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Photocathode for High Brightness Electron Beams Sources Workshop on Laser Laser on Workshop Photocathode for high brightness Particle electron beams Based Topical 1st D. Sertore INFN Milano - LASA Beam Brightness • Beam Brightness measures the number of generated electrons per Sources bunch w.r.t. beam divergence 푁푝푎푟푡 퐼 퐵 = ≈ 퐴 Ω 휖푥휖푦 Workshop on Laser Laser on Workshop Δ푄 Particle – Peak current 퐼 = where Q is the extracted charge from the cathode in Δt the interval t – The emittance term is the sum of different terms Based Topical 2 2 2 2 휖 = 휖푅퐹 + 휖푆퐶 + 휖푡ℎ + 휖푟표푢푔ℎ + ⋯ 1st The beam brightness generated at the Injector of a linac accelerator is the ultimate value and can only be spoiled along the accelerator The request of small emittances is a MUST also for FEL ϵn λFEL < γ 4 π Electron production effects • Thermoionic 휙 Sources − 2 푘 푇 – 푗푇ℎ(푇) = 퐴푅퐿퐷 푇 푒 퐵 2 (푘퐵 푒 푚) 퐴 • 퐴 = = 120.173 푅퐿퐷 2 휋2ℏ3 푐푚2퐾2 Workshop on Laser Laser on Workshop Particle • Field Emission 휙3 2 2 −퐵 Based Topical – 푗퐹퐸(퐸) = 퐴퐹푁 퐸 푒 퐸 푒3 1st • 퐴 = 퐹푁 8 ℎ 휋 휙 4 2푚 • 퐵 = 3 ℎ 푒 • Photoemission (for metal) 푞 2 – 푗 (휔) = 1 − 푅 휔 퐹 휔 ℏ휔 − 휙 퐼 푝ℎ ℏ휔 휆 휆 Ganter et al. NIMA 565 (2006) 423 Photocathodes • Photocathodes are materials that emit electrons Sources when light shines on them • Einstein postulated the Photoelctric effect in 1905 (Ann. der Phys. 17 (6) 132) and was awarded by Workshop on Laser Laser on Workshop Particle the Nobel Prize in 1921 퐾 = ℏ휔 − 휙 Based Topical 퐸 푒푓푓 1st • The «efficiency» of a photocathode is measured by its Quantum Efficiency # 푒푚푖푡푡푒푑 푒푙푒푐푡푟표푛 푄퐸 = #푖푛푐푖푑푒푛푡 푝ℎ표푡표푛푠 Quantum Efficiency • Often, specially for calculation, an “Internal” QE is defined Sources # 푒푚푖푡푡푒푑 푒푙푒푐푡푟표푛 #푒푚푖푡푡푒푑 푒푙푒푐푡푟표푛 푄퐸 = = 푛푡 #푎푏푠표푟푏푒푑 푝ℎ표푡표푛푠 1 − 푅 #푖푛푐푖푑푒푛푡 푝ℎ표푡표푛푠 • Workshop on Laser Laser on Workshop In pratical units QE is Particle 푄 푛퐶 퐸푝ℎ 푒푉 푄퐸 % = 퐸푙푎푠푒푟 휇퐽 10 Based Topical • For a typical 4th harmonic of a Nd laser (l = 262 nm) 1st 푄 푛퐶 4.72 푄퐸 % = 퐸푙푎푠푒푟 휇퐽 10 and hence we need 1 휇J to produce 0.472 푛퐶 having 1% QE A deeper look in the photoemission process for metal* Sources • We assume a metal photocathode and use the Spicer’s “Three Step Model” Workshop on Laser Laser on Workshop 1. Light absorption and electron excitaction Particle 2. Electron drift to the surface 3. Electron emission Based Topical 1st *D. Dowell et al. PRSTAB 12, 074201 QE calculation • Inside the metal electrons obey Fermi Dirac distribution 1 Sources 푓 = 퐹퐷 퐸−퐸퐹 1 + e 푘푇 • The potential at the surface boundary is given by Workshop on Laser Laser on Workshop Particle 푒퐹 휙푒푓푓 = 휙푤 − 휙푆푐ℎ표푡푡푘푦 = 휙푤 − 푒 4 휋 휖0 푀푉 휙푒푓푓 푒푉 = 휙푤 푒푉 − 0.037947 퐹푎 [푒푉] Based Topical 푚 1st QE calculation • The general expression for the QE is given by Absorption Sources ∞ 1 2 휋 푑퐸 1 − 푓퐹퐷 퐸 + ℏ휔 푓퐹퐷 퐸 푑 cos 휃 퐹푒−푒 퐸, 휔, 휃 푑Φ 퐸퐹+휙푒푓푓−ℏ휔 cos 휃푚푎푥 퐸 0 푄퐸 휔 = 1 − 푅 휔 ∞ 1 2 휋 푑퐸 1 − 푓퐹퐷 퐸 + ℏ휔 푓퐹퐷 퐸 푑 cos 휃 푑Φ 퐸퐹−ℏ휔 −1 0 Workshop on Laser Laser on Workshop Particle 1. Absorption of photon – It depends on the density of states of the starting state to the ending states (JDOS). The accessible energy range is starting from 퐸퐹 + 휙푒푓푓 − ℏ휔 Based Topical 2. Transport to surface 1st – Electrons, in their path to the surface, scatter mainly due hits with other electrons. The probability to reach the surface without collision is Fe-e. This is the case for metals. 3. Escape over barrier – The electron can overcome the surface barrier if the energy is above it. The criterion for escaping the barrier is 푝2 푛표푟푚푎푙 ≥ 퐸 + 휙 2 푚 퐹 푒푓푓 QE Calculation • The above formula can be reduced to a more manageable form Sources 2 1−푅 휔 퐸퐹+ℏ휔 퐸퐹+휙푒푓푓 푄퐸 휔 = 1 − 2 ℏ휔 휙 휙 2 ℏ휔 퐸퐹+ℏ휔 휆표푝푡 휔 푒푓푓 푒푓푓 Workshop on Laser Laser on Workshop 1+ 1+ Particle 휆푒−푒 퐸푚 3 ℏ휔 2 퐸푚 휆푙푎푠푒푟 – 휆 휔 = remembering that 푛 = 푛 + 푖푘 is the complex index of 표푝푡 4 휋 푘 Based Topical refraction – 휆푒−푒 is the electron scattering length 1st • If we expand QE as function of ℏ휔 − 휙푒푓푓 we obtain 2 1 − 푅 휔 ℏ휔 − 휙푒푓푓 푄퐸 휔 = 휆 휔 8 휙 퐸 + 휙 1 + 표푝푡 푒푓푓 퐹 푒푓푓 휆푒−푒 휔 Cs2Te QE @ FLASH • Cs2Te QE is routinelly measured in the FLASH RF GUN • It is measured at nominal phase (38 deg w.r.t. zero crossing), not Sources corresponding to maximum extracted charge 2 QE = 9.2 % nel 1.8 Workshop on Laser Laser on Workshop Particle QE nph 1.6 QCE eV 1.4 QE%100 ph Based Topical 1.2 Ecath J Q nC 1 space charge 1st QE % 0.47 0.8 Charge (nC) Charge effect Ecath J 0.6 0.4 푟2 퐸 − 푚 푙푎푠푒푟 @ 262 nm 2 푒퐸푙푎푠푒푟 2 푄 = 휋 푟 퐸 휖 퐹 sin 휙 + 푄퐸 푒 2 휎푟 푚 푙푎푠푒푟 0 ℏ휔 0.2 for gaussian laser beam 0 0 0.05 0.1 0.15 0.2 0.25 0.3 charge trend at low charge fitted Laser Energy (uJ) Graph from S.Lederer PPP 2012 Workshop Cs2Te QE vs Field @ FLASH m q F sin Generalized formula QE A h E E q e Sources G A e for semiconductor 4 0 QE @ zero gradient = 11.2 % Workshop on Laser Laser on Workshop Particle W = EG+EA = 3.5 eV = 4.7 Based Topical QE @ zero gradient = 4.5 % 1st W = EG+EA = 3.8 eV = 12.7 → QE decreased → EG+EA increased → field enhancement increased S.Lederer PPP 2012 Workshop Thermal Emittance • The emittance is the area occupied by the electron beam in the phase space p 1 x Sources 2 2 2 휖 = 푥 푝 − 푥 푝 푥 훽훾푚푐 푥 푥 • If we assume no correlation between position and momentum the second term under the Workshop on Laser Laser on Workshop square root vanishes and we get for x Particle the normalized emittance 2 푝푥 휖 = 훽훾휖 = 휎 Based Topical 푛 푥 푥 푚푐 푝2 1st 푥 • If we now define 휎 ≡ 푝푥 푚푐 • In term of rms quantity we can express emittance as 휖푛 = 휎푥휎푝푥 • We have then to calculate the variance of the electron momentum to have the normalized emittance Thermal emittance derivation • To derive thermal (electron distribution related) emittance, we calculate the variance of electron momentum ∞ 1 2 휋 푑퐸 1 − 푓 퐸 + ℏ휔 푓 퐸 푑 cos 휃 푑Φ 푝2 Sources 퐹퐷 퐹퐷 푥 퐸푓+휙푒푓푓−ℏ휔 cos 휃푚푎푥 퐸 0 2 휎푝 = 푥 2 ∞ 1 2 휋 푚푐 푑퐸 1 − 푓퐹퐷 퐸 + ℏ휔 푓퐹퐷 퐸 푑 cos 휃 푑Φ 퐸푓−ℏ휔 cos 휃푚푎푥(퐸) 0 • As for the QE derivation, the maximum emission angle qmax is given by the Workshop on Laser Laser on Workshop Particle energy in the direction normal to the barrier to be larger that barrier itself 2 푝푧 ≥ 퐸 + 휙 2 푚 푓 푒푓푓 Based Topical • No dependence from the electron-electron scattering probability • After some math we get 1st ℏ휔−휙푒푓푓 휎 = 푝푥 3 푚 푐2 • The thermal emittance is then given by ℏ휔 − 휙푒푓푓 휖 = 휎 푡ℎ 푥 3 푚 푐2 Thermal Emittance Measurement • RF Gun Approach Sources – Minimize all contributions to emittance and scan emittance versus laser spot size Workshop on Laser Laser on Workshop Particle M. Otevrel et al., FEL 2011 • Momentron – Correlate position Based Topical and momentum 1st (T. Vecchione et al. FEL2011) • Angular Resolved Photo Emission Spectroscopy – Time of Flight-INFN Milano LASA 1 2 2 EKin 2 x r cos q 2c m0 QE vs thermal emittance 푒퐹 휙푒푓푓 = 휙푊 − 푒 4 휋 휖0 2 Sources 1 − 푅 휔 ℏ휔 − 휙 푒푓푓 ℏ휔−휙푒푓푓 푄퐸 휔 = 휖 = 휎 휆 휔 8 휙 퐸 + 휙 푡ℎ 푥 3 푚 푐2 1 + 표푝푡 푒푓푓 퐹 푒푓푓 휆푒−푒 휔 . QE and emittance Workshop on Laser Laser on Workshop Particle have the same dependency on photon energy. Based Topical . We can reduce 1st emittance at the expense of very low QE. Free knobs are the optical properties and scattering parameters inside the material!!! Other cathode contributions to intrinsic emittance • Cathode “not” uniformity (F. Zhou et al., PRSTAB 5, 094203) Sources Workshop on Laser Laser on Workshop Particle Based Topical • Cathode roughness (D. Xiang et al., PAC07) 1st 2 푒휋 푎푛퐸푅퐹 sin 휃푅퐹 휖푛푠 = 휎 2 2 푚 푐 휆푛 yn(x)=an cos(2 /ln) cos(x) an l n x Photocathode Request • Quantum Efficiency Sources – Highest at longest wavelengths – Fast response time (< 100’s fs) – Uniform emission (space charge effects) Workshop on Laser Laser on Workshop Particle – Constant charge along the train – Low dark current • Based Topical Intrinsic Emittance – As low as possible 1st – Eventually tunable (see conflict with QE) • Operation – Operational lifetime > months • UHV required – Possible cleaning and/or rejuvenation – Reliable installation and replacement Photocathodes • Metal – Cu Sources – Mg – Superconductor • Nb Workshop on Laser Laser on Workshop Particle • Pb • Semiconductor Based Topical – PEA • Cs2Te 1st • K2CsSb • Cs3Sb – NEA • GaAs and strained • Here after I made a «very» personal selection of some of the materials and labs D. Dowell et al., NIM A 622(2010) 685 Metal Photocathode Sources Workshop on Laser Laser on Workshop Particle • These are the cathode used in normal conducting low Based Topical repetition rate micro bunch RF gun.
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