Tight-Focusing of Short Intense Laser Beams in Particle-in-Cell Simulations of Laser-Plasma Interaction

Transcription

1 28/03/2017, CTU in Prague Tight-Focusing of Short Intense Laser Beams in Particle-in-Cell Simulations of Laser-Plasma Interaction Bc. Petr Valenta Supervisors: doc. Ing. Ondrej Klimo, Ph.D. Dr. Stefan Andreas Weber Date: Page:

2 Content: 1) Goals & guidelines 2) Motivation 3) Particle-in-cell method 4) Paraxial approximation 5) Maxwell consistent approach 6) Implementation 7) Evaluation 8) Results 9) Conclusion 10) References Date: Page: 2

3 1) Goals & guidelines: Date: Page: 3

4 2) Motivation: High laser intensities required for exploring of specific themes of the ultra-relativistic regime of laser-matter interaction Laser intensity depends on energy, duration and size of focus of laser pulse Strong nonlinearities of the basic equations governing laser-plasma interaction - numerical simulation codes have become an indispensable tool (accompanying the experiments for analysis and interpretation) In order to simulate tightly-focused pulses, laser fields at boundaries have to be consistent with Maxwell equations Source: [1] Date: Page: 4

5 3) Particle-in-cell method: Date: Page: 5

6 Main computational cycle of particle-in-cell method: 1) Integrate the equations of motion (usually Leap-Frog scheme) 2) Particle weighting (interpolate charge and current densities to grid) 3) Solve the field equations (FDTD solver on staggered grid) 4) Field weighting (interpolate fields to particle positions) 3) Particle-in-cell method: Date: Page: 6

7 3) Particle-in-cell method: Code EPOCH (Extendable PIC Open Collaboration project) [2]: multi-dimensional, relativistic, electromagnetic PIC code for plasma physics simulations Explicit, 2 nd order of accuracy written in FORTRAN and parallelized using MPI, dynamic load balancing FDTD field solver (using H. Ruhl scheme [3]) Relativistic particle pusher (Birdsall & Landon type [4], Villasenor & Buneman current weighting [5]) Instrumented to enable in situ visualization of the EM fields using ParaView Catalyst Date: Page: 7

8 4) Paraxial approximation: Date: Page: 8

9 4) Paraxial approximation: Date: Page: 9

10 5) Maxwell consistent approach: Several solutions to overcome drawbacks of paraxial approximation already proposed: 1) higher order approximations for Gaussian beams (complicated, not easy to implement, explicit analytical does not have to exist for other beam types) 2) Focusing geometry with perfectly reflecting mirrors to introduce tightly focused beam into the simulation domain (restricted to specific shapes) 3) Direct evaluation of Stratton-Chu integrals (computationally expensive) 4) Simple and efficient algorithm for a Maxwell consistent calculation of the EM fields at the boundaries of the simulation domain - Laser Boundary Conditions (LBC) Algorithm can describe any kind of laser pulses, in particular tightly focused, arbitrarily shaped and polarized ones - the solution of the Maxwell s equations is performed in a frequency space Calculations adapted from the work of I. Thiele et al. from CELIA, Bordeaux (2016) [6] Date: Page: 10

11 5) Maxwell consistent approach: Date: Page: 11

12 5) Maxwell consistent approach: Date: Page: 12

13 6) Implementation: 2D version, written in C++, object oriented to be easily extended to 3D Linked into EPOCH as a static library (in order not to disturb the code, added support for CMake) Parallelized using hybrid techniques (OpenMP + MPI computation time in most cases negligible in comparison with the main simulation) Fourier transforms can be computed using Intel MKL library, FFTW library or without any library (compile-time option) Computed fields dumped into shared files using binary coding (speed up output, save disk storage) Only transverse component of electric field (Ex) passed to the EPOCH at each time step (no significant slowdown or memory overhead), other fields computed by EPOCH All new parameters needed for tight-focusing (w0, focus distance, etc.) may be specified via input file, implementation works generally regardless the number of lasers in the simulation or boundaries that they are attached to Date: Page: 13

14 Test simulation parameters: 7) Evaluation: Date: Page: 14

15 7) Evaluation: Transverse (Ey) and longitudinal (Ex) electric laser fields at focus in the case of paraxial approx. (a), (b) and Maxwell consistent approach (c), (d) In the case of paraxial approx. Ex, Ey reveal strong distortions and asymmetry w.r.t focus, the corresponding amplitude significantly lower Date: Page: 15

16 7) Evaluation: Transverse and longitudinal slices of the transverse electric laser field (Ey) at focus in the case of paraxial approx. (a), (b) and Maxwell consistent approach (c), (d) In the case of paraxial approx. strong side-wings in the beam profile (a), asymmetry of the field in the longitudinal line-out (b) Date: Page: 16

17 7) Evaluation: Time evolution of transverse (Ey) (a) and longitudinal (Ex) (b) electric laser field at the boundary according to the Maxwell consistent approach Evaluation of the beam symmetry - transverse (a) and longitudinal (b) slice of the transverse electric laser field (Ey) at the front (blue) and rear (red) boundary Date: Page: 17

18 7) Evaluation: Transverse (a) and longitudinal (b) slice of the transverse (Ey) electric field at focus according to paraxial (red) and Maxwell consistent (blue) approach for the beam with focus size one order of magnitude larger than the laser wavelength (a) Spot size parameter according to Maxwell consistent approach. (b) Transverse (Ey) electric field amplitude w.r.t. distance from focus. Date: Page: 18

19 8) Simulations of tightly focused beams: Several smaller test simulations of laser-matter interaction to identify the effects of tight-focusing Studied influence of the laser focal spot size in terms of laser energy absorption efficiency in plasma Domain: size 15 x 40 μm with N x = 1875 (δx = 10 nm), N y = 5000 (δy = 10 nm), T = 200 fs (δt = 0.01 fs) Plasma: Solid target made of e -, H + with thickness = 2.0 μm, density = 100 critical laser density, 2000 electrons per cell, 100 ions per cell Laser: λ = 0.8 μm, T = 30 fs (in FWHM), w 0 = 0.5, 1.0, 2.0, 4.0 μm, simulations with const. intensity (1e20 W/cm 2 ) or const. energy (2.84e4 J), p-polarization, focal spot 8 μm from left boundary 1) E = const. (E = 2.84e4 J) w 0 = 0.5 μm: absorption = % w 0 = 1.0 μm: absorption = % w 0 = 2.0 μm: absorption = 8.31 % w 0 = 4.0 μm: absorption = 6.19 % 2) I = const. (I = 1e20 W/cm 2 ) w 0 = 0.5 μm: absorption = % w 0 = 1.0 μm: absorption = % w 0 = 2.0 μm: absorption = % w 0 = 4.0 μm: absorption = % Date: Page: 19

20 8) Simulations of tightly focused beams: x vs. px of electrons dependency for w0 = 0.5 μm (a) and w0 = 2.0 μm (b) in the case of laser intensity I = 1e20 W/cm 2 and time t = 100 fs px vs. py of electrons dependency for w0 = 0.5 μm (a) and w0 = 2.0 μm (b) in the case of laser intensity I = 1e20 W/cm 2 and time t = 100 fs Date: Page: 20

21 8) Simulations of tightly focused beams: Distribution function of angle between electron px and py splited in three energetic intervals for w0 = 0.5 μm (a) and w0 = 2.0 μm (b) in the case of laser intensity I = 1e20 W/cm 2 and time t = 100 fs (a) Distribution function of electrons at time t = 100 fs. (b) Distribution function of protons at time t = 200 fs in the case of laser intensity 1e20 W/cm 2 Date: Page: 21

22 8) Simulations of tightly focused beams: Contour of critical proton density in the case of laser intensity 1e20 W/cm 2 (a) and 1e21 W/cm 2 (b) at the time t = 100 fs. Light pressure bores a hole of specific shape Electron trajectories from the source localized at focus (0.1 x 0.1 μm) in case of w0 = 0.5 μm (a) and w0 = 2.0 μm (b). Laser intensity is 1e21 W/cm 2 in both cases, captured time 6 fs (t = fs) Date: Page: 22

23 9) Conclusion: Propagation of tightly focused laser pulses cannot be described by paraxial approximation For the beams focused to a spot with the size comparable to a center laser wavelength, paraxial approximation leads to: 1) Shifted location of the focus 2) Asymmetric laser field profiles with distortions 3) Lower field amplitude These deviations are far from negligible and have strong impact on the lasermatter interaction results Propagation of tightly focused Gaussian laser beams prescribed at boundaries according to the Maxwell consistent approach proven to be correct Tight-focusing seems to have large influence on the laser energy absorption efficiency Date: Page: 23

24 10) References: [1] P. Gibbon, Short Pulse Laser Interactions with Matter, Imperial College Press, 2005 [2] T. D. Arber et al. Contemporary particle-in-cell approach to laser-plasma modelling. Plasma Physics and Controlled Fusion, 57(11):113001, [3] H. Ruhl et al. The plasma simulation code: A modern particle-in-cell code with load-balancing and GPU support [4] C. K. Birdsall, A. B. Langdon. Plasma Physics via Computer Simulation. Series in Plasma Physics. CRC Press, [5] J. Villasenor, O. Buneman. Rigorous charge conservation for local electromagnetic field solvers. Computer Physics Communications, 69(2-3), [6] I. Thiele, S. Skupin, R. Nuter. Boundary conditions for arbitrarily shaped and tightly focused laser pulses in electromagnetic codes. J. Comp. Phys. 321, 1110, 2016 Date: Page: 24

25 Thank you for your attention Date: Page: