WAKEFIELD LOSS ANALYSIS OF THE ELLIPTICAL 3.9 GHZ THIRD HARMONIC CAVITY

Third harmonic 3.9 GHz elliptical cavities are planned to be used in many particle accelerator projects such as XFEL, NGLS, and ASTA. In this paper, the wakefield losses due to bunches from 8 mm down to ultra short bunches of 10 μm are analysed. Both the loss and kick factors are numerically calculated for bunches of relatively long length (>1 mm) using CST wakefield solver. The data is then used to asymptotically extrapolate the values for ultra-short bunches by finding the wake functions. These calculations are essential to estimate the cryogenic losses in cryomodules and for beam dynamic analysis. INTRODUCTION Third harmonic cavities are commonly used in the particle accelerators of light sources to improve the bunch stability and compensate for the distortion that could happen between the sinusoidal accelerating field and the relatively long beam bunches [1-6]. Third harmonic 3.9 GHz cavities are currently under production for several projects. For instance, DESY’s XFEL and FNAL’s ASTA. Other future light sources (like NGLS) are also planning to use the third harmonic cavities. In collaboration with DESY, Fermilab constructed a third harmonic cryomodule for the Free electron LASer in Hamburg (FLASH) facility [1-4]. Each cryomodule contains four superconducting radio frequency (SRF) cavities operating at 3.9 GHz. The third harmonic 9-cell cavities are designed to operate at 2 K in the TM010 πmode at an accelerating gradient of 14 MV/m, summing up to a total energy gain of 20 MeV per cryomodule. These cavities operate in a decelerating phase of 179o relative to the beam phase, and are optimized for 9 mA of beam current. In addition, another cryomodule will be fabricated for Fermilab Advanced Superconducting Test Accelerator (ASTA). ASTA plans to deliver 50 MeV beam for a broad range of beam-based experiments to push limits of particle-beam generation, acceleration and manipulation. ASTA plans to employ Superconducting 3.9 GHz cavities for bunch linearization. Before accelerating beam with third harmonic cavities, it is imperative to estimate the cryogneic losses by analysing the wakefield losses. This paper reports on an extensive wakefield analysis, carried out on these third harmonic cavities, including the simulated loss and kick factors for sub cm beam bunches. Based on the simulated data and using an asymptotic approximation, we estimate the loss and kick factors for sub mm beam bunches. WAKEFIELD SIMULATION FOR SUB CM BEAM BUNCHES Figure 1 shows the geometry of the third harmonic 3.9 GHz 9-cells elliptical cavity. In different to the wakefield analysis in [5], we resorted to CST microwave studio to compute the wakefields inside a single cavity due to relatively long bunches, where the structure is excited by a longitudinal line current [7]. The line current is placed on the beam axis for the loss factor calculations, while the line is displaced off axis for the kick factor calculations. In both cases, the line current representing the beam is formed with a longitudinal, Gaussian shaped charge distribution. Accuracy of the analysis was checked versus the mesh size. Typically, the ratio between the bunch sigma (standard deviation of the Gaussian distribution) to the mesh step size in the longitudinal direction Sigma/h is used to check the accuracy of the analysis with conventionally using Sigma/h of 20 as a satisfactory level of mesh refinement. In this analysis, we have used a Sigma/h of 30, as shown in Fig. 2. Mesh size of approximately 70 million elements (per quarter of cavity) was needed for the relatively short RMS bunch length of 2 mm, as shown in Fig. 2. Figure 1: Geometry of the third harmonic 3.9 GHz cavity. Figure 2: Sigma/h and number of mesh elements vs. bunch sigma. ________________________________________________________________________________________________________________ *Operated by Fermi Research Alliance, LLC, under Contract DE-AC02-07CH11359 with the U.S. DOE #mhassan@fnal.gov Proceedings of PAC2013, Pasadena, CA USA WEPAC32 07 Accelerator Technology T07 Superconducting RF ISBN 978-3-95450-138-0 847 C op yr ig ht c © 20 13 C C -B Y3. 0 an d by th e re sp ec tiv e au th or s Figure 3 shows the wake potential both in longitudinal and transverse directions for various RMS bunch lengths ranging from 8 mm to 2 mm. As expected, the peak absolute value of the wake potential increases as the RMS bunch length decreases. The longitudinal wake potential increases from 5 V/pC to 16 V/pC as the RMS bunch length decreases from 8 mm to 2 mm. On the other hand, the transverse wake potential increases from 0.4 V/pC/mm to 0.6 V/pC/mm as the RMS bunch length decreases from 8 mm to 2 mm. The peak of the longitudinal wake potential happens at approximately 2 mm distance for all bunch RMS lengths, while the peak transverse wake potential happens at approximately12 mm distance. The loss and kick factors are shown in Fig. 4 (a) and (b), respectively. The loss factor varies from 3.5 V/pC to 10.5 V/pC as the RMS bunch length decreases from 8 mm to 2 mm, as shown in Fig. 4(a). On the other hand, the kick factor decreases from 0.22 V/pC/mm to 0.17 V/pC/mm over the same range. ASYMPOTITIC APPROXIMATION FOR SUB MM BEAM BUNCHES Computing the wakefield losses for ultra-short bunches is not possible using CST because of the mesh size limitation (for sub mm bunches, the mesh size would be in microns). In such case of ultra-short bunches, asymptotic approximation is typically used, where we could approximate the loss and kick factors by [8]