COST Meeting Krakow May 2010 Temperature and Ka-Yield

COST Meeting Krakow May 2010 Temperature and Ka-Yield radial distributions of laser-produced solid-density plasmas Ulf Zastrau X-ray Optics Group - IOQ - Friedrich-Schiller-University Jena

Contents • Physics of “Warm Dense Matter“ (WDM) • WDM generated by relativistic electrons using High-Intensity Lasers • Summary Ulf Zastrau 1

Warm Dense Matter Condensed Matter <> Warm Dense Matter <> Ideal Plasma Etherm ~ EFermi High Electron Density: 1. . 100 e. V Access of plasma parameters only possible by short wavelength radiation (w > w. P) r. WDM ≈ rsolid penetration up to critical density nc = w²e 0 m/e² strong coupling G ≥ 1 Ecoulomb ~ Etherm after R. W. Lee Ulf Zastrau 2

Spectroscopy of Solid Density Plasmas by X-ray Photons Absorption length of l=0. 27 nm in Titanium (Z=22) : ~ 20 µm in laboratory always transient micro-plasmas with strong gradients spectroscopy with high spatial and temporal resolutions Ulf Zastrau 3

Contents • Physics of “Warm Dense Matter“ (WDM) • WDM generated by relativistic electrons using High-Intensity Lasers • Summary Ulf Zastrau 4

Relevance of Laser-produced Plasmas Fundamental Parameter: Brightness number of X-ray photons time [s] emitting size [mm²] divergence [mrad²] spectral bandwidth [%] ü time-resolved X-ray diffraction ü point-source for radiography ü backlighter for Thomson scattering ü electron and ion acceleration (TNSA) ü laser-fusion and the „Fast Ignitor“-scheme © Wilks Ulf Zastrau 5

Physics of IR-Laser-Target Interaction Ponderomototive Potential Thot ~ fpond ~ √Il² 1019 W/cm² IR-laser pulse creates fast electrons with energies up to Me. V heat the cold target by collisions Ti Ka ne High Density & Fields, refluxing, filamentation, … Hybrid PIC-fluid model: Evans et al. , HEDP 2 (2006) electrons with E > 5 ke. V in Titanium are capable of K-shell ionization we observe Ka-emission from the heated target Ulf Zastrau 6

Experiment at 100 TW Laser, LULI 100 TW Laser standard operation (w) and frequency doubling (2 w) to obtain higher prepulse contrast Ti: Sa + Nd: Glas LASER 11° 1057 nm central wavelength 330 fs pulse duration max. 13 J energy in focus 8 µm focal diameter Intensity ~ 5· 1019 W/cm² X-ray Spectrometer X-ray film x’ toroidal bent Ga. As crystal a=50° y Ti-Ka 2 p-1 s d y r x z Titanium Foil different titanium samples: massive (bulk) and foils of 25, 10 und 5µm U. Zastrau et al. , PRE 81 (2010), 026406 1 -4 Ulf Zastrau 7

2 D inverse Abel transformation 5· 1019 W/cm² - single pulse spectra y r lateral Spectrum (y) assuming cylindrical symmetry radial Spectrum (r) 10µm Ti foil, 45° obvervation r = y = spatial resolution: 13. 5µm Ulf Zastrau 8

Radial Temperature Distribution 10 µm foil transition from cold to warm Titanium plasma: blue-shift due to thermal M-shell ionization Model: Laser µm-Foil bulk Theoretical line shape models: Stambulchik, . . , Zastrau, et al. , J. Phys. A 42 (2009), 214061 1 -5 Sengebusch, . . , Zastrau, et al. , J. Phys. A 42 (2009), 214056 1 -10 U. Zastrau et al. , PRE 81 (2010), 026406 1 -4 Ulf Zastrau 9

Global Parameter: Ka-Yield and Refluxing Ee > 100 ke. V e- leave the foil Ee < 100 ke. V e- stays in foil, mean free path ~ 20µm strong electric field ~ Me. V/µm hinders slow electrons to escape from the foil. Fit-Parameter: Ee < 100 ke. V Ulf Zastrau 10

Spatially integrated spectra Spectrum of a simple, spatially integrating spectrograph yields 3 x lower temperature ! Ulf Zastrau 11

Summary -LP Titan-Plasmas: radial Distribution of the Plasma Temperature with Dr = 13. 5 µm - Toroidally bent crystal X-ray spectrometer - Single-pulse spectra - 2 D Abel-inversion - Homogeneously heated central region at k. BT = 30 e. V - up to 10 x the laser focal diameter in size - spatially integrated spectra show a 3 x lower plasma temperature Ulf Zastrau 12

Thanks to international Collaborations High Energy Density Physics – Peak-Brightness Collaboration • AG Röntgenoptik, IOQ, Universität Jena E. Förster, S. Höfer, T. Kämpfer, R. Loetzsch, I. Uschmann, O. Wehrhan, colleagues, workshop • Universität Rostock G. Röpke, A. Sengebusch, Thanks to DFG • Weizmann Institute of Science, Israel I. Maron, E. Kroupp, E. Stambulchik • LULI, Ecole Polytechnique, Palaiseau, France P. Audebert, E. Brambrink Ulf Zastrau 13

Thank you for your attention. Ulf Zastrau 14

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High Resolution X-ray Spectroscopy Ulf Zastrau 16

Blueshift of Ka lines <> M-shell ionization ion-temperaturesensitive! Ka 1 & K a 2 start of significant L-shell ionization ~100 e. V Ulf Zastrau 17

Modeling of Ti Ka radiation results by E. Stambulchik et al. , Weizmann Institute In bulk titanium, delocalized quasi-free electrons have to be taken into account. A low-temperature-limit charge-state is Ti V (four-times ionised, Ti 4+). The Ka emission duration is ≤ 1 ps ( Ti = Te is assumed) Ulf Zastrau 18

Hansen et al. Accurycy of the method: COMET laser, LLNL, Kalifornien 1057 nm, 3 -6 J, 500 fs, 1019 W/cm² Hansen et al. , PRE 72, 036408 (2005) Ulf Zastrau 19

Electron Cross Sections Ulf Zastrau 20