# Two Design Options for Compact Linear Accelerators for High Flux Neutron Source
###### Abstract  
We describe and compare two optimized design options of RF linear accelerators with different resonant frequencies at 162.5 MHz (f\({}_{0}\)) and 325 MHz (2-f\({}_{0}\)). The RFQ + DTL linacs have been designed to provide 13 MeV acceleration to a proton beam for achieving a fast neutron yield of not lower than 10\({}^{13}\) n/s via \({}^{9}\)Be(p, n)\({}^{9}\)B reaction in pulsed-mode operation. Our design studies show that none of the two options is better than the other, but that the choice of operating frequency will mainly be determined by the accelerator length and RF cost consideration. This study can serve as a basis for the design of an initial stage of a new high brilliance Compact Accelerator-driven Neutron Source (CANS), aiming to use neutron scattering techniques for studying material properties in fundamental physics, materials science, nuclear energy, as well as for industries and societal challenges.  
particle beam transport; RF cavities; power RF sources; medical accelerator technology; accelerators for industry; accelerators for materials science +
Footnote †: journal: Applied Sciences  
**Citation:** [PERSON]; [PERSON].;  
[PERSON]; [PERSON] Two Design Options for Compact Linear Accelerators for High Flux Neutron Source. _Appl. Sci._**2022**, 12, 386.  
However, beryllium and lithium have different properties. Due to the low melting point (453.65 K) and thermal conductivity (85 W m\({}^{-1}\)K\({}^{-1}\)) and the high-power density deposited in the target material, it can be difficult to keep the lithium target solid, which leads to the selection of liquid lithium (LiLiT) in the target design [13; 14]. Moreover, the residual radioactivity of product nucleus, \({}^{7}\)Be, should be carefully handled in the target system.  
In contrast, beryllium is strong, more elastic than steel, does not oxidize in air, and has more favorable thermodynamic properties, which make this material ideal for a water-cooled neutron source [15]. Proton reactions at low energy favor lithium from a consideration of neutron yield alone. However, as the proton beam moves to higher energy, the neutron yield from beryllium is superior to lithium.  
Considering the requirements of input proton beam current and bombarding energy, the total neutron yields have been collected from the literature for proton energies up to 23 MeV. Figure 2 shows the total neutron yield from Be(p, xn) across a region of proton energy accessible to the accelerator system [16]. An empirical formula for the total neutron yield, \(Y_{N}\), as a function of the proton energy, \(E_{p}\) in MeV, is [17],  
\[Y_{N}\big{(}E_{p}\big{)}=3.42\times 10^{8}\big{(}E_{p}-1.87\big{)}^{2.05}\ [ \mathrm{n}/\mathrm{\SIUnitSymbolMicro C}] \tag{1}\]  
Although the neutron production rate increases monotonically with proton energy, there is a factor of four increase going from 7 MeV to 13 MeV. However, a clear drawback of the \({}^{9}\)Be target at energies above 13 MeV is the production of \({}^{7}\)Be via (p, t), (p, nd) and (p, 2 np) reactions [18; 19]. Threshold energies for these reactions are 13.4 MeV, 20.4 MeV and 22.8 MeV, respectively. The half-life of \({}^{7}\)Be is 53 days while it is 12.3 years for tritium.  
Since the threshold for the 9 Be(p, t)7 Be reaction is 13.4 MeV, and if we wish to minimize target activation, the maximum proton energy should not exceed 13.4 MeV. This choice of maximum proton energy is used in the rest of the paper for the design of the presented accelerating structures for ABNS Linacs.  
Figure 1: Schematic diagram of the ABNS layout: (**Upper**) a 162.5 MHz design option, (**Lower**) a 325 MHz design option.