Simulation of Laser-Driven Ion Acceleration in Double-Layer Relativistic-Transparent Plasma Gauss Centre for Supercomputing e.V.


Simulation of Laser-Driven Ion Acceleration in Double-Layer Relativistic-Transparent Plasma

Principal Investigator:
Bin Liu

Helmholtz Institute, Jena

Local Project ID:

HPC Platform used:

Date published:


With the development of ultra-intense laser technology, laser-driven plasma-based ion acceleration has attracted much attention. High-energy high-quality controllable ion beams with particle energy hundreds of MeV have important applications in many areas including medical treatment of cancer, matter detection, nuclear physics, and high energy physics. Ultra-thin foil is the most considered target configuration [1] in which the acceleration is usually a result of the combination of the mechanisms of hole-boring, light-sail, and target-normal-sheath field. On the other hand, theoretical analysis and simulations have shown that foam-like plasma targets is also promising for generating high-energy ion beams via ion wave breaking acceleration (IWBA) [2].  In this work, with the help of three-dimensional (3D) particle-in-cell (PIC) simulations, we have investigated laser-driven ion acceleration in a double-layer target which combines a ultra-thin solid-density foil and a foam slab. This work provides helpful information for the future experiments on high-energy ion acceleration.

When propagating an ultra-intense laser pulse in a foam-like plasma target in the relativistically-transparent regime, electrons are piled up at the laser front edge, forming a high density electron layer. A localized charge-separation field created in the region just behind of the electron layer co-moves with the laser front edge. Background ions can be self-trapped in the field via ion wave breaking and then be accelerated to velocities far beyond the velocity of the laser front edge. The trapping happens localized close to the laser axis, resulting in highly directed ion beams. The output ion beam is adjustable by tuning the laser intensity or the plasma density. This allows designing controllable laser-plasma ion accelerators. However, in laboratories, it is extremely difficult to prepare a foam-like target standalone with a relatively steep boundary which is crucial for breaking an ion wave at the initial stage. A foam-like carbon nano-tube target is usually produced on a solid-density substrate foil which usually makes the density of the foam have a step-like boundary on the foil side. This inspires us to investigate IWBA in such two-layer configuration.

Results and Methods

Simulation method

The particle-in-cell (PIC) code EPOCH has been used for our project. It is an open source code for high energy density physics and able to solve complicated problems utilizing many processor cores. A simulation box is covered by uniform spacial grid. Dynamics of the electric field E and magnetic field B is defined by the Maxwells equations solved on the grid using the FDTD method. More details of the algorithm can be found in Ref. [3].


We have carried out 3D PIC simulations with the parameters of the POLARIS laser system. The laser pulse is chosen as a circularly polarized gaussian pulse with total energy 16J. The target is assumed to be combined by a solid-density ultra-thin carbon foil and a uniform foam with a thickness 20um. The foam is assumed to be hydrogenated so that it is composed of fully ionised hydrogen and carbon atoms. Simulations show that IWBA survives in such a double-layer target as long as the foil is thin enough (in our case, less than 15 nanometers) so that the incident laser pulse can penetrate through it. This allows an experimental implementation of IWBA. Furthermore, we have found that the optimal proton acceleration happens when the foam density is about 10 times of the critical density and the corresponding maximum proton energy is about 150 MeV, as is shown in Fig. 1 (b).

The energy of the accelerated ions depends on the propagating velocity of the driving laser in the foam. We have developed a theoretical model for the propagating velocity. A series 1D, 2D and 3D PIC simulations have been carried out to verify that our theoretical prediction works well for a large range of laser intensities, as is published in Ref. [4]. This is important for understanding and estimating the acceleration of ions in foam-like targets.


[1] Qiao, B. et al. Revisit on ion acceleration mechanisms in solid targets driven by intense laser pulses. Plasma Phys. Control. Fusion 61, 014039–14 (2018).

[2] Liu, B. et al. Ion wave breaking acceleration. Phys. Rev. Accel. Beams 19, 073401 (2016); Liu, B., Meyer-ter-Vehn, J. and Ruhl, H. Self-trapping and acceleration of ions in laser-driven relativistically transparent plasma. Physics of Plasmas 25, 103117–14 (2018).

[3] Arber, T. D. et al. Contemporary particle-in-cell approach to laser-plasma modelling. Plasma Phys. Control. Fusion 57, 113001–27 (2015).

[4] Liu, B., Meyer-ter-Vehn, J., Ruhl, H. and Zepf, M. Front edge velocity of ultra-intense circularly polarized laser pulses in a relativistically transparent plasma. Plasma Phys. Control. Fusion 62, 085014 (2020).

Project Team

Dr. Bin Liu (PI)1, Bifeng Lei1
Helmholtz Institute, Jena (Germany)

Scientific Contact

Dr. Bin Liu
Helmholtz Institute Jena
Helmholtzweg 4, D-07743 Jena (Germany)
e-mail: Bin.Liu [@]

JSC project ID: iwba2layer

December 2020

Tags: JSC EPP HI-Jena