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Core brightness in presence of space-charge

Core brightness in presence of space-charge. Jorge Giner -Navarro Pietro Musumeci Workshop on Methods in Collective and Nonlinear Effects in Bright Charged Particle Beams University of Chicago – October 28 th , 2017. Outline. Motivation Brightness, emittance and photocathodes

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Core brightness in presence of space-charge

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  1. Core brightness in presence of space-charge Jorge Giner-Navarro Pietro Musumeci Workshop on Methods in Collective and Nonlinear Effects in Bright Charged Particle Beams University of Chicago – October 28th, 2017

  2. Outline • Motivation • Brightness, emittance and photocathodes • Simulations GPT in space-charge scenarios • Core brightness computation • Simulations and analysis • Experimental techniques • Pepper-pot • TEM grids • Slit + deflector system • Summary J.Giner-Navarro. Workshop: Methods in Collective and Nonlinear Effects in Bright Charged Particle Beams.

  3. Motivation • Brightness represents the charge density in phase-space . • According to Liouville’s theorem, phase space density for a Hamiltonian system is invariant throughout the accelerator. • Under linear forces: rms emittance is conserved • Under non-linear forces (e.g. space-charge): • rms emittance is not conserved but… • …“core” emittance is conserved J.Giner-Navarro. Workshop: Methods in Collective and Nonlinear Effects in Bright Charged Particle Beams.

  4. Motivation • The simulations presented here aim at finding a transport invariant quantity in presence of strong space-charge forces, rather than the rms emittance. • C. Gulliford et al, APL 106 - 094101 (2015): found core 2D-emittance preservation of 80-90% in DC gun-based photoinjector. • Figure of merit should be found in 6Dphase-space core density (difficult to verify experimentally) • An invariant core phase-space density means that it contains information about the beam source: cathode thermal emittance. Experimental possibilities of new cathode physics. px Photocathode -Ez x electrons Laser J.Giner-Navarro. Workshop: Methods in Collective and Nonlinear Effects in Bright Charged Particle Beams.

  5. GPT simulations and analysis • Simulations were made with General Particle Tracer (GPT) to evaluate the core-brightness as figure of merit for different transport optics: • Drift + Solenoid + Drift • Drift +Solenoid + Drift + RF-LINAC + Drift • Initial particle distribution: full 6D gaussian • Energy 5 MeV • Total charge 1 pC • Beam size 100x100x300 um • Transverse normalized emittance 10 nm rad • Energy spread 0.01% • Number of simulated macro-particles: 5000 – 25000 • Space-charge is implemented with GPT built-in routines: • spacecharge3Dmesh: solves Poisson’s equations on a mesh adapted to the beam geometry, with coordinates and fields in rest frame. • spacecharge3D: point-to-point particle relativistic interaction. J.Giner-Navarro. Workshop: Methods in Collective and Nonlinear Effects in Bright Charged Particle Beams.

  6. Simulations and analysis Core-brightness computation Coordinates Covariance matrix Normalized distance: defines a distance with respect to the center or reference (r0) taking into account the geometry and orientation of the distribution in the 6D phase space. This distance is used to sort and filter the particles of the “core”. J.Giner-Navarro. Workshop: Methods in Collective and Nonlinear Effects in Bright Charged Particle Beams.

  7. Simulations and analysis • Blue: all particles • Red line: contour full distribution • Pink: filtered particles (4%) • Green line: contour filtered distribution Core-brightness computation J.Giner-Navarro. Workshop: Methods in Collective and Nonlinear Effects in Bright Charged Particle Beams.

  8. Simulations and analysis Core-brightness computation The core-brightness is extrapolated to the center () with a linear fit between the number of particles and the volume occupied in 6D phase space. Method 1: fraction Method 2: subset emittance Volume is proportional to and it is used as a fraction factor of the rms emittance of the full distribution: Volume is calculated as the rms emittance of the subset of smallest that contains particles J.Giner-Navarro. Workshop: Methods in Collective and Nonlinear Effects in Bright Charged Particle Beams.

  9. Simulations and analysis Core-brightness computation The center of the distribution is not clearly defined. We compare the microscopic density at the average position and at the neighboring particles. We can take either the maximum density or an average. Maximum density at R=0 Particle distribution with respect to neighboring particles J.Giner-Navarro. Workshop: Methods in Collective and Nonlinear Effects in Bright Charged Particle Beams.

  10. Simulations and analysis Initial distribution One remark, one may consider relevant for the space-charge models and density analysis that the finite number of simulated particles (<0.1%) requires a suitable sampling to minimize statistical errors. GPT includes Hammersley sequences that generates a quasi-random initial 6D distribution. No sampling With Hammersley sampling From GPT User Manual J.Giner-Navarro. Workshop: Methods in Collective and Nonlinear Effects in Bright Charged Particle Beams.

  11. Simulations and analysis Drift + Solenoid + Drift Solenoid: Main body field 0.8T, Length 50cm, Aperture 5cm Space-Charge MESH routine Analysis: The average is considered here as the center of the distribution in order to calculate normalized distances. The maximum local core brightness is taken among a small subset in the center. Random initial distribution Hammersley sampling ~70% core brightness preserved rms emittance x40 J.Giner-Navarro. Workshop: Methods in Collective and Nonlinear Effects in Bright Charged Particle Beams.

  12. Simulations and analysis Drift + Solenoid + Drift Solenoid: Main body field 0.8T, Length 50cm, Aperture 5cm Space-Charge MESH routine Analysis: The first 1000 macro-particles with respect to average of the first frame are tracked to compute the core brightness. Random initial distribution Hammersley sampling well preserved rms emittance x40 J.Giner-Navarro. Workshop: Methods in Collective and Nonlinear Effects in Bright Charged Particle Beams.

  13. Simulations and analysis Drift + Solenoid + Drift Solenoid: Main body field 0.8T, Length 50cm, Aperture 5cm Space-Charge POINT-to-POINT routine Loss core brightness to 4% • (blue) of each frame • (red) track same 1000 particles of the first frame rms emittance x130 Jumps in rms emittance at the waist of the beam (~10um) as evidence of very strong space-charge forces. Core brightness calculations follow the same jumps: no preservation. (Jump x4) J.Giner-Navarro. Workshop: Methods in Collective and Nonlinear Effects in Bright Charged Particle Beams.

  14. Simulations and analysis Drift + Solenoid + Drift + Linac + Drift - Solenoid: Main body field 0.8T, Length 50cm, Aperture 5cm - Linac: PEGASUS linac field map (S-band, SW, 10-cell) Space-Charge MESH routine rms emittance x70 RF Linac does not perturb core emittance. Solenoid Linac • Hammersley sampling • Track of the filtered 1000 particles in the first frame J.Giner-Navarro. Workshop: Methods in Collective and Nonlinear Effects in Bright Charged Particle Beams.

  15. Simulations and analysis Drift + Solenoid + Drift Solenoid: Main body field 0.8T, Length 50cm, Aperture 5cm Space-Charge MESH routine Higher charge (x100)  Stronger space charge forces! x0.0001 Core brightness drops dramatically even at drift sections. Bad discretization (more charge means more particles) rms emittance x2000 J.Giner-Navarro. Workshop: Methods in Collective and Nonlinear Effects in Bright Charged Particle Beams.

  16. Experimental techniques • In order to measure the core density we need an experimental technique to reconstruct the phase space density. • Pepper-pot and TEM grid techniques allow the reconstruction of the transverse phase space density (4D) Simulation Pepper-pot TEM grid R.K. Li et al, PRSTAB 15, 090702 (2012) J.Giner-Navarro. Workshop: Methods in Collective and Nonlinear Effects in Bright Charged Particle Beams.

  17. Experimental techniques TEM grid: 4D transverse phase-space 4D transverse phase space density reconstruction Projected 2D phase-space Analysis of the “core” emittance using reconstructed phase space J.Giner-Navarro. Workshop: Methods in Collective and Nonlinear Effects in Bright Charged Particle Beams.

  18. Experimental techniques TEM grid: 4D transverse phase-space J. Giner-Navarro, D. Marx, P. Musumeci We developed analysis algorithms to reconstruct 4D emittance (including correlations) from TEM grid images. Simulation Correlation terms: J.Giner-Navarro. Workshop: Methods in Collective and Nonlinear Effects in Bright Charged Particle Beams.

  19. Experimental techniques Slit + Deflector: Longitudinal phase-space Simulation High charge transmission and single-shot 4D reconstruction allows the extension to 6D phase-space using the slit+deflector system. A slice of the beam is striked to measure the temporal distribution. ~4.5 ps J.Maxson, D. Cesar, P. Musumeci (2016) TEM Grid XTCAV Slit (10 J.Giner-Navarro. Workshop: Methods in Collective and Nonlinear Effects in Bright Charged Particle Beams.

  20. Summary • Numerical simulations have been performed using GPT to analyse the evolution of the “core” 6D-brightness in beam transport systems in presence of non-linear space-charge forces. • Mesh routines of space-charge forces show fair agreement of core brightness preservation, rather than point-to-point interaction routines which demand larger number of particles and computation time. • Ultimate goal is the use of this invariant for the characterization of new photocathodes from the analysis of the produced beam properties in the diagnostics section. • The use of TEM grids combined with a slit-deflector system is presented to be a good candidate for phase space density reconstruction and analysis of the core 6D brightness. J.Giner-Navarro. Workshop: Methods in Collective and Nonlinear Effects in Bright Charged Particle Beams.

  21. Thank you for your attention! J.Giner-Navarro. Workshop: Methods in Collective and Nonlinear Effects in Bright Charged Particle Beams.

  22. BACK UP Slides: J.Giner-Navarro. Workshop: Methods in Collective and Nonlinear Effects in Bright Charged Particle Beams.

  23. Simulations and analysis Drift + Solenoid + Drift Solenoid: Main body field 0.8T, Length 50cm, Aperture 5cm • First check: no space-charge forces! • Rms emittance is doubled as it enters inside the solenoid but is back to initial value at the output. • Core brightness keeps constant as expected. J.Giner-Navarro. Workshop: Methods in Collective and Nonlinear Effects in Bright Charged Particle Beams.

  24. Simulations and analysis Drift + Solenoid + Drift Solenoid: Main body field 0.8T, Length 50cm, Aperture 5cm Space-Charge MESH routine To consider statistical density in the vicinities of the “core center”, we can take an average of the fitted brightness (first 20 particles here). First 1000 particles of the first frame Reference: of each frame J.Giner-Navarro. Workshop: Methods in Collective and Nonlinear Effects in Bright Charged Particle Beams.

  25. Technique

  26. Technique

  27. Technique We are fitting a range of parameters for and looking for minimum. Problem is has very shallow minimum.

  28. Experimental techniques TEM grid: 4D transverse phase-space Reconstruction in ASTRA simulations: Simulation D. Marx Energy 3.05 MeV, Bunch charge 1 pC, TEM grid: 83um pitch/ 25um bar width Transverse beam emittance measurements at Pegasus beamline (Aug 2017) Oblique incidence (elliptical) TEM grid (300): 54um pitch/ 31um bar width J.Giner-Navarro. Workshop: Methods in Collective and Nonlinear Effects in Bright Charged Particle Beams.

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