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Scaling laws for the effective charge of heavy ions penetrating gas or plasma targets

Published online by Cambridge University Press:  09 March 2009

Th. Peter
Th. Peter
Affiliation:
Max-Planck-Institut für Quantenoptik, D-8046 Garching, Germany
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Abstract

Until now a theoretical derivation of scaling laws for the effective charge Zeff of heavy ions penetrating matter has been lacking, although for cold gaseous targets there are well-established empirical relations of the form Zeff/Zp = f (up/ZpγZtδ), where vp and Zp are, respectively, the velocity and nuclear charge of the projectile ion, Zt, is the nuclear charge of the target atoms, and γ and δ are the scaling exponents. We show that the scaling exponents may be derived from an investigation of loss and capture rates. The treatment is based on the Bohr-Lamb criterion. This very crude criterion yields γ = 2/3. Our analysis allows the formulation of a modified criterion, yielding γ = 0.528 for cold gas, which deviates by only 2% from the often-used empirical Betz formula. The dependence on Zt, in cold gas is oscillatory and cannot be described by a simple exponent δ. The treatment is also applied to a fully ionized plasma, resulting in Zerf/Zp = f (upZt0.27/Zp1.39).

Type
Research Article
Information
Laser and Particle Beams , Volume 8 , Issue 4 , December 1990 , pp. 643 - 658
Copyright
Copyright © Cambridge University Press 1990

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