An efficient solution for accelerating very high intensity beams in the low and medium energy regime

Taking advantage of the 0{\deg} synchronous phase, the KONUS ("Combined 0{\deg} Structure"translated from German"Kombinierte Null Grad Struktur") beam dynamics strategy enables long accelerating sections with lens-free slim drift tubes in the low and medium energy regime. It has successfully realized worldwide many room temperature H-type linacs with compact layouts and good beam performance. In this paper, a further development of this solution i.e. to combine the KONUS dynamics with the young superconducting CH (Crossbar H-Type) structure for accelerating very high intensity beams is being presented. The efficiency of the new solution has been shown by the systematic design studies performed for a 150mA, 6MW deuteron linac.


I. INTRODUCTION
For the production of various useful high intensity secondary beams e.g. neutrons, the development of MW-class linear accelerators has become very attractive since several decades. Serving as drivers of large-scale facilities for modern scientific and civil applications, this kind of linacs usually need to deliver very powerful light ion beams e.g. H + , H -, D + to bombard a certain target. Having been put into operation already in the early 1970s, the LANSCE linac [1] formerly known as LAMPF can provide protons with an average beam power up to ~0.8MW. Different from the full room temperature (RT) LANSCE linac, the ~1.4MW Spallation Neutron Source (SNS) linac [2] built in 2006 started to employ the superconducting (SC) radio frequency (RF) technology for the beam acceleration in the high β region. So far, many modern facilities based on this kind of high power driver linacs (HPDL) have been realized e.g. J-PARC [3] or proposed e.g. MYRRHA [4] worldwide, with the tendency to start the cold part already in the low and medium β region.
The average beam power is given by Eq. (1): Average beam power = beam energy × beam current × beam duty factor (1) To reach the beam power in the order of MW, there are typically the following several ways to combine these three factors for a modern HPDL machine:  high energy × modest current × low duty factor: e.g. LANSCE and SNS.
 low energy × very high current × CW: e.g. LEDA [6] and this study. For proton and ion linacs, the classic beam dynamics strategy applies negative synchronous phases typically -30° ~ -40° to the accelerating cells. It provides the beam longitudinal stability but at the same time RF defocusing effects in the transverse planes. In case of high currents, space charge effects are also a big concern for the low and medium energy beams, especially when β≤0.2.
Based on the classic beam dynamics strategy, two well established solutions for the conventional low and medium energy linacs are as follows: However, the separatrix that exists at negative synchronous phases e.g. -30° will shrinks to zero at 0° (see FIG. 3). To solve this problem, KONUS uses only the area marked by blue arrows in the longitudinal phase space, which means that the synchronous particle defining the geometrical layout of the drift tube array and the bunch center (BC) particle are decoupled. The energy shift at the beginning of a 0° section is realized by setting W s < W BC , while the phase shift is obtained by adjusting the tank RF phase or the geometrical length of the transition cell when the transition happens between cavities or inside a cavity, respectively. In short, the beam is injected into a 0° section asynchronously with a surplus in bunch energy and with a proper phase slip against the synchronous particle. This concept has been first applied in combination with an IH (Interdigital H-Type) structure for the heavy ion post-accelerator at the Munich tandem laboratory [9]. TABLE I shows a list of existing and planned KONUS-based H-Type DTLs worldwide. It can be seen that the development of this kind of machines is not only towards higher β but also towards higher current. So far, all realized and to-be-realized KONUS machines are normal conducting accelerators.

II. KONUS AND SC CH DESIGN FOR A 6MW DRIFT-TUBE LINAC
To challenge very high intensity and very high power beams, a 175MHz, 150mA, CW deuteron drift tube linac aiming to increase β from 0.07 to 0.20 is chosen for this study. The total beam power of this DTL will be considerably high as 6MW. For a convenient description, this linac will be called as the 6MW-DTL in the following text.
To avoid the safety and reliability problems e.g. activation and SC quenching which can possibly be caused by beam losses for such a very high power linac, good beam quality has to be ensured during acceleration. Therefore, a very careful design with special optimization concepts will be required for the 6MW-DTL. The primary guideline for our design is to be very conservative and to be fault-tolerant.
The considerations for the general layout of this 6MW-DTL are the follows:  The main beam acceleration (β = 0.10 ~ 0.20) will be accomplished by superconducting CH cavities.
 To be fault-tolerant, in front of the SC part, it's decided to add a warm transition section consisting of a 2-cell rebuncher and an IH cavity (β = 0.07 ~ 0.10) to filter possible notwell-accelerated particles from upstream.
 Quadrupole lenses and solenoids will be used as transverse focusing elements in the RT and SC parts, respectively.

III. BEAM DYNAMICS SIMULATION RESULTS
The beam transport simulation along the 6MW-DTL has been performed with LORASR [17], a dedicated computer code for the KONUS dynamics using H-type structures. The input distribution including ~1 million macro-particles has been obtained from the simulation of a β=0.07 deuteron RFQ accelerator [18] at 150mA. The phase spread is ±30° and larger than the ideal range i.e. ±15° for the KONUS dynamics. FIG. 8 shows also the output phase spaces of the 6MW-DTL. It can be seen that after the acceleration, the particle distributions are still very concentrated in both transverse planes. Although some small halos can be found in the longitudinal plane, they are still in the acceptable range. Hofmann Chart itself has been generated using the TraceWin code [19]. It can be seen that most of the beam trajectories are well confined in the clean area around the equipartitioning line on the chart, except a short trip into the neighboring resonance peak in the second lattice period (this is caused by the rebuncher as mentioned in the previous paragraph). In this way, good beam quality has been ensured.

IV. ERROR STUDIES
For the design stage, only perfect accelerator components and ideal operating conditions have been taken into account. In reality, however, more or less perturbations to the design case are inevi- For the LORASR code, the following kinds of errors can be implemented [20,21]:  Transverse offsets of magnetic lenses (LOFF).

 Rotations of magnetic lenses in all directions (LROT).
 Voltage amplitude errors for accelerating cells and tanks (VERR).
 Phase errors for tanks (PERR).   is <95% and <130% in the transverse and longitudinal planes, respectively. A further particle tracing study proves that those large longitudinal additional growths are contributed by only a few off-energy particles. Generally speaking, therefore, the beam quality stays still good in the presence of mixed errors.

V. CONCLUSIONS
In the last several decades, the combination of KONUS dynamics strategy and room temperature H-type structures has been developed as an efficient solution for accelerating low and medium β beams. To challenge very high intensity beams, a new idea to combine the KONUS dynamics with the young SC CH structure has been proposed and investigated.
The investigation is based on a 150mA, 6MW deuteron linac. To ensure a safe and reliable CW operation at such a very high intensity and mainly at 4.2K, 1) a carefully design guideline "to be very conservative and to be fault-tolerant" has been followed; 2) very conservative design choices e.g. E a and starting Δ and ΔW for the 0° sections have been adopted; 3) and special design concepts e.g. adding a warm transition section, introducing "super 0° sections", and trying to confine the beam footprints inside the largest safe area on the Hofmann Chart have been applied.
Due to the feature of the long lens-free sections allowed by the KONUS dynamics and the high accelerating gradient provided by the SC CH structure, a very compact layout (only ~12m long) with a low number of accelerator components has been realized for the 150mA, 6MW DTL by the new solution. Detailed analyses show that the emittance transfer has been minimized and good beam quality has been ensured. In addition, benefitting from the fewer components, the design shows also large tolerances against possible errors.