Laser Plasma Section

Simulation activity at Ti:Sapphire Laser Laboratory

Laser-plasma Simulations Simulation is an indispensable tool in designing experiments and understanding the experimental results. PIC simulation requires expertise in formulating simulation parameters and post-processing the results, along with huge computational resources. Over last few years, we have gained some expertise in this field. We have been carrying out 2D and 3D particle-in-cell (PIC) simulations relevant to the experimental parameters at RRCAT for laser-plasma based electron acceleration from gas-jet plasma. In addition to this simulations on high energy proton acceleration from foil targets are also carried out. We use hydrodynamic code medusa and radiation hydrodynamic code MULTI to study the time and space evolution of plasma density, material density and electron-ion temperature for long-pulse as well as short-pulse laser plasma interactions. The simulation group is actively involved in the simulation studies related to:

  • Electron acceleration in SMLWFA & Bubble and other novel regimes
  • Proton / ion acceleration in RPA & TNSA and other novel regimes
  • THz generation from two colour lasers
  • Hydrodynamics of plasma in nanosecond, picosecond and femtosecond regime, and hot electron transport.
The codes used for these simulations are:

PIC Codes:
  • VORPAL-3D (Tech-X Corp., 256 core) installed on Kshitij-3 HPC cluster
  • VLPL-3D (Prof. Pukhov, unlimited node) installed on Kshitij-4 HPC cluster
  • EPOCH-3D (unlimited node) installed on Kshitij-4 HPC cluster
  • FISCOF-1, 2D (Prof. Sakagami) installed on LPL workstation
  • PICCANTE-3D (unlimited node) installed on Uday HPC cluster
Hydrodynamic / Fluid Codes:
  • Multi – 2D: installed on LPL workstation
  • BOPS : installed on LPL workstation
  • MEDUSA 103 : installed on LPL workstation
For more details contact Dr. Ajit Upadhyay (ajitup@rrcat.gov.in)



Simulation of Electron Acceleration

The commercially available PIC code VORPAL and PIC code of Prof. Alexander Pukhov “Virtual Laser Plasma Laboratory (VLPL)” are installed on our 768 core (8 TFlops/Sec) computing cluster Kshitij-3. The 256 cores of Kshitij-3 was used to carry out 2D simulations using the code VORPAL and 3D simulations using the code VLPL respectively for the parameters reported below. The choice of laser and plasma parameters is based on our experiments demonstrating high quality mono-energetic electron acceleration. The choice of grid parameters has been done keeping in mind the computational hardware limitation, however grid spacing are sufficient enough to resolve the laser wavelength, plasma wavelength and spatial dimensions of interest.

For VORPAL simulation in 2D, a pre-formed plasma of density 6x1019cm-3 interacts with a Gaussian laser pulse of a0 ~ 1.65 (ILL~9μm, τL ~45fsec). The plasma has a linear ramp of length 100μm followed by 540μm long uniform density plasma of ne~6x1019cm-3. The laser pulse enters from the left boundary of the 2D rectangular moving window simulation box of 30x70μm2. The grid spacing is kept at λL/36 in the longitudinal direction and λL/6 in the transverse direction, and each cell contains 9 particles. The time step is deduced from Courant condition. For 3D simulations using VLPL, the laser and plasma parameters are kept same, the only difference is that the uniform density plasma column is 1 mm long in the case of VLPL simulations. Here also, the laser pulse enters from left boundary in the 3D simulation box of size 48x48x80μm3 which moves with the laser pulse. The grid spacing is λL/20 in longitudinal direction and λL/5 in transverse directions, the time step is < λL/20c which satisfies the Courant condition, and each cell contains 12 particles.

The 2D simulations shows that the laser pulse undergoes strong self-modulation and breaks into small pulses in longitudinal as well as transverse direction, and several cavity like structures are formed in longitudinal and transverse directions that evolve in due course as shown in fig. 1. After a travel of ~410 μm, the right-most axial fragment of laser pulse causes a cavity like structure which grows and forms a clear bubble, and one observes injection of electrons at a distance of 420 μm. This bubble like structure is sustained till the pulse travels to 460 μm, after which the structure breaks down (fig.1). The longitudinal electric field inside the cavity for the distance from 420μm to 460μm is in the range of 1MV/μm (fig.2), and trapped electrons are expected to have energy up to 40 MeV.

Fig.1  The electron density snapshots at 4884, 20350, 21164, 22792 time-steps.
Fig.1 The electron density snapshots at 4884, 20350, 21164, 22792 time-steps.


Fig.2  The longitudinal electric field snapshots at 20350 (410μm), 21164 (430μm), 22792 (460μm) time-steps.
Fig.2 The longitudinal electric field snapshots at 20350 (410μm), 21164 (430μm), 22792 (460μm) time-steps.

The results of 3D simulation using the code VLPL corroborate the results of 2D simulations of VORPAL. Here also we observe fragmentation of laser pulse in longitudinal and transverse dimension leading to multiple cavity like structures in the initial phase of simulation. The electron density snap-shots (fig. 3) show that a stable cavity starts developing at a distance of 390μm. This is due to a small axial fragment of laser pulse of size ~ 4μm diameter (base to base width of ~ 10 femtosecond) being stably guided from ~330μm to ~470μm.

Fig.3  Snapshot of plasma density and laser pulse intensity at 50, 200, 450, 480 time-steps
Fig.3 Snapshot of plasma density and laser pulse intensity at 50, 200, 450, 480 time-steps

From electron density snapshots, we observe that the electron injection starts at ~435μm (time-step 457) and closes at 440μm (time-step 472) and these self-injected electrons get accelerated till 470μm (time-step 500) beyond which the bubble structure starts breaking. The typical field inside the bubble is of the order of 1MV/μm (fig.4).

Fig.4  Longitudinal electric field at 450 time-step
Fig.4 Longitudinal electric field at 450 time-step

The electron energy spectrum is shown in fig. 5. We observe that as soon as the electrons are injected inside the cavity a small peak starts forming (time-step 460) whose energy grows to form a clear mono-energetic peak at 29MeV (step 480) and subsequently to 32 MeV with almost a flat top.

Fig.5  Electron energy spectrum at time-steps 460 – 500.
Fig.5 Electron energy spectrum at time-steps 460 – 500.

The energy spread in both the cases is ±3MeV. At later time steps multiple injection starts taking place and also the bubble structure breaks down leading to loss of mono-energetic feature beyond 500 time-steps.

Proton acceleration for CH foil in radiation pressure acceleration (RPA) regime, using 3D VLPL code:

  • Initially a pure hydrogen foil (500nc density, where nc is critical density of plasma) was taken and it was observed that R-T instability at later times of RPA acceleration disrupts radiation pressure interface thereby resulting in poor monoenergetic spectrum of protons.
  • Subsequently, a C-H foil (two layered) of 5 micron thickness (320nc density, where nc is critical density of plasma). The insertion of C layer between hydrogen and the laser pulse helps in controlling the R-T instability of the thin hydrogen layer, leading to
  • Laser intensity : 1023 W/cm2 (a0 = 100), Pulse duration : 25 fs
Quasi-mono-energetic protons at 200 MeV with a maximum energy of protons extended up to 800 MeV was observed in the simulation.

The proton energy spectra at different times for a thin hydrogen target.
The proton energy spectra at different times for a thin hydrogen target.


Proton Acceleration via Target Normal Sheath Acceleration (TNSA)

  • Simulations were carried out using 2D & 3D PIC code EPOCH for proton acceleration from 6.5m thin Aluminium Foil using 10 TW Ti:Sapphire Laser System.
  • Snapshot of laser intensity, electron density, proton density and proton energy spectrum evolution is shown below

Exotic Targets:

  • 3D – PIC simulation of Carbon Nanotubes, Nano-holes and nano-spheres using VLPL
  • 2D & 3D PIC simulation (using EPOCH) of structured target like 10nm diameter Gold nanoparticles embedded in 30 nm thick Carbon layer deposited on a Silicon sheet.

Hydrodynamic Simulation: Role of target material in proton acceleration from thin foils irradiated by ultra-short laser pulses

Using the one dimensional hydrodynamic code MULTI-1D, we have studied the propagation of the shock wave caused by the ASE pre-pulse inside the foil. A 1.5 ns duration ASE pre-pulse with temporal shape exactly matching with the experimentally measured value of our 10TW laser and having a peak intensity of 2×1012 W/cm2 (obtained from the measured contrast of the laser pulse) was used in the simulation. Fig. 1 shows the density profiles at the end of the pre-pulse for Al foils of different thickness. The “+” mark on each curve shows the initial position of the rear surface of foil. Wherever the rear surface survives (either in solid or a solid-liquid mixed phase) after the pre-pulse, the same has been shown in figure with a dotted vertical line. In some cases, the rear surface seems to have shifted during the laser pre-pulse, which is due to conservation of total mass, as the foil has melted and expanded in 1D code. The dash-dot horizontal line shows the density of solid Al (2.7 g/cm2). As seen from this figure, for 1.5 μm and 1 μm Al foil, the whole foil gets vaporized and no rear surface exists. For the 2 μm thick foil, a small region with gas-vapour mixture occurs inside the rear surface. It is clear that for the foil thicknesses < 2.5 μm, the rear surface of the foil evaporates (note the overall reduction in density as compared to pristine density 2.72 gcm-3). As the thickness is increased, till 6 μm, the rear surface appears to survive. However, for higher foil thicknesses >6 μm, the rear surface is not perturbed. Thus, for thicknesses less than 6 μm, the proton energy/flux decreases due to pre-plasma formation on the rear side of the foil. For higher thicknesses, the absorption of the hot electrons within the foil increases and the proton flux decreases. Therefore, the Al foil of 6.5 μm comes out as an optimal foil thickness for efficient acceleration of ions, as is observed in experiments.

FIG. 1: 1-D hydrodynamic simulation of the electron density evolution in the foil and the shock wave caused by a 1.5 ns ASE pre-pulse with intensity 2 x 1012 W/cm2, for Al foils of different thicknesses.
FIG. 1: 1-D hydrodynamic simulation of the electron density evolution in the foil and the shock wave caused by a 1.5 ns ASE pre-pulse with intensity 2 x 1012 W/cm2, for Al foils of different thicknesses.

The role of laser pre-pulse is expected to be different for different target material as the shock pressure and the shock velocity strongly depend on target atomic number and density. Therefore, in order to mitigate the effect of laser pre-pulse, a Ni foil was used. Figure 2 shows the one dimensional hydrodynamic simulation of density evolution and the shock wave caused by a 1.5 ns ASE pre-pulse with intensity 2x1012 W/cm2 for Ni foils of different thicknesses. We can see that for foil thicknesses below 0.5 µm, the foil is compleatly destroyed and no rear surafce exists. One may note the overall reduction in the density, as compared to the pristine density of 8.91 gm/cm3). For 1 µm foil, the shock wave just reaches the rear surface causing slight vaporization, whereas the 2 µm foil rear surface looks intact, unaffected by the laser pre-pulse. Therefore, for Ni target, 1-2 µm seems to be optimum thickness.

FIG. 2: One dimensional hydrodynamic simulation of density evolution and the shock wave caused by a 1.5 ns ASE pre-pulse with intensity 2x1012 W/cm2, for Ni foils of different thicknesses
FIG. 2: One dimensional hydrodynamic simulation of density evolution and the shock wave caused by a 1.5 ns ASE pre-pulse with intensity 2x1012 W/cm2, for Ni foils of different thicknesses









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