Advanced Numerical Modelling of the PHOENIX-SPES charge

breederA. Galatà1, D. Mascali2, L. Neri2, G. Torrisi2, and L. Celona2

1INFN - Laboratori Nazionali di Legnaro, Viale dell’Università 2, 35020 Legnaro (Padova), Italy2INFN - Laboratori Nazionali del Sud, Via S. Sofia 62, 95123 Catania, Italy

Outline

• Description of SPES and its Charge Breeder.

• Background theory and its numerical implementation.

• The code and its results.

• Conclusion and perspectives.

Cyclotron: p 70MeV, 750μA

Radio Frequency Quadrupole-Cooler

High Resolution Mass Spectrometer (1/20000)

Post-Acceleration: new RFQ+ALPI

• Up to 1013 proton induced fissions/s; A = 80 ÷ 160

ECR-based Charge Breeder

• Production, Ionization and Post-Acceleration of Radioactive Species

Target-Ion-Source system

The SPES Project

Target-Ion-Source system

SPES: ECR-based CB (SPES-CB)

• Upgraded version of Phoenix by LPSC.

• Agreement signed in June 2014.

• Acceptance tests in Spring 2015 (see ThuPE26).

• Delivery at LNL in Autumn 2015 .

EFFICIENCY* [%]

ION Q SPES req

Best LPSC

SPES-CB

Cs 26 ≥ 5 8,6 11,7Xe 20 ≥ 10 10,9 11,2Rb 19 ≥ 5 6,5 7,8Ar 8 ≥ 10 16,2 15,2*results obtained for the same 1+

injected current

Optimized position of iron rings

New extraction system

Almost all metal sealings

SPES-CB performances

• The performances of Phoenix got better during the years.

• Room for improvements still exists (gaseous Vs condensable).

• Previous work by M. Cavenago et al.

Numerical simulations can be a powerful tool to optimize the charge breeding process

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).

• 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.

Multiple Coulomb collisions

ECR-CB peculiarity

CsCharge breeding

Thermalization

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.

Perp. diffusion: <(Δv⊥)2>=D⊥ Par. diffusion: <(Δv//)2>=D//

τs τD τE

90° Degree Deflection Energy ExchangeSlowing Down

Characteristic times

Dynamical Friction: <Δv//>

• Equations

• Trends

• Limits

Φ-GG

Always increasing

Similar to ΔV

v0: no friction; isotropic diffusion v∞: transversal diffusionHeavy particles dominated by friction

Friction and Diffucion Coefficients

Implementation of Coulomb collisions

• Forward Difference method:

• MC approach fails Langevin Formalism

v(t+1)=v(t) + a*Tstep x(t+1)=x(t)+ v*Tstep

ΔvLang= v(t+1)-v(t)= - νsv(t)*Tstep+vrand

Slowing down Diffusion

Friction: a=- νsvRandom vector vrand

A benchmark for the code: case study

• Rb charge breeding within EMILIE* Optimum ΔVopt ~ -12 V. Global capture < 50%.

• Anomalous ΔV curves for Rb1+

Rb1+ efficiency some % @ ΔVopt. Efficiency increases with ΔV.

• Weakly interacting 1+ ions Rb1+ cb time plasma on and off τcb: 500 μs

NUMERCAL SIMULATIONS GOALS• Reproduction of Rb1+ ΔV curve• Tspan= 500 μs

• Global capture≥ 40 % @ ΔVopt ~ -12 V

• Rb1+ efficiency few % @ ΔVopt ~ -12 V*O. Tarvainen et al, PSST (2015), 24 035014

*Thanks to J. Angot and T. Lamy

VCB2 EinzelRb1+ @ 20 keV

plasma

VP

SIMION CODE

• Starting conditions Simulation of Rb1+ injection in experimental conditions. Characterized by Einj=E-Vp*q → ΔVsim=Vp-E/q. ΔVexp=VCB-E/q < ΔVsim (plasma potential?)

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<4→extracted.

2/8.617

)(

)22(2)('2

2)('2

mTS

zpBz

yxSzpy

yB

Sxyzpx

xB

Ions starting conditions for the numerical code

Analytical formulas for the magnetic field components

Simulated curves will be allowed to shift towards more negative ΔV

Plasma modeling

• BASIC PLASMA MODEL (BPM)plasmoid/halo scheme (nhalo=nplasmoid/100)Boris method for B motionlosses

v(t+1)-v(t)=ΔvLang + a*Tstep (Tstep=100 ps)plasma

Rb1+ @ different Einj

v(t+1)-v(t)= ΔvLang + q/m[E+v(t)xB] *Tstep

nplasmoid

nhalo

Becr

v(t+1)-v(t)= ΔvLang + 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 τioniz(q) Ionization applied through MC

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

YesChecks

for saving

Removes them from the

calculation

No

Checks for losses

Stores their positions and

velocities

Yes

No

BPM: flow diagram

BPM: results @ KTi=1 eV

• Capture is low, independent from n and weakly on Einj

• Ions residence time: plasma state?→υcoll Vs υcycl

υcoll ≤ υcycl all n

Magnetic Regime

ncore=i*nco

Einj = 2:5:22 eV •nco=2.6∙1018 m-3

•i=1, 0.6, 0.3, 0.1•<z>=2.5

•τmag=Rl/vT ~ 400-600 μs

•Agreement with Tspan

•τmag independent from n

1000 Rb1+ ions

BPM: results @ KTi=0.376 eV

• Overall confinement increased

• Different behaviour between low and high density

υcoll Vs υ cycl

υcoll <~ υ cycl @ low dens (see KT=1 eV)

υcoll > υ cycl high dens → Collisional Regime

Hardly applicable to 1+ ions!

ncore=i*nco

Einj = 2:5:27 eV •nco=2.6 ∙1018 m-

3

•i=1, 0.6, 0.3, 0.1•<z>=2.5

1000 Rb1+ ions

BPM: Rb1+ efficiencyKT=1 eV KT= 0.376 eV

For both temperatures no Rb1+ ions extracted unless n<0.3*nco

Similar trends but no agreement

BPM: summary

• 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.

• no Rb1+ efficiency unless n<0.3*nco.

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

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

YesChecks

for saving

Removes them from the calculation

No

Checks for losses

Stores their positions

and velocities

Yes

No

CPM: flow diagram

Checks for ioniz

Yes

No

q=q+1

BMP

+ po

tent

ial d

ip +

ioni

zatio

ns

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 [%] ε1+ [%]

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

n=0.1*nco n=0.075*nco

<z>=3 from a spectrum supposed ΔE=2 eV for Rb1+ beam KTi=0.3 eV

Shift -1.5 V

Shift -4 V

Einj [eV] Captures [%] ε1+ [%] ΔVsim [V]

10 44.71 2.16 -11.5

Einj [eV] Captures [%] ε1+ [%] ΔVsim [V]

7 47.64 0.80 -11

10 39.51 9.28 -14

GOALS ACHIEVED !

Distribution of captured particles Ionizations Distribution of losses

Most of the particles are within the plasmoid

First ionizations take place in agreement with the estimated ionization times Losses are mostly radial

CPM: details for n=1.95∙1017 m-3; ΔVsim= -11V

DENSITY MAP

10 eV 15 eV

resonance

2 eV 5 eV

THE OPTIMUM INJECTION ENERGY IS

EVIDENT

CPM: details for n=1.95∙1017 m-3; ΔVsim= -11V

• Injected particles release energy inside the plasma.

• The effect on the plasma can be experimentally observed

Xe injection

resonance

CPM: details for n=1.95∙1017 m-3; ΔVsim= -11V

Oxygen CSD

HIGHLY LOCALIZED ENERGY RELEASE

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

• 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• ECRIS (ECR-CB) and MDIS• Implementation of several processes (Coulomb, ioniz., excit., ecc..)• External electromagnetic fields (static, variable)

Perspectives

(TuePE11)

A lot of work to do!!!

THANK YOU VERY MUCH FOR YOUR

ATTENTION