Advanced Numerical Modelling of the PHOENIX-SPES charge breeder A. Galat1, D. Mascali2, L. Neri2, G. Torrisi2, and L. Celona2 INFN - Laboratori Nazionali di Legnaro, Viale dellUniversit 2, 35020 Legnaro (Padova), Italy 1 INFN - Laboratori Nazionali del Sud, Via S. Soa 62, 95123 Catania, Italy 2 Outline Description of SPES and its Charge Breeder. Background theory and its numerical implementation. The code and its results. Conclusion and perspectives. The SPES Project Production, Ionization and Post-Acceleration of Radioactive Species

Up to 1013 proton induced fissions/s; A = 80 160 Target-Ion-Source system Cyclotron: p 70MeV, 750AA Radio Frequency Quadrupole-Cooler Target-Ion-Source system High Resolution Mass Spectrometer (1/20000) ECR-based Charge Breeder Post-Acceleration: new RFQ+ALPI SPES: ECR-based CB (SPES-CB) Upgraded version of Phoenix by LPSC. Almost all metal sealings Agreement signed in June 2014. New extraction system Optimized position of iron rings

Acceptance tests in Spring 2015 (see ThuPE26). Delivery at LNL in Autumn 2015 . EFFICIENCY* [%] SPES Best SPESION Q req LPSC CB Cs 26 5 8,6 11,7 Xe 20 10 10,9 11,2 Rb 19

5 6,5 7,8 Ar 8 10 16,2 15,2 *results obtained for the same 1+ injected current SPES-CB performances The performances of Phoenix got better during the years. Room for improvements still exists (gaseous Vs condensable). Numerical simulations can be a powerful tool to optimize the charge breeding process Previous work by M. Cavenago et al. Here we present a new numerical approach to the charge breeding process, with the analysis of the influence of different beam and plasma parameters ECR-based charge breeding process Focusing. Deceleration (V,B).

Thermalizatio n Interaction with the plasma. Multiple Coulomb collisions ECR-CB peculiarity Creation and destruction of charge states: Step-by-step ionizations. Charge reduction (charge exchange, electron capture...). In common with conventional sources. Cs Charge breeding Background theory of Coulomb collisions Chandrasekhar (General), Spitzer (Charged Particles). Collisions are described by the Fokker-Plank equation. The coefficients are determined supposing a background of thermal ions. Dynamical Friction: s

Slowing Down Perp. diffusion: <(vv)2>=D Characteristic times Par. diffusion: <(vv//)2>=D// D E 90 Degree Deflection Energy Exchange Friction and Diffucion Coefficients Equations Trends -G G Always increasing

Similar to vV Limits v0: no friction; isotropic diffusion Heavy particles dominated by friction v: transversal diffusion Implementation of Coulomb collisions Forward Difference method: v(t+1)=v(t) + a*Tstep x(t+1)=x(t)+ v*Tstep MC approach fails Langevin Formalism vvLang= v(t+1)-v(t)= - sv(t)*Tstep+vrand Slowing down Diffusion Random vector vrand Friction: a=- sv A benchmark for the code: case study Rb charge breeding within EMILIE*

Optimum VVopt ~ -12 V. Global capture < 50%. Anomalous VV curves for Rb1+ Rb1+ efficiency some % @ VVopt. Efficiency increases with VV. Weakly interacting 1+ ions Rb1+ cb time plasma on and off NUMERCAL SIMULATIONS GOALS Reproduction of Rb1+ VV curve Tspan= 500 As Global capture 40 % @ VVopt ~ -12 V Rb1+ efficiency few % @ VVopt ~ -12 V cb: 500 ss *O. Tarvainen et al, PSST (2015), 24 035014 Input parameters Geometry: Cylinder l=288 mm r=36 mm between magnetic filed maxima. Injection, radial and extraction losses. If lost at extraction but r<4extracted.

Analytical formulas for the magnetic field components Starting conditions Simulation of Rb1+ injection in experimental conditions. Characterized by Einj=E-Vp*q VVsim=Vp-E/q. VVexp=VCB-E/q < VVsim (plasma potential?) Simulated curves will be allowed to shift towards more negative vV Rb1+ @ 20 keV 2 Einzel VCB plasma VP Ions starting conditions for the numerical code x p' ( z ) 2 Sxy 2 y B y p ' ( z ) 2 S ( x 2 y 2 ) 2

Bz p( z ) B x SIMION CODE *Thanks to J. Angot and T. Lamy S 617.8T / m 2 Plasma modeling Rb1+ @ different Einj v(t+1)-v(t)=vvLang + a*Tstep (Tstep=100 ps) plasma BASIC PLASMA MODEL (BPM) plasmoid/halo scheme (nhalo=nplasmoid/100) Boris method for B motion losses nh alo

Becr np la s m o id v(t+1)-v(t)= vvLang + q/m[v(t)xB] *Tstep COMPLETE PLASMA MODEL (CPM) Potential dip for electrostatic ion confinement. Complete Lorentz force. nwarm=ncold/10, nwarm distributed as ncold KTwarm=1/0.1 keV, ionizations (Lotz) Tabulated values for ioniz(q) Ionization applied through MC v(t+1)-v(t)= vvLang + q/m[E+v(t)xB] *Tstep BPM: flow diagram Loads starting conditions Yes Checks for saving

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

BPM: results @ KTi=1 eV Einj = 2:5:22 eV 1000 Rb1+ ions ncore=i*nco Capture is low, independent from n and weakly on E inj Ions residence time: plasma state?coll Vs cycl coll cycl all n mag=Rl/vT ~ 400-600 ss Agreement with Tspan Magnetic Regime mag independent from n nco=2.61018 m-3 i=1, 0.6, 0.3, 0.1 =2.5 BPM: results @ KTi=0.376 eV Einj = 2:5:27 eV

ncore=i*nco 1000 Rb1+ ions Different behaviour between low and high density coll <~ cycl @ low dens (see KT=1 eV) coll Vs cycl Hardly applicable to 1+ ions! 3 i=1, 0.6, 0.3, 0.1 =2.5 Overall confinement increased coll > cycl high dens nco=2.6 1018 m- Collisional Regime

BPM: Rb1+ efficiency KT=1 eV KT= 0.376 eV Similar trends but no agreement For both temperatures no Rb1+ ions extracted unless n<0.3*nco BPM: summary Plasma Temperature KTi is a key parameter for a good capture. KTi has to be low (0.376 eV) in order to have a capture comparable with experiments. KT=1 KT=0.376 Magnetized plasmafor all n

Low confinement Constant losses for all energies High n Low n Collisional plasma Magnetized plasma Higher confinement Optimum injection energy Higher capture than high n and KT=1 no Rb1+ efficiency unless n<0.3*nco.

Weaker frictional force at the lowest density CPM: flow diagram Loads starting conditions ti o ns on iz a +i ld ip No Stores the entire workspace on a file Collocates the particles inside or outside the resonance, solves the Langevin equation and applies the Boris method po te n

t ia BM P+ Yes Checks for saving Checks for losses Yes No q=q+1 Yes Checks for ioniz No Updates positions and velocities that become the starting conditions for the next iteration

Stores their positions and velocities Removes them from the calculation CPM Vs BPM @ KTi=1 eV and nco Capture increases up to a factor > 3 Ionizations take place CPM: KTi=0.376 eV and n=0.1nco The capture is still too low Rb1+ efficiency agrees with experiments n=0.1*nco Einj [eV] Losses [%] Captures [%]

1+ [%] 2 59.70 44.62 0.16 7 60.80 39.93 0.64 12 58.00 18.70 11.68

17 59.80 3.20 27.76 22 59.60 0.40 44.72 Requirements not completely fulfilled yet CPM: refinements supposed vE=2 eV for Rb1+ beam =3 from a spectrum n=0.1*nco

KTi=0.3 eV n=0.075*nco GOALS ACHIEVED ! Shift -4 V Shift 1.5 V Einj [eV] Captures [%] 1+ [%] vVsim [V] 10 44.71 2.16 -11.5

Einj [eV] Captures [%] 1+ [%] vVsim [V] 7 47.64 0.80 -11 10 39.51 9.28 -14

CPM: details for n=1.951017 m-3; vVsim= -11V Distribution of captured particles Ionizations Distribution of losses First ionizations take place in agreement with the estimated ionization times Losses are mostly radial Most of the particles are within the plasmoid CPM: details for n=1.951017 m-3; vVsim= -11V 2 eV 5 eV DENSITY MAP THE OPTIMUM INJECTION ENERGY IS EVIDENT 10 eV

resonance 15 eV CPM: details for n=1.951017 m-3; vVsim= -11V Injected particles release energy inside the plasma. Xe injection The effect on the plasma can be experimentally observed HIGHLY LOCALIZED ENERGY RELEASE resonance Oxygen CSD Conclusions 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 Perspectives Improvement of the plasma-target model: Electromagnetic calculations (see ThuPE27). ECR heating and Coulomb collisions. Self consistent calculations of the electron density map. Warm electrons density estimations. Multipurpose Simulation Tool

(TuePE11) ECRIS (ECR-CB) and MDIS Implementation of several processes (Coulomb, ioniz., excit., ecc..) External electromagnetic fields (static, variable) f o t o l A ! ! ! o d o work t THANK YOU VERY MUCH FOR YOUR ATTENTION