A comparison of the maximum proton energy in the TNSA simulation and experiment [57, 58] for a different thickness and contrast (in the experiment) or paraplasmic state (in our simulation). We changed the thickness and density of the artificial hydrogen layer on the back side from 10 nm to 80 nm, and from 4nc to 20nc, respectively.
Introduction
In order to overcome low conversion efficiency of TNSA and experimental difficulty of RPDA, attention has been paid to ion acceleration in near-critical density plasma. There are three acceleration regimes in near-critical density plasma (n=1~10nc); electrostatic shock ion acceleration [ 45 ], magnetic vortex acceleration [ 46 – 48 ], and breakout afterburner [ 49 , 50 ].
Background
- Temperature
- Debye sheath
- Ponderomotive force
- Pre-plasma
Unlike electric and magnetic fields, the ponderomotive force is not relevant to the sign of charged particles. On the other hand, charged particles are continuously pushed by ponderomotive force with a small velocity spread when CP pulse is irradiated.
Particle-in-cell code
This is an intended time sequence to reduce numerical errors in FDTD and called the leapfrog method (see Fig. 3.4). It is possible to exchange positions between E and B. Numerical error can be evaluated by comparing theoretical dispersion relation and numerical dispersion relation [99]. Discretized version of dispersion relation in a free space can be obtained by inserting the numerical expression into the wave equation using the centered difference.
Acceleration regimes
Target-normal-sheath-acceleration
- Description
- Issue
But every time the hot electrons return to the target from the inside out, the electrostatic field decreases. The direction of the sheath field is normal to the surface, because the electron sheath surrounds the entire surface of the plasma. In this sense, the surface ions are mainly accelerated in the direction normal to the target at first.
Having arrived at the rear side, the population and energy of hot electrons become a Gaussian profile in the transverse direction during laser irradiation. If not, the initial temperature is zero before the laser-plasma interaction, the hydrogen layer at the front is accelerated in the forward direction and penetrates the target in the simulation; this is not true. When the initial temperature is given, the hydrogen layer at the front is accelerated in the backward direction.
Radiation pressure dominant acceleration
- Description
- Issue
A neighboring charged particle is affected by the shock's electrostatic field with speed vs. However, the combined effects of the substrate thickness and the areal density of the proton layer have not been systematically investigated previously. 5.3: (a) Longitudinal fields for different substrate thicknesses, for l=10 nm, n=2nc, during the laser-target interaction (48 fs). b) The number of electrons on the back side of the substrate during the laser-target interaction.
From this figure it is clear that the average proton energy decreases with increasing layer surface density (along the abscissa), while a higher proton energy is achieved by decreasing the thickness of the substrate (along the ordinate). Meanwhile, the reflected part of the pulse energy contributes to the initial pistoning of an ion density point. Accordingly, the electrostatic field also oscillates, which is eventually smeared by the shock density point.
Electrostatic shock ion acceleration
Control of the charge and energy of the proton beams from a laser-driven double-layer
Introduction
69] studied the scaling of proton energy by varying the laser intensity for the different surface densities of the target. 70, 71] investigated the effects of the layer thickness, where they found that the maximum proton energy increased as the layer thickness increased up to a certain level. 72] analytically studied the influence of the surface density of the proton-ion composite (mixture) target on the proton energy spectrum.
Motivated by this, we naturally propose a separate control of the charge of the proton beam by the surface density of the layer, as well as the beam energy through the thickness of the main target (from now on called a substrate). This conclusion indicates that σ and L can be used as design parameters of the beam charge and energy in the double-layer scheme. In section 5.3 the effects of the surface density of the layer are briefly discussed, together with ours.
Simulation set up
The different initial temperature of each layer used in our simulations does not significantly affect the calculation, since the target temperature increases very quickly to MeV as soon as the laser pulse irradiates the target. Usually, in one-dimensional simulations, the acceleration field is permanently maintained in the TNSA regime, since the expansion of the mantle field in the radial direction at the trailing side cannot be properly accounted for. To avoid overestimating the proton energy with such an artifact, the simulation must be stopped at a certain point.
61], where mantle expansion is considered, is known to be consistent with many simulations and experiments for a short driving laser pulse, as in our work. The formula is described by tacc = α(τL+tmin), where tacc is the acceleration time on the rear surface, tmin. Based on the time the pulse took to reach the front, we stopped the simulations after 153–156 fs, depending on the target thickness.
Effects of the areal density of the proton layer
This result can be explained by considering the maximum electric field at the edge of the proton beam presented [70, 71]. Note that the maximum field described by the above equation depends on the product of n and l, i.e. since the protons with the highest energy come from the edge of the layer, the part of which this largest field is most strongly accelerated, it is consequently necessary to determine the maximum energy of the protons by the surface density.
Effects of the substrate thickness
Therefore, for a fixed laser mode with a high contrast ratio as in our case, the substrate thickness and the areal density of the proton layer can be considered as independent control parameters of the total proton charge and beam energy. In our simulations, the highest average energy of the proton beams was measured to be more than 10 MeV for a 200 nm thick substrate. The origin of the oscillation-like pattern in the maximum energy of the proton in the region of high areal density in Fig.
5.5 we investigated the fractional spectral width (εmax - εmin)/εavg of the proton beams depending on the substrate thickness and the areal density of the layer, where εmax, εmin and εavg are the maximum, minimum and average proton beam energy, respectively. The smaller the spectral width, the more quasi-monoenergetic the proton beam. As a consequence, the results presented in this section indicate that the effects of the substrate thickness and the areal density of the layer do not interfere strongly with each other.
Conclusion
Another condition for shock formation is that the piston speed of the peak is large enough to match the shock speed. Note that step (c) only occurs after the pulse has completely disappeared, indicating that the shock is electrostatic. The existence of the shock could also be verified qualitatively by measuring the Mach number of the density peak and velocity doubling of incident ions in phase space.
The relativistic transparency, which is proposed as one of the most important steps for the shock formation, is determined dominantly by the electron density. 6.6 (b)] in front of the density peak near the laser axis is a result of velocity doubling by reflection of incoming ions from the shock front. The shock could persist for a long time, even in the absence of the driving pulse, due to the tapered density of the extended target.
Shock ion acceleration by an ultrashort circularly polarized laser pulse via relativistic
Introduction
One-dimensional simulation
Therefore, the ions expand due to the non-uniform electrostatic field of the sheath, where the ions at the boundary of the sphere reach the maximum speed. Cold plasma can be considered before the arrival of the main pulse on the target. If the duration of the laser pulse is long enough for the density peak to reach the rear side of the target, the LS starts there.
There are two problems in the RPDA experiment, one is the laser contrast ratio and the other is the normal condition of the incident laser pulse. The first and second targets are defined by a reflection of the laser pulse in the plasma, where the laser pulse compresses the plasma by transferring its momentum. On the other hand, in RPA an ultra-high contrast ratio of more than 10-11 of the driving pulse is required.
For lf = 2 μm, it is found that the shock velocity is reduced only slightly even after complete preloading of the laser field at t=200 fs. Due to the combination of shock and sheath acceleration, the lf = 2 μm plasma generated the highest maximum ion energy at 780 MeV. When the transparency of the laser pulse was too high (lf = 3 μm), the high electron temperature led to a thermal energy spectrum of the ion beam.
Furthermore, the reduction of the target density must be accompanied by the reduced a0, which will necessarily lower the accelerated beam charge.
Two- and three- dimensional simulation
Note that the asymmetric target profile with a slightly longer rear face used in the three-dimensional simulation may not be easily realized in the laboratory. The shock absorber is designed mainly in the front, so the rear side dimension is not so influential. Since the sheath effect can be suppressed with a longer trailing tail, a symmetric target with a shorter three-dimensional simulation lf in out should result in a slightly increased maximum ion energy and higher energy consumption due to the increased sheath effect.
Conclusion
Reducing the target plasma density to induce an RT circularly polarized pulse can be achieved by expanding the exploded targets. The partially rebound part of the pulse drives the initial density jump in piston speed via the hole-drilling mechanism. When the reflected and transparent parts of the driving pulse are properly selected, the Mach number of the initial density peak satisfies the shock criterion, i.e. M > 1.5, which turns it into an electrostatic shock.
The ions in the upstream direction are reflected by the shock front and form a localized energetic ion beam. The use of a circularly polarized pulse significantly reduces the high pulse power demand required for compression of the initial density peak, i.e. to 1 PW (or slightly larger). A parametric study of TNSA using a bilayer target provides information on the independence between the areal density of the second layer and the thickness of the first layer on an accelerated proton beam.
Summary
![Fig. 2.4.2: A comparison of the maximum proton energy in TNSA simulation and experiment [57, 58]](https://thumb-ap.123doks.com/thumbv2/123dokinfo/10531017.0/21.892.244.633.145.464/fig-comparison-maximum-proton-energy-tnsa-simulation-experiment.webp)
![Fig. 3.1: Concept of finite-difference method [98].](https://thumb-ap.123doks.com/thumbv2/123dokinfo/10531017.0/22.892.113.786.295.453/fig-3-concept-of-finite-difference-method-98.webp)
