2.1WS2011/12

2. Ionization

- Electron impact ionization & Photo ionization -

2.2WS2011/12

Overview

1. Atomic processes in plasma

2. Rate equation

3. Electron impact ionization

4. Photo ionization

5. Summary

Example EBIT, Charge Exchange, Radiative Recombination

Ionization mechanism: Multistep ionization, Ionization factor, approximation for cross section (Lotz formula), Carlson correction, optimal electron energy, application (electron target)

Basics, cross section, application (RILIS)

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AZ+: Atom of species A with charge state Ze’ : electron changed energy

2.1. Overview: Atomic processes in a plasma

collisions with

electron

scollisions w

ithp

ho

ton

s

Impact Ionization Three-Body-Recombination (TBR)

Impact excitation Impact disexcitation

Photo ionization Radiative Recombination (RR)

Excitation Spontaneous emission

Photo absorption Bremsstrahlung

Non-radiative transition

Line spectrum

The electron changes from one free state to another free state with lower energy.

Continuous spectrum

In most ion sources, ions are produced in a plasma. The basic atomic processes (selection) in plasmas are:

'''1 eeAeA ZZ

'eAeA ZZ

eAhA ZZ 1

ZZ AhA

'eAehA ZZ

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From these multiple processes arise the dynamic balance quantities:

• Distribution of the abundance of all charge states Z (=0...Zmax), Ionization equilibrium

• Number of emitted and absorbed photons per time interval, Radiative equilibrium

sinkssouces dt

dn

TBRzzezzezez nnvnndt

dn,111

1

The density of the particle species are determined from so-called rate equations:

Example: impact ionization:

2.2. Rate equation

ß z+1, TBR : rate coefficient for Three-Body-Recombination (TBR)

The rate coefficients often not be calculated with sufficient precision; experimental data are only available to a limited extent. Therefore one tries to obtain data from thermo dynamical equilibrium.

With decreasing electron density the TBR drops, so that the impact ionization is not in equilibrium with the TBR anymore. The RR rate also decreases but not as strong. With decreasing ne also the photo ionization becomes unlikely. As result the impact ionization and the RR-process dominate. The photons leave the plasma without being re-absorbed.

2.5WS2011/12

: averaged thermal ion velocity

: cross sections for impact ionization, RR and charge exchange by collisions with residual gas

: collision rate for all Coulomb collisions of ions with charge state i

: depth of the electrostatic potential (radial and axial),

: thermal energy of the ions heated by Coulomb collisions

: electron density and velocity

: neutral particle density

i

ion

w

ion

w

collii

chexiii

chexiiionoi

RRiii

RRii

ioniii

ioniiee

i n

kT

ieU

kT

ieU

nnnnnnndt

dn

exp

111111111

Example EBIT:

een on

ionionionion MkT2

colli

ionkTWU

The solutions of the linear system of equations provides the charge state distribution in dependence on the ionization factorej

TOP: Ionization of pulsed injected argon gas by an electron beam with an energy of 3.9 keV, which inhibits the ionization of the charge state Ar17+ (EBIS-Mode with breeding at the shell closure).

BOTTOM: Capture and ionization for the case of continuously injected argon atoms and 6 keV electron beam energy (EBIT-Mode without RR and charge exchange with residual gas).

%

20

40

60

80

-3 -2 -1 0 1 2log(J*TAU)

8

0

16

-4-4

-3-3

-2-2

-1-1

-3-3 -2-2 -1-1 00 11 22 33log(J*TAU)log(J*TAU)

8

16

ARGONARGON log(n /n )i ma x

%

20

40

60

80

-3 -2 -1 0 1 2log(J*TAU)

8

0

16

-4-4

-3-3

-2-2

-1-1

-3-3 -2-2 -1-1 00 11 22 33log(J*TAU)log(J*TAU)

8

16

ARGONARGON log(n /n )i ma x

2.6WS2011/12

276.2,

17.1121 1043.1 cmEi gasion

exii

0 20 40 60 80

10-12

10-9

10-6

10-3

10 A/cm2

100 A/cm2

Pre

ssu

re (

mb

ar)

Pb Charge states

For the approximation of the charge exchange cross section, commonly the equation by Müller and Salzborn is used:

Therein i describes the charge state of the highly charged ion and Eion, gas is the ionization potential of the

gas atoms interacting with the ion.

Example: Reachable charge states depending on the current density and the pressure

Charge exchange:

2.7WS2011/12

For the approximation of the RR cross sections the semi-classical expression by Kim und Pratt is used. Their formula bases on the first theoretical description of the Radiative Recombination by Kramers (1923):

Radiative Recombination (RR):

with

Ry: Rydberg energy 13,6 eV: fine structure constant 0 ratio between the numbers of occupied and unoccupied statesZ: nuclear chargeq: charge staten: main quantum number(e)r : reduced Compton-wavelengthE: electron energy

with:

• the effective nuclear charge to take into account the shielding of the nuclear potential by the bound electrons

• the effective main quantum number

to include the capture into states with different angular momentums

2.8WS2011/12

2.3. Electron impact ionization

The electron impact ionization is the most fundamental ionization process for the operation of ion sources.

• The cross section for the impact ionization is by orders of magnitudes higher than the cross section for the photo ionization.• The cross section depends on the mass of the colliding particle. Since the energy transfer of a heavy particle is lower, a proton needs for an identical ionization probability an ionization energy three orders of magnitudes higher than an electron

Why?

2.9WS2011/12

There are two different possibilities to produce multiple charged ions:

• in a collision where many electrons are removed from the ion (double-ionization, triple-ionization, …)

• multistep or successive ionization, where only one electron is removed per collision and high charge states are produced in different collisions

For energetic reasons the ionization releasing only one electron from the atomic shell is the most probable process. To produce highly charged ions the kinetic energy of the projectile electrons has to be at least equivalent to the n-th ionization potential.

Electron impactSingle ionization

Electron impactDouble ionization

Mechanism for the impact ionization

Cro

ss s

ectio

n

C

ross

sec

tion

electron energy electron energy

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Ionization energies up to 100 keV (U91+ → U92+)

→ shell structure of the atomic shells is clearly visible

Ionisation energies by C. Moore

1E+0

1E+1

1E+2

1E+3

1E+4

1E+5

1E+6

0 10 20 30 40 50 60 70 80 90 100OXGAS2.XLS R. Becker, 31.07.99 Z

eV

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1111

1

qqeqqeeqq

qqq j

e

vn

n

Successive ionization:

The probability for removing one electron and changing the charge state of the ion from q q+1 is determined by the cross section qq+1 [cm2].

Are the cross sections for the successive ionization known, the average ionization time of the ions with charge state q can be approximated from the collision frequency:

The time between to ionizing collisions is

This applies to electrons with a defined kinetic energy.

11

qqqqe

ej

sm

vnn qqeqeqq 311

1

The average ionization time in the charge state q depends only on the cross section and the current density. This expression is called IONISATION FACTOR. (Sometimes it is defined as only the inverse cross section!)

Principle of electron impact ionization

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Approximation of the cross section and the ionization time for the production of bare ions from H-like ions using the Mosley’s lawfor X-ray frequencies emitted in transitions from the continuum to the K-shell:

][6.13)( 2 eVZZE ki 4

17

4214

1

109

6.13

ln105.4

ZZe

ezz

)(ZEeE ki

zzzz

ezz e

j

111

1

4

17

4

11 5109

ZeZej

zzzze

wherein

1

0 1

1

01

1q

i iie

q

iiiq j

e

Example on the right side:The ionization factor je* for different charge states of Xe depending

on the electron energy.

The average time necessary to reach the charge state q is therewith:

Examples: Argon can be ionized by 10 keV electrons, ions of the heavy elements by up to 100 keV electrons and Uranium by 150 keV electrons. The resulting values for the ionization energy, cross section and ionization factor are summarized in the table on the left side.

2.13WS2011/12

N

ieii

N

iiqq q

111

)'(2

vvMh

q

nl

kin

nlkinnl

nli E

EEE

Zconst ln1

Approximation of the cross section in quantum-mechanical calculations done by Bethe (1930) using the Born Approximation:

Scattering of a matter wave at a central potential V(r) for Ekin >> Eion (perturbation theory).

All electrons in an atom or ion contribute with their individual ei to the total cross section , as long as

the kinetic energy Ekin of the projectile is larger then the ionization energy P i of these electrons.

All qi electrons of the subshell contribute to the i of the shell. The cross section for the ionization of the

(n, l) - shell results from integration of the transition probabilities over all states n’, l’ k und the integration over the collision vector

with v before and v’ after the collision. One receives

Bethe et al., Ann. Physik 5 (1930) 325

N = number of subshells

Approximation of the cross section for the electron impact ionization

2.14WS2011/12

2

1

141 cm

ln105.4

N

i ikin

i

kin

qq PE

PE

i

kin

P

Ex 1

2)1(ln

2xxx

kinPE

EP

kin

~)1(

105.4 21

1410

1

For practical reasons the semi-empirical formula developed by Lotz 1967 for the energy dependence of the cross sections for the elements from H to Ca and for energies < 10 keV is commonly used. The error is given by maximal 10%.

The Lotz formula for the case of high ionization energies Ekin >> Pi is:

For E Pi and with (x 0) , and with for x << 1

This means the cross section goes linear with E Pi to zero.

Examples for the dependence of the cross sections on the energy are shown for the case of He. The higher the initial charge state, the smaller is the cross section. Moreover the cross section is higher for atoms in an excited state.

Pi = Enl , N-subshells

This expressions is mostly used in calculations of the charge state distribution.

follows

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10-17

10-19

Single-ionisation: He + e → He+ + 2e Multi-ionisation: He + e → He2+ + 3e

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10-16 10-18

Ionization of singly charged HeIonization of the excited state

He (2s) + e → He+ + 2e He+ + e → He2+ + 2e

2.17WS2011/12

qiii EqWEP 00 )(

E0i : binding energy of an electron in the i-th shell of an atom

E0q : atomic binding energy of the electron, which is the weakest bound electron in the ion of the

charge state q Wi(q) : ionization energy of the ion (describes always the weakest bound electron)

inner electron i, to be removed

The ionization energies Pq,i for ions with different charge states q, which does not describe the weakest bound electron are sometimes difficult to find in literature. They can be approximated with the Carlson-Correction.

The ionization energy Pq,i is calculated from the ionization energy Wi(q) of the ion with charge state q and the atomic binding energies of the electrons as follows:

Carlson-Correction for ionization energies:

weakest bound electron q (ionization energy is known)

Ion: Aq+

E0q-E0i

2.18WS2011/12

0ln

105.41

141

N

i ikin

i

kin

zz

PE

PE

dE

d

dE

d

N

i i

N

i i

i

N

i i

N

i i

iN

i ii

P

PP

e

P

PP

EP

E

EP

1

1

1

1max

12

1

ln

exp1

ln1

exp0ln11

z

z

z

z

Pe

P

PP

eE

1

ln

expmax

Because (E) has a maximum at a certain energy, the ionization factor je* has a minimum there.

Basically the cross section for the last electron, which is removed, determines the ionisation time.

The optimal energy is given by

For the optimal energy of the last electron, which is removed, follows:

Therewith the optimal energy is nearly e-times the ionization energy of the last electron that is removed from the ion with the charge state z.

Optimal electron energy

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Ionization factor and optimal electron energy

el

ectr

on e

nerg

y

ionization factor

2.20WS2011/12

EBIS beam

+ + + + + +

+ + +

Fast ions

Slow ions

Slow electrons

Fast electrons

ECR plasma

MI

MI

MIFast electrons

Slow ions+

+ +

+ +

++

+ +

+ +

+

Stripper foil

EBIS beam

+ + + + + +

+ + +

Fast ions

Slow ions

Slow electrons

Fast electrons

ECR plasma

MI

MI

MIFast electrons

Slow ions+

+ +

+ +

++

+ +

+ +

+

Stripper foil

Application of the electron impact ionization for the production of ions

• Plasma confinement by magnetic fields of different structure (cusp, magnetic mirror, …) (see next lectures)

• The efficiency of the electrons in the plasma and the charge state can be increased by using the electron several times, by: - reflection of the electrons, e.g. reflection discharge or penning discharge - magnetic confinement, e.g. by magnetic mirrors

2.21WS2011/12

Further application of electron impact ionization

Example: electron target

Investigation of electron-ion-collisions:

• Investigation of electron impact ionization • Investigation of recombination processes• Investigation of excitation processes

Measurement of rate coefficients R

rdrnrnR ie3

and therewith cross sections:

rrrrr vdf 3vvvv

An+

An+

Important is the overlap of ion and electron beam

iv

ev

rv

: cross sectionne: electron densityni: ion densityvr: collision velocity / relative velocityf(vr): distribution function of the relative velocity

2.22WS2011/12

• “crossed beams technique”• better energy resolution then gas target• 10-15 cm long interaction region• spectroscopic access is possible• electrostatic focusing

BUT:• lower interaction rate as longitudinal electron target or gas target

Transversal electron target Longitudinal electron target

• „Merged beams“.• also used as cooler for ion beams • 2-2.5m long interaction region

BUT:• limited access for spectroscopy

0.061A/cm, R=8.19 mesh units, J=0.2 A/cm2

2.23WS2011/12

Atoms of a gas can be ionized by an intensive beam of photons with the adequate energy (photo ionization). Therefore the photon energy has to be .

The energy of a photo electron is:

eAhA

iqeh ,

iqehmv ,2max2

1

The reaction is:

2.4. Photo ionization

• For a given atomic shell the cross section p is the largest close to threshold, meaning where the

photon energy reaches the ionization energy I (resonance/ threshold behavior):

MLKmax I ,I ,I :

Cross section p:

• p has a strong dependence on the photon energy and the nuclear charge Z: 2/7

54

)(

Z

p

• Description of p as time-inverse effect

to the radiative recombination by the Milne-formula:

• For high photon energies the ionization of the s-orbital is most probable and the K-shell ionization delivers the dominant contribution:

KI ω

K3n n

1 p K1

3K2021.1

n

1p

npp

Pq

eRRq g

Ecmg 2

2

1 2

with g: statistical weights

→

pn : cross section for RR into the K-shelln: main quantum number

2.24WS2011/12

RILIS (Resonant ionization laser ion source) Ionization via resonant excitation with three laser beams of frequencies f1 – f3, as shown in the following scheme.

Application of photo ionization for the production of ions

1 eV l = 1.24 mm (IR-radiation), 5 eV l = 248 nm (close UV)

For direct ionization photons from the UV – x-ray region are necessary.

2.25WS2011/12

In reality there a many more effects to be takeen into account:

Excitation schemes used for resonant laser ionization

• Excitation into auto-ionizing state (AIS) with typical lifetimes of 10-15 – 10-10 s

• Excitation in Rydberg-states n = n*

3*0 )(nLifetime

Binding energy

Radius of Rydberg atoms

2*

2

)(n

Z

mM

MRE

e

2*0 )(nar

R = Rydberg constant

Orders of magnitudes for the cross sections:

• non-resonant (direct ionization): = 10-19 – 10-17 cm2

• AIS: = 1.6 x 10-14 cm2

• Rydberg states: ~ 10-14 cm2

2.26WS2011/12

A prominent example for a RILIS is at ISOLDE/CERN (see picture).

Advantages of a RILIS:• high selectivity

• separation of surface-ionizing contaminations by adjusting the temperature of the cavity

• high efficiency

2.27WS2011/12

Processes increasing the charge state Processes decreasing the charge state

2.5. Summary: Ion production

• Ionization - single-ionization - double-ionization The production of higher charge states is a successive process

The ionization has energy threshold → higher charge states need higher projectile energies (electron energies)

• Charge exchange (for low charge states)

• Recombination - radiative recombination The cross section is larger for lower electron temperatures

- dielectronic recombination (resonant process)

• Charge exchange (for high charge states)

depending on the neutral particle density (residual gas)

cross section are larger for higher charge states

2.28WS2011/12

10. Spouses never need to worry about what their ion source physicist husband or wife is up to when they still aren’t home by

midnight...they know with great confidence that they’re just at the lab changing a source!

9. Between – the International Conference on Ion Sources, – the Workshop on Ion Source Issues Relevant to a Pulsed Spallation Neutron Source, – the ECR Ion Source Workshop, – The International Conference on Negative Ions, Beams and Sources, – the International Symposium on the Production and Neutralization of Negative Ions and Beams, – the Workshop on Negative Ion Formation and Beam Handling, – the International Conference on Sources of Highly Charged Ions,

the ion source community has the greatest number of conferences and workshops of any scientific discipline measured

per linear inch of subject matter

8. Endless hours can be devoted to the important philosophical meaning of “pi” as in “the output emittance is 0.2 pi-mm-mrad”

7. Believe it or not, sometimes the SNS ion source antenna picks up free Satellite Television!

6. High-voltage, hydrogen gas, antennas and power supplies: it’s every little kids dream!

5. In what other field can you acquire a Ph.D., and then spend your professional life practicing the occult?

4. When the phone rings during dinner time, you always know who it is: no its not a tele-marketer, it just the lab...the ion source went down!

3. In what other field could you advertise a workshop on “RF-driven, multicusp, Cesium-enhanced H-sources for the SNS”,

and have 50 people actually show up?

2. Job security...when was the last time you heard a manager say, “the ion source is running so well, we’re going to let the entire group go.”

1. It’s a subject in which anyone can make a contribution, and everyone has an opinion! Courtesy of Stuart Henderson/ORNL