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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
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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
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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
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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
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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
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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
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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
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Compression overcomes flow-cooling only in the focal region
Temperature evolution
Heat transfer to the plasma tail
Beam interacting with a finite size plasma
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More neutralization & less heating
Beam interacting with a e-source-like plasma
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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
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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