Expansion and Equilibration of Ultracold Neutral Plasmas

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1 Expansion and Equilibration of Ultracold Neutral Plasmas Thomas C. Killian Department of Physics and Astronomy 9 th NNP Conference, Columbia University

2 Access Ultracold Temperatures with Laser Cooled Strontium d~1mm, N~10 8, n~10 10 cm -3, T ~1 mk

3 Creation of an Ultracold Neutral Plasma through Photoionization Ionization Potential Photoionization 412 nm Rydberg Levels 1 P 1 Cooling 461 nm 1 S 0 Ground State

4 Initial electron kinetic energy, E e, equals excess photon energy ( K) Ions created with mk energies Ultracold neutral plasma! I. P. Kinetic energy, E e

5 Ultracold Neutral Plasma Interest Classical plasma physics Strongly coupled Coulomb systems Expansion Collective modes Recombination Ion-electron-atom collisions Two-component plasmas Equilibration and correlations Equilibration and correlations Thermal transport High energy density and warm dense matter physics Laser-produced plasmas Similar dynamics Applications Bright charged-particle beams Surprises?

6 1996 Contemporary Physics Education Project Neutral Plasmas Neutral Plasmas

7 Neutral Plasmas 1996 Contemporary Physics Education Project Strongly- Plasmas don t Coupled exist Plasmas 2 Γ = e 4 / k T > 1 π ε a 0 B

8 Model for Plasma Creation Electron Potential Energy Position electron kinetic energy At t=0: Just after photoionization, the plasma is neutral everywhere and the potential is flat.

9 Model for Plasma Creation Electron Potential Energy kinetic energy Position At t 1 ~10ns: Electrons escape due to their kinetic energy and a charge imbalance builds up until electrons are trapped.

10 Model for Plasma Creation Electron Potential Energy kinetic energy Position At t 1 ~10ns: Electrons escape due to their kinetic energy and a charge imbalance builds up until electrons are trapped.

11 Model for Plasma Creation Electron Potential Energy kinetic energy Position At t 1 ~10ns: Electrons escape due to their kinetic energy and a charge imbalance builds up until electrons are trapped.

12 Model for Plasma Creation Electron Potential Energy kinetic energy Position At t 1 ~10ns: Electrons escape due to their kinetic energy and a charge imbalance builds up until electrons are trapped.

13 Model for Plasma Creation Electron Potential Energy Position kinetic energy At t 1 ~10ns: Electrons escape due to their kinetic energy and a charge imbalance builds up until electrons are trapped.

14 Model for Plasma Creation Electron Potential Energy Position kinetic energy λ D ~10µm<<σ~1mm At t 2 ~.1-10µs: Ultracold plasma Neutral in center

15 Model for Plasma Creation Electron Potential Energy Position kinetic energy At t 2 >10µs: Ions cloud expands. Coulomb well depth increases.

16 Model for Plasma Creation Electron Potential Energy Position kinetic energy At t 2 >10µs: Ions cloud expands. Coulomb well depth decreases.

17 Model for Plasma Creation Electron Potential Energy Position kinetic energy At t 2 >10µs: Electrons can escape

18 Model for Plasma Creation Electron Potential Energy Position kinetic energy At t 2 >10µs: Electrons can escape, or be dragged out by residual electric fields.

19 Absorption Imaging 422 nm laser plasma y z false-color camera image Simien et al., PRL 2004

20 Image of Plasma Expansion

21 Expansion of Other Plasmas Short pulse irradiation of solid targets Inertial confinement fusion experiments

22 Expansion of the Plasma Expansion is driven by the pressure of the electron gas electrons ions

23 Exact Solution to the Vlasov Equations r u i r k T ( r, t ) rˆ B m σ 2 r u r ( r ) v ( r ) a r r t is time since photoionization i i e ( 0 ) This is not a heating of the ions. r r Heating is an increase in ( v ) 2 i u i. ( = local average a velocity t ) t Directed radial ion velocity r r, u i

24 Terminal Velocity initial electron energy with T. Pohl ion expansion energy Expansion reaches terminal velocity when all electron energy has been transferred to radial ion motion Electrons cool adiabatically v final i rm, = k B Te (0) m i

25 Theory predicts a self-similar similar Gaussian expansion for a neutral plasma N n( r, t) = Exp [ r 2 / 2σ 2 ( t)] 3 / 2 π σ 3 ( t) ( 2 ) σ σ σ

26 Self-Similar Similar Gaussian Expansion cross-section section Laha et al., PRL 2007

27 Limits of the Validity of the Exact Solution for the Expansion with T. Pohl ion expansion energy initial electron energy collisionless, exact solution colder and denser electrons

28 Plasma Ion Absorption Spectrum Imaging Camera Absorption (arbitrary units) Vary frequency of imaging laser beam

29 spectral linewidth measures the ion velocity and temperature Doppler Broadening σ D v 2 z T i ẑ typical velocity along laser direction cold hot

30 Rapid Heating of the Ions hot Ion Kinetic Energy(K) Disorder-induced heating cold potential energy position time

31 Rapid Heating of the Ions k T Coulomb = 2 e 4πε B 0 a τ ε m ω ne 0 i 1 = 2 pi time position Ion Temperature Kinetic Energy(K) potential energy

32 Strongly Coupled? Ion Ion Kinetic Temperature Energy(K) Γ ion 2.5 Disorder-induced heating 2 Γ = e / k T > 1 4 π ε a 0 B

33 Disorder-Induced Heating=Strong Coupling hot cold position time Ion Temperature Kinetic Energy(K) potential energy

34 Strongly Coupled Plasmas Γ 2 = e / k T > 1 4 π ε a 0 B Jupiter interior Wigner crystals of trapped ions (NIST, Boulder) Ions in an Ultracold Neutral Plasmas Dusty plasma crystals (Taiwan)

35 Kinetic Energy Oscillations: Heavily Damped Ion Plasma Oscillation Ion Kinetic Energy(K) ω pi = potential energy 2 ne m ε i 0 electrostatic kinetic electrostatic time position position

36 Equilibration and Oscillations in Other Systems Fast pulse irradiation of solid targets Inertial confinement fusion experiments Fast pulse ionization of clusters

37 We are interested in the long-time ion dynamics: Global Equilibrium, heat transport Ion adiabatic cooling Stronger ion Coulomb coupling k T 2 e 4πε a B i 0 higher density means higher equilibrium temperature central, high density outer, low density initial electron energy Expansion Dominates Pohl, Pattard, and Rost, PRL 92, (2004)

38 Fluorescence Imaging Separates Expansion from Thermal Motion 422 nm laser 1 mm z plasma y imaging optics

39 Ion Temperature at Later Times Observed temperature, excess heating Adiabtic cooling Disorderinduced heating Expected from electron-ion thermalization and adiabatic cooling

40 Anomalous Heating Rate Heating rate: Weak or no density dependence Linear with T e

41 Conclusions Ultracold neutral plasmas New regime Great experimental control and diagnostics Strong coupling - ion equilibration, screening, kinetic energy oscillations Dynamics of the expansion, recombination, electron oscillations Future plans Spatially resolve collective modes, shock waves Strongly coupled electrons and ions Thermal transport in strongly coupled systems Magnetic confinement, laser-cooling ions

42 Graduate Students Post Docs Clayton Simien Sarah Nagel Sampad Laha Priya Gupta Aaron Saenz Pascal Mickelson Y. Natalie Martinez Jose Castro Mi Yan V.S. Ashoka Ying Cheng Chen Hong Gao Undergrads Olen Rambow Yara Mejia Temple Keller Ian Stevenson Josh Dorr Meaghan Paceley Andrew Traverso Kris Zarling Aaron Dunn Adityah Sashi