equations.

Note that it is preferable that the quadrupole scan contains a focal point to increase the accuracy of the fit.

LPS diagnostic section

To find these unknown factors, we apply parametric fitting to the measurement data based on these equations. The fit returns the coefficients so that we can calculate the initial Twiss parameters as, .

Demonstration of multifunctional LPS manipulation via simulations

Injector simulation
Simulation results: Tunable bunch compression
Simulation results: Flexible chirp control simulation
Simulation results: Nonlinear LPS manipulation
Quadrupole alignment
TDC kick strength calibration
Dogleg dispersion calibration
Spectrometer dispersion calibration

So we can better measure the spread of the dogleg based on the change in the center of mass of the beam. As with the TDC, the dogleg must scan the beam energy to achieve the spread. The bending angle of the dipole is linearly proportional to the beam energy or the applied dipole current.

Consequently, the dipole current scan provides the mushroom distribution at the beam energy E0 and the bending angle of θ0.

Figure 20: The injector simulation for the DEEX experiment. (a) is xy beam image. (b) is longitudinal phase space

Experiment procedure

Experimental beamline setting

In our case, the scatter was calculated from the simulation because the spectrometer supplier provides the 3D field map. Using the screens on the straight, we set the RF phases of the TDCs. The opposite sign of the design κ produces a larger horizontal beam size due to the EEX condition.

The second quadrupole stretch was performed on the third and fifth quadrupoles and used the straight-section screen behind a fifth DEEX beamline dipole.

DEEX beamline tuning for experiment

Note that TDC has two crossings across zero (±κ) and can be distinguished by the first EEX beamline. The screens were installed immediately after the last quadrupole of Quad Array 1 and the first dipole of the DEEX beamline. The first quadrupoles in the Quad 2 set performed a quadrupole scan to achieve the initial beam condition.

Therefore, the first quadrupole was used to focus the vertical beam and the second quadrupoles performed the quadrupole scan for the optimization of the remaining quadrupoles.

Experimental data acquisition

By comparing theσx on the screen, one can estimate theσxandsx with the DEEX beam input. The last quadrupole did the quadrupole scan to evaluate the beam state at the second input of the EEX beam. In case of non-linear LPS manipulation, the vertical beam should be minimized to octupole.

Experiment results

Tunable bunch compression

Additionally, unlike conventional compressors, chirp control is not required for clutch compression. We observed both bundle compression and elongation in a scan of the last quadrupole magnet in the midsection. The effect of the coarse cavity in the second EEX can be minimized by using Quad set 1 before the DEEX beamline.

During the experiment, four matched quadrupole magnets in front of the beamline were positioned to reduce the effect of the thick cavity in the second EEX beamline.

Figure 29: Tunable bunch compression by DEEX beamline. The last quadrupole magnet in the middle section was scanned during the experiment

Flexible longitudinal chirp control

During the experiment, the four matching quadrupole magnets in front of the beamline were adjusted to minimize the effect of the coarse cavity on the second EEX beam. be written as a function of the length of the final bundle and the horizontal slope at position 3 in Fig. Similar to the tunable bunch compression described in Eq. 5.6), the final longitudinal chirp is controlled by the horizontal slope at the end of the middle section, which can be easily adjusted with quadrupole magnets. During the experiment, we used several different combinations of the last two quadrupole magnets in the Quad 2 array so that the chirp varied while the length of the final bundle remained constant.

The quadrupole magnets in the center section were initially set to generate the final beam distribution, as shown in Fig.

Nonlinear longitudinal phase space manipulation

Figure 31(f) shows the third-order coefficient from the polynomial fit of the measured LPS and the corresponding rms bunch length. When the input beam at the EEX beam line satisfies the minimum bundle length condition (sx=-R51/R52), the final bundle length can be expressed as. Limiting factors, higher order effects and CSR effects, increase the group length and emission at the same time.

In the previous section, we found that the CSR effect is negligible at the final set length.

Figure 32: Layout of single EEX beamline. The beamline consists of two doglegs, a TDC, a fundamental mode cavity and three sextupoles.

Correlated energy spread suppression for XFEL-O

We removed both group 1 and 2 compressors in the original LCLS-II HE mesh and found a DEEX beamline at the position of the first group compressor. The beam energy from the injector is 100 MeV and is accelerated to 8 GeV. One sextupole and 12 quadrupoles make up the middle section of the DEEX beamline for coherent suppression of energy propagation.

Operation on the apex of linac 1 increased beam energy from 250 MeV to 311 MeV at the DEEX beamline entrance, while LPS imparts quadratic curvature as shown in Fig.

Figure 35: Longitudinal phase spaces at three points. (a) DEEX beamline entrance. (b) DEEX beamline exit

DEEX based LPS manipulation for multi-color X-ray

Theoretical background

They move to the zero crossing points of the sine curve and the density profile can converge when the appropriate R56 is introduced. Note that in the middle of the DEEX beamline there will be quadrupole magnets that can control these elements of the transfer matrix. The quadrupole magnets were optimized to create the coupling and the DEEX beamline provided the R-terms as listed in Table 4.

Similarly, in this table, R65 and R66 are matrix elements, the spectral bundling, and the other two elements are not listed.

Figure 36: Longitudinal phase spaces of numerically tracked beam. An artificially generated beam trav- trav-els through a 200 GHz dielectric structure and DEEX beamline to illustrate density and spectral bunching cases

Experimental demonstration in AWA

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