Roadmap for the increase of beam brilliance from ECRIS and Microwave Discharge Ion Sources

The requirements for future accelerator chains need to increase the injected beam brilliance significantly, still keeping high the beam quality in terms of reliability, reproducibility and stability. A roadmap for ion source development may consist of several steps: plasma simulation, multiphysics simulation of each system component, high-level control system, plasma characterization, beam characterization, data analysis and, again, plasma simulation. The cycle starts and ends with plasma simulation because it is the instrument that shows how different phenomena take part in the plasma and beam formation and because, in such a way, the accuracy grows with each cycle. Commercial multiphysics simulation tools are essential for adequately designing all ion source equipment: magnets, intense electrostatic field regions, microwave propagation and coupling, thermal dissipation and vacuum. The dependence of source performances from source parameters (magnetic field profile, gas pressure, microwave power) has been widely investigated using a high-level control system[1] able to test tens of thousands of source configurations without human interaction. This characterization technique allowed us to identify a new magnetic configuration, High Stability Microwave Discharge Ion Sources[2], that produces a beam with high stability, intensity and brilliance. The plasma simulation tool we developed discloses the role of two types of electrostatic waves in plasma formation and their correlation to stability. The simulation provides a complete view of ions and electrons energy and density distributions, the formation of the plasma meniscus and the beam extraction. The paper will present the results obtained with this development procedure on Microwave Discharge Ion Sources and how we started to apply it to the Electron Cyclotron Resonance Ion Sources development.


Introduction
Electron Cyclotron Resonance (ECR) is one of the most convenient methods to excite the plasma in ion sources.The magnetic field value is chosen to achieve gyrofrequency close to the electromagnetic field frequency: The electric field component of the electromagnetic field, orthogonal to the magnetostatic field, produces an acceleration along a circular orbit orthogonal to the magnetostatic field.If the particles move in a magnetic field equal to the resonance value, the gyrofrequency and the electromagnetic frequency are the same and the electrons are subjected to continuous acceleration.If the magnetic field is close but not equal to the resonance value, the gyrofrequency and the electromagnetic frequency differ.At the beginning of the electron motion subjected to the electromagnetic field, the electrons move orthogonally to the magnetic field in phase with the electromagnetic field.During the motion, due to the difference between gyrofrequency and electromagnetic frequency, the phase between the motion and the electromagnetic field increases, reducing the energy gain from electromagnetic waves.When a condition of counter phase is reached, the electromagnetic field decelerates the electrons.Inside the ion sources, even if the magnetic field value is close but not equal to the resonance value, acceleration can occur due to the collisions and the magnetic field variation along particle trajectory that continuously vary phase between the circular orbit and the electromagnetic wave oscillation.Furthermore, the electromagnetic field in plasma converts to other waves that show strong components in the direction parallel to the magnetic field so that the magnetic field does not affect the acceleration produced by the electromagnetic field.
We distinguish two types of sources in such a complex mixture of phenomena.Microwave Discharge Ion Source (MDIS) refers to Electron Cyclotron Ion Sources (ECRIS) working at 2.45GHz, having only a solenoidal field, designed to produce high current of low charge state beams.The ECRIS acronym is prevalently used for sources operating at higher frequencies (more than 10 GHz) having a magnetic system allowing radial and axial confinement.The scaling low provides a rough description of the source behaviours: ‫ܫ‬ ∝ ே ் ; ‫〉ݍ〈‬ ∝ ܰܶ Where I stay for Ion Current, ‫〉ݍ〈‬ is the averaged charge state, T is the confinement time, and N is the plasma density.MDIS use a magnetic system with only an axial component to achieve low confinement time and high extracted current.In contrast, ECRIS are designed with a magnetic system composed of axial and radial components to increase the confinement time and achieve high charge states.
The magnetic configuration of MDIS was introduced in 1991 by Taylor and Wills [3] following experimental evidence.It comprises a magnetic field with an ECR value close to the two ends of the plasma chamber and a slightly higher value in the rest.

Roadmap
The commissioning of the Proton Source for the European Spallation Source (PS-ESS) [4,5], was the context that allowed the INFN-LNS ion source group to disclose a new magnetic configuration showing extreme stability, low emittance and easy variation of the extracted current.With the following High Stability Microwave Discharge Ion Sources (HSMDIS) project, we disclosed the physics behind this evolution and the possibility of further improvements.If one considers that the physics behind the two types of sources is the same, it is reasonable to state that the same approach used during the PS-ESS commissioning can be used for ECRIS development.This paper presents the roadmap followed for MDIS development and the considerations about application on ECRIS development.

Multiphysics simulations of each element of the source and the LEBT
When approaching a new experimental setup, many existing elements or designs were often used without considering that they were designed long ago with rudimental computational capability.Using modern simulation tools, we can improve all equipment's performance and robustness to the level other roadmap steps require.This task requires time and money to purchase updated equipment but is crucial to enable the next steps of this roadmap.A brief overview of the different simulations we have performed to design all equipment of the PS-ESS ion source is shown in Fig. 1.For ECRIS development, the magnetic systems must have a high magnetic field value and flexibility.Furthermore, technical choices must be focused to speed up the magnetic field variation.The extraction system needs to be carefully simulated, considering several species and charge states extracted simultaneously.Custom code must be developed for this task because commercial tools consider only one species and one charge state per time.For high total extracted current, space charge needs also be considered.To produce high charge states, vacuum simulations inside the plasma chamber and LEBT [6] are required to ensure a good vacuum and, therefore, minimize neutral-high charge state collisions, responsible for decreasing the mean charge state in ECRIS.Indeed, because it is currently impossible to insert vacuum sensors within the plasma chamber, only simulation can evaluate pressure there.
This type of source works with high RF power.The heat transfer from plasma to chamber walls is not homogeneous.Consequently, detailed plasma chamber cooling simulations are crucial.Regions of the plasma chamber that are hit by a large amount of fast electrons and, consequently, are subjected to significant heating have to be designed carefully.RF-matching without plasma must be performed to prevent unwanted behaviours with ancillary equipment and vacuum pumps present in the injection side of the ECRIS plasma chamber.RF to plasma matching must be carefully designed because by increasing the frequency, we go from the case of a stationary electromagnetic wave coupled with the plasma chamber to a high-frequency propagating wave that can be directly absorbed at the plasma surface.

Non-plasma-perturbative diagnostics for plasma and beam
Plasma chambers are small and invasive diagnostics like the Langmuir probe perturb the plasma locally and globally due to the electromagnetic perturbation it introduces.However, since the ion beam (and not plasma) is our primary outcome, it is not a showstopper if all plasma parameters are not precisely known.Beam diagnostics should have higher priority.
The Optical Emission Spectroscopy (OES) diagnostics setup [7] used in PS-ESS commissioning is shown in Fig. 2. From OES spectra, it is possible to evaluate plasma temperature and density and estimate some beam parameters [8].Unfortunately, we did not have the time to make this diagnostic compatible with the high voltage required for the extraction.More information on OES can be found in Refs.[9][10][11][12].Different instruments were installed for beam diagnostics (see Fig .3), and a high-accuracy and fast electronic system was chosen.The total current coming out from the source was measured by an ACCT installed on the cable of the high-voltage power supply.The relative amount of the different species composing the beam (H + , H2 + , H3 + ) was evaluated using the Doppler shift measurement [13].The beam's emittance was measured with an emittance meter [14].A Faraday cup was installed to measure the extracted beam current.For ECRIS development, OES can provide interesting information.Still, the desirable measurements are those providing spatial information.Although it is a challenge from the mechanical point of view, plasma imaging, from visible to hard X-ray, is expected to be the best option for plasma diagnostics [15].Due to the space limitation and the constraint of not perturbing plasma, interchangeable devices should be selected.Beam diagnostics might be enriched with a dipole, and the emittance needs to be evaluated with a Pepperpot device instead of an Alison scanner due to the non-axial symmetry expected beam.

High-Level Control System for a wide characterization
Fast improvements in software capabilities are an opportunity we cannot miss.A high-level control system [1] can be connected to the standard control system to change the configuration parameters and record the behaviour of the source.If the ion source equipment were upgraded (point 1 of the roadmap) to be robust and not damaged by those configurations that don't work properly, the characterization could be automated.There can exist configurations where the source does not produce a beam.Configurations with extremely unstable plasma and sparks in the extraction system.Configurations where a significant part of the microwave power is reflected toward the RF power supply.The most important advance of this approach is that the characterization result is fast and provides quantitative analysis.On the contrary, an operator can store less information and is much slower than a software.
We developed high-level interfaces and codes that interact with the standard control system to commission PS-ESS.One is shown in Fig. 4, allowing the operator to direct control of the magnetic field inside the plasma chamber.There are buttons with which it is possible to rise or decrease the magnetic field in one of three points of interest, at 0 mm, 35 mm and 84 mm from the injection flange.These points are along the plasma chamber axes.The code behind the interface checks if the chosen values are compatible with the magnetic system and show the operator the magnetic configuration closer to the selected one.The interface offers the possibility to send to the main control system the exact value of the currents needed to produce the selected magnetic field identified by the code behind the highlevel control interface.In such a way, the operator has a clear idea of the magnetic field used and can relate it to the ion source behaviour.Furthermore, a direct correlation between magnetic field value and ion source behaviour is used instead of a nonlinear correlation if the three coil energization values are used.
In MDIS development, the ion source configuration was identified by the value of five parameters: the value of the magnetic field in the three points, the microwave power and the gas flux directly proportional to the pressure inside the plasma chamber.For ECRIS development, three more parameters must be added to properly define the ion source configuration: the RF frequency, the gas mixing value and the bias disk voltage.It is important to note that a high reproducibility condition must be achieved before characterization, such as cleaning the plasma chamber.The order in which the configuration parameters are changed during the characterization must consider the time required for the shift.For example, bias disk voltage can be changed rapidly, and magnetic field can be changed slowly, mainly if superconductive magnets are used.Due to cost and simplicity, many sources use permanent magnets for the hexapole field, substantially limiting the source characterization.
There are two types of working configurations.Some configurations can start from an empty plasma chamber; others need a preexisting plasma density to be switched from.This distinction is essential to define the procedure to map the ion source configuration space.It is clear evidence of the additional difficulties we will encounter in applying this roadmap to ECRIS development compared to MDIS development.
20th International Conference on Ion Sources Journal of Physics: Conference Series 2743 (2024) 012022 IOP Publishing doi:10.1088/1742-6596/2743/1/0120226 2.4.Multiparameter data analysis to disclose correlations Ion source configuration spans a multidimensional space where each axis is a configuration parameter like magnetic field values, RF power, pressure, frequency, and other parameters peculiar to the experimental setup.Configurations where the source does not produce a beam, make an unstable plasma density or have a strong generation of hard X-rays are considered non-working conditions.Their identification is essential because it defines the working regions.The analysis of the profiles of these regions is required to understand the physical phenomena that permit the source to operate better.On the contrary, even if an optimization tool tests fewer source configurations to improve source performances, the outcome will be a relative maximum of source performance that does not provide information on the physics behind it and does not guarantee that it is a global optimum instead of a local optimum.
The complex data set collected during the characterization requires a multiparameter data analysis to disclose the correlations between the parameters and the behaviour of the source.The choice of the coordinate system to analyze source behaviour is significant.For example, Fig. 5 shows the behaviour of the ion source (beam current measured on the Faraday cup and the ACCT, beam stability) versus the magnetic field configuration expressed by the magnetic field value at two coordinates along the plasma chamber axis.This visualization exposes a clear source behaviour trend versus the magnetic configuration.On the contrary, the same data plotted versus the coil current on the power supply does not produce any significant representation.The magnetic field is not linearly correlated to the coils' current due to the overlapping of the magnetic field produced by the three coils of the magnetic system and the presence of iron in between.
For ECRIS development, the ion source configuration is defined by more parameters, and the performance of the source is more complex to describe due to the different charge states produced.The data analysis will be more complex and funnier because more surprising results will emerge.IOP Publishing doi:10.1088/1742-6596/2743/1/0120227 2.5.Plasma simulations to understand observed behaviour Our group has been active in plasma simulation since 2010 [16][17].The last version of the simulation code developed at INFN-LNS is based on a Particle In Cell (PIC) approach.The different blocks constituting our tool and the interplay are shown in Fig. 6.Electrons are moved with 10 -11 s, ions with 10 -10 s, coulomb collisions and reactions are computed every 10 -9 s, and the electromagnetic simulation is updated every 10 -7 s circa.The wall interaction and the electrostatic simulation are done every time step.The total time evaluated in the simulation is one millisecond.Tensorial permittivity, self-consistent electric field and computation efficiency are the central values of our PIC code, which can evaluate the ion source behaviour from plasma formation to beam extraction.The tensorial permittivity formulation considers the magnetic field map and the plasma density distribution and uses the electron temperature distribution to evaluate the electron collision rate.The electromagnetic simulation highlights the change of wave propagation in correspondence with different regions of the CMA diagram [18].
For ECRIS development, we can take advantage of the actual capabilities of our simulation tool to check from the beginning if some part of the source can be done differently or which part of the plasma chamber volume is more interesting to investigate with plasma diagnostics tools.

Conclusion
The roadmap followed for the development of MDIS will be highly useful for developing ECRIS if we can handle a higher level of complexity.However, we can profit from a validated work organization and a simulation tool that has already achieved reasonable reliability.Simulation of plasma formation and beam extraction can be inserted for ECRIS development as the first step of the roadmap, which becomes 1) Plasma simulations, 2) Non-plasma-perturbative diagnostics, 3) Multiphysics simulations of each element of the source and the LEBT, 4) High-Level Control System, 5) Multiparameter data analysis, 6) Plasma simulations.
Following this roadmap requires additional effort compared to how normally a new source prototype is developed for studying purposes.Still, it was proved that the outcome would produce a better comprehension of the phenomena acting inside the source and the capability to find configurations where the source behaviour is more stable and produces a higher brilliance beam.

Figure 1 .
Figure 1.Overview of the different simulations performed to optimize the design of the various equipment.

Figure 3 .
Figure 3. Main parts of the ion source and the beam diagnostics.

Figure 4 .
Figure 4. High-level control interface developed for direct control of the ion source magnetic configuration.

Figure 5 .
Figure 5. Example of multiparametric analysis of the data collected with the automatic characterization. 4.