Investigations on Transverse Beam Break Up Using a Recirculated Electron Beam
Investigations on Transverse Beam Break Up Using a Recirculated Electron Beam
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使用循环电子束研究横向束分裂
DOI：
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发表时间：
2015
期刊：
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通讯作者：
N. Pietralla
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作者：
T. Kürzeder;M. Arnold;M. Gros;F. Hug;L. Jürgensen;J. Pforr;N. Pietralla
自 1991 年以来，循环超导加速器 S-DALINAC 为达姆施塔特大学的核物理实验提供高达 130 MeV 的电子束。它由一个 10 MeV 注入器和一个 40 MeV 主直线加速器组成，并使用最多两个再循环路径达到其最终设计能量。超导主直线加速器装有八个在 3 GHz 和 2 K 下运行的 20 单元 SRF 腔。此外，再循环直线加速器设计，发生束流破裂的阈值电流非常低，仅为几 μA，为 ERL 社区提供了一个独特的机会，可以在该加速器上通过实验测试避免束流破裂的不同策略，并对有关该主题的束流动力学模拟进行基准测试。为了最大限度地减少 HOM 对循环电子束的影响，我们将在加速器中放置倾斜四极和六极磁铁，并测试它们对阈值电流的影响。我们将报告有关其在加速器中的使用的束流动力学模拟的状态，并提供倾斜四极杆定位的实际计算。将给出对 S-DALINAC 未来活动的展望。简介 横向束分裂（BBU）是现代超导能量回收直线加速器的主要问题之一。 [1] 显示了 ERL 中 BBU 不稳定性的理论。当电子束穿过加速腔并激发其中的高阶偶极子模式 (HOM) 时，就会发生这种情况。这些 HOM 具有较大的品质因数，因此在超导腔中的使用寿命较长。该束将被该模式的电磁场偏转。在再循环设计中，这种情况会变得更糟，因为同一束可以由同一 HOM 沿同一方向偏转。因此，每个循环直线加速器中可传输和加速的最大束流受到限制。该限制称为 BBU 阈值电流。对于全球范围内计划或已经在建设的 ERL 来说，这是一个至关重要的参数，因为它们产生 10-100 mA 及以上的束流。相反，在早期的 SRF 直线加速器中，由于 BBU [2,3]，只能产生几μA 的束流。当在再循环模式下运行时，S-DALINAC [4] 的束流也受到限制。目前在长期实验中达到的最高稳定电流为5μA[5]，远低于20μA的设计值，但方便了实验的进行。 S-DALINAC 的低阈值电流允许进行横向束破裂实验，而不会损坏加速器。 S-DALINAC 超导达姆施塔特直线加速器 (S-DALINAC) 为达姆施塔特大学的核和天体物理实验提供电子束。它由一个超导 10 MeV 注入器和一个 40 MeV 直线加速器组成。主直线加速器具有两条再循环光束线，最多可使用 3 次。作为电子源，可以选择热离子和光枪，它们也可以产生极化电子[6]。这种布局最初设计用于提供高达 130 MeV 的束能量和单程模式下 60 μA 的束电流或再循环两次时 20 μA 的束电流。但如上所述，循环运行时的设计束流目前还无法实现。为了加速波束，使用了 12 个 20 单元 SRF 腔，工作频率为 3 GHz。这些空腔是在 20 世纪 90 年代产生的，并且从未在 HOM 抑制方面进行过优化。此外，不能使用 HOM 耦合器，因为大多数 HOM 被捕获在这些长 20 单元腔的中间单元内。 2015 年 8 月，将开始安装额外的再循环光束线，并计划于 2016 年 1 月完成 [7]。 S-DALINAC 的平面图如图 1 所示。在当前只有两个再循环的设置中，当在最大梯度下使用时，腔体向氦浴消耗的功率太高，因为腔体的品质因数小于最初计划的 [8]。进行升级是为了在连续运行中达到 130 MeV 的设计能量，每个腔的加速梯度更小。 BBU 抑制已经做出了许多努力，并且仍在继续提高 BBU 阈值电流。有两种策略可以解决该问题。作为基础，ERL 的空腔被设计为阻尼高阶模式。还将使用 HOM 耦合器。第二种方法是匹配光束传输系统的光学器件。我们计划通过操纵再循环回路中的光束光学器件来增加 S-DALINAC 的低阈值电流。横向相位超前的变化 在[9]中，建议以提供 HOM 激励的负反馈的方式匹配 ERL 中的横向相位超前，这可以增加 ___________________________________________ *BMBF 通过 05K13RDA kuerzeder@ikp.tu-darmstadt.de TUICLH2032 Proceedings of ERL2015, Stony Brook, NY, USA ISBN 支持的工作978-3-95450-183-0 30 版权 © 20 15 CC -B Y3。 0 以及 WG2ERL 光学与光束动力学：集体效应/多通道/光环模拟阈值电流的具体作者。此外，[9] 中的模拟表明，横向运动的 x 和 y 平面的耦合可以进一步增加阈值电流。我们将测试这些方法，并在 2016 年将 S-DALINAC 作为单次或三次再循环直线加速器运行时尝试达到更高的电流。完整相空间的交换将在第二再循环路径中完成。因此，我们的 FODO 晶格中需要实现三个倾斜四极磁体。为了实现垂直和水平相空间的交换，需要4x4旋转矩阵。这样的矩阵可以像[10]中那样进行分析计算。对于我们的例子，我们选择了一个最适合我们常规晶格的晶格。三个倾斜四极杆的分布方式是，在它们彼此距离的一半之间分别定位一个传统四极杆（第一聚焦，第二散焦）（SFSDS）。斜四极杆的位置在图1中被标记为绿色。这种系统的解析解（薄透镜近似）[10]提供了偏斜四极杆的折光力 s = 1/s√2 和传统四极杆的折光力 F/D = ±√2/s。束流能量为 68.85 MeV，每个磁体焦平面之间的漂移为 s = 1.981 m，则可以轻松计算出梯度 Gs = 0.4184 T/m 和 GF/D = ±1.4206 T/m。最后，使用优雅的代码 [11] 进行了数值优化，以便找到旋转系统 5 个磁铁的精确值（参见表 1）。表 1：相空间旋转系统的优化四极杆梯度 聚焦/散焦四极杆 ±1.082 T/m 斜四极杆 1&3 0.4408 T/m 斜四极杆 2 0.4347 T/m 斜磁铁已经制造出来，目前正在 S-DALINAC 的第一次再循环中进行测试（见图 2）。它们将于 2015 年夏季在 BBU 上进行首次实验，然后在安装新的再循环光束线期间被重新安置到优化位置。色度的变化 在[12]中表明，具有足够高色度 Ψ 的再循环光束线让电子“忘记”任何偶极子模式获得的反冲。 [12] 中也给出了该行为必须满足的条件：
The recirculating superconducting accelerator S-DALINAC provides electron beams of up to 130 MeV for nuclear physics experiments at the University of Darmstadt since 1991. It consists of a 10 MeV injector and a 40 MeV main linac and reaches its final design energy using up to two recirculation paths. The superconducting main linac houses eight 20-cell SRF cavities operated at 3 GHz and 2 K. The very low threshold current of only a few μA for the occurrence of beam break up in addition with the recirculating linac design gives a unique opportunity to the ERL community for testing different strategies of avoiding beam break up experimentally at this accelerator and to benchmark beam dynamics simulations concerning this topic. To minimize the impact of HOMs on the recirculating electron bunches we will place skew quadrupole and sextupole magnets in our accelerator and test their effect on the threshold current. We will report on the status of beam dynamics simulations concerning their use in the accelerator and present actual calculations for the positioning of the skew quadrupoles. An outlook on the future activities at the S-DALINAC will be given. INTRODUCTION Transverse beam break up (BBU) is one of the main problems of modern superconducting energy recovery linacs. A theory of BBU instability in ERLs was shown in [1]. It occurs when an electron bunch travelling through an accelerating cavity excites higher order dipole modes (HOM) in it. These HOMs can have a large quality factor and thus a long lifetime in superconducting cavities. The bunch will be deflected by the electro-magnetic field of the mode. In a recirculating design this gets even worse as the same bunch can be deflected by the same HOM in the same direction. Thereby the maximum beam current which can be transported and accelerated is limited in every recirculating linac. This limit is called the BBU threshold current. For ERLs worldwide which are planned or already under constructions this is a crucial parameter as they yield for beam currents of 10-100 mA and above. On the contrary in early SRF linacs only a few μA of beam current were possible because of BBU [2,3]. Also the S-DALINAC [4] is limited in its beam current when operated in recirculating mode. The highest stable current achieved so far in a long term experiment accounts for 5 μA [5], which was well below the design value of 20 μA but convenient for the experiments carried out. The low threshold currents at the S-DALINAC allow to carry out experiments on transverse beam break up without the risk of damaging the accelerator. S-DALINAC The Superconducting Darmstadt LINear Accelerator (S-DALINAC) provides electron beams for nuclearand astrophysical experiments at the University of Darmstadt. It consists of a superconducting 10 MeV injector and a 40 MeV linac. With two recirculation beam lines the main linac can be used up to 3 times. As electron sources a thermionic and a photo gun, which can also produce polarized electrons [6], can be chosen. This layout was originally designed to provide beam energies of up to 130 MeV and beam currents of either 60 μA in single pass mode or 20 μA when recirculated twice. But as mentioned above, the design beam current in recirculating operation could not be achieved so far. For acceleration of the beam twelve 20-cell SRF cavities are used on an operation frequency of 3 GHz. These cavities have been produced in the 1990s and have never been optimized with regard to HOM suppression. Furthermore no HOM couplers can be used as most HOMs are trapped within the middle cells of these long 20-cell cavities. In August 2015 the installation of an additional recirculation beam line will begin and is scheduled to be finished in January 2016 [7]. A floor plan of the S-DALINAC is shown in Fig. 1. In the current setup with only two recirculations the power dissipated by the cavities to the helium bath was too high when used at maximum gradient as the quality factor of the cavities is smaller than originally planned [8]. The upgrade is done in order to reach the design energy of 130 MeV in c.w.-operation with a smaller accelerating gradient per cavity BBU SUPPRESSION Many efforts have been made and are still going on to raise the BBU threshold currents. There are two strategies to address the problem. As a basis, cavities of ERLs are designed to damp the higher order modes. Also HOM couplers will be used. The second approach is matching the optics of the beam transport system. We are planning to increase the low threshold current of the S-DALINAC by manipulating the beam optics in the recirculation loops. Variation of the Transverse Phase Advance In [9] it is proposed to match the transverse phase advance in an ERL in a way that a negative feedback of the HOM excitation is provided which can increase the ___________________________________________ *Work supported by BMBF through 05K13RDA kuerzeder@ikp.tu-darmstadt.de TUICLH2032 Proceedings of ERL2015, Stony Brook, NY, USA ISBN 978-3-95450-183-0 30 Co py rig ht © 20 15 CC -B Y3. 0 an d by th er es pe ct iv ea ut ho rs WG2ERL Optics & Beam Dynamics: Collective Effects/Multi-passes/Halo Simulations threshold current. In addition simulations in [9] show that a coupling of the x and y planes of transverse motion could increase the threshold current even further. We will test these approaches and try to reach for higher currents when running the S-DALINAC as a single or three times recirculating linac in 2016. The exchange of the complete phase space will be done in the second recirculation path. Therefore three skew quadrupole magnets need to be implemented in our FODO lattice. In order to achieve the exchange of vertical and horizontal phase spaces a 4x4 rotation matrix is needed. Such a matrix can be calculated analytically like in [10]. For our case we chose a lattice, which fits best into our regular lattice. The three skew quadrupoles are distributed in a way that between half of their distance to each other respectively one conventional quadrupole (first focussing, second defocussing) will be positioned (SFSDS). The positions of the skew quadrupoles are marked green in Fig.1. The analytical solution (thin lens approximation) for such a system [10] provides the refractive power for the skew quadrupoles of s = 1/s√2 and for the conventional quadrupoles of F/D = ±√2/s. With a beam energy of 68.85 MeV and a drift of s = 1.981 m between each magnet’s focal plane the gradients easily can be calculated to Gs = 0.4184 T/m and GF/D = ±1.4206 T/m then. Finally a numerical optimization using the elegant code [11] has been carried out in order to find the exact values for the 5 magnets of the rotation system (see Table 1). Table 1: Optimized Quadrupole Gradients for the Phase Space Rotation System Focussing/Defocussing Quadrupoles ±1.082 T/m Skew Quadrupole 1&3 0.4408 T/m Skew Quadrupole 2 0.4347 T/m The skew magnets have been manufactured already and are currently undergoing tests in the first recirculation of the S-DALINAC (see Fig. 2). They will be used for first experiments on BBU in summer 2015 and then be relocated to their optimized positions during installation of the new recirculation beamline. Variation of Chromaticity In [12] it is shown that a recirculation beam line with high enough chromaticity ξ let electrons “forget” the kick obtained by any dipole mode. The condition which has to be fulfilled for that behaviour is also given in [12]: