Models for Cathode Roughness Models for Cathode Roughness David H. Dowell 1,2 in collaboration with H. Padmore 1, T. Vecchione 1 and J. F. Schmerge 2 & W. Wan 1 1 Lawrence Berkeley Laboratory 2 SLAC National Accelerator Laboratory Presented at the Photocathode Physics for Photoinjectors (P3) Workshop Cornell University Ithaca, NY October 9, 2012

D. H. Dowell -- P3 Workshop2 Complete Physics Theory and/or Simulation: Contains all the physics so it’s exact Complicated and difficult to solve Complete Physics Theory and/or Simulation: Contains all the physics so it’s exact Complicated and difficult to solve Simplified Models: Strips down physics to essentials Applicable over limited variable regime Focuses on just a few important phenomena Simple expressions for QE, emittance, etc. Straightforward to implement in simulation codes Simplified Models: Strips down physics to essentials Applicable over limited variable regime Focuses on just a few important phenomena Simple expressions for QE, emittance, etc. Straightforward to implement in simulation codes Experimental Analysis: Model formulae allow fast, easy data analysis Testing of model assumptions Aids experiment design Experimental Analysis: Model formulae allow fast, easy data analysis Testing of model assumptions Aids experiment design Motivation for Model Analysis of Photoemission create heuristic model

D. H. Dowell -- P3 Workshop3 Emittances Near the Cathode Intrinsic (aka Thermal) Emittance,  intrinsic : Cathode’s material properties (E F,  w, E G,E A, m *,…) Cathode temperature, phonon spectrum Laser photon energy, angle of incidence and polarization Intrinsic (aka Thermal) Emittance,  intrinsic : Cathode’s material properties (E F,  w, E G,E A, m *,…) Cathode temperature, phonon spectrum Laser photon energy, angle of incidence and polarization Rough Surface Emittance: Electron and electric field boundary conditions important Surface angles washout the exit cone Coherent surface modulations enhances surface plasmons Three principle emittance effects: Surface tilt washes out intrinsic transverse momentum > escape angle increases Applied field near surface has transverse component due to surface tilt Space charge from charge density modulation due to E x surface modulation Rough Surface Emittance: Electron and electric field boundary conditions important Surface angles washout the exit cone Coherent surface modulations enhances surface plasmons Three principle emittance effects: Surface tilt washes out intrinsic transverse momentum > escape angle increases Applied field near surface has transverse component due to surface tilt Space charge from charge density modulation due to E x surface modulation Bunch Space Charge Emittance: Large scale space charge forces across diameter and length of bunch Image charge (cathode complex dielectric constant) effects space charge limit Emittance compensation Bunch shaping (beer-can, ellipsoid) to give linear sc-forces Bunch Space Charge Emittance: Large scale space charge forces across diameter and length of bunch Image charge (cathode complex dielectric constant) effects space charge limit Emittance compensation Bunch shaping (beer-can, ellipsoid) to give linear sc-forces

D. H. Dowell -- P3 Workshop4 Emittance Due to a Tilted Surface T  in  out Vacuum Metal Continuity of transverse momentum at surface: Surface momentum: Max angle of incidence:

D. H. Dowell -- P3 Workshop5 (Intrinsic Emittance) 2 (Intrinsic Emittance) 2 Near Threshold: Emittance due to intrinsic + tilt: Normalized Emittance:

D. H. Dowell -- P3 Workshop6 Choose a functional form for the surface roughness: The first derivative of the surface height function gives the tilt angle, T: Which can be simplified by assuming the surface tilt is small, specifically a n k n < 1, therefore This leads to an awkward sine-function of a sine-function: and Emittance due to intrinsic + cosine-modulated surface:

D. H. Dowell -- P3 Workshop7 Emittance Due to an Applied Electric Field The transverse momentum due to an applied electric field is given by the integral of the acceleration along the electron’s trajectory, (x(t),z(t)). [D. J. Bradley et al., J. Phys. D: Appl. Phys., Vol. 10, 1977, pp ], The transverse momentum due to an applied electric field is given by the integral of the acceleration along the electron’s trajectory, (x(t),z(t)). [D. J. Bradley et al., J. Phys. D: Appl. Phys., Vol. 10, 1977, pp ], At large distances from the surface, z > a few n, the transverse field vanishes and transverse momentum gained in the field becomes constant. The variance of this transverse momentum, p x,field, gives the emittance due to the applied field [See D. Xiang et al., Proceedings of PAC07, pp ], This is the emittance only due to the transverse component of the applied field. To include cross terms between the intrinsic, tilt and applied field, sum all the transverse momenta and compute the variance of the sum,

D. H. Dowell -- P3 Workshop 8 Squaring and dropping terms proportional to sink n x since its average when computed over one wavelength is zero gives, By numerical integration it can be shown that the third term inside the square brackets is quite small with respect the other terms and can be ignored. The variance of the transverse momentum is then And the total emittance becomes

D. H. Dowell -- P3 Workshop9 ~10 microns ~35 nm AFM of LCLS cathode sample What is the Size of These Emittances? LCLS cathode & gun parameters

D. H. Dowell -- P3 Workshop 10 Generally the roughness of a real surface is much more complicated than a simple cosine-like function. The effect of all spatial frequencies can be included by Fourier transforming the AFM image and then summing the emittance at each spatial frequency in quadrature, FFT of AFM image Use model to compute emittance vs. wavenumber and sum emittances Use model to compute emittance vs. wavenumber and sum emittances 57.5 MV/m 0 V/m Inverse sum from high to low wavenumber: 10 microns

D. H. Dowell -- P3 Workshop at Cornell 11 Charge Density Modulations Produced by Surface Roughness Due to this crossover, space charge forces and other effects such as Boersch-scattering need to be investigated. Since this ‘surface lens’ is non-linear it can also produce geometric aberrations and increase the emittance. Plus the time dependence of the RF field which changes the focus with time. Rich area of study! Electrons are focused and go through a crossover a few mm from the cathode.

D. H. Dowell -- P3 Workshop12 The space charge emittance near the cathode is driven by: -Roughness focusing the beam to produce density modulations near the cathode. -Non-uniform emission due to patchwork of QE variations from different work functions of grain and crystalline orientations as well as due to local contamination. The space charge emittance near the cathode is driven by: -Roughness focusing the beam to produce density modulations near the cathode. -Non-uniform emission due to patchwork of QE variations from different work functions of grain and crystalline orientations as well as due to local contamination. Additional Space Charge Considerations compliments of H. Padmore, ALS-LBNL PEEM image of Cu cathode ~15 microns

13 I=100 A I=50 A I=10 A The spatial frequency, f s,(modulations/radius)is the number of vertical surface modulations or waves across the radius of emission. The emittance due to space charge expansion of an initial modulation with spatial frequency f s and total beam current, I, is QE and Charge Density Uniformity: Estimating Space Charge Emittance Near the Cathode I 0 is the characteristic current: emittance for 100% modulation depth D. H. Dowell -- P3 Workshop work in progress!

D. H. Dowell -- P3 Workshop14 Other Roughness Models M. Krasilnikov, ‘Impact of the cathode roughness on the emittance of an electron beam,’ Proc. FEL 2006, Berlin, pp M. Krasilnikov, ‘Impact of the cathode roughness on the emittance of an electron beam,’ Proc. FEL 2006, Berlin, pp Model developed to compare 2D and 3D roughness effects. Also numerically computed the field emittance for an isolated protrusion. The 2D roughness emittance where 3D rough surface emittance is and Found that for the same roughness parameters : 2D Surface 3D Surface

D. H. Dowell -- P3 Workshop15 Field only Roughness only Krasilnikov Cathode field (MV/m) Comparison of Roughness Models Krasilnikov model Current model The Krasilnikov model because of it’s assumptions it doesn’t give the roughness/tilted surface emittance, instead it is more like the field emittance.

D. H. Dowell -- P3 Workshop16 Other Roughness Models S. Karkare and I. Bazarov, ‘Effect of nano-scale surface roughness on transverse energy spread from GaAs photocathodes’, arXiv: v1 [physics.acc-ph] 23 Feb 2011] Numerical simulations of electron trajectories from a tilted surface with an applied field to get the tilt and field emittances vs. photon wavelength. Roughness map from AFM image of GaAs surface before and after heat cleaning and activation. Simulations showed the tilt+field emittance overestimates the data but adding narrow cone emission 1 (due to m * effects) and phonon scattering can explain the expt. results. 1 Z. Liu et al., ‘Narrow come emission from negative electron affinity photocathodes’, J. Vac. Sci. Technol. B 23(6), pp

D. H. Dowell -- P3 Workshop17 -The electric field term dominates the roughness emittance. Surface roughness most important at high fields. -The term given by the product of the excess energy and roughness shows that decreasing the intrinsic emittance will relax the roughness required to achieve a desired emittance (Karkare & Bazarov). -The 2D emittance is approximately 40% higher than the 3D emittance for a surface with the same roughness parameters for Krasilnikov. -The surface field enhancement can strongly focus the beam to modulate the charge density with high spatial frequency. This can generate geometric and space charge emittance as well as slice emittance. The size of these emittances and the downstream effects requires further study. -The electric field term dominates the roughness emittance. Surface roughness most important at high fields. -The term given by the product of the excess energy and roughness shows that decreasing the intrinsic emittance will relax the roughness required to achieve a desired emittance (Karkare & Bazarov). -The 2D emittance is approximately 40% higher than the 3D emittance for a surface with the same roughness parameters for Krasilnikov. -The surface field enhancement can strongly focus the beam to modulate the charge density with high spatial frequency. This can generate geometric and space charge emittance as well as slice emittance. The size of these emittances and the downstream effects requires further study. Conclusions