Influence of SXFEL resistive wall wakefield on beam phase space distortion

Youwei Gong; Wencai Cheng; Minghua Zhao; Xuan Li; Duan Gu; Meng Zhang

doi:10.11884/HPLPB202234.210491

Journals >High Power Laser and Particle Beams >Volume 34 >Issue 6 >Page 064007 > Article

High Power Laser and Particle Beams
Vol. 34, Issue 6, 064007 (2022)

Influence of SXFEL resistive wall wakefield on beam phase space distortion

Youwei Gong^1、2, Wencai Cheng^1、2, Minghua Zhao¹, Xuan Li³, Duan Gu³, and Meng Zhang^3、*

Author Affiliations

¹Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China

²University of Chinese Academy of Sciences, Beijing 100049, China

³Shanghai Advanced Research Institute, Chinese Academy of Sciences, Shanghai 201210, China

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DOI: 10.11884/HPLPB202234.210491 Cite this Article

Youwei Gong, Wencai Cheng, Minghua Zhao, Xuan Li, Duan Gu, Meng Zhang. Influence of SXFEL resistive wall wakefield on beam phase space distortion[J]. High Power Laser and Particle Beams, 2022, 34(6): 064007 Copy Citation Text

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Abstract

X-ray free-electron laser (XFEL), due to its ultra-high brightness, ultra-short pulse and other characteristics, has been built worldwide. Based on the theory of wakefield, we calculate the resistive wall wakefield from the linear accelerator (linac) exit to the end of the undulator in Shanghai X-ray free electron laser (SXFEL) with bunch traveling through the 245 m stainless steel transfer line and copper beamline in undulator. Then we analyze the resistive wall wakefields which eventually lead to the distortion of the longitudinal phase space within the bunch. Finally, the theoretical predictions of influence of resistive wall wakefield are compared with experiment results on SXFEL, which shows great agreement. The detailed research provides a direction for subsequent FEL optimization.

Keywords

energy distribution distortion longitudinal phase space resistive wall wakefield SXFEL

$ \begin{gathered} {w_\delta }(s) = \dfrac{{4{Z_0}c}}{{\pi {a^2}}}\Bigg( \dfrac{1}{3}{{\text{e}}^{ - \tfrac{s}{{{s_0}}}}}\cos \Bigg(\dfrac{{\sqrt 3 s}}{{{s_0}}}\Bigg) - \dfrac{{\dfrac{{\sqrt 2 }}{{\text{π }}}\displaystyle\int_0^\infty {{\text{d}}x{x^2}{{\text{e}}^{ - \tfrac{{s{x^2}}}{{{s_0}}}}}} }}{{{x^6} + 8}} \Bigg) \\ {s_0} = {(2{a^2}/{Z_0}{\sigma _c})^{1/3}} \\ \end{gathered} $

(1)

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$ {W_\delta }(s) = \displaystyle\int_0^s {\lambda (s - s')} {w_\delta }(s){\text{d}}s' $

(2)

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$ \left\{ \begin{array}{l} k = {\omega }/{c} \hfill \\ {u^*} = 1 - {{{\text{i}}\omega l}}/{{{v_{\rm{F}}}}} \hfill \\ {\delta ^{{\rm{NSE}}}} = \sqrt {\dfrac{{2c}}{{{Z_0}{\sigma _c}\omega }}} \hfill \\ \xi = \dfrac{{(1 - {\text{i}})\omega {\delta ^{{\rm{NSE}}}}\sqrt u }}{{2c}} \hfill \\ Z(k) = \dfrac{{{Z_0}}}{{2{\text{π }}a}}\displaystyle\int_0^\infty {\dfrac{{{\text{d}}q}}{{\cosh (q)}}{{\Bigg[\dfrac{{\cosh (q)}}{{\xi (k)}} - \dfrac{{{\text{i}}ka}}{q}\sinh (q)\Bigg]}^{ - 1}}} \end{array} \right. $

(3)

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$ {W_\delta }(s) = \dfrac{c}{{2{\text{π }}}}\displaystyle\int_0^s {\lambda (s)\displaystyle\int_{ - \infty }^\infty {Z(k){{\text{e}}^{ - {\text{i}}k(s - s')}}{\text{d}}k{\text{d}}s'} } $

(4)