Dynamics of neutralizing electrons and focusability of intense ion beams

A.F. Lifschitza, G. Maynarda and J.-L. Vayb

aLGPG, Universitė Paris Sud, Orsay, FrancebLBNL, 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 2-½ 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:

1. Isolated beam

2. Beam interacting with a finite size plasma created by gas ionization

3. Beam interacting with a electron-source-like plasma

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

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

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

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

Beam interacting with a e-source-like plasma

SummaryIsolated 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

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