Online electron beam trajectory correction in free-electron lasers via adaptive dictionary learning

During accelerator operation, the beam trajectory in free-electron laser (FEL) facilities frequently drifts from its predefined path due to machine instabilities and environmental factors, thereby degrading beam quality. In this work, we propose an online trajectory correction method based on dictionary learning, which significantly reduces data requirements and allows real-time, continuous updates of the response matrix. Simulation studies under static and drifting conditions demonstrate that the dictionary learning method achieves a root-mean-square error of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mn>0.2</a:mn> <a:mtext> </a:mtext> <a:mtext> </a:mtext> <a:mrow> <a:mi mathvariant="normal">m</a:mi> <a:mo>/</a:mo> <a:mi>rad</a:mi> </a:mrow> </a:mrow> </a:math> or lower for response matrix elements, using only <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:mrow> <d:mo>∼</d:mo> <d:mn>1000</d:mn> </d:mrow> </d:math> trajectory-excitation data pairs. Experimental validation at the Shanghai Soft X-ray Free Electron Laser (SXFEL) further demonstrates its robustness, achieving a correction precision better than 0.01 mm and confirming its suitability for online implementation in advanced XFEL facilities.