Design and Simulations of the Source of Polarized Slow Positrons at ELI-NP Nikolay Djourelov ELI-NP, IFIN-HH, 30 Reactorului Str, MG-6 Bucharest-Magurele, Romania * E3 Positron source

AE1GOAL: Build a laboratory for spectroscopy with spin polarized slow positron beam of high intensity METHOD: ( , e + e - ) reaction of  -beam of I  = 2.4×10 10 s -1 and E  < 3.5 MeV with circular polarization incident on W-converter Fig. Gamma Beam Timing Positron Spectroscopy Laboratory

Electrostatic focusing (copied from PULSTAR Nuclear Reactor e + source) solenoid Adiabatic Magnetic Guidance to the Positron Laboratory Hall Converter/Moderator Assembly Extraction grid γ-beam Beam formation

Fig. γ ‑ beam energy Fig. Compton scattering of laser- light off a high-energy electron beam Fig. Energy vs scattered angle, θ, of the γ ‑ rays at the interaction point. Gamma Beam Characteristics Fig. γ ‑ beam intensity profile at 4 m from IP FWHM = 6.1 mm at 4 m (from IP) Fig. Scheme for GEANT4 simulation of the γ-beam energy cut by a tungsten collimator. The sizes are in mm.

. Fig. The polar angle distribution of the momentum direction of the created fast e + in the W target. Fig. Energy spectrum of the created fast e + in the W target Converter geometry Fig. One-side-open Venetian blind geometry of the proposed CMA (converter/moderator assembly). The γ-beam propagates along z-axis. Converter Sizes Optimization necessary!

Implementation of e + moderation in GEANT 4 e+e+ track e+e+ slow fast GEANT 4 Theory

Improved Slow-Positron Yield using a Single Crystal Tungsten Moderator. Vehanen, A., Lynn, K.G., Schultz, P.J., Eldrup, M. Applied Physics A, Vol. 32, No. 3, 1983, p Co source W reflection m R = 3.8×10 -3 Validation of e + moderation implemented in GEANT 4 GEANT 4 (our simulation) Experimental results Development and use of a thin‐film transmission positron moderator K. G. Lynn, B. Nielsen and J. H. Quateman, Appl. Phys. Lett. 47, 239 (1985) 22 Na source W d = 0.5 µm transmission m T = 4×10 -4 m T = 6.1×10 -4 m R = 2.8×10 -3 Used e + energy spectrum

Extraction of Moderated Positrons Moderated positrons are emitted normal to the surface with E + = 3 eV. Reflection with 60% survival. U (V) No segmentation Segmentation into 6 insulated layers

L = 30 cm FIXED (FOCUSING) Length L = 30 cm FIXED (FOCUSING) (H:G) = 3:1 FIXED (EXTRACTION) Aspect ratio (H:G) = 3:1 FIXED (EXTRACTION) W = 16 mm Optimized Gap width W = 16 mm (Optimized) d = 80 µmOptimized Foil thickness d = 80 µm(Optimized) H = 6 mm Optimized Gap height H = 6 mm (Optimized) N144Calculated Number of gaps N = L / (d+G) = 144 (Calculated) Analytical optimization is then completed with GEANT4 simulations including physics to take into account e + moderation process. Optimization of Converter Sizes d G H w L = N*(d+G) D fwhm Cumulative thickness N*d (mm) Fast e + in bulk Used

d (mm) h (mm) × × × × × × × × × × × × × × ×10 -5 Table: The absolute γ ‑ to ‑ slow positron conversion efficiency, Γ, at selected values for the CMA height, h, and foil thickness, d, for CMA width b=16 mm and length L =300 mm, and γ-beam intensity profile with Dγ=6.1 mm, as obtained by GEANT4 simulation. Optimization by GEANT4 Efficiency e + s /γ = 8.2×10 -5 Slow positrons = 1.6×10 6 e + s /s

solenoid Beam spot of 2.5 cm (FWHM) COMSOL simulations Beam Formation (Focusing) For converter length of 30 cm 87% transmission Focusing quality is limited mainly due to the spread of the transversal energy which is gained during the extraction (Liouiville’s theorem) Electrostatic focusing (reproduced from PULSTAR Nuclear Reactor e + source) Followed by transport in solenoid magnetic field. x-z plane y-z plane Results from Extraction

e + (fast in the bulk) e + (moderated) Spin Polarization (transversal) Polarization Transfer The influence of slowly varying electric and magnetic fields on polarized electron beams is described in [H.A. Tolhoek, Electron Polarization, Theory and Experiment, Rev. Mod. Phys. 28 (1956) ]. Few cases are described : a)Deflecting low energy electrons by electric filed over an angle of π/2 change the longitudinal polarization to transversal (or the opposite); b)acceleration electric field (longitudinal) leaves the electron polarization unchanged; c)transverse magnetic field rotates the direction of the beam at the same rate as the electron spin, so that a magnetic field leaves the state of transverse polarization unchanged; d)longitudinal magnetic field does not change the direction and magnitude of the momentum but the electron spin precesses about the propagation axis. Circular polarization Spin Polarization (longitudinal)

Design for Spin Polarized Positron Beam Negligible depolarization effect on beam formation

Fig. Energy vs scattered angle, θ, of the γ ‑ rays at the interaction point. FACT Nuclear Physics Experiments require narrow energy band width γ ‑ beam! Fig. γ ‑ beam energy Attenuated γ ‑ beam due to interaction with CMA γ ‑ beam for Nuclear Physics Experiments slow positrons CMA with holes - 1 mm in diameter 10% less e + intensity of the beam but available in parasitic mode ELI-NP International Scientific Advisory Board contribution

AE1 EXPECTATIONS: Moderated (slow) positron intensity 1.4×10 6 s -1 Degree of spin polarization 31% ADVANTAGES to use γ-beam: 100 times higher intensity of polarized positrons than isotope based source of polarized positrons in operation for material studies Independent from the only supplier (iThemba) of 22 Na sources Negligible heating of the converter/moderator assembly Easy access for upgrade of the converter/moderator assembly compare to reactor based sources SPECTROMETERS: CDBS – Coincidence Doppler Broadening Spectroscopy PALS – Positron Annihilation Lifetime Spectroscopy AMOC – Age MOomentum Correlation TOF-PAES – Positron annihilation initiated Auger Electron Spectroscopy GiPALS – Gamma induced PALSSUMMARY

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