Nonideal complex Plasmasin the Universe and in the lab

Michael BonitzInstitut für Theoretische Physik und Astrophysik

Christian-Albrechts-Universität zu Kiel

2nd Summer Institute „Complex Plasmas“, Greifswald, 4 August 2010

PlasmaPlasma

I. Langmuir/L. Tonks (1929): ionized gas - „plasma“

„4th state of matter“: solid fluid gas plasmaideal hot classical gas

made of electrons and ions

= System of many charged particles, dominated by Coulomb interaction

Wikipedia: „More than 99 % of the visible matter in ouruniverse is in the Plasma state“

OccurencesOccurences of Plasmaof PlasmaContemporary Physics Education Project (CPEP)http://www.cpepweb.org/

NonidealLaboratory & astrophysicalplasmas

PlasmaPlasma

I. Langmuir/L. Tonks (1929): ionized gas - „plasma“„4th state of matter“: solid fluid gas plasma

ideal hot classical gasmade of electrons and ions

BUT: there exist unusual („complex“) plasmas which- are „non-ideal“, - often contain non-classical electrons,[- may contain other particles, chemically reactive]

= System of many charged particles, dominated by Coulomb interaction

ContentsContents

1. Introduction: Examples of nonideal plasmas

3. Computer simulations of quantum plasmas

- matter at extreme density

- White dwarf and neutron stars

2. Plasma physics approach to dense matter

Stars in Stars in thethe MilkyMilky wayway

Milky Way Central Bulge, viewed from the inside. It is a vast collection of more than 200 billion stars,

planets, nebulae, clusters, dust and gas.

Stars in Stars in thethe MilkyMilky wayway

Milky Way, Southern part, red emission nebulae, bright star clouds Sagittarius and Scorpius, Red giant Antares

Stars Stars sortedsorted: : schematicschematic

Hertzsprung-Russel-Diagram

Stars Stars sortedsorted: : observationsobservations

22000 stars from the Hipparcos Catalogue together with 1000 low-luminosity stars (red and white dwarfs) from the Gliese Catalogue of Nearby Stars.

Source: Wikipedia

WhyWhy therethere areare different Starsdifferent Stars

• All Stars contain the same matter as we know on Earth

• Origin of different Stars:

- different mixture of elements (composition)- different physical state of matter (temperature, density)- different physical processes (nuclear fusion)

• All Stars undergo similar evolution (only few options)

Compact Stars: Compact Stars: dwarfsdwarfs

• There is a close connection between size R and mass M:

Example water:

R, M 2 R, 8 MconstRM

=ρ

3~

Stars: The smaller a star, the larger its mass!

R, MR/2, 8 M

6

3

~~

−

−

RRM

ρ

White White dwarfsdwarfs• Balance of gravity and Fermi pressure of electrons

3~ −RM

Relativistic electrons

ChandrasekharLimiting mass

Source: Wikipedia

363 10~~

−cmgRM

EARTH

SUNρ

5000km

10000km

0.5M_sun 1.0M_s

Picture of a Picture of a whitewhite dwarfdwarf

White dwarf in the planetary nebula NGC 2440 (“cocoon”)In center of Milky Way. The hottest star? Surface T~200,000KCredit: H. Bond (STSci), R. Ciardullo (PSU), WFPC2, HST, NASA

WhatWhat isis insideinside a a whitewhite dwarfdwarf??

White Dwarf in NGC 2440. 250 time brighter than our Sun Image: Hubble Space Telescope.

• Spectroscopy: Core: carbon, oxygen, …

• Seismology: core crystalline

In In thethe newsnews ((BBC 16 Feb 2004BBC 16 Feb 2004))„Diamond star thrills astronomers“

„Twinkling in the sky is a diamond starof 10 billion trillion trillion carats, astronomers have discovered.“

The cosmic diamond is a chunk of crystallisedcarbon, 4,000 km across, some 50 light-yearsfrom the Earth in the constellation Centaurus. It's the compressed heart of an old star that was once bright like our Sun but has since fadedand shrunk.

Astronomers have decided to call the star "Lucy" after the Beatles song Lucy in the Sky with Diamonds.

White Dwarf BPM 37093,T. Metcalfe, Harvard-Smithsonian

„A diamond that is almost forever“

„The diamond star completely outclassesthe largest diamond on Earth, the 546-carat Golden Jubilee (South Africa).“

DensityDensity of of compactcompact starsstars

• How does matter behave at such extreme densities??

363 10~~

−cmgRM

EARTH

SUNWDρ

The answer is given by plasma physics!

White Dwarfs:(M

OccurencesOccurences of Plasmaof PlasmaContemporary Physics Education Project (CPEP)http://www.cpepweb.org/

White dwarfs

Plasma theory of white dwarfs• Starting in the 1960s: Van Horn, DeWitt, Ichimaru, Chabrier…

• Energy of electron-ion plasma (neutral) in thermodynamic equilibrium:

K – kinetic energy, G – gravitation, U – Coulomb interaction

eiiieeieei UUUGKKH +++++= +

• At extreme densities matter is expected to be fully ionized… (?)

Plasma theory of white dwarfsK – kinetic energy, G – gravitation, U – Coulomb interaction

eiiieeieei UUUGKKH +++++= +U (small)constMnH ≈)]([0

• One-component plasma model (OCP, jellium), TD equilibrium:

[ ]),(1),( ,0 nTKUKUHnTH iiiibacke Γ+=+=−−

Plasma state defined by single „coupling“ parameter

• Electrons exptected to be spatially homogeneous, quantum degenerate, weakly interacting

Thermodynamics of OCP

Classical „one-componentplasma“ (OCP)

Liquid-solid transition below criticaltemperature (above critical couplingstrength).

2D MD simulation of OCP cooling/heating,Periodic b.c., Torben Ott

See lectures by P. Hartmann and T. Ott

rTke

EU

BKIN

2||==Γ

)137:2(175 Dcr ≈Γ

Predicted by Wigner 1934 for theelectron gas in metals.

Wigner crystals in the laboratory

Tne

rTke

EU

BKIN

3/122||∝==Γ

Ways to achieve:

1. cooling

Need: crΓ≥Γ

Ideal gas behavior

Strongly

coupled

plasma

Wigner

(Coulom

b) cryst

al)

White dwarfs

Physically equivalent systems

Ion crystals in traps1987 first realization in Paul trap and laser cooling (Ca, Mg,…)Bollinger et al. (NIST), Walther et al. (true 1-component plasma)

Today many active groups in Innsbruck (Blatt), Aarhus (Drewsen)…

Ions in storage rings, U. Schramm, LMU München

Drewsen

Ion crystals in traps (2)

Applications: atomic physics, quantum optics, collective excitations, quantum computing…

R. Blatt, Uni Innsbruck

Measured oscillation of bi-crystal, Drewsen, Aarhus

Wigner crystals – solution 2

Tne

rTke

EU

BKIN

3/122||∝==Γ

2. Charge increase

Ways to achieve:

1. cooling

Need: crΓ≥Γ

Ideal gas behavior

Strongly

coupled

plasma

Wigner

(Coulom

b) cryst

al)

Trapped ions

White dwarfs

Physically equivalent systems

StronglyStrongly correlatedcorrelated CoulombCoulomb Systems Systems

Trapped ions

Tne

rTke

EU

BKIN

3/122||∝==ΓNeed: crΓ≥Γ

Ways to achieve:

1. cooling

2. Charge increase

„Dusty plasma“

Lectures on Monday, Tuesday

WignerWigner crystallizationcrystallization byby compressioncompression

Trapped ions

Tne

rTke

EU

BKIN

3/122||∝==ΓNeed: crΓ≥Γ

Ways to achieve:

1. cooling

2. Charge increase

3. compression

Dusty plasmas

semiconductors

MesoscopicMesoscopic quantumquantum CoulombCoulombclustersclusters in in quantumquantum dotsdots

quasi-2-dimensional system,

Density increase quantum („cold“) melting of „crystal“

Phys. Rev. Focus (April 2001), Sciences et Avenir, Scientific American, FAZ 1.8. 2001…

First-principle path integral Monte Carlo results

Prediction of electron crystallization: A.Filinov, MB, Yu. Lozovik, PRL 86, 3851 (2001)

compression

Quantum Quantum couplingcoupling parameterparameter3/1

3/2

3/122

~|| −∝∝=Γ n

nne

rEe

EU

FKIN

QNeed: crsB

sQ r

arr ≥∝=Γ

DeBrogliewave length

Tmkh Bπλ 2/=

r

λ

3λχ n=

Quantum degeneracy

Wigner crystal)2(37...34 Dr crs ≈Ceperley et al.,A. Filinov, MB

Ferm

iliq

uid

Ferm

igas

Universality of one-component plasmas

OCP with same coupling parameter(s) show same behavior

M. Bonitz, Physik Journal 7/8 (2002)

„Artificial atoms“ (electrons in quantum dots)

Noneq.-Green functions-Simulation: Lasse Rosenthal (length 0.001mm, T=1K)

„Mendeleyevtable“

Dusty plasmaexperiments byA. Melzer et al.

Length: 10mm,T~300K

Classical 2D finite Coulomb Clusters

Summary: Universal behavior of OCP

• classical plasma described by single parameter• quantum OCP described by two parameters

Application:

Mapping of white dwarf properties on entirely different laboratory plasmas

Γ

But: does the OCP model apply to real plasmas in stars??

Phase diagram of 2-comp. plasmas

Whitedwarfs

Neutronstars

157,000K~1 RydAtoms, molecules

weakly correlated!

Plasma theory of white dwarfs (2)

K – kinetic energy, G – gravitation, U – Coulomb interaction

eiiieeieei UUUGKKH +++++= +

Include: • Dynamics of electrons (no rigid background)• Formation of atoms, molecules; partial ionization• quantum and spin effects of electrons• quantum and spin effects of ions

Need: Selfconsistent first-principle approach to equilibriumproperties quantum Monte Carlo

Ultradense neutral plasmas

157,000K~1 RydAtoms, molecules

Pressure ionizationof atoms (Mott effect)

classical ion crystal +quantum electron gas

Filinov, Bonitz, Fortov, JETP Letters 72, 245 (2000)

ConditionsConditions forfor TCPTCP CoulombCoulomb crystalscrystals

I. strong ion coupling (OCP): )3(100,175 Drr crsshcr

h ≅≥≅Γ≥Γ

II. no Coulomb bound states:

h

e

e

h

e

h

TT

qqZ

mmM =Θ== ,,

Additional parameters in TCP: mass, charge and temperature asymmetry

2.1/ ≅≤= MottsBese rarr,23 Be EkT ≥

Analytical Results: Bonitz et al. PRL 95, 235006 (2005)

1. Classical system:finite temperature range for crystal orminimum charge Z

secr

B

e

rZ

EkT

ΓΘ

≤≤3/22

32

Quantum Quantum TCPTCP CoulombCoulomb crystalscrystals

h

e

e

h

e

h

TT

qqZ

mmM =Θ== ,,mass, charge and temperature asymmetry

AnalyticalAnalytical ResultsResults (2): Quantum system(2): Quantum system

1)(

)(3/4

−=≥e

Motts

crs

ecr

TrZrTMM• Critical mass ratio:

• Maximum temperature: crs

crB

eB

rMZ

ETk

Γ+Θ

=)1(4

2

• Finite density range: Mottcre

Mott nMMnn

3

11⎟⎠⎞

⎜⎝⎛

++

≤≤

Applies to White dwarf stars

White White dwarfdwarf starstar

D. Schneider, LLNL

classicalfluid and crystalin „quantum sea“of electrons

Size ~ our EarthMass ~ our Sun

density:

ERDEρρ610≅

Diamond???Diamond???„Diamond star thrills astronomers“

White Dwarf BPM 37093,T. Metcalfe, Harvard-Smithsonian

„A diamond that is almost forever“

Diamond:Melting point: 3820K

35.3 −≈ gcmρ

White dwarf:

Crystal of bare C6+ nuclei!

3610 −≈ gcmρ

KT 610≈

WhatWhat happenshappens to to thetheplasmaplasma uponupon furtherfurther

compressioncompression??

FromFrom whitewhite dwarfsdwarfs to to neutronneutron starsstars

Quantum Quantum meltingmelting of of ionion crystalcrystalReduce ion mass from M=1856 to M=100to simulate density increase 2/3

3 ~m

nnΛ=χ

Quantum Quantum meltingmelting of of ionion crystalcrystalReduce ion mass to M=25 and M=5

to simulate density increase

2/33 ~

mnnΛ=χ

Ion liquid Ion gas

Neutron Neutron starstarcrystal and quantum fluidof Fe-nuclei

in „quantum sea“of electrons

Radius ~ 10kmMass ~ our Sun

31510 −≅ cmgρ

Source: Coleman, UMD

Ato

ms

Elec

tron

-ion

plas

ma

e &

nuc

lei

(e &

pro

tons

&) n

eutr

ons

3

17.0fmbaryons

N =ρ

MeVTcmfm

C 175101 13

== −

Dwarfstars

Neutronstars

e &

ion

crys

tal

Compression, de-trapping:new states of charged matter

T_c

FromFrom nucleinuclei to to nuclearnuclear mattermatter

CanCan oneone reproducereproducethethe twotwo--componentcomponent plasmaplasmaof of compactcompact starsstars on Earth?on Earth?

OurOur simulationssimulations predictpredictpossiblepossible systemssystems and and

parametersparameters..

PredictedPredicted parametersparameters of of TCP TCP CoulombCoulomb crystalscrystals

][ 3max−cmn ][max KT][ 3min −cmn

+6C Ions(white dwarfs)

91026102 ⋅ 33106.3 ⋅

Are there candidates for laboratory TCP crystals?

TCP TCP CoulombCoulomb crystalscrystals

][ 3max−cmn ][max KT

Protons(hydrogen)

][ 3min−cmn

+6C Ions(white dwarfs)

91026102 ⋅ 33106.3 ⋅

24105⋅ 28100.1 ⋅ 000,66

Laser or ion beam compression experiments (?)

Lecture by Dirk Gericke

TCP TCP CoulombCoulomb crystalscrystalsin in thethe laboratorylaboratory??

][ 3max−cmn ][max KT

Protons(hydrogen)

Semiconductors(M=100)

][ 3min−cmn

+6C Ions(white dwarfs)

91026102 ⋅ 33106.3 ⋅

24105⋅ 28100.1 ⋅ 000,66

0.920102.1 ⋅ 20101.2 ⋅

Phase Phase diagramdiagram of hole of hole crystalcrystal

Bonitz, Filinov, Fortov, Levashov, and Fehske, Phys. Rev. Lett. 95, 235006 (2005)

Re E

kTT23

=3/11 n

ra

r eB

se

∝=

11++

= crMMK

Θ= 2

1Z

α

)2(60),3(83 DDM cr =• for Z=1 (e.g. electron-hole plasma):

Animation: G. Schubert, M=5,12,25,50,100

Band structure& collective

hole behavior

Increase of M: Increasing hole localization

Hole Fermi gas Fermi liquidWigner crystal

Animation: G. Schubert, M=5,12,25,50,100

Early predictions of hole crystal: Halperin/Rice, Abrikosov, ...PIMC simulations Filinov, Bonitz 2005

Experimental verification?High temp. Superconductivity?

Dec 2 2005Deutschlandfunk, NDR

BBC FocusSuperconductor Weekca. 100 online Science pages.......

New Scientist

Our results in the news

„The Hole crystal“

Ato

ms

Elec

tron

-ion

plas

ma

e &

nuc

lei

(e &

pro

tons

&) n

eutr

ons

3

17.0fmbaryons

N =ρ

MeVTcmfm

C 175101 13

== −

Dwarfstars

Neutronstars

e &

ion

crys

tal

Compression, de-trapping:new states of charged matter

FromFrom nuclearnuclear matter to matter to quarksquarks

Qua

rk-g

luon

plas

ma

Nρ)10...5(deconfinement

T_c

Big bang: Big bang: trappingtrapping of of chargedcharged mattermatter

Source: RHIC web site

Quark-gluon plasma realized at:Relativistic Heavy ion collider, BrookhavenLarge Hadron collider, CERN

Crystal of nuclei, ions

Can one verify this experimentally ?

To produce a quark-gluon plasmahuge densities and

particle energies are needed

big particle colliders in the U.S. and Europeaim at producing and studying the properties

of the quark-gluon plasma

G. Baym

G. Baym

G. Baym

Quark-gluon plasma

It is believed that of the quark-gluon plasmahas been seen at RHIC

(Relativistic Heavy Ion Collider) and will soonbe produced at the LHC at CERN

The particles in the QGP plasma interactvia the (color) Coulomb potential

First results were surprising: the QGP is a non-ideal plasma, liquid-like

New applications of non-ideal plasma physics!See e.g. V. Filinov et al., Contrib. Plasma Phys. 49, 536 (2009)

SummarySummary

One-component plasma model: universal phase diagram, Similar plasma behavior in trapped ions, dusty plasmas etc.

Coulomb crystal in neutral/Two-component plasmas:Ion crystal in Fermi sea of electronshole crystal in semiconductors (for M>80), superconductivity?

http://www.theo-physik.uni-kiel.de/~bonitz

Nonideal plasmas: exist in planets, white dwarf and neutron stars, quark-gluon plasma highly organized, collective particle behavior

SummarySummary

Theoretical approaches to nonideal plasmas:Lecture this afternoon

For more information see:

„Introduction to Complex Plasmas“, M. Bonitz, N. Horing and P. Ludwig (eds.), Springer 2010

http://www.theo-physik.uni-kiel.de/~bonitz

PlasmaOccurences of PlasmaPlasmaContentsOccurences of PlasmaPlasma theory of white dwarfs Plasma theory of white dwarfs Thermodynamics of OCPWigner crystals in the laboratoryIon crystals in trapsIon crystals in traps (2)Wigner crystals – solution 2Strongly correlated Coulomb Systems Wigner crystallization by compression Mesoscopic quantum Coulomb clusters in quantum dots�Quantum coupling parameter Universality of one-component plasmas„Artificial atoms“ (electrons in quantum dots) „Mendeleyev table“ Phase diagram of 2-comp. plasmasPlasma theory of white dwarfs (2) Ultradense neutral plasmasConditions for TCP Coulomb crystalsQuantum TCP Coulomb crystalsWhite dwarf starFrom white dwarfs to neutron starsQuantum melting of ion crystalQuantum melting of ion crystalNeutron starFrom nuclei to nuclear matterPredicted parameters of �TCP Coulomb crystalsTCP Coulomb crystalsTCP Coulomb crystals�in the laboratory?Phase diagram of hole crystalBand structure �& collective �hole behaviorOur results in the newsFrom nuclear matter to quarksBig bang: trapping of charged matterCan one verify this experimentally ?Quark-gluon plasma