Tailored Density Profile Research Articles

Additive manufacturing of functionally graded foams: Material extrusion process design, part design, and mechanical testing

Functionally graded foams (FGFs) were in-situ fabricated via material extrusion (MEX) additive manufacturing (AM) process. Foamable filaments loaded with thermally expandable microspheres (TEMs) at 8.0 wt% was first fabricated using a single screw extruder. The correlations between the resultant foam density and process factors, namely nozzle temperature (NT) and flow rate (FR) were established using a statistical analysis and the density predictability of the model was verified by experiment. With concurrent control of NT and FR, FGFs with density ranges as high as 0.86 g cm−3 were achieved within a single print. Various FGFs were designed using linear, concave, and convex density gradient functions. The density-process correlation model was then used to obtain the NT and FR parameters needed to produce the density values as demanded by the part design. FGFs along with their single density foam (SDF) counterparts were successfully printed with good dimensional stability. Under quasi-static compression testing, all FGFs showed higher energy absorption capacity at low stress levels, as compared to their SDF counterparts. Moreover, under impact conditions, a significant loading direction dependency was found for the FGFs. Overall, this work demonstrates the AM feasibility of FGFs as a single print with tailored density profiles which can be used in generative design optimization of AM parts for enhanced mechanical performance and other functionalities.

Plasma density profile reconstruction of a gas cell for Ionization Induced Laser Wakefield Acceleration

Laser-driven plasma wakefields can provide hundreds of MeV electron beam in mm-range distances potentially shrinking the dimension of the actual particle accelerators. The plasma density plays a fundamental role in the control and stability of the acceleration process, which is a key development for the future electron injector proposed by EuPRAXIA.A gas cell was designed by LPGP and LIDYL teams, with variable length and backing pressure, to confine the gas and tailor the gas density profile before the arrival of the laser. This cell was used during an experimental campaign with the multi TW-class laser at the Lund Laser Centre. Ionization assisted injection in a tailored density profile is used to tune the electron beam properties. During the experiment, we filled the gas cell with hydrogen mixed with different concentration of nitrogen. We also varied the backing pressure of the gas and the geometrical length of the gas cell. We used a transverse probe to acquire shadowgraphic images of the plasma and to measure the plasma electron density.Methods and results of the analysis with comparisons between shadowgraphic and interferometric images will be discussed.

Impact of the radial density profile on the Z-pinch stability at a microsecond rise time of the driving current

This paper considers the instabilities of imploding aluminum metal-puff Z-pinches with an outer plasma shell. An experiment was performed on the GIT-12 generator (3.2–3.6 MA, ∼1 μs implosion times, and ∼15 cm initial Z-pinch radius). It was shown that the density profile of the Z-pinch material had the dominant effect on the growth and suppression of instabilities. Two Z-pinch load configurations were used. The first configuration provided a tailored density profile (TDP) [A. L. Velikovich et al., Phys. Rev. Lett. 77, 853 (1996)], which ensured the suppression of the magneto-Rayleigh–Taylor (MRT) instability in the Z-pinch. For the second configuration, the density profile was changed in such a way that a density notch from 10 to 0.5 μg/cm3 occurred at a radius of about 3 cm from the Z-pinch axis. The notch in the density profile and the nonmonotonic increase in density resulted in a completely unstable compression of the Z-pinch. This gave rise to large-scale instabilities, which were detected by optical diagnostics. The instabilities grew and were not suppressed even in the stagnation phase, despite a sharp increase in the density of the Z-pinch material near the axis. The results were interpreted using the model proposed by Curzon et al. [Proc. R. Soc. London A 257, 386 (1960)]. The total instability amplitude is the sum of the amplitudes of MRT and magneto-hydrodynamic (MHD) instabilities. The growth of the total instability in the density notch region is due to the development of MRT instability. Thus, if the density profile has a notch, the Z-pinch compression in the stagnation phase occurs under strong perturbations at the magnetic field/plasma interface. This results in a dramatic growth of MHD instabilities. Hence, a stable implosion of a Z-pinch with TDP is possible only if the density increases monotonically toward the axis.

Photon Acceleration from Optical to XUV.

The propagating density gradients of a plasma wakefield may frequency upshift a trailing witness laser pulse, a process known as "photon acceleration." In uniform plasma, the witness laser will eventually dephase because of group delay. We find phase-matching conditions for the pulse using a tailored density profile. An analytic solution for a 1D nonlinear plasma wake with an electron beam driver indicates that, even though the plasma density decreases, the frequency shift reaches no asymptotic limit, i.e., is unlimited provided the wake can be sustained. In fully self-consistent 1D particle-in-cell (PIC) simulations, more than 40 times frequency shifts were demonstrated. In quasi-3D PIC simulations, frequency shifts up to 10 times were observed, limited only by simulation resolution and nonoptimized driver evolution. The pulse energy increases in this process, by a factor of 5, and the pulse is guided and temporally compressed by group velocity dispersion, resulting in the resulting extreme ultraviolet laser pulse having near-relativistic (a_{0}∼0.4) intensity.

Effect of tailored density profiles on the stability of imploding Z-pinches at microsecond rise time megaampere currents

To study the effect of the radial density profile of the material of a metal-plasma Z-pinch load on the development of magneto-Rayleigh–Taylor (MRT) instabilities, experiments have been performed at the Institute of High Current Electronics with the GIT-12 generator which produces microsecond rise time megaampere currents. The Z-pinch load was an aluminum plasma jet (PJ) with an outer plasma shell. This configuration leads to the formation of a uniform current sheath in a Z-pinch load upon application of a high-voltage pulse. It was successfully used in experiments with hybrid deuterium gas-puffs (Klir et al 2020 New J. Phys. 22 103036). The initial density profiles of the Z-pinch loads were estimated from the pinch current and voltage waveforms using the zero-dimensional ‘snowplow’ model, and they were verified by simulating the expansion of the PJ formed by a vacuum arc using a two-dimensional quasi-neutral hybrid model (Shmelev et al 2020 Phys. Plasmas 27 092708). Two Z-pinch load configurations were used in the experiments. The first configuration provided tailored load density profiles, which could be described as ρ(r) ≈ 1/r^s for s > 2. In this case, MRT instabilities were suppressed and thus a K-shell radiation yield of 11 kJ cm−1 and a peak power of 0.67 TW cm−1 could be attained at a current of about 3 MA. For the second configuration, the radial density profiles were intentionally changed using a reflector. This led to the appearance of a notch in the density profiles at radii of 1–3 cm from the pinch axis and to magnetohydrodynamic instabilities at the final implosion stage. As a result, the K-shell radiation yield more than halved and the power decreased to 0.15 TW cm−1 at a current of about 3.5 MA.

Multiple species laser-driven ion-shock acceleration

Two-dimensional particle-in-cell simulations are used to explore laser-driven collisionless shock acceleration of ions in a multi-species plasma. Simple plasma slab simulations consisting of electrons, protons, and fully ionized carbon are used, varying the carbon ionization state, the relative fraction of ions, and the ratio of downstream to upstream plasma density. We find that two shocks can simultaneously propagate with different velocities defined by the dominant ion species reflected by each shock. The appearance of two shocks allows for ions to be accelerated twice, but can also cause trapping and heating of ions. We modify the current collisionless electrostatic shock theory where ions are treated as a single fluid to include a second ion fluid. This fluid model is unable to calculate the Mach number at which both ions will reflect, therefore we propose a kinetic model that may better model multi-species shocks. Scans are also performed in simulations with a laser pulse and realistic density profile that show reduced proton peak energies with the inclusion of carbon ions. Double shocks are only seen in simulations with steep density profiles, demonstrating the experimental importance of tailored density profiles.

Laser-accelerated protons using density gradients in hydrogen plasma spheres

The effect of different density profiles on micron-sized hydrogen plasma spheres is investigated when the plasma gets irradiated with an ultrashort circularly polarized laser. In this study, we show that significant improvement in the characteristics of the accelerated protonsviz.maximum proton energy, as well as their monoenergetic behaviour, is possible by using a plasma sphere having a tailored density profile. A linear-shaped density inhomogeneity is introduced in the plasma sphere such that the density is peaked at the centre and gradually dropping outwards. The density gradient is tuned by changing the peak density at the centre. The optimum regime of steepness is found for the maximum energy attained by the protons where the target is opaque enough for the radiation pressure to play its role, however not too opaque to inhibit efficient target heating. A novel Gaussian-shaped density profile is suggested which plays an important role in suppressing the sheath field. With a decreased rear-side field, a visible improvement of the monoenergetic feature of the protons is observed.

Studies on the implosion of pinches with tailored density profiles

This paper presents the results of experimental and theoretical studies of imploding metal-puff Z-pinches. The experiments were carried out on the MIG high-current pulse generator at a current level of about 2 MA and a current rise time of about 100 ns. A plasma gun was used to produce a plasma column with a tailored density profile through which the main electromagnetic pulse of the MIG generator was passed. The experiments have shown that pinches of this type, being compressed, are resistant to dynamic magneto-Rayleigh–Taylor (MRT) instabilities. The experimental results were analyzed using one-dimensional radiation magnetohydrodynamic simulations. It has been shown that in a pinch with a tailored density profile, the formation of a high-temperature plasma at the pinch axis and the generation of x-rays occur at the stagnation stage, i.e. under conditions close to Bennett equilibrium. At this stage, flute-like MRT instabilities develop, causing the pinch to decay.

Trajectory of a flying plasma mirror traversing a target with density gradient

It has been proposed that laser-induced relativistic plasma mirror can accelerate if the plasma has a properly tailored density profile. Such accelerating plasma mirrors can serve as analog black holes to investigate Hawking evaporation and the associated information loss paradox. Here we reexamine the underlying dynamics of mirror motion in a graded-density plasma to provide an explicit trajectory as a function of the plasma density and its gradient. Specifically, a decreasing plasma density profile (down-ramp) along the direction of laser propagation would in general accelerate the mirror. In particular, a constant-plus-exponential density profile would generate the Davies–Fulling trajectory with a well-defined analog Hawking temperature, which is sensitive to the plasma density gradient but not to the density itself. We show that without invoking nano-fabricated thin-films, a much lower density gas target at, for example, ∼1×1017cm−3, would be able to induce an analog Hawking temperature, kBTH∼3.1×10−2eV, in the far-infrared region. We hope that this would help to better realize the experiment proposed by Chen and Mourou.

Formation of double shell during implosion of plasma metal puff Z-pinches

This work presents the results of experimental and theoretical research of impact of tailored density profile and application of external axial magnetic field on initial spatial distribution of the plasma density in the plasma metal puff Z-pinch and on its implosion dynamics. It has been discovered that upon implosion of the plasma metal puff Z-pinch some stripes interpreted as the system of two coaxial shells appear on the optical images. With the help of numerical simulation, the formation of the plasma liner consisting of a mixture of carbon and bismuth ions and formed by the expansion of the plasma jet of the arc burning on the bismuth electrode has been considered in this work. It has been shown that the lightweight carbon ions facilitate formation of the density distribution smoothly decreasing with the increase in radius, that, in turn, leads to suppression of the Rayleigh–Taylor instability in the current sheath upon further implosion. It has also been demonstrated that availability of the two types of ions in plasma considerably different in mass leads to formation (in the compression phase) of a double shell with externally located heavy ions. It has also been revealed that the application of the external axial magnetic field leads to reduction in the plasma metal puff Z-pinch initial diameter.

Collisionless shock acceleration of quasimonoenergetic ions in ultrarelativistic regime.

Collisionless shock acceleration of carbon ions (C^{6+}) is investigated in the ultrarelativistic regime of laser-plasma interaction by accounting for the radiation reaction force and the pair production in particle-in-cell simulations. Both radiation reaction force and pair-plasma formation tend to slow down the shock velocity, reducing the energy of the accelerated ions, albeit extending the timescales of the acceleration process. The slab plasma target achieves a lower energy spread while the target with a tailored density profile yields higher ion acceleration energies.

Two-stage laser acceleration of high quality protons using a tailored density plasma

A new scheme of proton acceleration from a laser-driven near-critical-density plasma is proposed. Plasma with a tailored density profile allows a two-stage acceleration of protons. The protons are pre-accelerated in the laser-driven wakefields, and are then further accelerated by the collisionless shock, launched from the rear side of the plasma. The shock has a small transverse size, and it generates a strong space-charge field, which defocuses protons in such a way, that only those protons with the highest energies and low energy spread remains collimated. Theoretical and numerical analysis demonstrates production of high-energy proton beams with few tens of percents energy spread, few degrees divergence and charge of few nC. This scheme indicates the efficient generation of quasi-monoenergetic proton beams with energies up to several hundreds of MeV with PW-class ultrashort lasers.

Optimization of laser-plasma injector via beam loading effects using ionization-induced injection

Simulations of ionization-induced injection in a laser driven plasma wakefield show that high-quality electron injectors in the 50–200 MeV range can be achieved in a gas cell with a tailored density profile. Using the PIC code Warp with parameters close to existing experimental conditions, we show that the concentration of N2 in a hydrogen plasma with a tailored density profile is an efficient parameter to tune electron beam properties through the control of the interplay between beam loading effects and varying accelerating field in the density profile. For a given laser plasma configuration, with moderate normalized laser amplitude, a0=1.6 and maximum electron plasma density, ne0=4×1018 cm-3, the optimum concentration results in a robust configuration to generate electrons at 150 MeV with a rms energy spread of 4% and a spectral charge density of 1.8 pC/MeV.

Dynamics of electron injection and acceleration driven by laser wakefield in tailored density profiles

The dynamics of electron acceleration driven by laser wakefield is studied in detail using the particle-in-cell code WARP with the objective to generate high-quality electron bunches with narrow energy spread and small emittance, relevant for the electron injector of a multistage accelerator. Simulation results, using experimentally achievable parameters, show that electron bunches with an energy spread of $\ensuremath{\sim}11%$ can be obtained by using an ionization-induced injection mechanism in a mm-scale length plasma. By controlling the focusing of a moderate laser power and tailoring the longitudinal plasma density profile, the electron injection beginning and end positions can be adjusted, while the electron energy can be finely tuned in the last acceleration section.

Study of the stability of Z-pinch implosions with different initial density profiles

Stability of metal-puff Z pinches was studied experimentally. Experiments were carried out on a facility producing a load current up to 450 kA with a rise time of 450 ns. In a metal-puff Z pinch, the plasma shell is produced due to evaporation of the electrode material during the operation of a vacuum arc. In the experiment to be reported, a single-shell and a shell-on-jet pinch load with magnesium electrodes were used. Two-dimensional, 3 ns gated, visible-light images were taken at different times during the implosion. When the shell was formed from a collimated plasma flow with small radial divergence, Rayleigh–Taylor (RT) instability typical of gas-puff implosions was recorded. The RT instability was completely suppressed in a mode where the initial density distribution of the shell approached a tailored density profile [A. L. Velikovich et al., Phys. Rev. Lett. 77, 853 (1996)].

Aluminum integral foams with tailored density profile by adapted blowing agents

The goal of the present work is the variation of the structure of aluminum integral foams regarding the thickness of the integral solid skin as well as the density profile. A modified die casting process, namely integral foam molding, is used in which an aluminum melt and blowing agent particles (magnesium hydride MgH2) are injected in a permanent steel mold. The high solidification rates at the cooled walls of the mold lead to the formation of a solid skin. In the inner region, hydrogen is released by thermal decomposition of MgH2 particles. Thus, the pore formation takes place parallel to the continuing solidification of the melt. The thickness of the solid skin and the density profile of the core strongly depend on the interplay between solidification velocity and kinetics of hydrogen release. By varying the melt and blowing agent properties, the structure of integral foams can be systematically changed to meet the requirements of the desired field of application of the produced component.

Laser imprint reduction with a short shaping laser pulse incident upon a foam-plastic target

In the previous work [Metzler et al., Phys. Plasmas 6, 3283 (1999)] it was shown that a tailored density profile could be very effective in smoothing out the laser beam nonuniformities imprinted into a laser-accelerated target. However, a target with a smoothly graded density is difficult to manufacture. A method of dynamically producing a graded density profile with a short “shaping” laser pulse irradiating a foam layer on top of the payload prior to the drive pulse is proposed. It is demonstrated that the intensity and the duration of the shaping pulse, the time interval between the shaping pulse and the drive pulse, and the density ratio between the foam and the payload can be selected so that the laser imprint of the drive pulse is considerably suppressed without increasing the entropy of the payload. The use of the foam-plastic target and a shaping pulse reduces the imprinted mass perturbation amplitude by more than an order of magnitude compared to a solid plastic target. The requirements to the smoothing of the drive and “shaping” laser beams and to the surface finish of the foam-plastic sandwich target are discussed.

Reduction of early-time perturbation growth in ablatively driven laser targets using tailored density profiles

The effects of tailoring the density profile in a laser target in order to decrease imprinting of mass perturbations due to the long-wavelength modes are investigated analytically and numerically. Inverting the acceleration of the ablation front during the shock transit time could reduce the early-time mass perturbation amplitudes developed in the target after the shock transit. This principle was first suggested for mitigating the Rayleigh–Taylor (RT) instability of imploding Z-pinches [Velikovich et al., Phys. Rev. Lett. 77, 853 (1996); Phys. Plasmas 5, 3377 (1998)]. As the shock wave slows down propagating into higher density layers, the effective gravity near the ablation front has the same direction as the density gradient. This makes the mass perturbations near it oscillate at a higher frequency and at a lower amplitude than they normally would due to the “rocket effect” caused by mass ablation [Sanz, Phys. Rev. Lett. 73, 2700 (1994); Piriz et al., Phys. Plasmas 4, 1117 (1997)]. So, tailoring density profiles instead of using flat densities is demonstrated to reduce the “seed” mass perturbation amplitude at the onset of the exponential RT growth.

Stabilized radiative Z-pinch loads with tailored density profiles

Mitigation of the Rayleigh–Taylor (RT) instability of Z-pinch loads imploded from large initial radii through tailoring initial load density profiles in radial and axial directions is studied numerically. These methods could be helpful for a variety of applications of high-power Z-pinches, from producing large amounts of K-shell radiation to imploding inertial confinement fusion pellets. Radial density tailoring is demonstrated to delay the onset of the RT instability development at the expense of reducing the energy available for conversion into radiation. Axial density tailoring can fully stabilize acceleration of a fraction of the initial load mass. For a better tradeoff between stability and radiative performance of the loads, the density profiles could be tailored in two dimensions, combining the advantages of both methods. Post-processing of the radiation-magnetohydrodynamic simulation results demonstrates that an appreciable K-shell argon radiation power could be generated with a stabilized argon load imploded by a 5 MA current from a ∼10 cm initial radius in about 0.5 μs.

Suppression of Rayleigh-Taylor Instability in Z-Pinch Loads with Tailored Density Profiles.

A load structure with tailored density profile which delays the onset of the Rayleigh-Taylor instability development in imploding {ital Z} pinches by inverting acceleration of the magnetic field/plasma interface is proposed and studied numerically. This approach makes it possible to start gas-puff implosions from large radii (say, 8cm) and produce significant {ital K}-shell yield with current pulse duration of 250ns and longer. It could also be used to mitigate imprinting of initial perturbations into laser fusion targets. {copyright} {ital 1996 The American Physical Society.}