Nonideal complex Plasmas in the Universe and in the lab
Michael Bonitz Institut für Theoretische Physik und Astrophysik Christian-Albrechts-Universität zu Kiel
2nd Summer Institute „Complex Plasmas“, Greifswald, 4 August 2010 PlasmaPlasma
= System of many charged particles, dominated by Coulomb interaction
Wikipedia: „More than 99 % of the visible matter in our universe is in the Plasma state“
I. Langmuir/L. Tonks (1929): ionized gas - „plasma“
„4th state of matter“: solid Æ fluid Æ gas Æ plasma ideal hot classical gas made of electrons and ions OccurencesOccurences ofof PlasmaPlasma
Contemporary Physics Education Project (CPEP)http://www.cpepweb.org/
Nonideal Laboratory & astrophysical plasmas PlasmaPlasma
= System of many charged particles, dominated by Coulomb interaction
I. Langmuir/L. Tonks (1929): ionized gas - „plasma“ „4th state of matter“: solid Æ fluid Æ gas Æ plasma ideal hot classical gas made 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] ContentsContents
1. Introduction: Examples of nonideal plasmas
- White dwarf and neutron stars
- matter at extreme density
2. Plasma physics approach to dense matter
3. Computer simulations of quantum plasmas StarsStars inin 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. StarsStars inin thethe MilkyMilky wayway
Milky Way, Southern part, red emission nebulae, bright star clouds Sagittarius and Scorpius, Red giant Antares StarsStars sortedsorted:: schematicschematic
Hertzsprung- Russel- Diagram StarsStars 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 differentdifferent StarsStars
• 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) CompactCompact Stars:Stars: dwarfsdwarfs
• There is a close connection between size R and mass M:
3 Example water: ~ RM ρ = const R, M 2 R, 8 M
Stars: The smaller a star, the larger its mass!
~ RM −3 ρ ~ R−6 R/2, 8 M R, M WhiteWhite dwarfsdwarfs • Balance of gravity and Fermi pressure of electrons
Chandrasekhar Limiting mass
−3 10000km M ~ R
5000km Relativistic electrons
0.5M_sun 1.0M_s M SUN 6 −3 ρ 3 10~~ cmg R EARTH Source: Wikipedia PicturePicture ofof aa whitewhite dwarfdwarf
White dwarf in the planetary nebula NGC 2440 (“cocoon”) In center of Milky Way. The hottest star? Surface T~200,000K Credit: H. Bond (STSci), R. Ciardullo (PSU), WFPC2, HST, NASA WhatWhat isis insideinside aa whitewhite dwarfdwarf??
• Spectroscopy: Core: carbon, oxygen, …
• Seismology: core crystalline
White Dwarf in NGC 2440. 250 time brighter than our Sun Image: Hubble Space Telescope. InIn thethe newsnews ((BBCBBC 1616 FebFeb 20042004)) „Diamond star thrills astronomers“
„Twinkling in the sky is a diamond star „A diamond that is almost forever“ of 10 billion trillion trillion carats, astronomers have discovered.“ The cosmic diamond is a chunk of crystallised carbon, 4,000 km across, some 50 light-years from 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 faded and shrunk.
„The diamond star completely outclasses White Dwarf BPM 37093, the largest diamond on Earth, T. Metcalfe, Harvard-Smithsonian the 546-carat Golden Jubilee (South Africa).“
Astronomers have decided to call the star "Lucy" after the Beatles song Lucy in the Sky with Diamonds. DensityDensity ofof compactcompact starsstars
M White Dwarfs: SUN 6 −3 ρWD 3 10~~ cmg (M<1.4 M_sun) R EARTH
M Neutron stars: SUN 15 −3 ρ NS ~ 3 10~ cmg (M~1.4…2.1 M_sun) km)10(
M~2.1…3 M_sun: quark star (?)
• How does matter behave at such extreme densities??
Æ The answer is given by plasma physics! OccurencesOccurences ofof PlasmaPlasma
Contemporary Physics Education Project (CPEP)http://www.cpepweb.org/
White dwarfs Plasma theory of white dwarfs
• Starting in the 1960s: Van Horn, DeWitt, Ichimaru, Chabrier…
• At extreme densities matter is expected to be fully ionized… (?)
• Energy of electron-ion plasma (neutral) in thermodynamic equilibrium:
K – kinetic energy, G – gravitation, U – Coulomb interaction
= + + + + + +UUUGKKH eiiieeieei Plasma theory of white dwarfs
K – kinetic energy, G – gravitation, U – Coulomb interaction
= + + + + + +UUUGKKH eiiieeieei
0 )]([ ≈ constMnH U (small)
• Electrons exptected to be spatially homogeneous, quantum degenerate, weakly interacting
• One-component plasma model (OCP, jellium), TD equilibrium:
),( ,0 backe [ Γ+=+=−− iiii nTKUKUHnTH ),(1 ]
Æ Plasma state defined by single „coupling“ parameter Thermodynamics of OCP
Classical „one-component plasma“ (OCP)
U || e2 ==Γ EKIN B rTk
Liquid-solid transition below critical temperature (above critical coupling strength).
Γcr ≈ D )137:2(175 2D MD simulation of OCP cooling/heating, Periodic b.c., Torben Ott Predicted by Wigner 1934 for the electron gas in metals. See lectures by P. Hartmann and T. Ott Wigner crystals in the laboratory
U || e2 ne 3/12 Need: Γ ≥ Γcr ∝==Γ EKIN B rTk T
Ways to achieve:
Ideal gas behavior 1. cooling
ma as pl l) led sta up ry co ) c ly b ng lom ro ou St (C er ign W White dwarfs
Physically equivalent systems Ion crystals in traps
1987 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)…
Drewsen
Ions in storage rings, U. Schramm, LMU München 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
U || e2 ne 3/12 Need: Γ ≥ Γcr ∝==Γ EKIN B rTk T
Ways to achieve:
Ideal gas behavior 1. cooling a sm l) 2. Charge pla ta d rys ple ) c increase ou b c lom gly ou on (C Str er gn Wi White dwarfs
Physically equivalent systems
Trapped ions StronglyStrongly correlatedcorrelated CoulombCoulomb SystemsSystems
U || e2 ne 3/12 Need: Γ ≥ Γcr ∝==Γ EKIN B rTk T
Ways to achieve:
1. cooling
2. Charge increase
„Dusty plasma“
Lectures on Monday, Tuesday Trapped ions WignerWigner crystallizationcrystallization byby compressioncompression
U || e2 ne 3/12 Need: Γ ≥ Γcr ∝==Γ EKIN B rTk T
Ways to achieve:
1. cooling
2. Charge increase Dusty plasmas 3. compression semiconductors
Trapped ions MesoscopicMesoscopic quantumquantum CoulombCoulomb clustersclusters inin quantumquantum dotsdots
Prediction of electron crystallization: A.Filinov, MB, Yu. Lozovik, PRL 86, 3851 (2001) quasi-2-dimensional system, First-principle path integral Monte Carlo results compression
Density increase Æ quantum („cold“) melting of „crystal“
Phys. Rev. Focus (April 2001), Sciences et Avenir, Scientific American, FAZ 1.8. 2001… QuantumQuantum couplingcoupling parameterparameter
Q r cr 2 3/12 Q U || e ne − 3/1 Need: rs ≥∝=Γ rs =Γ ~ ∝∝ n a 3/2 B EKIN F rE n Quantum degeneracy = nλχ3 r DeBroglie wave length λ
= 2/ πλBTmkh
cr Fermi gas
Wigner crystal Fermi liquid rs ≈ D)2(37...34 Ceperley et al., A. Filinov, MB 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) Classical 2D finite Coulomb Clusters
„Mendeleyev table“
Length: 10mm, T~300K
Dusty plasma experiments by A. Melzer et al. Summary: Universal behavior of OCP
• classical plasma described by single parameter Γ • quantum OCP described by two parameters
Application:
Mapping of white dwarf properties on entirely different laboratory plasmas
But: does the OCP model apply to real plasmas in stars?? Phase diagram of 2-comp. plasmas
157,000K Atoms, molecules ~1 Ryd weakly correlated! White Neutron dwarfs stars Plasma theory of white dwarfs (2)
K – kinetic energy, G – gravitation, U – Coulomb interaction
= + + + + + +UUUGKKH eiiieeieei
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 equilibrium properties Æ quantum Monte Carlo Ultradense neutral plasmas
157,000K Atoms, molecules ~1 Ryd
classical ion crystal + quantum electron gas
Pressure ionization of atoms (Mott effect)
Filinov, Bonitz, Fortov, JETP Letters 72, 245 (2000) ConditionsConditions forfor TCPTCP CoulombCoulomb crystalscrystals
Additional parameters in TCP: mass, charge and temperature asymmetry m q T M h Z h ,, =Θ== e me qe Th
cr cr I. strong ion coupling (OCP): h ,175 rr ssh ≅≥≅Γ≥Γ D)3(100
II. no Coulomb bound states: 3 Mott 2 ≥ EkT Be , / rarr sBese ≅≤= 2.1
Analytical Results: Bonitz et al. PRL 95, 235006 (2005)
1. Classical system: 2 kT 2ΘZ 3/2 Æ finite temperature range for crystal or e ≤≤ Æ minimum charge Z cr 3 EB Γ rse QuantumQuantum TCPTCP CoulombCoulomb crystalscrystals
m q T mass, charge and temperature asymmetry M h Z h ,, =Θ== e me qe Th
AnalyticalAnalytical ResultsResults (2):(2): QuantumQuantum systemsystem M +1 3 • Finite density range: Mott ⎛ ⎞ Mott nn e ≤≤ ⎜ ⎟ n ⎝ M cr +1⎠ r cr cr TMM )( =≥ s −1 • Critical mass ratio: e 3/4 Mott s TrZ e )(
Tk 2 MZ +Θ )1( eB = 4 • Maximum temperature: cr cr EB Γ rs
Applies to White dwarf stars WhiteWhite dwarfdwarf starstar
classical fluid and crystal in „quantum sea“ of electrons
Size ~ our Earth Mass ~ our Sun Ædensity: 6 ≅ 10 ρρERDE
D. Schneider, LLNL Diamond???Diamond??? „Diamond star thrills astronomers“
„A diamond that is almost forever“ Diamond: ρ ≈ 5.3 gcm−3 Melting point: 3820K
White dwarf: ρ ≈10 gcm−36 ≈106 KT Æ Crystal of bare C6+ nuclei! White Dwarf BPM 37093, T. Metcalfe, Harvard-Smithsonian WhatWhat happenshappens toto thethe plasmaplasma uponupon furtherfurther compressioncompression?? FromFrom whitewhite dwarfsdwarfs toto neutronneutron starsstars QuantumQuantum meltingmelting ofof ionion crystalcrystal
n Reduce ion mass from M=1856 to M=100 χ nΛ= 3 ~ to simulate density increase m 2/3 QuantumQuantum meltingmelting ofof ionion crystalcrystal
Reduce ion mass to M=25 and M=5 to simulate density increase
Ion liquid n Ion gas χ nΛ= 3 ~ m 2/3 NeutronNeutron starstar
crystal and quantum fluid of Fe-nuclei
in „quantum sea“ of electrons
Radius ~ 10km Mass ~ our Sun
ρ ≅ 1015 cmg −3
Source: Coleman, UMD T_c T C fm From = From e ttso hre matter of charged states new Compression, de-trapping: = 175 101 MeV − 13 cm nuclei nuclei to to
Atoms ρ nuclear nuclear N =
17.0 Electron-ion plasma baryons fm Dwarf stars
3 e & ion crystal matter e & nuclei matter Neutron stars
(e & protons &) neutrons CanCan oneone reproducereproduce thethe twotwo--componentcomponent plasmaplasma ofof compactcompact starsstars onon Earth?Earth?
OurOur simulationssimulations predictpredict possiblepossible systemssystems andand parametersparameters.. PredictedPredicted parametersparameters ofof TCPTCP CoulombCoulomb crystalscrystals
−3 −3 min cmn ][ max cmn ][ max KT ][
6+ C Ions 9 ⋅102 26 ⋅106.3 33 10 (white dwarfs)
Are there candidates for laboratory TCP crystals? TCPTCP CoulombCoulomb crystalscrystals
−3 −3 min cmn ][ max cmn ][ max KT ][
6+ C Ions 9 ⋅102 26 ⋅106.3 33 10 (white dwarfs)
Protons 28 ⋅105 24 ⋅100.1 000,66 (hydrogen)
Laser or ion beam compression experiments (?)
Æ Lecture by Dirk Gericke TCPTCP CoulombCoulomb crystalscrystals inin thethe laboratorylaboratory??
−3 −3 min cmn ][ max cmn ][ max KT ][
6+ C Ions 9 ⋅102 26 ⋅106.3 33 10 (white dwarfs)
Protons 28 ⋅105 24 ⋅100.1 000,66 (hydrogen) Semiconductors ⋅102.1 20 ⋅101.2 20 0.9 (M=100) PhasePhase diagramdiagram ofof holehole crystalcrystal
M +1 K = M cr +1 1 α = Z 2Θ
3 kT Te = 2 E 1 a 3/1 R B ∝= n rse re
• for Z=1 (e.g. electron-hole plasma): M cr = DD )2(60),3(83
Bonitz, Filinov, Fortov, Levashov, and Fehske, Phys. Rev. Lett. 95, 235006 (2005) Band structure & collective hole behavior
Increase of M: Increasing hole localization
Hole Fermi gas Æ Fermi liquid Æ Wigner crystal
Early predictions of hole crystal: Halperin/Rice, Abrikosov, ... PIMC simulations Filinov, Bonitz 2005
Experimental verification? High temp. Superconductivity? Animation: G. Schubert, M=5,12,25,50,100 Our results in the news
Dec 2 2005 Deutschlandfunk, NDR „The Hole crystal“ New Scientist BBC Focus Superconductor Week ca. 100 online Science pages ...... T_c T C fm From From = e ttso hre matter of charged states new Compression, de-trapping: = 175 101 MeV − 13 cm nuclear nuclear deconfinement matter to
Atoms matter to ρ N =
17.0 Electron-ion plasma baryons fm Dwarf stars
3 e & ion )10...5(
ρ crystal N quarks e & nuclei quarks Neutron stars
(e & protons &) neutrons
Quark-gluon plasma BigBig bang:bang: trappingtrapping ofof chargedcharged mattermatter
Crystal of nuclei, ions
Quark-gluon plasma realized at: Relativistic Heavy ion collider, Brookhaven Large Hadron collider, CERN Source: RHIC web site Can one verify this experimentally ?
To produce a quark-gluon plasma huge densities and particle energies are needed
big particle colliders in the U.S. and Europe aim at producing and studying the properties of the quark-gluon plasma G. Baym G. Baym G. Baym Quark-gluon plasma
ÆIt is believed that of the quark-gluon plasma has been seen at RHIC (Relativistic Heavy Ion Collider) and will soon be produced at the LHC at CERN
ÆThe particles in the QGP plasma interact via the (color) Coulomb potential
ÆFirst 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
Nonideal plasmas: exist in planets, white dwarf and neutron stars, quark-gluon plasma Æ highly organized, collective particle behavior
One-component plasma model: universal phase diagram, Similar plasma behavior in trapped ions, dusty plasmas etc.
Coulomb crystal in neutral/Two-component plasmas: Æ Ion crystal in Fermi sea of electrons Æ hole crystal in semiconductors (for M>80), superconductivity?
http://www.theo-physik.uni-kiel.de/~bonitz SummarySummary
Theoretical approaches to nonideal plasmas: Æ 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