Modeling Auger processes DUE to high Intensity, ultrafast x-ray pulses SULI Program Modeling Auger processes DUE to high Intensity, ultrafast x-ray pulses drhgfdjhngngfmhgmghmghjmghfmf Ray sullivan Undergraduate Intern Under supervision of Antonio Picón Argonne National Lab, Lemont IL

Outline Introduction and Background Information What is an ultrafast x-ray source? What are Auger processes? Theoretical Model Time dependence Ansatz Auger spectrum Simulation Results Pulse Length effects Intensity effects Conclusion

Introduction & Background Information

Ultrafast x-ray Sources Synchrotron x-ray sources, such as the Advanced Photon Source at Argonne National Laboratory, produce x-rays with 100ps pulse length, which are suitable for time- resolved experiments such as chemical dynamics in solution. Free-electron lasers, such as LCLS at SLAC, produce x- rays with 10fs pulse length, which allows the extension of time-resolved experiments to the femtosecond timescale, and then study fundamental electron relaxation processes.

Auger Processes When an x-ray interacts with an atom or molecule, it excites one of the core shell electrons into continuum or valence orbitals. This leaves a vacancy in the core shell. A higher shell electron falls into the vacant lower-energy state, releasing energy. Energy is released either as a photon (fluorescence) or as an electron (Auger electron). The Auger electron can be excited to a valence orbital (Resonant Auger) or to the continuum (Normal Auger)

Auger Process Diagram of the Auger Process  Vakgroep META  Vrije Universiteit Brussel

Auger Processes Diagram of Coincidence Measurement

What we did Want to create a time-dependent code that describes both the x-ray excitation and the Auger processes. This code currently allows us to explore normal Auger processes in a neon atom. We have observed effects on the Auger spectrum as a result of excitation by ultrashort x-ray pulses. Pulse duration effects Intensity effects

THEORETICAL MODEL

Time-dependent model Introduction With the program we are able to describe the first step, ionization, and the second step, Auger decay. We are able to track all the Auger pathways. The plot is the Auger spectrum for neon when the 1s orbital has been ionized.

Time-dependent model b0 is the ground state bεεa;ij is the final state Ansatz Wavefunction for the system Hartree-Fock ground state One electron and two electron excitations: b0 is the ground state bε;i is the core-excited state bεεa;ij is the final state

Time-dependent model Schrödinger Equation Schrodinger equation for this system is By including the ansatz into the Schrödinger equation, we derive the following equations of motion

Time-dependent model Auger Spectrum Two-electron (photoelectron and Auger electron) coincidence is given by By assuming that the pulse length for the square x-ray pulse is T, the amplitude of the final state can be written as First two terms are the coupling of the ground, core-hole and final states Third term is a Sinc function, relating to the bandwidth of the pulse Fourth term is Lorentzian, related to decay of core-hole state

Time-dependent model Auger Spectrum By plotting We obtain the Auger spectrum. We are only looking at the first peak (781 – 792.96 eV). Select for a specific photoelectron energy for the coincidence measurement. Plot the integral of over the boundaries of the photoelectron spectrum to simulate the total auger spectrum measurement.

Computer Simulation

Computer simulation Program Information Antonio’s program is a numerical solution of the equations of motion mentioned earlier. Instead of an idealized square pulse, which was used for preliminary calculations, the program uses a Gaussian pulse shape.

Computer simulation Background Used the LCRC (Laboratory Computing Resource Center) to run our program, using the Blues cluster. ~350 public nodes 64 GB (Intel Sandy Bridge) of memory on each node 16 cores (Intel Sandy Bridge) per compute node Over 6,000 compute cores available Had to compile the program to a much newer computer, so we had to spend a substantial amount of time troubleshooting the code and making sure it was working properly. The ALCF (Argonne Leadership Computing Facility) group that we worked with parallelized the code so that we could utilize all 16 processors on a node. Once the code worked properly, the program ran much quicker, and we were able to collect almost all of our data within a week.

Computer simulation Pulse length effects Computer simulation data for the pulse length effects. Intensity of the pulse is 1015 W/cm2. A visible broadening is observed due to bandwidth effects.

Computer simulation Intensity effects This is the Auger spectrum for increasing intensities. The more intense pulse results in a broader spectrum.

Conclusion

Conclusion We discovered that the length of the pulse, and the intensity of the pulse, affect the lifetime of the core-hole state of the Auger process. It took a long time, but we discovered that this is due to a bandwidth effect. These are preliminary predictions for next-generation x-ray sources, as we currently cannot produce x-ray pulses of .1fs.

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Appendix: Square Pulse results

Analytical Solution Pulse duration effects – photoelectron-coincidence Auger spectrum This is a plot of the Auger spectrum for .1,1,10 and 100 fs pulses with an intensity of 1015 W/cm2. A noticeable bandwidth effect is visible, the spectrum broadens as the pulse length decreases.

Analytical Solution Pulse duration effects – total Auger spectrum This is a plot of the Auger spectrum for .1,1,10 and 100 fs pulses with an intensity of 1015 W/cm2. The four Auger spectra show complete overlap, and show no dependence on pulse length. The bandwidth information evidently is lost when taken over whole photoelectron spectrum

Analytical Solution Intensity effects – photoelectron-coincidence Auger spectrum This is the photoelectron-coincidence Auger spectra. The pulse length is 10fs. There is a visible broadening in the tail of the spectra for the 1020 W/cm2 pulse. The spectra exhibit a dependence on the intensity of the x-ray pulse.

Analytical Solution Intensity effects – total Auger spectrum The total Auger spectrum for 10fs pulses with different intensities. The two spectra overlap, and exhibit no dependence on the pulse intensity.

Total Auger vs. Coincidence measurement We can see from the graph, how the sum of the coincidence measurements produces the total Auger spectrum. This is why the lineshape information is lost during the total measurement.