1. Dynamics of neutralizing electrons and focusability of intense ion beams A.F. Lifschitz a, G. Maynard a and J.-L. Vay b a LGPG, Universitė Paris Sud, Orsay, France b LBNL, Berkeley, USA

2. 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 T e is relevant when: a) global neutralization is good (f ≥90 %) b) transversal temperature is high (T e ≥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

3. 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

4. Isentropic process → Electrons behave as an ideal gas under a adiabatic bidimensional compression → 2.5 MeV Xe +, I b =2.5 kA r b0 =5 cm, L b =50 cm (8 ns) L f =3 m Isolated beam Temperature evolution

5. 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

6. 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

7. Neutralization by gas ionization Beam interacting with a finite size plasma t<(σ n g v b ) -1 N e / N b « 1 t>(σ n g v b ) -1 Plasma and beam compete for picking-up electrons + gas density  + neutralization

8. Compression overcomes flow-cooling only in the focal region Temperature evolution Heat transfer to the plasma tail Beam interacting with a finite size plasma

9. More neutralization & less heating Beam interacting with a e-source-like plasma

10. 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

11. Neutralization Initial evolution of temperature is determined by neutralization evolution  Long term neutralization t>(σ n g v b ) -1  Short term neutralization t<(σ n g v b ) -1 N e « N b neutralization limit for interaction with a electron-source-like plasma approximation for gas ionization plasma Independent of gas density Isolated beam