# Presentation: 320202

## Dynamics of neutralizing electrons and focusability of intense ion beams

- A.F. Lifschitza, G. Maynarda and J.-L. Vayb
- aLGPG, Universitė Paris Sud, Orsay, France
- bLBNL, Berkeley, USA

## Introduction

-  Even when the beam is globally neutral, neutralization is not perfect due to the transversal electron temperature → finite screening length
-  The limit to the neutralization due to finite Te is relevant when:
-          a) global neutralization is good (f ≥90 %)
-          b) transversal temperature is high  (Te≥10 keV)
-  Electron transversal temperature is determined by:
-            a) heating by compression
-            b) flow of electrons into the beam
-                 beam electrostatic potential → neutralization degree
-            c) heat exchange with the beam surrounds

## This work

- Fully-electromagnetic 2-1⁄2 PIC simulations (BPIC code) including:
- a) beam ionization by collision with background gas
- b) background gas ionization by collision with beam ions and electrons

- We study the parallel evolution of the temperature and neutralization:
- Isolated beam
- Beam interacting with a finite size plasma created by gas ionization
- Beam interacting with a electron-source-like plasma

## Isolated beam

- Isentropic process →
- Electrons behave as an ideal gas under a adiabatic bidimensional compression →                      

- 2.5 MeV Xe+ , Ib=2.5 kA
- rb0=5 cm, Lb=50 cm (8 ns)
- Lf=3 m

**Isolated beam**

**Temperature evolution**

## Departures from 2D compression

- Close the focal point:
- 1) Large gradients of density and temperature
- 2) Electron temperature uncorrelated with density
- 3) Transfer of energy from radial to axial direction

**Isolated beam**

## Neutralization

**Neutralization**

- Good values for the neutralization can be obtained assuming:
- a) infinite beam
- b) electrons in thermal equilibrium

- Assuming

- →

- Solutions of 1D Poisson-Boltzmann equation:

**Isolated beam**

## Neutralization by gas ionization

**Neutralization by gas ionization**

**Beam interacting with a finite size plasma**

-  t<(σ ng vb )-1    Ne / Nb« 1

-  t>(σ ng vb )-1

- Plasma and beam compete for picking-up electrons

- + gas density
-           
-  + neutralization

## Temperature evolution

- Compression overcomes flow-cooling only in the focal region

**Temperature evolution**

- Heat transfer to the plasma tail

**Beam interacting with a finite size plasma**

## More neutralization & less heating

**More neutralization & less heating**

**Beam interacting with a e-source-like plasma**

## Summary

**Summary**

- Isolated beam:
- Isolated beam behaves as a 2D-adiabatic system.
- Neutralization values are close to infinite beam in thermal equilibrium.
- Departures from 2D compression only visible at the focal region.
- Beam interacting with gas ionization plasma:
- Neutralization degree proportional to background gas density for early times and  independent for later times due to plasma pick-up.
- Cooling by electron flow into the beam more significant than compression except in the focal region
- Heat transfer to the plasma tail reduces electron temperature inside the beam
- Beam interacting with an external plasma:
- Gas ionized tail close to an electron source improves beam neutralization and reduces heating by compression

## Neutralization

**Neutralization**

- Initial evolution of temperature is determined by neutralization evolution

-  Long term neutralization     t>(σ ng vb )-1

-  Short term neutralization     t<(σ ng vb )-1    Ne « Nb

- neutralization limit for interaction with a electron-source-like plasma

- approximation for gas ionization plasma

- Independent of gas density

**Isolated beam**