Dynamics study of a drift tube linac for both heavy ions and proton

An accelerator complex for Space Environment Simulation and Research Infrastructure (SESRI) has been designed by Institute of Modern Physics (IMP) and will be constructed in Harbin Institute of Technology (HIT). This accelerator consists of an ECR ion source, a linac injector, a synchrotron and 3 experiment terminals. As an important part of the complex, the linac injector should provide both proton and different kinds of heavy ions, from helium to bismuth, with energy of 5 MeV and 1 MeV/u respectively for the synchrotron. In order to provide beams with the mass to charge ratio (A/Q) range from 1 to 6.5 (for proton to 209Bi32+) by only one linac injector, a special solution of the main acceleration section DTL is carried out. The relevant dynamics calculations, such as beam matching, stripping process of the hydrogen molecule ion and beam energy spread reducing, are performed by Particle in Cell (PIC) method.


Introduction
In order to simulate and research the damage to the electronic equipment and organism on the spacecraft by high energy particles in the universe, Harbin Institute of Technology (HIT) proposed building an accelerator based nuclear irradiation source named Space Environment Simulation and Research Infrastructure (SESRI). The accelerator complex of SESRI is designed and constructed by Institute of Modern Physics (IMP) which contains an ECR ion source, a linac injector, a synchrotron and 3 experiment terminals [1] as shown in figure 1. The ECR ion source can provide mostly all stable ions from proton to bismuth. These ions are accelerated by the linac injector to the injection energy of the synchrotron. The synchrotron accelerates different kinds of ions to specific energy and then slowly extracts them to the experiment terminals. The design of the linac injector must meet the requirements of the synchrotron, which is listed in table 1. For this linac injector, the main problem is how to accelerate both very heavy ions like 209 Bi 32+ and lightest ion proton, and also make it as compact as possible. Between the linac injector and the synchrotron, there is a long beam transport line used for vacuum-level transition.
According to the project requirement, preliminary dynamics design of the DTL has finished. And then, beam dynamics tracking with a PIC simulation code for different operation mode alone the main acceleration section is accomplished. The simulation takes beam matching into account and verifies the preliminary design. On the other hand, effects of stripping foil on the 2 ) are studied. A short beam transport line used for reducing the beam energy spread of proton and heavy ion is also designed in the PIC simulation.

Preliminary dynamics design of the DTL
The R/Q of the injected ion into the synchrotron ranges from 1 to 6.5 and it is too large for a normal conducting muticell linac, because the cavity power is proportional to squared of the R/Q. The whole RF system cannot operate stably in such a large power range. So in order to provide proton beam to the synchrotron, H + 2 is accelerated to 1 MeV/u by RFQ and DTL1 firstly and then be stripped to proton to ulteriorly accelerate by DTL2. In this way, the R/Q range of the RFQ and the first DTL will be only from 2 to 6.5. Beam extraction energy of the RFQ is set to 300 keV/u for H + 2 and other heavy ions. The RF frequency is 108 MHz for the whole linac injector, and for DTL cavity interdigital H-mode (IH) structure is employed because of its high shunt impedance. So both of the two DTLs are based on π-mode structure.
KONUS beam dynamic concept [2] and LORASR code [3] are adopted to make the preliminary dynamics design of the DTL for the linac injector. On the basis of the injection energy requirements of the synchrotron for proton and heavy ions, this linac injector contains two DTL cavities. All heavy ions including H + 2 can be accelerated to 1 MeV/u by the DTL1 which contains an inner focusing quadrupole triplet. There is also an quadrupole triplet between DTL1 and DTL2. DTL2 is only used to accelerate the proton from 1 MeV to 5 MeV. For heavy ions, it is just treated as a drift section. Design parameters of both DTL1 and DTL2 are shown in table 2. The maximum on-axis electric field values of each accelerating gap are optimized to 8.5 MV/m by tuning the gap length and integral voltage. Between the two DTLs, there must be a foil for stripping H + 2 to proton. For simplicity, the effects of stripping foil on the H + 2 are ignored in the preliminary design.  In the dynamics calculation, the tracking particle is set to be proton, but the maximum values of gap voltage and quadrupole magnet strength about DTL1 must be reasonable when 209 Bi 32+ is accelerated. The Kilpatrick factor is less than 2.1 and the maximum pole face magnetic field of all quadrupole magnets is not larger than 0.9 T. Beam transverse and longitudinal phase space distribution at the entrance of DTL1 is set to a uniform distribution where the RMS emittance is 0.2 πmm·mrad and 0.45 πns·keV/u respectively as shown in figure 2. Transverse envelope of 90% beam is shown in figure 3. DTL2 is followed by a quadrupole triplet. Energy spread and bunch length boundary of the beam relative to the synchronous particle can be seen in figure  4. The normalized RMS emittances relative increase is small in the transverse planes but a little larger in the longitudinal plane as shown in figure 5. Nevertheless, the synchrotron cares more about the transverse emittance, especially the horizontal one, and beam energy spread. As shown in figure 6, the minor axis of longitudinal phase ellipse is short and it will benefit us in reducing the beam energy spread which will be discuss later.

Beam tracking for 209 Bi 32+
The preliminary design of the beam dynamics in the RFQ has been finished and the phase space distribution of the extracted beam of the RFQ is shown in figure 7. Water bag distribution is chosen for generating the particle coordinate in each phase space plane. The transverse normalized RMS emittance is 0.15 πmm·mrad. And longitudinal RMS emittance is 14 πDeg.·keV/u. Between the RFQ and DTL1, there is a 1.5 meter-long beam transport line including 5 quadrupole magnets and a 2 gap buncher named Buncher1. When doing the simulation of 209 Bi 32+ , DTL2 is treated as a drift section. The second buncher behind DTL2 is used for reducing the beam energy spread of heavy ions extracted from DTL1. The PIC simulation is performed by BEAMPATH code. [4] The transverse beam envelope, bunch length and energy spread along the main acceleration section are shown in figure 8. At the exit of the linac injector, energy spread of 209 Bi 32+ is less than ±0.3%. In this simulation, transverse normalized RMS emittance increases by about 28% which is larger than preliminary design result. On the basis of the requirement of synchrotron, the normalized RMS emittance of heavy ion beam extracted from RFQ must be less than 0.125 πmm·mrad.

Beam tracking for H + 2 /proton
Because the RFQ and DTL1 are designed for H + 2 and the DTL2 is designed for proton beam, a stripping foil is needed to convert H + 2 to proton. It will enlarge the transverse beam emittance  and energy spread. On the other hand, the holistic beam energy would be lower slightly. These trouble must be considered in dynamics tracking. According to literature research [5], a 15 µg/cm 2 carbon foil is chosen, and the stripping efficiency approaches 100% for 1 MeV/u H + 2 . Its influence on H + 2 beam is calculated by LISE ++ code [6] as shown in table 3, which will be used in the beam tracking. The beam tracking calculation of 500 eµA H + 2 /proton is also performed by BEAMPATH code. Monte Carlo method is adopted for the charge stripping process. Buncher3 is placed behind DTL2 with a distance of 2.5 m for reducing the energy spread of proton. The transverse beam envelope, bunch length and energy spread of H + 2 /proton can be seen in figure 9. Energy spread of 100% beam is too large for the synchrotron. But after removing the 20% particles having large energy spread, the rest of the beam can satisfy the energy spread requirement of the synchrotron. Transverse emittances of H + 2 /proton are shown in figure 10. The local saltation of beam emittance is because of the long bunch not enter into a quadrupole magnet entirely [7]. Because the injection design of synchrotron demands painting in horizontal direction, vertical emittance growth is acceptable. Based on the above beam tracking, proton beam extracted by the linac injector can meet the design requirements.

Conclusion
Dynamic design and tracking calculation of the DTL for the linac injector of SESRI complex has been finished which can provide 1 MeV/u heavy ion and 5 MeV proton beam for the synchrotron. Beam matching section between RFQ and DTL1, stripping foil and energy spread  Figure 9. Beam envelope and energy spread of H + 2 /proton along the main acceleration section.

Figure 10.
Normalized emittances of H + 2 /proton along the main acceleration section.
reducing section are design and simulated. The transverse emittances of heavy ion and proton beam are both less than 13 πmm·mrad and satisfy the injection demand of the synchrotron. Beam energy spread of extraction beam of this linac injector can also meet the requirements of synchrotron basically. The RF structure design of these two DTLs is in progress.