Abstract
1 Introduction
Over the past 15 years, the generation of multi-MeV proton and ion beams with unique properties has attracted intense interest due to the numerous fundamental and applicative prospects these beams offer[
Although in most previous studies of ion acceleration solid targets are used, gas targets may provide debris-free acceleration and a reduction of unnecessary secondary radiation, such as bremsstrahlung. Gas jets are also considered as sources of high-purity high-
The generation and subsequent properties of shock accelerated ion beams are highly dependent on the initial plasma density distribution[
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In the present study, which is based on the work of Tresca et al.[
Considering the case of the BNL
2 Physical modelling
In the first stage of the laser–gas interaction, the main mechanism of energy absorption is the inverse bremsstrahlung heating. Electrons gain energy from the incident optical high power laser pulse via collisions. At a very high field strength, gases break down, i.e., they become highly ionized, accompanied by a light flash. The electron–ion collision frequency is given by[
In the frame of the present work, after the initial energy deposition, the heated plasma hydrodynamically expands into the surrounding ambient medium as a blast wave in a similar way to the Sedov or adiabatic stage of supernova or atomic explosions[
The expansion velocity
The expansion rate of the shock is described by
The density scale length is a parameter of major importance in controlling the properties of accelerated ions and is the distance over which the density decreases by a factor of
The density profiles of a blast wave, corresponding to the BNL
3 Numerical modelling
The modular, parallel, multiphysics simulation code FLASH was used for our simulations[
This partial differential equation system of the Euler equations is solved using an unsplit hydrodynamic solver with third-order interpolation which corresponds to the piecewise parabolic method (PPM). The PPM scheme is a higher-order extension of Godunov’s method[
A major advantage of the FLASH code is that the simulation domain is discretized and refined by the help of an adaptively mesh refined (AMR) grid. The application of AMR grid is based on an initial Eulerian grid where the regions that require finer resolution are identified and finer sub-grids (extra computational cells) are generated. This refinement process is controlled by the help of a local truncation error estimator[
FLASH includes two AMR algorithms, the default PARAMESH package that was used in our study and CHOMBO[
4 Numerical hydrodynamic simulations
An analytic model developed for this study is based on a customized version of the Sedov model, as described in detail in Ref. [
The boundary conditions are reflecting on the axis of the cylinder, on the left of the domain, to model the cylindrical symmetry. Outflow boundary conditions (zero-gradient boundary conditions) are applied to the rest of the three sides, allowing shocks to leave the computational domain without any reflections.
As depicted in the right part of Figure
Alongside with the initial conditions of the numerical problem, the throat and exit diameters as well as the length of the nozzle are set. The nozzle simulated is a so called ‘1 mm’ nozzle, with a throat diameter of 0.5 mm, an exit diameter of 1 mm and length of 4 mm. The longitudinal density profile can be approximated as a triangle[
The initial grid of cells that models the computational domain for all of the simulations performed had an initial uniform discretization of
5 Results and discussion
5.1 BNL
The simulations performed focused on the investigation of the density profiles of the blast waves and the determination of the time over which the main pulse irradiates the overdense plasma. The FLASH code is set to output data files at every nanosecond simulated, the wavelength to
A comparison example for the case of
Following this, four energies of 1, 5, 20 and 100 mJ were studied. The results of the blast wave radii and the corresponding ratio of the peak electron density to the critical density are presented in Figure
The time frame within which the main pulse interacts with the target is highly dependent on the region where the prepulse is focused. In Figure
On the contrary, if we deposit the energy very close to the jet’s throttle, there is the risk of never creating an overdense plasma, especially for high pulse energies, as shown in Figure
The main conclusion from the above results is that for lower, medium and high laser pulse energies, the target is overcritical. Hence, there is no necessity to apply the main pulse at later times having to deal with unnecessary long density scale lengths. Hydrogen would be a good choice for these experiments. In earlier works where helium was used[
It is of great importance that the scale length values, for the three energies, are relatively low and permit the production of monoenergetic ion beams since scale lengths lower than
5.2 Vulcan laser
The simulation results for targets suitable for experiments using the Vulcan laser at Rutherford Appleton Laboratory are presented here. The FLASH code is set again to output data files at every nanosecond simulated, the wavelength to
A maximum initial electron density of
The time evolution for the ratio of the peak electron density to the critical density in the shock is presented in Figure
Following the same concept of the results visualization used for the BNL case in Figure
6 Conclusions
The use of a lower energy prepulse to create a blast wave in the gas jet, thus shaping the target, has been proposed in the literature. Following the prepulse, the higher energy main pulse finds a sharpened density gradient that facilitates ion acceleration[
The critical plasma density is highly dependent on the laser wavelength. We chose to investigate these two particular laser systems, BNL
The analysis of the variables of interest indicates that, depending on the energy absorbed and the deposition position, gas targets can be shaped suitably and thus an identical temporal window may be determined for the acceleration considering both the necessary overdense state of plasma and the required short scale lengths for monoenergetic ion beams. The new simulation results offer valuable data for the optimization of future experiments since new conditions including scanning of the initial density and energy deposited for two different wavelength regimes have been explored here. This will help future experiments determine the plasma heating requirements for generating density profiles favourable for quasimonoenergetic ion beam generation.
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