## Code-Library Based on the Particles-on-Cell Method

#1087

Numerical Simulation and Optimization of Ion Accumulation and Production Processes in Multicharged Ion Sources and Electron Beams for Electron Cooling Applications

**Tech Area / Field**

- PHY-PFA/Particles, Fields and Accelerator Physics/Physics

**Status****8** Project completed

**Registration date****15.08.1997**

**Completion date****14.05.2002**

**Senior Project Manager**

Malakhov Yu I

**Leading Institute**

Joint Institute of Nuclear Research, Russia, Moscow reg., Dubna

**Supporting institutes**

- VNIIEF, Russia, N. Novgorod reg., Sarov

**Collaborators**

- Institute of Physical and Chemical Research (RIKEN), Japan, Saitama, Wako

**Project summary**

A goal of the project, proposed to the ISTC, is the development of theoretical and numerical methods of simulation and optimization of ion accumulation and production in ECR ion sources and electron beams for the electron cooling application.

The ECR ion source is one of the most widely used ion sources with step-by-step ionization by electron impact. In the ECR ion source the plasma is confined in an open magnetic trap.

For the physical modeling and numerical simulation of the ECR plasma properties the so-called “Classical model of ion confinement and losses” has been applied successfully during several last years. In this model processes of ion accumulation and production in the plasma of ion sources with electron impact ionization, have 'been described with a set of nonlinear differential balance equations for ail ionic charge states and neutrals present in the source. The balance equations include all inelastic processes between particle and ion losses from the source.

The electron cooling method is widely used now to reduce transverse beam dimensions and particle energy spread in the proton and ion storage and collide rings of low and intermediate energies. The cooling electron beam accumulates positive ions from the residual gas in the accelerator chamber during the cooling cycle. The space charge neutralization of cooling beam is used to reduce the electron energy spread and enhance the cooling ability. The Electron Beam Ion Sources and Traps (EBIS and EBIT) as well as the electron beams for electron cooling application have the beam parameters in the same ranges of magnitudes. Several relatively simple models based on the balance equations for ionic charge states are used now to describe the ion accumulation and space charge neutralization in these electron beams.

The balance equations used for studding ECR plasma and electron beams assumed the homogeneous ion and electron densities in the plasma or beam volumes. These models don't take into account the real spatial distribution of electric and magnetic fields as well as field boundary conditions. The ECRIS, for example, has very complicate specific field distribution inside.

The present numerical simulations are able to model the average values only such as mean ion and electron densities, output currents, a total value of potential or potential dip in the plasma or beams. Some of the general effects for hole plasma or beam volume (ion mixing or so-called afterglow effects for example) could be simulated with the present models. But one should has the detailed notion of the beam or plasma structure, field and particle distributions, especial in a case of the stage of design, tuning or optimization of an experimental set up. There are a number of very important effects connected with local particle generation or shape of field distributions in the plasma. The peculiarities of spatial distribution of particles and fields are very important for the processes of ion accumulation and neutralization of electron beams for electron cooling and ion source applications.

This project proposes to create a new generation model and codes for ion production and accumulation based on the model of finite particles in sells. The finite particle method allows studying the detailed beam characteristics, the distribution function of particles, the ion transitions from one charge state to another, to consider the nonlinear self and external fields. This method is successfully used for the simulation of the motion of continuous medium, gasdynamics, dynamics of charged particle beams.

The finite particle method is most powerful method now for the numerical simulation of continuous medium. The numbers of finite particles and cells of mesh determine the capacity, accuracy and resolution of simulation procedure.

The goal of proposed project is the creation of a new generation model and codes for the numerical simulation based on 'the method of particles in sells for the multicomponent ECR plasma and electron-ion beams. This new numerical model will be used To study the detailed plasma and beam characteristics, the distribution function of panicles, the ion transitions from one charge state to another, inelastic collisions of particles, to consider the nonlinear self and external fields. This technique should allow providing very precise numerical simulation and optimization of ECR and electron beam sources, electron cooling systems.

Capabilities of the project participants are confirmed by the following high qualification and experience of the JINR, VNIIEF and RIKEN scientific experts in numerical simulations, plasma, atomic and particle beams physics. The most perfect present model and simulations of the ion production in ECRIS based on the balance equation method were developed in JINR. The method of particles-in-sells was sufficiently developed in RIKEN for the simulation of charged particle beam transportation.

During the project realization new level code library for the multicomponent plasma and electron-ion beams will be developed and applied for the scientific research program at RIKEN in the frame of new RIKEN Project of Radioactive Ion Beam Factory, The outcome of the collaboration will have the following benefits:

- the creation a code library based on the particle-on-cell method for the multicomponent hot plasma and multicomponent electron-ion beams;

- the preparing of recommendations to design and improve the ECR ion source and neutralized electron beams for the electron cooling system of RIKEN RI Beam Factory Project.

*The Role of Foreign Collaborators:*

Within the framework of the present project RIKEN is responsible for organization and support of the numerical simulation and optimization of ECRIS and electron cooling set-ups. The RIKEN scientific contributions to the project are the following:

- Development of computer codes for ECR plasma and electron-ion beams;

- Numerical simulation of ECRIS and electron cooling beams at RIKEN;

- Development and optimization of ECRIS and electron cooling beams at RIKEN.

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