This post covers work from 10/21-11/01. I did some more of my dissertation, read a lot of papers, and made some minor edits to papers.

Contributions to Plasma Physics Paper

The paper finally got accepted! It will probably take at least a few weeks for the editors to publish in a journal and I need to do some procedural stuff like signing license/copyright agreements.

arXiv Papers

Collimated gamma-flash emission along target surface

This paper reports on the production of gamma photons from a high-power laser with a solid target. There is a nice paper which motivates theoretically a significant enhancement in electron energies when the laser pulse is at grazing incidence as $\gamma_{max} = 1 + \frac{4 a_0 \cos(\theta_n)}{1 - \sin(\theta_n)}$. This can be compared to the typical ponderomotive scaling of electrons $\gamma = \sqrt{1 + a_0^2}$ where $\theta_n$ is the angle of incidence (w.r.t the laser axis and not the target).

They used 3D PIC simulations to see a collimated gamma photon beam along the target surface without having to use grazing incidence. They found this mostly at oblique incident (45 degrees). They say that although the use of a larger incident angle results in higher electron energy (motivated by the other paper), the gamma photon beam collimation and conversion efficiency significantly decreases as the angle approaches 60 degrees. This is also for p-polarization and s-polarization and circular polarization results in a much broader distriburtion with lower energies.

Titan Sims Plots

Efields

Above is a plot that shows the electric field in the normal direction to the target at 500fs for the four simulations (a) single (b) double (c) single with preplasma (d) double with preplasma. The plots in the bottom row show the electric field that is zoomed in (corresponding to the green square in the plots in the top row). I zoomed in because the region of interest is right at the interface between the solid and vacuum where the TNSA fields should be the strongest to drive the protons to the highest energies. Interestingly, it looks like the preplasma sims actually seem better in the sense that they are more uniform. Additionally, we can see a clear enhancement between the double pulse and the single pulse in both cases.

Bfields

I have a similar plot that shows the magnetic field at 1000fs for the four simulations. An interesting thing to note is that the single pulse with pre-pulse had some very strong magnetic fields that were not symmetric.

Electron Spectra

I computed the electron spectrum by assessing the energies of the particles currently in the simulation. First, I looked at the electrons

where the left (right) column is single (double) pulse and the top (bottom) row is flat (expanded) target. We can see that the electron generation is slightly higher for the double pulse with the flat target, but interestingly, the electron generation is slightly higher for the single pulse. Overall, there are significantly more electrons generated for the expanded target in comparison to the flat target.

Additionally, I computed the estimate of the hot electron temperature. Assuming the distribution of electrons above a certain energy range follows a maxwellian

\begin{equation} \frac{dN}{dE} = C \exp(-E / (k_B T_h)) \end{equation}

then

\begin{equation} \log(\frac{dN}{dE}) = \log(C) - E / (k_B T_h) \end{equation}

which means that the slope of the log dN/dE curve should be $-1/(k_B T_h)$.

The hot electron temperature is just under 2 MeV for all but the single pulse with preplasma which had a temperature closer to 3 MeV. This is the simulation that also had the highest amount of ionization (35 vs 30 for the rest). My guess is that the preplasma negates the double pulse enhancement, but since the 41 degree pulse is better than the 20 degree pulse, we see slightly better results for the single pulse.

Proton Spectra

I computed the proton spectra in a very similar way

where it appears that the amount of protons is actually very similar with the expanded target. There is this curious bump at around 2.5 MeV for both expanded target simulations and the single pulse expanded target sim had a small bump around 8.5 MeV. We can see a clear cutoff in the proton energy which is to be expected from TNSA protons.

Ferri 2019

I have been trying to read Ferri’s 2019 paper to get some more insight into what I observed in the Titan simulations. He comments that there is a judicious balance between plasma expansion from the front and back side which could enhance hot electron generation (and therefore sheath fields) but also degrade the quality of the TNSA beam if the protons on the rear surface have pre-expanded. The double pulse (assuming same timing) does not modify the density profile any differently, it merely relies on the enhanced constructive interference at the front of the target. Note that there’s also enhanced destructive interference. But the enhanced constructive interference increases the peak electric field while maintaining the same overall laser energy. And it is this peak electric field that is responsible for the highest energy protons.

My findings overall agree with Ferri in that the double pulse sees enhanced proton energies. However, the results with the expanded target I don’t think are directly comparable. He uses the vacuum heating (Brunel) justification for absorption which only applies to a flat planar target with a steep density gradient: not true for our simulations. Additionally, the long picosecond pulse basically heats up and expands the entire target before the fields have a chance to fully develop. Ferri mentions that for pulses with greater than 10J, the proton layer on the rear side starts to entirely disconnect from the bulk of the target during the acceleration which causes the proton energies to saturate and lower than expected.

Ferri claims that the double pulse offers a symmetry that keeps Bz 0 at certain positions that suppress the v cross B force. He also claims that the v cross B force inhibits the force due to the electric field in the x direction.

So, I don’t think a Brunel-like model would be capable of explaining my work. I already feel like the single and double pulse with preplasma are explainable: the long preplasma negates the flat profile which the double pulse enhancement is reliant on.