Astrophysik mit hochgeladenenIonen: Theorie und Experiment

José R. Crespo López-UrrutiaZoltán Harman

Max-Planck-Institut für KernphysikHeidelberg

Highly charged ions exist wherevernucleosynthesis occurs

All atoms are born equal, as naked nuclei, and decay from their pristine highly charged state

to their neutral chemical configuration

new generation of high resolution x-ray and VUV satellites in space

observed: wavelength, line ratios and line widths... inferred: identification of species, temperature, magneticfield, plasma density...

Why highly charged ions (HCI)?

• Natural, abundant, neither exotic nor artificial:

Universe is full of HCI !

• Relativistic, QED-”fully loaded” bound electrons in HCI are interesting for theory

• Technically relevant: fusion research

Why photon spectroscopy beyond H?

- Non-perturbative QED: coupling constant Zα ≈ 1

Bound electron expanded: sum of free electron propagators

Many virtual photons, each interaction Z times stronger than in H

•Few-particle QED unexplored

•Theory of (non-perturbative) QED in high fields still under construction; general scaling law ~Z 4

•Large nuclear size effects

The classic ideal: H-like ions

Two-body-Coulomb-Problem ⇒ analytical solution

Scaling factors from H to U91+ :•Level energy En ~ Z2 ´ 8⋅103

Transition probability Aik :• E1 ~ Z4 a factor of ´ 7⋅107

• 2E1 ~ Z6 ´ 6⋅1011

• M1 ~ Z10 ´ 4⋅1019

• M2 ~ Z8 ´ 5⋅1015

• hyperfine splitting ~ Z3

• nuclear size effects ~ Z6

• QED contributions ~ Z4

• PNC contributions ~ Z5

„forbidden“ lines

∅(Sun)/∅(H atom)

Why highly charged ions?

Schrödinger Dirac QED

n=1

p3/2

s1/2, p1/2

n=2

p1/2

s1/2

p3/2

115 keV

132.3 keV131.8 keV

+radiation fieldEn = Ry. Z2/n2

1s Lamb shift

n=3

s1/2

+ relativity

for U92+ 468 eV

Lamb shift

Li: 0.002% of 1.85 eV

Fe23+: 1% of 48.6 eV

U89+: 15% of 280 eV

Li-like

» QED QED Lamb shift

Lamb shift

H-like

Lamb shift in hydrogen- and lithium-like ions

QED contributions:

Ionization potential rises from 10 to 130000 eV

0 10 20 30 40 50 60 70 80 90 100

0.01

0.1

1

10

100barium

tungsten

krypton

neon

argon

uraniumIo

niz

atio

n p

ote

ntial

(ke

V)

Ion charge state q+

Sequential electron impact ionization

As the ion charge state goes up:• growing ionization potential:

10 eV → 130000 eV• diminishing cross section:

10-16 cm2 → 10-24 cm2

continuum

130 keV

31 keV

12 keV

n=1

n=2 n=3

beam electronwith energy Ek

Competing processes: recombination

n n

n

n

n

n n

n

n

n

Ne9+

Ncharge exchange with restgas neutral atoms

solution: vacuum 10-13 Torr

capture of free electrons

n n

n

n

n

solution: raising electronbeam energy

(1000 atoms/cm3)

γ radiative recombination (RR)

• Relevant and precise experimental data needed for theory tests

• Fundamental phenomena become accessibleto observation:

•simpler electronic structure•scaling with high powers of Z

Need for experimental data

• In the electron beam ion source (EBIS), a fast, dense, electron beam interacts with atoms and produces ions.

• Ions are confined radially by the potential well in the electron beam and axially by ring electrodes.

• Ions can be accumulated in or expelled out of it.

• As the interaction time between electrons and ions defines the highest charge state achievable, high current density (of the order of 1000A/cm2) electron beams are required.

• Since normal cathodes are limited to less than 10A/cm2, beam compression by means of a strong magnetic field is needed.

Electron beam ion source

Poisson‘s equation in cylindrical coordinates

Resulting potential with boundary conditions taken into account

Space charge potential: a line charge

1000 2000 30000

20

40

60

80

100

120

140

center drift tube radiusspace charge potential

electron density(normalized to 50)

Spac

e ch

arge

pot

enti

al (V

)

Distance from axis (μm)

Ebeam=2162 eVIbeam=40 mA

Space charge potential of the electron beam

0.1 1 10 100 1000

0

20

40

60

80

100

120

140

center drift tube radius

electron beam radius

space charge potential

electron density(normalized to 50)

Spac

e ch

arge

pot

enti

al (V

)

Distance from axis (μm)

Ebeam=2162 eVIbeam=40 mA

Space charge potential of the electron beam

• As electrons collide with the ions in the beam, they stripoff electrons until the energy required to remove the nextelectron is higher than the beam energy.

• The original LLNL EBIT (1986) is capable of an electronbeam energy of about 30 keV, enough to make neon-likeuranium (U82+, or a uranium atom with only 10 of theusual 92 electrons).

• From this EBIT-I, a high-energy EBIT, named SuperEBIT, was built. It has an electron gun that can achieve an electron beam energy of 200 keV, enough to make bare uranium (U92+).

The electron beam ion trap (EBIT)

Production of HCI with an electron beam ion trap

radially: electron beamspace charge

total trap potential Utrap ≈ 200 V

(Utrap× ion charge) ≈ 10000 eV

15000 A/cm2

ne ≈ 1013 e-/cm3

axially: electrodes

I=450 mAE= 5 keV

Section through the HD-EBIT I (1999)

HD-EBIT III(2006)The first EBIT

(LLNL,1986)

0.01 0.1 1 100.0

0.1

0.2

0.3

Hg10+

Hg20+Hg30+

Hg40+

Hg78+

Hg70+

Ch

arg

e st

ate

frac

tion

Ionization time (s)

Hg52+

Time evolution of the charge state

Calculated for Hg ions at 50 keV electron beam energy by numerically solving a set of coupled differential equations for the ionization and recombination processes:

Evaporative cooling

• heavy, highly charged ions (e.g. Ba53+ ) remain trapped indefinitely

Evaporative cooling• collisions with beam electrons heat up ion ensemble• light, less tightly trapped ions (e.g. Ne10+ ) evaporate removing thermal energy: a single Ne10+ takes away 2 keV (1 second additional life for a heavy ion)

Ion temperatures from 1000 eV to 10 eV

Doppler width Δλ/λ ≈ 1/20.000 (Ba53+)

High resolution spectroscopy

0

500

1000

1500

2000

0.0 0.2 0.4 0.6 0.8 1.0

D B

Relative energy distribution function

Pote

ntia

l ene

rgy

(arb

. uni

ts)

Trapping potential

Evaporating fraction

Light ions

Heavy ions

Evaporative cooling: energy distributionfunction relative to trapping potential

EBITs are good to reproduce the conditionsprevailing in astrophysical plasmas

transientplasmas, strong densityandtemperaturegradients

EBITs:stationary,homogeneousconditions

Density and temperature space sampled by different spectroscopic light sources

P. Beiersdorfer, Annu. Rev. Astron. Astrophys. 41 (2003) 343-390

11 12 13 14 15 16 17 18 19 20 21 22 23 24 2550

100

150

200

250

300

Wavelength (nm)

Elec

tron

ene

rgy

(eV)

Ba under conditions from 105 K to 106 K

18.0 18.5 19.0 19.5 20.0 20.5 21.0 21.5 22.050

100

150

200

250

300

350

400

Wavelength (nm)

Elec

tron

ene

rgy

(eV)

Fe under conditions from 105 K to 106 K

16.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0

101

102

II

Fe V

III

Fe V

III

Fe V

III

Fe V

III

Fe V

III

Fe V

III

Fe V

III

X

Fe I

X

II

Fe X

Fe

X

Fe X

VI

I VI

I II

Fe

X

Fe X

I

Fe X

I

Fe X

Fe

XI

Fe

XI

Fe

XI

Fe X

I

Fe X

II

Fe X

Fe

XI

Fe

VII

III

Fe

VII

IFe

XII

Fe

VII

IFe

XII

Fe

XI

Fe X

Fe V

III

Fe X

II

Fe X

I

Fe X

II Fe

VII

IFe

VII

IFe

XII

Fe

XII

Fe

VII

Fe

VII

IFe

VII

IFe

VII

I

Int

ensi

ty (c

ount

s)

Wavelength (nm)

Fe under conditions from 105 K to 106 K

X-ray diagnostics: Bragg’s law

Flat crystal x-ray spectrometer

Laboratory setup

Absolute x-ray spectroscopy

Bruhns, Braun et al., Rev. Sci. Inst. 76, 073105 (2005)

A novel methoderemoves the largest errorsources found in crystalspectrometers

x-ray source(EBIT)

laser

light beams crystal

x-ray line fiducial 1

fiducial 2

CCD

mirror

The Lyman-α spectrum of hydrogenic Ar

The Lyman-alpha spectrum of hydrogenic Ar

~2 eV

How are X-rays reflected from a surface?

The reflection of X-rays from a solid surface is caused by the electrons in the atoms of the solid, which give it a refractive index which is less than one at X-ray wavelengths(solids have refractive indices greater than one at optical wavelengths).

This means that X-rays striking air-metal or vacuum-metal interfaces are going from optically more-dense to optically less-dense media. In these circumstances total internal reflection of the light can occur.

If the incidence angle is great enough (or the grazing angle is small enough) the X-rays are reflected from the surface. The value of the critical angle depends on the electron density of the mirror material. This number is particularly large for gold, platinum, iridium.

0 2000 4000 6000 8000 1000010-5

10-4

10-3

10-2

10-1

100

Refl

ecti

vity

of

a go

ld m

irro

r

Photon energy (eV)

Incidence angle

90o

2o

0.5o

12,5 13,0 13,5 14,0 14,5

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

Refl

ecti

vity

Wavelength (nm)

Reflectivity of a molybdenum/silicon multilayer mirrorwith 40 layers of 6.9 nm

The reflectivity of X-rays from a solid surface can be enhanced by using multilayers with nanometer spacing.

Multilayer optics for X rays

Multilayer optics for X rays

Reflection grating spectrum

Seya-Namioka VUV spectrometer

The Seya-Namioka mounting is used at wavelengths > 30 nm and is a special case of the Rowland mounting with an acceptable spectral resolution. It is widely used in plasma diagnostics and at synchrotrons.

The HETG gratings have a period of 0.2µm or 2000Å for the high-energy gratings, and 0.4µm or 4000Å, for the medium energy gratings.

Transmission gratings for x-rays

Schematic diagram of an X-ray experiment with a two pinhole grating (labeled a and b) spectrograph. PFS is a plasma focus x-ray source; C is the capacitor; SH is the shutter; PH is the pinhole;PG is the pinhole grating.

A pinhole transmission grating spectrometer

Grazing incidence soft-x-ray spectrometer

•At wavelengths shorter than 30 nm, small grazing angles are needed. •Detectors are mounted on the Rowland circle and moved under vacuum with bellows. •Curved photographic plates can also be used.

Grazing incidence imaging optics

Kirkpatrik-Baez

Each of the two cylindrical mirrors focuses in one coordinate.

Grazing incidence mirror telescope with concentric conic surfaces having a single common point: a paraboloid-hyperboloid combination with two internal reflections.

Wolter telescope

Wolter telescope and Rowland spectrometer

Chandra’s Wolter telescope

Image of a point source at 3 keV

Coronal Diagnostic Spectrometer (CDS) on SOHO (ESA/NASA Solar and Heliospheric Observatory)

Two compementary systems; the Normal Incidence Spectrometer (NIS) and the Grazing Incidence Spectrometer (GIS).

Spectral range of operation

Space based x-ray telescopes

Spectral imaging with XMM and Chandra

Images of a supernova remnant at different soft x-ray wavelengths

Composite image

Diagnostics of fusion plasmas with VUV and X-rays