Recombination in laser-heated molecular clusters Pierfrancesco Di Cintio 1,* , Ulf Saalmann 1 & Jan-Michael Rost 1 1:MPIPKS N¨othnitzer Straße 38, D-01187, Dresden Germany; *:pdicint@pks.mpg.de Short and intense X-ray pulses enhance unconventional dynamics in both atomic and molecular clusters. Multiple single photon K-shell ionization in species such as Carbon or Oxygen and fast Auger decay release several electrons within a few femtoseconds. • Species segregation in heterogeneous clusters [1]. • Surprisingly in experiments at LCLS [2] and [5] on methane clusters, no or small carbon signal in ions spectrum, albeit carbon being the main photon absorber → ultra-fast recombination. • Molecular clusters are suitable prototypes for imaging of biological samples with XFEL pulses. We study numerically the interaction of clusters of hydrogenated molecules such as CH 4 and H 2 O with short (10 fs) and intense X-ray lasers pulses (I ∼ 10 17 - 10 20 W/cm 2 ) with an hybrid quantum- classical model [3], [4]. Photoionization and Auger decay are modeled with rate equations and Monte Carlo samplings and the charged particles are propagated with simple ab initio molecular dynamics. Photionization and Auger decay • Cross-sections for K-shell photoionization σ 1s are given in the limit of high photon energy (ω = 1keV) by σ 1s = 256π 3 αZ -2  |E 1s | ω  7/2 a 2 0 • Probabilities p for photoionization asa function of the laser inten- sity I in a timestep Δt are computed via p 1s = I σ 1s Δt ω and then used in the Monte Carlo procedure. K-shell L-shell photoelectron X-ray photon • We derive the probability for Auger decay from the average lifetime τ of the K-shell holes and the electronic structure of the ion with Γ= n e (n e - 1) n(n - 1) τ -1 ; p = ΓΔt. K-shell L-shell Auger e - refilled hole • Since we consider finite systems (clusters), the number of pro- duced photoelectrons saturates with intensity in both atomic and molecular clusters. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 10 17 10 18 10 19 10 20 absorbed photons per carbon I 0 [W/cm 2 ] C 689 (CH 4 ) 689 Dynamics • Faster free photoelectrons having absorbed 1 keV photons have typical kinetic energies around 700 eV then we are essentially in the classical regime. • Charged particles are evolved as integrating their classical equa- tions of motion with a simple direct N -body solver. • When a ionization takes place an electron is created and added to the simulation with the correct value of kinetic energy taking into account impulse and energy conservation. The model The dynamics of the explosion of atomic or molecular clusters heated by XFEL pulses is followed during the interaction with the laser (i.e. photoabsorption) and after the pulse is over for about half ps. The picture for atomic and molecular clusters is sensibly different. Principal phases of the dynamics • Photoionization and subsequent Auger decay of the holes produce a deep cluster potential (∼ r 2 inside and ∼ 1/r outside) Φ r r Harmonic core Coulomb tail released e - trapped e - electrons with energies inferior to the potential barrier are trapped to form a nanoplasma • The cluster undergoes Coulomb explosion, in methane or water clusters, protons are emitted faster than heavier ions. -2 -1 0 1 2 T = 0 fs t = 15 fs -2 -1 0 1 2 -2 -1 0 1 2 t = 350 fs -2 -1 0 1 2 t = 430 fs -0.2 0.8 1.8 2.8 0 1 2 3 v/v typ r/r 0 t = 430 fs -0.2 0 0.2 0.4 0 0.5 1 1.5 v/v typ t = 0 fs • The protons outflow in hydrogenated clusters lowers the collec- tive potential, hotter electron thermally evaporate. The left-over nanoplasma has a lower electron temperature. Evolution of the charge • In the first 15 fs the charge in the cluster reaches its maximum due to the combined effect of photoionization and Auger decay that have the roughly same time scale (pulse length 10 fs and τ ∼ 8 fs). 0 0.2 0.4 0.6 0.8 1 photon absorption XFEL pulse 0 0.2 0.4 0.6 0.8 1 charge ultra-fast neutralization! -20 0 20 40 60 80 time [fs] 0 1 2 3 radius carbon in (CH 4 ) 297 C 297 hydrogen in (CH 4 ) 297 • Due to the lower charge density the expansion of the cluster is slower in the molecular case than in the atomic case. • After the massive proton emission the charge in the core lowers dramatically leading to a lower electron temperature. Cluster in strong XFEL pulses Numerical simulations shower more efficient recombination in molec- ular clusters. This is in agreement with experimental findings. We argue that more efficient K-shell refilling via auger decay and lower electron temperature are the key. Ionization vs recombination • Smaller electron typical kinetic energy than in pristine atomic cluster 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 100 200 300 400 <K e > [eV] time [fs] C 297 (CH 4 ) 297 • The recombination rate dR/dt grows as the electron (pseudo)temperature stops increasing. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 dR/dt [fs -1 ] 0.01 0.1 1 dI/dt [fs -1 ] Photo-ionization Auger decay Field-ionization Cumulative 0 0.2 0.4 0.6 0.8 1 1.2 -20 0 20 40 60 80 <K e > [eV] time [fs] • After the pulse the ionization is only due to field ionization bal- anced by recombination, Boltzmann-Saha regime? n r +1 n e n r = G r +1 g e G r (2πm e kT e ) 2/3 h 3 exp  - ΔE (r +1,r ) kT e  Final charge states • More efficient recombination in both methane (left) and water (right) clusters with respect to carbon and oxygen atomic clusters 0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 5 6 n(Q)/N Q I 0 =10 17 W/cm 2 0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 5 6 n(Q)/N Q I 0 =10 17 W/cm 2 0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 5 6 n(Q)/N Q I 0 =10 18 W/cm 2 0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 5 6 n(Q)/N Q I 0 =10 18 W/cm 2 0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 5 6 n(Q)/N Q I 0 =10 19 W/cm 2 0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 5 6 n(Q)/N Q I 0 =10 19 W/cm 2 0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 5 6 7 8 n(Q)/N Q I 0 =10 17 W/cm 2 0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 5 6 7 8 n(Q)/N Q I 0 =10 17 W/cm 2 0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 5 6 7 8 n(Q)/N Q I 0 =10 18 W/cm 2 0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 5 6 7 8 n(Q)/N Q I 0 =10 18 W/cm 2 0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 5 6 7 8 n(Q)/N Q I 0 =10 19 W/cm 2 0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 5 6 7 8 n(Q)/N Q I 0 =10 19 W/cm 2 • Strong dependence on the pulse intensity • Good agreement with experimental results [2] • Similar mechanism in biomolecules containing hydrogen? Recombination [1] Popov K.I., Bychenkov V. Y., Rozmus W., Kovalev V.F. and Sydora R.D., 2009, Laser and Particle Beams 27, 321. [2] Kandadai N. et al., 2011, In preparation. [3] Di Cintio P.F. et al., 2011, in preparation. [4] Gnodtke C, Saalmann U., and Rost J.M., Phys. Rev. A 79, 041201, 2009. [5] T. Ditmire, M. Hohenberger, D. R. Symes, K. W. Madison, F. Buersgens, R. Hartke, J. Osterhoff, A. Henig, and A. Edens, in Super- strong Fields in Plasmas, Vol. 827 of AIPC Series, 2006, 109. References View publication stats View publication stats