Table Of ContentGrigory D. Shirkov · Günter Zschornack
Electron Impact Ion
Sources for Charged
Heavy Ions
Grigori D. Shirkov
Gunter Zschornack
Electron Impact Ion Sources
for Charged Heavy Ions
Grigori D. Shirkov
Gunter Zschornack
Electron Impact Ion
Sources for Charged
Heavy Ions
I I
VI&Weg
All rights reserved
© Springer Fachmedien Wiesbaden 1996
Originally published by Friedr. Vieweg & Sohn Verlagsgesellschaft mbH,
Braunschweig/Wiesbaden in 1996
No part of this publication may be reproduced, stored in a retrieval system or
transmitted, mechanical, photocopying or otherwise, without prior permission of
the copyright holder.
Produced by Hubert & Co., Gottingen
ISBN 978-3-663-09898-0 ISBN 978-3-663-09896-6 (eBook)
DOI 10.1007/978-3-663-09896-6
Preface
Presently many different types of ion sources exist worldwide for producing highly charged
ions. The object of the present book is the treatment of electron impact ion sources like
ECR (Electron Qyclotron .Resonance) ion sources, EBIS (Electron .B_eam Ion S.ources),
EBIT Electron .B_eam Ion Irap) and ERIS (Electron .Ring Ion S.ources), which altogether
are able to produce ions of high charge states. This criterion delimits the book according
to classic ion sources, which as a rule can deliver high currents of low charged ions.
In the last decades there has been an intense development and building-up of sources
of highly charged ions. The first impetus to the building of such sources came from heavy
ion accelerator centers, since the effectiveness of a heavy ion accelerator is predominantly
determined by the available ion sources. Thereby, the critical criterions for the operation
of an ion source are the charge state distribution of the ions produced and the intensity
of the extracted ion currents. Besides the employment of sources of highly charged ions
in accelerator centers such sources increasingly are inserted separately from accelerators
for basic investigations in atomic physics, surface physics and related areas.
In the present book ECR ion sources, EBIS, EBIT and ERIS are treated. Besides
the fundamental theory for the description of ionization processes in electron impact ion
sources the individual sources are described and discussed using the characteristics of
actual sources. Thereby, laser ion sources are not discussed, because the ion production
here differs greatly from those sources named above and thus their treatment would widen
the frame of the existing book.
Besides the treatment of electron impact ion sources for the production of highly
charged ions characteristic diagnostics methods arc described for these sources, which
are applied in different laboratories to diagnose the operating conditions. Thereby, be
sides the direct source diagnostics the diagnostic methods used often have relations to
diagnostics methods in plasma physics and in particularly to the diagnostics of fusion
plasmas.
Subsequently applications of sources of highly charged ions are discussed without
wanting to reach here completeness. However, we examined the comprehensive work at
the EBIT of the LLNL, which now makes it possible to accomplish X-ray investigations
of highly charged ions into an unique way.
The authors cordially thank Dr.K.Wong from the LLNL, who kindly took over the
proofreading of the english text and gave a lot of valuable references for the formation of
the present book.
One of the authors (G. Z.) dedicates this book to his late wife Gisela, who contributed
to the success of the work with her great understanding for the time demands of working
on this book.
Dubna and Dresden, March 1996
G.D.Shirkov and G.Zschornack
Contents
1 Elementary Processes 1
1.1 Collisions of Charged Particles 1
1.2 Ionization by Electron Impact . 3
1.3 Ion-Atom Collisions ..... . 7
1.4 Elastic Collisions of Charged Particles 12
1.5 Balance Equation for Ion Charge States 19
1.6 Problems in Producing Multiple-Charged Ions . 22
2 Ion Distribution Function 28
2.1 Ion Distribution Function in Electron Beams 28
2.1.1 Kinetic Vlasov Equations ...... . 28
2.1.2 Ion Distribution Function in Electron Beams 29
2.1.3 Electron Beams with Constant Density 31
2.1.4 Electron Beams of Gaussian Density ... 33
2.2 Momentum Method and Distribution Function . 36
2.2.1 Movement of Beams of Charged Particles 36
2.2.2 Moments of the Distribution Function . . 38
2.2.3 One-Dimensional Non-Relativistic Case . 39
2.2.4 The Two-Dimensional Non-Relativistic Problem 40
2.2.5 Moments of Second Order for Annular Beams . . 42
2.2.6 Multicomponent Beams of Charged Particles .. 47
2.2.7 Numerical Modelling with the Momentum Method 49
2.3 Method of Finite Particles . . . . . . . . . . . . . . . . . . 52
3 Production of Multiply Charged Ions in Relativistic Electron Rings 59
3.1 Collective Ion Acceleration in Electron Rings . . . . . . . . 59
3.1.1 The Collective Method of Ion Acceleration . . . . . 59
3.1.2 The Heavy Ion Collective Electron Ring Accelerator 62
3.2 Ion Storage in Electron Rings . . . . . . . . . . . . . . 67
3.2.1 Ion Storage from the Residual Gas ......... . 67
3.2.2 Calculation of Ion Charge State Distributions . . . . 69
3.2.3 Ion Accumulation from a Beam of Neutral Particels 72
3.2.4 Diagnostic Methods for Electron-Ion Rings . . . . . 74
3.3 Particularities of the Production of Highly Charged Ions in Electron Rings 76
3.3.1 Basic Problems . . 76
3.3.2 Physical Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Contents VII
3.4 The Electron Ring Ion Source ERIS 83
4 Electron Beam Ion Sources 90
4.1 The Electron Beam Method for the Production of Highly Charged Ions 90
4.1.1 History and Operation Principles . . . . . . . . . . . . 90
4.1.2 The Construction of an EBIS . . . . . . . . . . . . . . 91
4.2 Production and Storage of Multiply Charged Ions in an EBIS 93
4.3 Heating and Cooling of Ions in an EBIS . . . . 100
4.3.1 Electron Losses from the Electron Beam . . . . . . 100
4.3.2 Cooling of Multiply Charged Ions . . . . . . . . . . 105
4.3.3 Ion Cooling at Continuous Injection of Light Ions . 107
4.4 The Electron Beam Ion Trap . . . . . . . . . . . . . . . . 111
4.4.1 The Construction of an EBIT . . . . . . . . . . . . 112
4.4.2 Mathematical Modelling of the Ion Storage in the EBIT 114
4.4.3 Experimental Investigations of Highly Charged Ions 122
5 Electron-Cyclotron Resonance Ion Sources 123
5.1 Operation Principles of Electron-Cyclotron Resonance Ion Sources 123
5.1.1 Principle Function of an ECR Ion Source . . . . . . . . . . 125
5.1.2 High Frequency Heating of Electrons in the Plasma of an ECR Ion
Source ....................... . 126
5.1.3 Storage of Charged Particles in a Magnetic Trap 128
5.2 Storage of Ions in ECR Ion Sources . . . . . . . . . 130
5.2.1 Ion Confinement Time .............. . 130
5.2.2 Balance Equations for the Ion Components .. . 133
5.2.3 Calculations of the Ion Charge State Distribution . 136
5.3 Production of Multiply Charged Ions in ECR Ion Sources 142
5.3.1 Ion Cooling . . . . . . . . . . . . 143
5.3.2 Pulsed Working Regime ..... 146
5.3.3 Pulsed Regime with Ion Cooling 150
6 Plasma Diagnostics Related to Ion Sources 153
6.1 Introduction . . . . . . . . . . . . 153
6.2 Diagnostics of ECR Ion Sources ...... . 154
6.2.1 Plasma Models . . . . . . . . . . . . 154
6.2.2 Magnetic and Electrical Diagnostics 160
6.2.3 Microwave diagnostics .. 180
6.2.4 Spectroscopic Diagnostics 185
6.3 Diagnostics of EBIS and EBIT 234
6.3.1 Diagnostic Methods ... 234
6.3.2 Ion Cooling Diagnostics . 234
6.3.3 Electron Beam Current Density . 238
6.3.4 Electron Energy in Electron-Ion Collisions . 240
6.3.5 Magnetic Measurements . . . . . . . . . . . 243
6.3.6 Electron Beam Geometry in EBIS . . . . . 243
6.3.7 Diagnostics of Extracted Ion Beams from EBIS 245
VIII Contents
6.3.8 Diagnostics of the Ionization Process . 246
6.3.9 Ion Capacity of the EBIS ..... 248
7 The Use of Electron Impact Ion Sources 251
7.1 Introduction ................ . 251
7.2 Application of Electron Impact Ion Sources to Heavy Ion Accelerators 252
7.3 Investigations on Highly Charged Ions . . . . . . . . . . . . . . . . 254
7.3.1 Atomic Structure of Highly Charged Ions . . . . . . . . . . 254
7.3.2 Investigations for Thermonuclear Fusion and Astrophysics 270
7.3.3 Ion-Surface Interactions . . . . . 273
7.3.4 Electron-Ion Interaction Studies . . . . . . . . . . . . . . 287
Chapter 1
Elementary Processes
1.1 Collisions of Charged Particles
Positive charged ions are formed as a result of electron impact ionization of atoms or
molecules in ion sources. Hereby electrons and ions are confined by external e.lectric and
magnetic fields. Multiply charged ions are created as a result of successive ionization
processes.
In this chapter we will describe and classify as simple as possible the main physical
processes taking place in the working area of ion sources, where ions are created and
confined.
Neutral particles, ions and electrons in the plasma are in continuous motion, colliding
with one another. In this context collisions mean Coulomb interactions between charged
particles. Charged particles produce an electric field in their surrounding. When moving
in the fields of other particles, they will change their trajectory, affecting other particles by
their eigenfields. In this way energy is exchanged and redistributed between the colliding
particles. These processes we shall name Coulomb collisions of charged particles .
If the internal states of electron shells change due to an electron or ion collision with the
electron shell of another atom or ion, the impact is called an inelastic collision. Inelastic
collisions can increase the total energy of the atomic electron shells. This process is
named an excitation process and is characterized by
A+B-+ A+B*. (1.1)
The impact of an electron on a neutral particle can produce an electron which energy is
higher than the binding energy of the respective electron in the atom. This electron is
then transferred to the continuum of unbound states and lost by the atom, e.g. it means
an ionization of the electron. As a result of such a process the neutral atom is changed
into a positively charged ion
(1.2)
The ionization process of an ion of charge i caused by electron impact can be described
in like manner
(1.3)
2 Chapter 1 Elementary Processes
If, resulting from an interaction, there is an ionization of several electrons, it is a multiple
ionization process. In generalized form this ionization process due to an electron impact
is described as follows
(1.4)
The character of interaction between electrons and between ions and neutral particles
depend on their energy and the distance of interaction. In addition to processes of
excitation and ionization, it is possible that the collision partners exchange one or more
electrons. This process - charge exchange - is most likely to be found between neutral
particles and ions. All interactions in which electrons are redistributed between the
atomic shells of the reactances may be described in the following general form
(1.5)
In case of ionization (j + n - i - k) greater 0 is valid. If (j + n - i - k) = 0 holds, with
i =f. j and k =f. n as restraints, a charge exchange process is involved.
Single ionization and single charge exchange are the most likely processes. As the
ionization energy increases and the degree of ionization of the atom becomes larger,
ionization of additional electrons from the ion will be less and less probable. So the
probability of ionization decreases with an increase in ionic charge. For the same reason
electron transitions between ions are not probable. On the contrary, the probability of
charge exchange processes between neutral particles and ions is sufficiently high.
If the velocity of free electrons is lower than the characteristic electron velocity in
the atomic orbitals, it is possible that an ion will be able to catch a free electron. This
process is referred to as recombination.
If, as a result of an interaction, only energy or the momentum direction of the whole
particle is changed without excitation of internal degrees of freedom, it. will be a matter
of elastic collisions.
On what exactly do the probabilities of collision processes depend? For an answer, a
particle A will be considered. It is supposed that as a result. of a collision with a particle
B, particle A will be ionized. In that case the probability of ionization P of particle A
by particle B at time interval /:it is dependent on
• density nB of particle B in the volume surrounding particle A (number of particles
B per unit of volume);
• relative velocity v between particles A and B;
• effective interaction cross-section a- for the process considered (here: ionization
cross-section of particle A by particle B).
So, for the probability of ionization
(1.6)
holds.
The total effective cross-section a- of any impact process can be simply described as
1f(i .
(J =
The quantity 12 describes the maximum distance or the impact parameter· at which the
process considered is still possible.
