Novel modelling of metal atoms diffusion and ion transport in ECR plasma relevant to ion sources and in-plasma nuclear physics studies

Metals can be injected into electron cyclotron resonance ion sources (ECRIS) via different techniques, among which resistive ovens are used to vaporize neutral materials, later captured by the energetic plasma that will step-wise ionize them, hence giving multiply charged ion beams for accelerators. Recently, PANDORA, a novel ECR plasma trap, has been conceived to perform interdisciplinary research spanning from nuclear physics to astrophysics, where in-plasma high charge states of metallic species are demanded. However, a full knowledge on the vaporization method and on the coupling of neutral atoms with plasma and its overall dynamics is still not available. Simulations, hence, are of fundamental relevance to improve the overall efficiency, reduce consumption of rare expensive isotopes, and to improve the ion source performance. We present a numerical study about metallic species suitable for oven injection in ECRIS, focusing on metals diffusion, transport, and wall deposition under molecular flow regime. We studied the metal dynamics with and without plasma. Results underline the plasma role on a space-dependent conversion yield, reflecting the strongly inhomogeneous ECR plasma. The plasma and its parameters have been modelled using an established self-consistent particle-in-cell model. The numerical tool is conceived for the PANDORA plasma trap but can be extended to other ECR plasmas and traps. As test cases we studied the 134Cs and 48Ca radioisotopes, as metals of interest for the modern nuclear physics. A focus is given on the β-decaying 134Cs, as an application case for PANDORA, providing quantitative estimates of the γ-detection signal-poisoning effect by neutral metals deposition at the chamber wall.


Introduction
The large variety of particle beams demanded by the nuclear physics community requires for continuous efforts in developing suitable technologies for injecting high-brightness ion beams into particle accelerators.Electron cyclotron resonance ion sources (ECRIS) are largely used as plasma-based injectors for accelerators, for producing multiply-charged and high-intensity ion beams [1].They are also considered for producing metallic ion beams, and to this aim, several metal injection techniques have been conceived.Among them, resistively heated ovens [2] can be employed to vaporize many metallic species, showing limitations in case of refractory elements.These systems are under continuous development [3,4], but very few is known on the oven-toplasma coupling, whose dynamics strongly impacts on the atom-to-ion conversion yield and on the plasma source stability.In this work, we numerically studied the metal diffusion dynamics via evaporation in an upcoming ECR facility at the INFN-LNS, the PANDORA plasma trap, which will make use of rare metallic radioisotopes for multidisciplinary experimental in-plasma studies.PANDORA is an INFN-leaded project [5,6] aiming at measuring, for the first time, possible variations of in-plasma β-decay lifetimes for isotopes of astrophysical interest, as a function of thermodynamic conditions of the in-laboratory controlled plasma environment.The physics cases considered in this study have been motivated both by the aim to improve the global conversion efficiency of rare and expensive isotope atom to ions (e.g., 48 Ca), and to explore viable ways to reduce the neutral metals deposition on the plasma chamber wall (e.g., by 134 Cs), the latter poisoning the signal-to-background ratios of certain measurements expected within the PANDORA project [6,7].We developed a MATLAB ® Monte Carlo code to study the impact of plasma ionization and charge-exchange in the atom-to-ion conversion/tracking dynamics.The numerical tool was conceived for the PANDORA plasma trap but can be extended to other ECR plasmas and traps.Results stress the role of the plasma which leads to a spacedependent atom-to-ion conversion yield, in fact reflecting the in-homogeneous ECR plasma features.The transport of ionized species is strongly driven by the confining magnetic field, and metal deposition maps on the chamber wall have been used to investigate on the γ-signal poisoning of 134 Cs decay's products, as an interesting application of the numerical tool.

Methods
The study has been performed considering a cylindrical vacuum/plasma chamber (radius, R = 140 mm, length, L = 700 mm) as simulation's geometry, resembling the PANDORA ECR plasma trap geometry, and the oven inlet, which is reduced only to an emitting surface (radius, r = 2.5 mm) at the edge of injection side of the chamber, at given pressure, p vap =10 −2 mbar, and temperature, T -see Fig. 1(a).This latter regulates the thermal speed (considering an isotropic emission with v = k B T /M , k B the Boltzmann constant, and M the mass of the metal) of evaporating N P particles moving in non-collisional regime, and changes from 134 Cs (T ∼ 420 K) to 48 Ca (T ∼ 770 K).The developed Monte Carlo code allows to integrate N P = 10 6 particle's motion equations, with thermal diffusing starting conditions; the evolution of particles' position, charge-state (from 0 to 1 + , and backward), and velocity (direction changed by the magnetic field) in the simulation space is followed till particles impinge on the wall or the end of simulation time (∼ 3 ms) is reached.A space-dependent ionization reaction rate of metallic atoms is computed, according to the plasma energy content and density.Those 3D reaction maps are based on data taken from self-consistent plasma simulations of electron dynamics in the PANDORA plasma trap [8,9,10].Further details can be found in [11].The electron-impact (EI) and charge-exchange (CEX) ionization cross sections, so as the reaction frequency are hence calculated from plasma's (ω RF = 18 GHz, P RF = 5 kW) simulated data, according to Lotz [12] and Müller-Salzborn [13] formalism.Due to typical in-homogeneous and anisotropic plasma parameters, this resulted in space-dependent reaction rate maps.Reaction rate maps are then used to compute a 3D probability map that thermally diffusing metal atoms go into reactions.Metal ions then start feeling the magnetic field lines, changing accordingly their motion in the space, continuing their diffusion inside the chamber or ending on the chamber wall, freezing and becoming in the end neutral.

Results
In Fig. 1(b) an example of neutral 134 Cs deposition at the chamber wall after only thermal diffusion is shown, i.e., no plasma is here considered.The colorbar of the plot indicates the log 10 [particle/s] deposited, adequately scaled to the mass-flow rate [kg/s] of material expected to be consumed during the experimental oven run.The peculiar deposition shape shows a maximum close to the oven's inlet, mostly caused to the non-axisymmetric position of the oven and to the isotropic emission of metal vapours.The 100% of simulated particles are in this case deposited.The tilting angle (∼ 10 • ) and the non-axisymmetric position considered in this study have been addressed as source of such anisotropy shown by the deposition maps.Including the plasma role in the metal diffusion, reaction, and transport, impacts on the deposited materials, strongly depending on both the plasma features (electron and ion density, energy, ion charge state distribution, magnetic field) and on the evaporated metallic species.The former ones impact on the ionization/capture efficiency of metallic neutral atoms, as well as on the metal ions transport; the latter introduce a different factor of ionization reactivity in plasma, mostly depending on their relative thermal speed compared to the plasma's ion speed and on their ionization potentials.Figures 1(c) and 1(d) show respectively the amount of deposited 134 Cs and 48 Ca material at the chamber wall, after considering the overall plasma role in the metal dynamics.The deposition pattern is mostly driven by the magnetic field lines, with higher particle concentration along the magnetic branches.Moreover, whereas for the 134 Cs case, the amount of reacting particles is ∼ 47%, and the deposited percentage is ∼ 78%, in the 48 Ca case, the reacting percentage is lower ∼ 33%, with a larger deposition percentage ∼ 90%.These two main results can be easily related to what above discussed: despite the plasma features are the same, starting thermal speed of the two species are very different, and so also their ionization potentials, which eventually change in the end their in-plasma reactivity.As an interesting application of the numerical model, we developed another Monte Carlo routine to calculate the 134 Cs radioisotope's daughter nuclei (i.e., 134 Ba) γ activity, depending on the continuous space-dependent deposition rate at the chamber wall of the β-decaying 134 Cs nuclei, as resulting from Fig. 1(c).This was very useful to make quantitative estimates for the PANDORA project's goals, in particular about the poisoning of the γ signal (E γ ∼ 795 keV), used as detectable tagging observable for investigating on the β-decay rate change in plasma.The contamination of the signal could come from deposited neutral decay's products of shortliving radioactive nuclei, as the 134 Cs (t 1/2 ∼ 2 years).Whether or not the additional background arising from deposited γ-decaying 134 Ba nuclei is important, was an aspect not quantitatively explored so far.Numerical results, accounting for the space-dependent deposition rates and detection efficiency, indicate that the detected contribution due to the γ decay of 134 Ba deposited at the wall is really negligible (∼ 0.007%), completely overwhelmed by the intense plasma selfemission in the same energy range.

Conclusions
In this work, we have reported on novel numerical simulations investigating the dynamics of metallic atoms evaporated into ECR plasmas, aiming at studying the impact of the plasma in the atom-to-ion conversion yield, which is of relevance for the ECRIS applications to accelerators and plasma research.Results underline the plasma role on a space-dependent conversion yield, reflecting the strongly anisotropic and inhomogeneous ECR plasma.The numerical study has been conceived and performed on the PANDORA plasma trap scenario, but can be extended to other ECR trap and ion sources.The metals' dynamics depends both on species and the plasma model.To corroborate the numerical predictions and reliability of plasma modelling, we plan to perform experimental measurements, in collaboration with the ion source department of the GSI.This will aim at improving the technique's efficiency, finding novel strategies for the evaporation system, especially relevant for reducing waste and consumption of expensive isotopes, as well as to increase the ECRIS performances.

Figure 1 .
Figure 1.(a) CAD of simulated domain reproducing the PANDORA plasma chamber and the oven inlet (red circle).The latter is in a non-axisymmetric position and tilted towards the center of the chamber (red arrow).Superimposed sliced magnetic field lines B(0, 0, 0) -in red (blue) to distinguish among the upper (lower) magnetic branches with respect the longitudinal z-axis -onto the isomagnetic surface at B = BECR = meωRF /e are shown.(b) Deposited 134 Cs map log10 [particle/s] (unwrapped cylinder coordinates, z-axis vs. azimuth angle), without plasma.(c) Same as (b) but including plasma and magnetic field' effects.(d) Deposited 48 Ca map log10 [particle/s] including plasma and magnetic field' effects.