Electron Beam Phase-Space Tomography Techniques
This content delves into electron beam phase-space tomography at the FAST Injector, discussing reconstruction methods, simulation setups, effects of quadrupoles, and changes in beam phase. Techniques such as algebraic reconstruction and filtered back projection are explored, alongside the impact of altering RF cavity phases and quadrupole strengths. The process of reconstructing phase space is detailed, showcasing steps involving rotation, measurements, and algorithmic applications for accurate results.
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Presentation Transcript
Electron Beam Phase-space Tomography at FAST Injector Tianyi Ge Charles Thangaraj
Tomography is a tool to reconstruct the phase space of a particle beam ? ? Longitudinal phase space Transverse phase space Changing the phase of a RF cavity Changing the strength of a quadrupole Projections 2
Techniques to reconstruct the phase space 1. Algebraic reconstruction technique 2. Simultaneous algebraic reconstruction technique 3. Filtered back projection 3
ELEGANT simulation setup Varying quad strength S C R E E N Q U A D ? Beam P L O T 4
x ELEGANT simulation plot of incoming phase x space X X (mm) 5
Effects of a quadrupole on electron beam* x The phase space of an electron beam undergoes the following mapping, as defined by the transportation matrix. x 0 e x x x x x x R R R R e 1 k 0 1 cos sin si cos n x x 0 0 0 11 12 1 = = = R 0 0 0 0 21 22 2 Rotation Shear Expansion Therefore, expansion constants and rotational angles can be expressed by and from ELEGANT. 12 R 11 R = + 2 2 e R R 1 11 12 R R ( ) = 1 tan 12 11 6 *
x Steps of reconstructing phase space x . 1e We first restore the rotation-only phase space with and = ( , ) ( , ), where rotation and meauserd projection at screen. p x e p e x p p 1 1 r k m k r m rp We apply the ART algorithm on and subsequently reconstruct the phase space . x x 7
Simulation of a quadrupole on phase space y(m) X X (m) X (m) 8
Changing the phase of a cavity is equivalent to rotating the phase space. dp/p (%) t (s) 9
Reconstructed phase space of one quad x x 5mm 10
Comparison of elapsed time and Twiss parameters for reconstructed phase space x x 11
x x ELEGANT simulation of 3 x 3 pixel phase space (same for ) y y X X (mm) 12
Reconstructed 3 x 3 pixel phase space x x 5mm 14
y Reconstructed 3 x 3 pixel phase y 5mm 15
Reconstructed 4 x 4 pixel phase space t p 5mm 17
Limitations, Advantages and Features Limitations Will need 180 degree coverage. Might need more quadrupoles for certain setups. Minimum number of angles to get a less noisy background is unclear. Open to study. THANKS .. to the Lee Teng Intern Program, Eric Prebys for this opportunity. Thanks to Sasha Valishev for providing the time to complete this work Background issues Advantages Can be implemented in the FAST injector. Quick technique < 1 minute for the reconstruction itself. Implemented in all 3 phase spaces. Features MATLAB code available at repository. Extensively commented. Video demo for the entire workflow. 18 Couple of features to be added in the final week
