Phase space analysis of velocity bunched beams

Peak current represents a key demand for new generation electron beam photoinjectors. Many beam applications, such as free electron laser, inverse Compton scattering, terahertz radiation generation, have efficiencies strongly dependent on the bunch length and current. A method of beam longitudinal compression (called velocity bunching) has been proposed some years ago, based on beam longitudinal phase space rotation in a rf field potential. The control of such rotation can lead to a compression factor in excess of 10, depending on the initial longitudinal emittance. Code simulations have shown the possibility to fully compensate the transverse emittance growth during rf compression, and this regime has been experimentally proven recently at SPARC. The key point is the control of transverse beam plasma oscillations, in order to freeze the emittance at its lowest value at the end of compression. Longitudinal and transverse phase space distortions have been observed during the experiments, leading to asymmetric current profiles and higher final projected emittances. In this paper we discuss in detail the results obtained at SPARC in the regime of velocity bunching, analyzing such nonlinearities and identifying the causes. The beam degradation is discussed, both for slice and projected parameters. Analytical tools are derived to experimentally quantify the effect of such distortions on the projected emittance.

Figure 1

Layout of SPARC linac and matching section. The two blue cylinders around the first two accelerating cavities represent the iron jokes of the TW solenoids.

Figure 2

Deflected 280 pC, 3 ps beam image (right picture) compared to nondeflected one (left picture).

Figure 3

Taken from 2. Measurement of compression factor (red points) and rms bunch length (black points) as a function of the compression phase. The dashed lines are PARMELA simulation [34], both from compression factor (red lines) and bunch length (black lines).

Figure 4

Comparison between measured longitudinal emittance and calculated system resolution. The three curves represent minimum longitudinal emittance measurable as a function of beam transverse emittance. The cyan curve represents the values we would measure for a zero beam longitudinal emittance. The red (blue) curve represents the case in which only the energy (time) resolution is hit. The blue (red) dot represents measured longitudinal emittance for (un)compressed beam where one expects to have a pulse duration (energy spread) smaller than the system resolution.

Figure 5

Simulation (PARMELA) of energy and energy spread as a function of compression phase for a 280 pC beam in the SPARC photoinjector. Red dotted lines show the values relative to the on-crest acceleration.

Figure 6

Instant current profile as a function of the compression phase for the measurements reported in Table . Simulated profiles (Parmela, red curve) are compared to the measured ones (black lines).

Figure 7

Analytical solution of the single particle longitudinal equations of motion along a TW cavity. The blue solid curve shows the relation between injection and extraction phase. The green dashed curve represents the normalized energy as function of extraction phase, i.e., the curvature of the output LPS. By selecting an injection phase interval and doing its projection on the $x$ axis via the blue curve, one can find the output phase interval. The intersection with the green curve gives the shape of the LPS. The lines plotted as an example are significative of the measured LPS reported in Fig. 8.

Figure 8

Measured longitudinal phase space and current profile for a compressed beam with $C=7$. The red line has been drawn as a reference to show the chirp deviation from linearity toward the bunch head, as predicted in Fig. 7. The top left corner shows the beam current profile.

Figure 9

Comparison between slice emittance of uncompressed beams, with TW solenoids on (red) and off (black). The points at $z=0$ represent the horizontal projected emittance reconstructed from the measured slice parameters. The green curve shows the current profile.

Figure 10

Slice emittance comparison for different gun solenoid strengths, and compression factor of 3. The points at $z=0$ show the horizontal projected emittances reconstructed from the slice parameters.

Figure 11

Mismatch parameter for the three cases of Fig. 10.

Figure 12

Gun solenoid scan of projected emittance with TW solenoids switched on and no rf compression. The black diamond represents the best horizontal and vertical emittance found with TW solenoids off.

Figure 13

Projected emittance of compressed beam as a function of gun solenoid field, for two different beam orbits along the linac. Dots represent emittance with beam orbit on the electromagnetic center of the cavities. Diamonds show the same measurements after the beam orbit has been reoptimized on the magnetic axis of the solenoids. As a comparison, horizontal and vertical projected emittance without compression are also shown.

Figure 14

Streak image of compressed beam at linac exit.

Figure 15

Reconstructed $x\mathrm{\text{−}}z$, $x^{\prime }\mathrm{\text{−}}z$ (left), and $x\mathrm{\text{−}}{x}^{\prime }$ (right) planes from quad scan technique. This last plane has been reconstructed from the other two. The slices have been undersampled for clarity.

Figure 16

Horizontal slice emittance and slice current for a 60 pC uncompressed beam. Black triangles (diamond) show the relative measured horizontal (vertical) projected emittance.

Figure 17

Compression factor versus rf injection phase for the 60 pC case. The red curve is the compression curve simulated by PARMELA. On the top-right shows the reported slice current for the maximum compression factor.

Figure 18

The $x\mathrm{\text{−}}t$ plane for a highly compressed low charge beam (60 pC). A nonlinear correlation is visible despite the low resolution.