PDF Emittance minimization by Courant-Snyder M 2 m M 6 U 0 0 1 0 0

Emittance minimization by Courant-Snyder parameter scan in energy recovery linac 황 지 광, 김 은 산, 가속기 물리 연구실 경북대학교 Tsukasa Miyajima Photon Factory, KEK, Japan. 연 구 목 표 현재 세계적으로 연구되고 있는 에너지 회수형 초전도 선형 가속기는 가로 방향 및 진행 방향의 높은 결맞음을 가진 높은 파워의 X-ray 생성을 위핚 방사광 가속기 중 하나이다. 현재 일본 KEK 연구소는 5 GeV에너지의 에 너지 회수형 초전도 가속기의 실증을 위핚 35 MeV의 낮은 에너지를 가지는 Prototype 가속기를 설계 및 건설 중 이다. 높은 파워 및 결맞음을 달성하기 위해서는 다음과 같은 사항들이 연구에 주요하다. 1. 높은 전하량 및 아주 작은 Emittance (<1 mm-mrad)를 가진 빔의 생성 및 전송 (Injector system and Merger section) 2. 5~35MeV 정도의 낮은 에너지에 의핚 큰 공간 전하 효과(Space charge effect)의 평가 및 보정. 3. 길이방향의 공간전하 효과에 의핚 에너지 spread 증가의 평가. 이러핚 연구 주제들 중 Injector에서 생성된 작은 Emittance의 빔을 Main Ring으로 전송하기 위핚 Merger 부붂의 최적화 연구를 일본의 KEK 연구소와 협력하여 수행하였다. 이에서 얻은 결과를 아래에 정리하였다.. 1. Introduction. Figure 1. Scheme of merger section. 0.8 0.6. 3. Numerical Calculation by using GPT -The emittance growth due to the space charge force was estimated by using the GPT[4], which be able to calculate 3-D space charge effect. 0.4 0.2. 1.9 10. 6. 0.0. 1.8 10. 6. 1.7 10. 6. 1.6 10. 6. 1.5 10. 6. 0.2 0.4 0.0. 0.5. 1.0. 1.5 2.0 s m. 2.5. 3.0. emittance m rad. Space Charge Dispersion m2. - The merger section consists of the three bending magnets. One of the bending magnet is sector type and others are rectangular type. The bending magnets has the edge angle to achieve the zero dispersion at the exit of merger section.[1] The scheme of the merger section shown in Fig. 1.. where and are the initial and final emittance as un-normalized values, respectively, is rms spreads of bunch slice displacement in phase space. The results shown in Fig. 4.. Figure 2. Space charge dispersion at the merger section.. 0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 Angle rad. Figure 5. The numerical calculation results. The initial normalized transverse emittance is 0.1 mm-mrad, bunch length is 3 ps (rms) and beam energy is 5 MeV.. 2. Space charge effect in merger section. -We get the 1.35 mm-mrad of minimum transverse emittance growth in merger section when vertical CS parameter was fixed at =9mm, =0. But the motions of electron of horizontal and vertical direction was coupled, the horizontal CS parameters are depends on the vertical CS parameters. The change of horizontal CS parameter and emittance growth due to the change of vertical CS parameter was investigated. The results shown in Fig. 6. 1.5 10. 6. 1.4 10. 6. 1.3 10. 6. 1.2 10. 6. 1.1 10. 6. x. m rad. -Analysis of emittance growth in the merger section using first-order theory was used.[2] The longitudinal space charge force (LSCF) is the main source of the emittance growth in low-energy beam. We assume that longitudinal and transverse beam size not largely changed in the merger section.. 4. Vertical CS parameter scan (Coupling). Figure 3. The first order calculation model of emittance growth in merger section The emittance growth due to the displacement of bunch slices in the phase space can be minimized by matching the displacement to the orientation of the phase ellipse at the exit of merger. The displacement of bunch slice laid on the . Therefore the angle of the displacements given by from the first-oder theory. In our calculation, the transfer matrix for each elements is derived by Green's function method[3].  cos     1 sin    MR   0  0   0 .  sin .  (1  cos  )  (1  cos  )  2 (  sin  ) . cos . sin . sin . 0. 1. 0. 0. 0. 1. 0. 0. 0.   (1  cos  )    0     1 . 1  0 M L  0  0 0 . L 0 0 0  1 0 0 0 0 1 0 0  0 0 1 0 0 0 0 1 . M Edge.  1       . 1 tan 0 0 0. 0 0 0 0  1 0 0 0  0 1 0 0 0 0 1 0  0 0 0 1 . The angle of the slices in phase space was calculated -0.53 rad. Using the above calculation parameters, the LSCF wake potential is , the . When the merger section is optimized for the envelope matching between the LSCF-induced dispersion function and the betatron function, all the bunch slices align along the orientation of the phase ellipse. The transverse emittance growth calculated by. (a). (b). 0.55. 0.50. 0.45 rad. 0.40. 0.35. Figure 6. The change of transverse emittance at the exit of merger section as function the orientation of the phase ellipse due to the change of vertical CS parameters. As shown in Fig. 6, the minimum horizontal emittance at the exit of merger was achieved at the -0.557 rad of angle of the slices in phase space. This angle is well corresponding to result of analytical calculation.. 5. Conclusion In this study, we performed the compensation of the emittance growth induced by LSCF in the merger section. As shown in results, the transverse normalized emittance at the exit of merger has larger than 1 mm-mrad at the 5 MeV case. The emittance growth mainly depend on the beam energy. Also, the coupling between the horizontal CS parameter and vertical CS parameter was investigated to compensate the emittance growth. The result well corresponding to the result of the analytical calculation.. Reference [1] M.Rihaoui et. al, Phys. Rev. ST Accel. Beams 12 124201 (2009). [2] Ryoichi HAJIMA, Jpn. J. Appl. Phys. Vol. 42 (2003) pp. L 974–L 976 [3] H. Wiedemann: Particle Accelerator Physics (Springer-Verlag, Berlin,1993) p. 107. [4] Pulsar Physics, http://www.pulsar.nl/gpt. Figure 4. Analytical calculation of the emittance growth: Initial beam energy (a) 5 MeV (b) 10 MeV.