# Conceptual and Technical Design Aspects of Accelerators for External Injection in LWFA
## 5 Challenges for Beam Stability, Control and Diagnostics
### Arrival Time Jitter  
Table 6 presents an overview of the typical tolerances and expected arrival time jitter for the different compression techniques. More information about the tolerances study can be found in [77]. A disadvantage of the velocity bunching scheme is the fact that the first traveling wave structure, acting as an RF-compressor, must be working around \(-90\) deg from the on-crest phase, resulting therefore in high sensitivity to the phase jitter of the cavity. A phase stability equal or better than \(0.008\) deg must be reached to allow the achievement of an arrival time jitter better than \(10\) fs RMS. Likewise, a stability of \(0.02\) deg would result in \(22\) fs arrival time RMS jitter.  
\begin{table}
\begin{tabular}{l c c c} \hline  & **MC** & **VB + MC** & **VB** \\ \hline Laser-to-RF [fs] & 5950 & 160 & 125 \\ Gun charge [\%] & 1.6 & 301.6 & 1010.1 \\ Gun phase [deg] & 0.78 & 0.61 & 0.49 \\ Gun Amplitude [\%] & 1.14 & 0.72 & 0.40 \\ TWS1 Phase [deg] & 0.021 & 0.011 & 0.010 \\ TWS1 Amplitude [\%] & 0.055 & 0.073 & 0.098 \\ TWS2 Phase [deg] & 0.022 & 0.13 & 4.21 \\ TWS2 Amplitude [\%] & 0.064 & 0.040 & 1.155 \\ Magnetic field [\%] & 0.030 & 0.030 & - \\ \hline \end{tabular}
\end{table}
Table 6: Comparison of the jitter tolerances corresponding to three typical working points in which the beam is compressed by velocity bunching (VB), magnetic compression (MC) or their combination (VB+MC). The tolerances have been studied in reference [77] using the code Elegant [79]. The elements in the table are defined in Figure 6. The line Magnetic field refers to the dipoles of the bunch compressor.  
\begin{table}
\begin{tabular}{l c c c} \hline  & **WP1** & **WP2* & **WP4** \\ \hline \(Q_{final}\) [pC] & 0.8 & 5.7 & 17.3 \\ \(Q_{initial}\) [pC] & 20 & 200 & 50 \\ \(t_{RMS}\) [fs] & 0.5 & 2 & 12 \\ \(E\) [MeV] & 101 & 102 & 101 \\ \(\Delta E/E\) [\%] & 0.17 & 0.43 & 0.27 \\ \(x_{RMS}\) [\(\mu\)m] & 1.0 & 3.3 & 3.4 \\ \(y_{RMS}\) [\(\mu\)m] & 1.3 & 1.7 & 2.1 \\ \(ne_{x}\) [\(\mu\)m] & 0.11 & 0.52 & 0.52 \\ \(ne_{y}\) [\(\mu\)m] & 0.10 & 0.43 & 0.94 \\ \(I_{p}\) [A] & 434 & 814 & 405 \\ \(B\) [A/m\({}^{2}\)] & 4 \(\times\) 10\({}^{16}\) & 5 \(\times\) 10\({}^{15}\) & 8 \(\times\) 10\({}^{14}\) \\ \hline \end{tabular}
\end{table}
Table 5: Summary of the beam characteristics after the bunch compressor for three working points. The peak current \(I_{p}\) is defined as \(I_{p}=Q_{final}/(3.5\cdot t_{RMS})\). The beam brightness is defined as \(B=I_{p}/(ne_{x}ne_{y})\). In the column with (*) 2% of the particles in the tail were removed.  
For the pure magnetic compression scheme, a challenging but more realistic phase jitter of 0.013 deg in both the traveling wave cavities would in this case be sufficient to achieve an arrival time jitter of the beam below 10 fs RMS.  
The arrival time jitter can also be reduced by adopting a jitter compensation scheme. At _SPARC_LAB_ it has been experimentally demonstrated that it is possible to fully compress the arrival time jitter of the photo-cathode laser by properly tuning the \(R_{56}\) of the dogleg and keeping a moderate compression of the electron bunch [80]. The tunability of the \(R_{56}\) in the chicane and dogleg at ARES will allow for testing those and other novel schemes [73].