This post covers work from 06/01 - 08/15. Recently, I have been working on the Titan Simulations and trying to understand how to simulate gold – a high-Z element in a way that makes sense. Due to its high density and atomic number, it is hard to keep track of every level of ionization and I would need a somewhat fine resolution grid. I made some minor updates to the data analysis code and some minor updates to the papers on overleaf.

Summary of Work During the Summer

1. I did some work on the synthetic data paper and submitted it to Contributions to Plasma Physics. I only made minor changes before submitting it.
2. I helped Jack work through revising the pre-pulse and pump-depletion model in his synthetic data paper. We have things mostly finished at this point, there are just a few things to sort out before we can start working on the paper.
3. At Wright-Patt, the PP angle issue was fixed. Now there is an accurate mapping between the voltage and angles. To alleviate the shots dropping issue, we decided to lower the acquisition rate to 10Hz. This also allows for a larger exposure time to better detect protons. Additionally, I found an error with my program that was merging data on the 2Hz rate of the WP which I’ve now fixed. We’ve had a 2 runs (06/14 and 08/02) that we’ve collected enough good electron signals, decent target stability, and done a full looping of parameters to now work on a paper.

Guide on OSC Cluster Resources

I’ve talked briefly about OSC before, but I’ll make a more in depth guide here. OSC has three different Clusters in order of increasing compute capability:

1. Owens
2. Pitzer
3. Ascend

Owens is the oldest cluster and will be discontinued at some point in the near future. In terms of CPU computing, it has 28 cores per node and a compute capability of 6.0. In terms of GPU computing, it has 1 Pascall P100 GPU of 16GB memory per node.

Pitzer has two different types of nodes: Skylake (2018) and Cascade Lake (2020). These have a compute capability of 7.0 and 2 Volta V100 GPUs per node. Skylake has 40 cores per node and 16GB memory per GPU while Cascade Lake has 48 cores/node and 32 GB memory per GPU.

Ascend is the newest cluster and has 88 CPU cores/node with a compute capability of 8.0. There are 4 Ampere A100 GPUs per node with 80GB memory each.

The cost breakdown can be seen in the following table:

Titan Simulations

Particle Probes

I decided to use the particle probe block in EPOCH. To make sure that I understood how it worked, I did a basic simulation which involved two populations of electron drifting rightward and leftward. Then, I put 4 probes in the simulation that account for both species of electron and both velocities that we can detect (east bound or west bound). Initially, I kept the left moving electrons on the right side of the grid

and the right moving electrons on the left side of the grid

I set up the simulation so that the particles drift with momentum 1e-23 which ends up being 1.098e7 m/s or 10 microns per picosecond. This is enough velocity to drift the whole length of the simulation over the full simulation time of 1 ps. From this exercise, I learned that when specifying velocity/momentum or getting the output of velocity/momentum, EPOCH returns the individual particle velocity/momenetum and not the macroparticle velocity/momentum. To obtain the quantities per macroparticle, you would have to multiply by the weight. Anyway, by setting up the simulation this way, I expected to see the rightward moving electron be detected at the 8 micron eastward facing gate at around 600fs and the leftward moving electrons be detected at the 5 micron westward facing gate at around 300fs.

This is exactly what I saw and we can see that the gates won’t detect electrons if they are crossing through the opposite orientation (off-diagonal plots).

Pre-Plasma

I’ve talked about the preplasma before and I’ve implemented it in the same way. Ferri talks about a 0.5 micron long plamsa gradient being formed on the front side of the target from his simulations which is cutoff below $0.2 n_c$. Nashad talks about how a preplasma can enhance TNSA when pulses arrive with a temporal delay. In my case with 2ps pulses, I feel that the pulses are sufficiently long so that this effect wouldn’t be there.

Nashad’s Appendix investigates the effect of a preplasma of scale length 0.4 microns

Ionization

The sims that Ricky had had Gold singly ionized and only tracked up to 5 levels of ionization. I realized in the simulation that, very quickly, all the gold ions became ‘fully’ ionized. I think due to the long nature of the simulation and high energy, we should expect gold to get ionized much more. This paper reports a formula for threshold intensity that ionizes an atom from field ionization to charge state $q$ and ionization energy $U_q$ as $I \approx 10^9 \frac{U_q^4}{q^2}$ W/cm2. Nashad keeps track of ionization in his paper for Carbon and Oxygen which is simpler because of using Ethylene Glycol which is comprised of low-Z elements.

To get intensities around $10^{19}$, I would need to use a charge state of around 43 with ionization energy of 2026 eV. This seems like there would be way too many electrons, so for now, I will try a charge state of +11 (the 6s electron and 10 5d electrons are fully stripped away). The 11th charge state has an ionization energy of 168 eV and 12th charge state has ionization energy of 248eV, so I can set the initial temperatures to 200 eV. Or, because there are so many electrons, it may not be worth keeping track of ionization, maybe it is enough to just start the gold in a highly ionized state.

The Ferri Papers simply assumed Aluminum was fully ionized which is not something we can do with gold (too many electrons, and not physically accurate to ionize that many electrons).

Density

Gold has a high density of 5.9e28 1/m3 or 19.32 g/cm3. This works out to around $59 n_c$ where $n_c \approx 10^{27}$ 1/m3 is the critical density for a 1.053 micron laser. Higher densities lead to smaller debye lengths and need a higher resolution grid to run simulations. As a result, I can consider lowering the density of gold. I wouldn’t want to lower it below the critical density, because the laser would pass right through and this wouldn’t be physical. Rusby does simulations on a 0.8ps micron laser using only 5 times the critical density for the tantalum targets when tantalum has a density of 55 times the critical density: a whole order of magnitude difference. Additionally, they only used 10 particles per cell and a resolution of around 20 cells per micron, whereas I have 50 cells per micron.

Accounting for Energy in Simulation

I ran a basic simulation without the target to keep track of laser energy in the simulation. This is for a benchmark to compare loss of energy conservation due to artifical heating of the particles. I ran a simple simulation with a target just so I could understand what to look out for in terms of energy conservation. Below, I have a plot that shows the various sources of energy

Additionally, I have another plot showing the total target simulation energy that accounts for particle energy, field energy, particle energy leaving the grid (through ejected_particles) and laser energy leaving the grid (through absorption).

Here, it looks like the energy accounted for matches up somewhat close to the theoretical energy. With a target, more energy could leave quicker than expected (e.g. reflections of the laser), so I think this makes qualitative sense and shows that we aren’t getting some runaway energy conservation error. And, this is using only 25 cells per micron which is half the resolution I was looking at before.