1. A. Galatà 1, D. Mascali 2, L. Neri 2, G. Torrisi 2, and L. Celona 2 1 INFN - Laboratori Nazionali di Legnaro, Viale dell’Università 2, 35020 Legnaro (Padova), Italy 2 INFN - Laboratori Nazionali del Sud, Via S. Sofia 62, 95123 Catania, Italy

2. Description of SPES and its Charge Breeder. Background theory and its numerical implementation. The code and its results. Conclusion and perspectives.

3. Post-Acceleration: new RFQ+ALPI ECR-based Charge Breeder

4. EFFICIENCY* [%] IONQSPES reqBest LPSCSPES-CB Cs26≥ 58,611,7 Xe20≥ 1010,911,2 Rb19≥ 56,57,8 Ar8≥ 1016,215,2 *results obtained for the same 1+ injected current

5. The performances of Phoenix got better during the years. Room for improvements still exists (gaseous Vs condensable). Previous work by M. Cavenago et al.

6. Focusing. Deceleration (V,B). Interaction with the plasma. Creation and destruction of charge states: Step-by-step ionizations. Charge reduction (charge exchange, electron capture...). In common with conventional sources. ECR-CB peculiarity Cs Charge breeding

7. Chandrasekhar (General), Spitzer (Charged Particles). Collisions are described by the Fokker-Plank equation. The coefficients are determined supposing a background of thermal ions. Perp. diffusion: =D ⊥ Par. diffusion: =D // τsτs τDτD τEτE Slowing Down Characteristic times Dynamical Friction:

8. Equations Trends Limits Φ-G G Always increasing Similar to ΔV v  0: no friction; isotropic diffusion v  ∞: transversal diffusion Heavy particles dominated by friction

9. v(t+1)=v(t) + a*T step  x(t+1)=x(t)+ v*T step Slowing downDiffusion Friction: a=- ν s v Random vector v rand

10. Rb charge breeding within EMILIE* Optimum ΔV opt ~ -12 V. Global capture < 50%. Anomalous ΔV curves for Rb 1+ Rb 1+ efficiency some % @ ΔV opt. Efficiency increases with ΔV. Weakly interacting 1+ ions Rb 1+ cb time plasma on and off τ cb : 500 μs *O. Tarvainen et al, PSST (2015), 24 035014

11. *Thanks to J. Angot and T. Lamy V CB 2 Einzel Rb 1+ @ 20 keV plasma VPVP SIMION CODE Starting conditions Simulation of Rb 1+ injection in experimental conditions. Characterized by E inj =E-V p *q → ΔV sim =V p -E/q. ΔV exp =V CB -E/q < ΔV sim (plasma potential?) Geometry: Cylinder l=288 mm r=36 mm between magnetic filed maxima. Injection, radial and extraction losses. If lost at extraction but r<4→extracted. Analytical formulas for the magnetic field components Simulated curves will be allowed to shift towards more negative ΔV

12. BASIC PLASMA MODEL (BPM) plasmoid/halo scheme (n halo =n plasmoid /100) Boris method for B motion losses v(t+1)-v(t)=Δv Lang + a*T step (T step =100 ps) plasma Rb 1+ @ different E inj v(t+1)-v(t)= Δv Lang + q/m[E+v(t)xB] *T step n plasmoid n halo B ecr v(t+1)-v(t)= Δv Lang + q/m[v(t)xB] *T step COMPLETE PLASMA MODEL (CPM) Potential dip for electrostatic ion confinement. Complete Lorentz force. n warm =n cold /10, n warm distributed as n cold KT warm =1/0.1 keV, ionizations (Lotz) Tabulated values for τ ioniz (q) Ionization applied through MC

13. Loads starting conditions Collocates the particles inside or outside the resonance, solves the Langevin equation and applies the Boris method Stores the entire workspace on a file Updates positions and velocities that become the starting conditions for the next iteration Yes Checks for saving Removes them from the calculation No Checks for losses Stores their positions and velocities Yes No

14. Capture is low, independent from n and weakly on E inj Ions residence time: plasma state? → υ coll Vs υ cycl υ coll ≤ υ cycl all n Magnetic Regime n core =i*n co E inj = 2:5:22 eV n co =2.6∙10 18 m -3 i=1, 0.6, 0.3, 0.1 =2.5 τ mag =Rl/v T ~ 400-600 μs Agreement with T span τ mag independent from n 1000 Rb 1+ ions

15. Overall confinement increased Different behaviour between low and high density υ coll Vs υ cycl υ coll <~ υ cycl @ low dens (see KT=1 eV) υ coll > υ cycl high dens → Collisional Regime Hardly applicable to 1+ ions! n core =i*n co E inj = 2:5:27 eV n co =2.6 ∙10 18 m -3 i=1, 0.6, 0.3, 0.1 =2.5 1000 Rb 1+ ions

16. KT=1 eVKT= 0.376 eV For both temperatures no Rb 1+ ions extracted unless n<0.3*n co Similar trends but no agreement

17. KT i is a key parameter for a good capture. KT i has to be low (0.376 eV) in order to have a capture comparable with experiments. no Rb 1+ efficiency unless n<0.3*n co. KT=1 KT=0.376 Magnetized plasmafor all n Low confinement Constant losses for all energies High n Low n Collisional plasma Magnetized plasma Optimum injection energy Higher capture than high n and KT=1 Higher confinement Weaker frictional force at the lowest density Plasma Temperature

18. Loads starting conditions Collocates the particles inside or outside the resonance, solves the Langevin equation and applies the Boris method Stores the entire workspace on a file Updates positions and velocities that become the starting conditions for the next iteration Yes Checks for saving Removes them from the calculation No Checks for losses Stores their positions and velocities Yes No Checks for ioniz Yes No q=q+1

19. Capture increases up to a factor > 3Ionizations take place

20. The capture is still too lowRb 1+ efficiency agrees with experiments n=0.1*n co E inj [eV]Losses [%] 259.70 760.80 1258.00 1759.80 2259.60 Requirements not completely fulfilled yet

21. n=0.1*n co n=0.075*n co =3 from a spectrum supposed ΔE=2 eV for Rb 1+ beamKT i =0.3 eV Shift -1.5 V Shift -4 V E inj [eV]Captures [%]ε 1+ [%]ΔV sim [V] 1044.712.16-11.5 E inj [eV]Captures [%]ε 1+ [%]ΔV sim [V] 747.640.80-11 1039.519.28-14

22. Distribution of captured particles Ionizations Distribution of losses

23. 10 eV 15 eV resonance 2 eV 5 eV

24. Injected particles release energy inside the plasma. The effect on the plasma can be experimentally observed Xe injection resonance

25. Slowing down and capture correctly implemented in a single particle approach: Model of increasing complexity. Agreement with theorectical expectations. Agreement with experiments for a narrow set of plasma parameters. Important outputs: Key role of ion temperature. Density estimation in agreement with experimental results within EMILIE. Energy deposition map. Predictive tool for the capture process: Influence of beam emittance. Influence of ion mass. Information about RIBs losses

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