## 4 RFQ-Decelerator for the GSI HITRAP Facility
### New RFQD Design Applying the DESRFQ Code  
On the basis of the carried-out numerical study and the experimental confirmation, the new RFQD decelerating-focusing channel has been developed. The main design goal was to decelerate U\({}^{92+}\) ions with the energy of 495 keV/u, corresponding to the optimum IH-DTL decelerator settings, down to the design beam energy of 6 \(\pm\) 1 keV/u. Simultaneously, the longitudinal acceptance of the RFQD should be increased to provide for a higher yield of the decelerated ions. Due to the already fixed input- and output-energies and with the fixed overall length of the rods (to be mounted into the same tank), such requirements lead to a nontrivial designing process and require the use of an advanced and reliable beam dynamics code.  
The image-oriented interactive code DESRFQ [34] was developed for advanced RFQ design efforts with a high level of reliability and visualization during all stages of the design process. The beam dynamics in each RFQ cell are calculated immediately after the definition of its parameters. Therefore, characteristics of the next cell can be chosen in accordance with the beam evolution in all previous cells. A typical screenshot (see Figure 6) illustrates the final stage of an interactive design process.  
The new HITRAP-RFQD channel was designed with the standard \"acceleration\" approach. Nevertheless, following the statements mentioned above, in a smart way such approach could be also implemented for the design of an RFQ Decelerator. New rods (mini-vanes) were developed with the constant average radius (average aperture) and the constant width/rounding of the mini-vanes along the channel. This simplifies the fabrication of the mini-vanes, as well as further machine tuning. The rf-voltage was increased from 77.5 kV to 89.5 kV, following experimental tests and dedicated calculations for the maximum electric field strength on the surface of the rods [57]. The main parameters for the original and the new RFQDs are presented in Table 1. The corresponding beam phase portraits, depicting the acceptance for each accelerating-focusing channel, are shown in Figure 7.  
Figure 6: A typical screenshot, illustrating cell-by-cell design process with the DESRFQ code; the longitudinal beam phase portrait (**left**) and the stability diagram (**right**) are shown.  
The RFQD with newly fabricated rods was commissioned and successfully tested at the HITRAP setup with heavy ion high charged beams [17]. A sufficient amount of heavy ions, decelerated to the design energy of 6 \(\pm\) 1 keV/u, were detected (Figure 8, upper spot). Due to unavoidable beam mismatch between IH-DTL and RFQD sections at the recent setup, a significant fraction of the beam could not be decelerated (Figure 8, lower spot). Therefore, a completely revised RFQD design has been recommended for a potential future upgrade of the HITRAP heavy ion linear decelerator.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Original** & **New** \\ \hline Input energy (keV/u) & 525 & 495 \\ Output energy (keV/u) & 6 \(\pm\) 1 (\({}^{\text{th}}\)) & 6 \(\pm\) 1 \\ Voltage (kV) & 77.5 & 89.5 \\ Average radius (cm) & 1.0–0.58–0.68 & 0.65 \\ Rods rounding and width & variable & constant \\ Max. modulation & 3.0 & 2.35 \\ Min. aperture (cm) & 0.34 & 0.39 \\ Frequency (MHz) & 108.408 & 108.408 \\ Max. field strength (kV/cm) & 220 & 238 \\ Kilpatrick factor (criterion 125 kV/cm) & 1.76 & 1.94 \\ Transv. total acceptance, 90\% (cm mrad) & 0.65 & 0.58 \\ Long. total acceptance, 90\% (keV/u-deg) & 177 & 357 \\ Electrode length (cm) & 198.1 & 198.1 \\ \hline \end{tabular} \({}^{\text{th}}\) No decelerated ions were observed behind the original RFQD, installed at HITRAP setup.  
\end{table}
Table 1: Main design parameters of the original and the new RFQD channels.  
Figure 7: Beam phase portraits depicting the acceptance of the original (**top**) and new (**bottom**) accelerating-focusing channels. The ellipses represent 90% of the beam intensity.