Laser ion acceleration studies at BELLA center (Conference Presentation)

When a plasma foil is irradiated by an intense laser pulse at a grazing angle, the pre-pulse of the laser evaporates the solid plasma and generates an expanding near-critical-density (NCD) layer. We consider the situation where the plasma density profile in this layer is strongly nonuniform (high-contrast laser), i.e., the density scale length is comparable to the laser spot size. In this case a relativistic electron vortex (EV) is excited in the NCD layer after the laser pulse depletion. It drifts perpendicular to the density gradient at a constant velocity, typically 0.2 - 0.3 times the speed of the light. The strong coupling between laser and NCD plasma gives rise to intense current density that generates significant magnetic field. The magnetic pressure leads to charge separation in the vortex, which can be used to accelerate protons. The basic mechanism of acceleration is different from the magnetic vortex acceleration (MVA), where a magnetic dipole vortex is generated in a uniform NCD target and acceleration only happens when it reaches the rear side of the target. In our work, the EV, or magnetic monopolar vortex, serves as a stable slow-moving structure in which protons can be captured and gain considerable kinetic energy from the charge separation field associated with the EV. Similarly to collisionless shock acceleration, protons initially at rest can be reflected to twice the EV drift velocity. The mechanism of EV drift in the strongly nonuniform plasma is different from the weakly nonuniform plasma that are mostly studied in the previous works. In order to obtain a deeper insight into the dynamics of EV drift, we perform 2-dimensional (2D) particle-in-cell (PIC) simulations and track the trajectories of a number of electrons that are trapped in the EV. Our results suggest the laser-driven electrons are subject to an E x B drift which drives the collective motion of the vortex structure. Based on this, an analytical model for the vortex velocity is derived in terms of laser and plasma parameters, the prediction of the model agrees well with the PIC simulations. It demonstrates that drift velocity of EV, and therefore the maximum proton energy, can be effectively controlled by the incidence angle of the laser and the plasma density gradient. A representative scenario is studied with 2D PIC simulations—with laser intensity at 10^21 W/cm^2 and incident at 10 degrees—is discussed, in which a quasi-monoenergetic proton beam is obtained with a mean energy 140 MeV and an energy spread of 10%. 3D effects are discussed briefly towards the end of the presentation.

Kinetic drift instabilities have been implicated as a possible mechanism leading to anomalous electron cross-field transport in E × B discharges, such as Hall-effect thrusters. Such instabilities, which are driven by the large disparity in electron and ion drift velocities, present a significant challenge to modelling efforts without resorting to time-consuming particle-in-cell (PIC) simulations. Here, we test aspects of quasi-linear kinetic theory with 2D PIC simulations with the aim of developing a self-consistent treatment of these instabilities. The specific quantities of interest are the instability growth rate (which determines the spatial and temporal evolution of the instability amplitude), and the instability-enhanced electron-ion friction force (which leads to “anomalous” electron transport). By using the self-consistently obtained electron distribution functions from the PIC simulations (which are in general non-Maxwellian), we find that the predictions of the quasi-linear kinetic theory are in good agreement with the simulation results. By contrast, the use of Maxwellian distributions leads to a growth rate and electron-ion friction force that is around 2–4 times higher, and consequently significantly overestimates the electron transport. A possible method for self-consistently modelling the distribution functions without requiring PIC simulations is discussed.

High-intensity ultrashort laser pulses focused on metal targets readily generate hot dense plasmas which accelerate ions efficiently and can pave way to compact table-top accelerators. Laser-driven ion acceleration studies predominantly focus on protons, which experience the maximum acceleration owing to their highest charge-to-mass ratio. The possibility of tailoring such schemes for the preferential acceleration of a particular ion species is very much desired but has hardly been explored. Here, we present an experimental demonstration of how the nanostructuring of a copper target can be optimized for enhanced carbon ion acceleration over protons or Cu-ions. Specifically, a thin (≈0.25 μm) layer of 25–30 nm diameter Cu nanoparticles, sputter-deposited on a polished Cu-substrate, enhances the carbon ion energy by about 10-fold at a laser intensity of 1.2×1018 W/cm2. However, particles smaller than 20 nm have an adverse effect on the ion acceleration. Particle-in-cell simulations provide definite pointers regarding the size of nanoparticles necessary for maximizing the ion acceleration. The inherent contrast of the laser pulse is found to play an important role in the species selective ion acceleration.

In order to further study the radiation of the relativistic electron beam-ion channel experimentally and theoretically, the propagation of a relativistic electron beam in neutral gas and its self-focusing process are investigated. Particle in cell (PIC) simulation shows that the electron beam can self-focus and transmit the dynamically loaded plasma through impact ionization. The transverse and the longitude inhomogeneities of the ion background have significant effects on the transport properties of the electron beam. Base on these researches, a model of transmission of electron beam in a transverse non-uniform ion background is supposed. And the condition of self-focus is given. The numerical results show that the transverse inhomogeneity will lead to the mixed phase transmission of the electron beam, and the inner electrons can defocus near the focus point, which is consistent with the PIC simulation. The PIC simulation also shows that due to the self-focusing of the electron beam, there are much more ions to be ionized at the focus point, which will capture the lower-energy electrons after collision, the capture electron effect will significantly reduce the efficiency of the transmission of the electron beam. But the distribution of the captured electrons in the longitude direction is quasi-periodic, which acts as the electrostatic Wiggler field. These may achieve the dynamical loading of the electrostatic Wiggler field. These results give new clues to the further study of electron beam-plasma system in experiment and the establishment of theoretical models.

This paper presents KlyH, a new 1D (one-dimensional) large-signal simulation software for klystrons, designed to deliver efficient and accurate simulation and optimization tools. KlyH integrates a Fortran-based dynamic link library (DLL) as its computational core, which employs high-performance numerical algorithms to rapidly compute critical parameters such as efficiency, gain, and bandwidth. Compared with traditional 1D simulation tools, which often lack open interfaces and extensibility, KlyH is built with a modular and open architecture that supports seamless integration with advanced optimization and intelligent design algorithms. KlyH incorporates multi-objective optimization frameworks, notably the Non-Dominated Sorting Genetic Algorithm II (NSGA-II) and Optimized Multi-Objective Particle Swarm Optimization (OMOPSO), enabling automated parameter tuning for efficiency maximization and interaction length optimization. Its bandwidth-of-klystron-analysis module predicts gain and output power across operational bandwidths, with optimization algorithms further enhancing bandwidth performance. A Java-based graphical user interface (GUI) provides an intuitive workflow for parameter configuration and real-time visualization of simulation results. The open architecture also lays the foundation for future integration of artificial intelligence algorithms, promoting intelligent and automated klystron design workflows. The accuracy of KlyH and its potential for parameter optimization are confirmed by a case study on an X-band relativistic klystron amplifier. Discrepancies observed between 1D simulations and 3D PIC (three-dimensional particle-in-cell) simulation results are analyzed to identify model limitations, providing critical insights for advancing high-performance klystron designs.

For many years, laser-driven ion acceleration, mainly proton acceleration, has been proposed and a number of proof-of-principle experiments have been carried out with lasers whose pulse duration was in the nanosecond range. In the 1990s, ion acceleration in a relativistic plasma was demonstrated with ultra-short pulse lasers based on the chirped pulse amplification technique which can provide not only picosecond or femtosecond laser pulse duration, but simultaneously ultra-high peak power of terawatt to petawatt levels. Starting from the year 2000, several groups demonstrated low transverse emittance, tens of MeV proton beams with a conversion efficiency of up to several percent. The laser-accelerated particle beams have a duration of the order of a few picoseconds at the source, an ultra-high peak current and a broad energy spectrum, which make them suitable for many, including several unique, applications. This paper reviews, firstly, the historical background including the early laser–matter interaction studies on energetic ion acceleration relevant to inertial confinement fusion. Secondly, we describe several implemented and proposed mechanisms of proton and/or ion acceleration driven by ultra-short high-intensity lasers. We pay special attention to relatively simple models of several acceleration regimes. The models connect the laser, plasma and proton/ion beam parameters, predicting important features, such as energy spectral shape, optimum conditions and scalings under these conditions for maximum ion energy, conversion efficiency, etc. The models also suggest possible ways to manipulate the proton/ion beams by tailoring the target and irradiation conditions. Thirdly, we review experimental results on proton/ion acceleration, starting with the description of driving lasers. We list experimental results and show general trends of parameter dependences and compare them with the theoretical predictions and simulations. The fourth topic includes a review of scientific, industrial and medical applications of laser-driven proton or ion sources, some of which have already been established, while the others are yet to be demonstrated. In most applications, the laser-driven ion sources are complementary to the conventional accelerators, exhibiting significantly different properties. Finally, we summarize the paper.

Recent advances on laser-driven ion accelerators have sparked an increased interest in such energetic particle sources, particularly towards the viability of their usage in a breadth of applications, such as high energy physics and medical applications. Here, we identify a new ion acceleration mechanism and we demonstrate, via particle-in-cell simulations, for the first time the generation of high energy, monochromatic proton micro-bunches while witnessing the acceleration and self-modulation of the accelerated proton beam in a dual-gas target, consisting of mixed ion species. In the proposed ion acceleration mechanism due to the interaction of an ultra-short, ultra-intense (2 PW, 20 fs) laser pulses with near-critical-density partially ionized plasmas (C & H species), we numerically observed high energy monochromatic proton microbunches of high quality (peak proton energy 350 MeV, laser to proton conversion efficiency ~10−4 and angular divergence <10 degree), which can be of high relevance for medical applications. We envisage that through this scheme, the range of attained energies and the monochromaticity of the accelerated protons can be increased with existing laser facilities or allow for laser-driven ion acceleration investigations to be pursued at moderate energies in smaller scale laser laboratories, hence reducing the size of the accelerators. The use of mixed-gas targets will enable high repetition rate operation of these accelerators, free of plasma debris and electromagnetic pulse disruptions.

The lack of understanding of the azimuthal instability and the resulting electron anomalous transport limits further improvement of Hall thrusters. Compared to theoretical and experimental approaches, the numerical particle-in-cell (PIC) simulation is a suitable and powerful tool, which has been widely applied to investigate the azimuthal instability, and great progress has been made in the past decades. However, PIC simulations are intrinsically computationally expensive, and it is realized that the Hall thruster azimuthal instability has a three dimensional nature. Therefore, massive 3D PIC simulation must be carried out to completely reveal the mechanism of the instability. In this paper, the effect of plasma initialization on 3D PIC simulation of Hall thruster azimuthal instability is studied as a starting point. It is found that by initializing with ion density and velocity fitting functions to the steady-state simulation results, a faster convergence can be obtained and the computational time can be reduced by about 1.5 times. Typical fitting functions of ion density, drifting velocity, and temperature are given, and the influence of different initialization profiles is presented.

The impact of contaminants on laser-driven ion acceleration is investigated using particle-in-cell simulations. The conventional ion acceleration mechanism, target normal sheath acceleration, has been revisited for targets with proton-rich contaminants in the form of water vapor. The targets considered have a deuterated plastic layer on the rear surface of an aluminum target, and the influence of the contaminant layer on the deuteron acceleration is investigated. In the early stage of ion acceleration, the space-charge electrostatic field on the rear target surface accelerates only the outermost, proton-rich layer of ions, which inhibits the deuteron acceleration by shielding it from the field. When the proton layer is depleted, the deuterons become exposed to the space-charge field and are promptly accelerated. This scenario was tested with a two-dimensional particle-in-cell simulation model by varying the contaminant layer thickness and laser fluence (laser energy per unit area). For laser fluences Flaser&amp;lt;1 J/μm2, the contamination layer over the surface inhibits the deuteron acceleration from the rear surface, while in the opposite case of laser fluences Flaser&amp;gt;1 J/μm2 deuterons and heavier ions can be successfully accelerated with conversion efficiency of laser energy into ions of more than 1%. Experimental data from a 6 μm thick aluminum foil coated with a 1 μm deuterated plastic layer on the back surface are suggestive of the detrimental role of contaminants on deuteron acceleration.

Laser-driven ion acceleration is capable of generating ion beams of MeV energy exhibiting unique attributes such as ultralow emittance. Research is still focusing on fundamental laser-target interactions to control further beam attributes. In this Letter we present the observation of directional ion acceleration of irradiated spherical targets through proton imaging. This feature, together with an earlier observed quasimonoenergetic proton burst makes spherical targets extremely attractive candidates for high quality, high repetition rate sources of laser accelerated particles.

The effect of an axial magnetic field on laser driven ion acceleration from a thin overdense plasma slab is investigated. The magnetic field modifies the refractive index of the plasma and the axial ponderomotive force. The latter compresses the electrons until the space charge field thus created offsets it. When the foil thickness is just bigger than the length at which this happens, the compressed electrons and a thin ion layer detach from the foil forming a double layer that gets accelerated by the laser radiation pressure force. The optimum thickness of laser foil, Δs, for maximum acceleration is sensitive to the polarization of the laser pulse. For right circular polarization it increases, while for left circular polarization it decreases with the magnetic field. The ion energy gain is sensitive to a02ω2∕Δsωp2 (where a0 is the laser field strength, ωp is the plasma frequency, and ω is the laser frequency) and can be tuned by varying the magnetic field.

Radiation reaction effects on electron nonlinear dynamics and ion acceleration in laser–solid interaction

Fully kinetic three-dimensional (3D) particle-in-cell (PIC) simulations are necessary to reveal the underlying physics of Hall thruster azimuthal instability. To better study the problem, a code named PMSL-PIC-HET-3D is developed recently specifically for simulating the Hall thruster, aiming at high computational efficiency and speed but less development effort. In this paper, the PMSL code is validated by comparison to the open-source PIC code WarpX, and its computation speed has reached the same level as WarpX. In addition, PMSL is able to combine cubic simulation domains such that the effect of the plume region arrangement is investigated in terms of the axial plume size and the location of the thruster exit relative to the peak magnetic field, i.e., the aft-loading magnetic field design. The simulation results indicate that the plume region arrangement has non-negligible effects on the global profiles, such as the plasma density and potential, but has a minor influence on the azimuthal instability properties. In addition, simulation results of larger plume angles are obtained for aft-loading cases, which are consistent with experimental observations.

Shock reformation involves regions of a shock undergoing periodic collapse and redevelopment on a time scale close to the ion cyclotron period. Reformation is often observed in one‐dimensional (1‐D) hybrid and particle in cell (PIC) simulations of quasi‐perpendicular collisionless shocks provided the Alfvén Mach number MA and ion plasma beta βi are sufficiently high and low, respectively. Initial 2‐D PIC simulations showed some evidence for shock reformation, with ion reflection providing the main energy dissipation mechanism, while recent spacecraft observations showed a reforming shock with large amplitude whistler waves in the foot region. While recent spacecraft observations showed an case with reforming shock crossing with whistler waves dominated in the foot region. However, recent 2‐D hybrid and PIC simulations suggest that reformation does not occur in exactly perpendicular 2‐D shocks. This paper re‐examines shock reformation in quasi‐perpendicular shocks using 1‐D and 2‐D hybrid simulations. We find that 2‐D quasi‐perpendicular shocks (θbn = 85°) indeed undergo cyclic reformation providing MA and βi are high and low enough, respectively. For low MA ≤ 4, 2‐D quasi‐perpendicular shocks are found to be quasi‐stationary, despite 1‐D simulations predicting reformation, confirming and extending recent work for perpendicular 2‐D shocks. The dynamics of reformation are quite different in 2‐D than in 1‐D: in 2‐D large amplitude whistler waves grow in the shock foot, have amplitudes of order the downstream magnetic field, and affect the reformation. The whistlers have almost zero phase speeds in the shock frame and oblique wave vectors with respect to the upstream magnetic field. The predicted reformation period increases in 2‐D compared with 1‐D and increases nonlinearly as MA decreases towards the reformation threshold.

RF phase Jitter is a very important parameter for a relativistic klystron amplifier, and it is closely related with the physical processes in the klystron. In view of the physical process in the klystron, the RF phase jitter is theoretically studied together with particle in cell （PIC） simulation. The main factor which affects the RF phase jitter is deduced and verified in the PIC simulation. The RF phase jitter is significantly affected by the fluctuation of the beam voltage at the steady state when the cavity is in resonanec. The relation is linear in a certain range.