2.1. Stimulated Brillouin Scatter

SBS [Reference Labaune, Fabre, Michard and Briand6, Reference Froula, Divol and Glenzer7] occurs when incident light transfers energy to an ion-acoustic wave, and it is expected predominately as backscatter, with a finite angular distribution that exceeds the cone angle of the incident, focused laser. While some SBS can happen in forward directions as well, the laser light will still be absorbed by the target and therefore contribute to the desired preheat. Forward scatter is not observable by the diagnostic suite presented in this study. In a homogeneous plasma, the growth rate for SBS is given by [Reference Montgomery8]

(1) $\begin{array}{}{\gamma }_0=\frac{k_{iaw}eE}{4m_e{\omega }_0}\sqrt{\frac{Z_i{\omega }_p^2{m}_e/m_i}{{\omega }_{iaw}{\omega }_s}}\text{,}\end{array}$

where k _iaw,ω _iaw are the wavenumber and frequency of the ion-acoustic wave, E, the electric field of the laser, e, m _e, the charge and mass of the electron, m _i, Z _i, the mass and charge state of the ion, and ω _p, ω ₀, ω _s, the plasma frequency and the frequencies of the incident laser and the scattered wave. This dependency would suggest a decrease of SBS growth with the nuclear charge Z ₀, since with increasing Z ₀, the mass of an ion species grows faster than the charge state, particularly for relatively low temperatures resulting in partial ionization. However, the growth of SBS can be reduced by Landau damping [Reference Landau9], which is more effective for lighter ions. Here, the ion-acoustic wave transfers energy to ions, which move with velocities close to the wave’s phase velocity. In general, the dominant ion-acoustic mode is expected to have a much faster phase velocity than any species’ average thermal velocity. Therefore, plasmas with lighter ions, exhibiting a higher fraction of the Maxwell–Boltzmann velocity distribution near the wave’s phase velocity, will experience stronger damping. For fusion-relevant plasmas such as those studied in this paper, a common ion temperature in the plasma is typically a valid assumption. As a result, a multispecies plasma will have multiple normal modes corresponding to isotope-specific thermal velocities [Reference Biskamp and Welter10]. These modes can compete and reduce SBS growth. Damping is particularly efficient for adding a (small) fraction of light ions to a heavier species, but the opposite has a potential for notable damping as well, specifically under the consideration of ion trapping [Reference Williams, Berger and Drake11].

2.2. Stimulated Raman Scatter

Stimulated Raman scattering (SRS) [Reference Wilks, Kruer and Denavit12] results from light transferring energy to an electron-plasma wave. Since electrons are several magnitudes lighter than ions, energy transfer is more efficient, and a scattered photon will be significantly red-shifted. The growth rate follows a similar pattern as SBS lowers the influence of charge state and mass ratio [Reference Montgomery8]:

(2) $\begin{array}{}{\gamma }_0=\frac{k_{epw}eE}{4m_e{\omega }_0}\sqrt{\frac{{{\omega }_p}^2}{{\omega }_{epw}{\omega }_s}}\text{,}\end{array}$

where k _epw and ω _epw denote the wavenumber and frequency of the electron plasma wave. As apparent from (2), the influence of the ion properties for SRS can only be a secondary effect, such as mass flow, where densification and rarefaction of ion density cause a modification of the electron density on grounds of charge neutrality in the plasma. SRS side scatter can also occur if the incident laser light is s-polarized with respect to a strong, oblique density gradient [Reference Drake, Turner and Lasinski13]. Side scatter would only be observed if light is s-polarized with respect to the object plane, because it is unlikely that any feature can be discriminated from primary laser interactions if it is caused by light being scattered towards or away from the detector. SRS is more prevalent at densities between 10% and 25% of the critical density, n _c , for a given laser wavelength. Since the experiments discussed in this paper use fill densities below 10% n _c , SRS will likely be a small contributor to energy loss¹.

2.3. Laser-Target Coupling

Coupling of laser energy into the gas is the primary objective of the laser preheat studies at Sandia, and the dominant process for laser deposition is absorption through inverse bremsstrahlung, characterized by the collisional absorption coefficient K [Reference Atzeni and Meyer-Ter-Vehn14]:

(3) $\begin{array}{}K=\frac{{\nu }_e{\omega }_p^2}{c{\omega }_0^2}\frac{1}{\sqrt{1-{{\omega }_p}^2/{\omega }_0^2}}\text{,}\end{array}$

where ω _p is the plasma frequency, and ν _e is the electron collision frequency as described by [Reference Atzeni and Meyer-Ter-Vehn14]

(4) $\begin{array}{}{\nu }_e\propto \frac{n_e{Z}_i\ln {\Lambda }_e}{{T_e}^{3/2}}\text{.}\end{array}$

Equation (4) assumes that the collision frequency is much smaller than the plasma frequency, and ln λ_e is the weakly temperature- and density-dependant Coulomb logarithm. Z _i stands for the ion charge. It becomes immediately clear that different target gases affect heating via a different ion charge state Z _i as noted in the introduction. This brings up a dilemma for surrogate gases: unless you end up with an identical ion charge (such as using hydrogen instead of deuterium-tritium), it is impossible to match both electron density and absorption. As a result, either heating or LPI, or both, will not exactly reproduce the physics of the target gas to be modelled. A best-case compromise is to be found for meaningful studies.

Besides deposited energy, specific coupling details such as the total range of deposition (maximum laser propagation depth) and X-ray brightness distribution of the laser-heated channel can be used to identify similarities and differences for various experimental scenarios. In our experiments, we chose to reduce the density of helium targets by 10%, which we empirically found to preserve the propagation depth of the laser and therefore the plasma volume. Electron densities stay far below the critical density for the laser frequency when fully ionized. D₂ at room temperature and 60 psi against vacuum results in 5% n _e/n _c for 527 nm laser wavelength, while 54 psi of He leads to 4.5% n _e/n _c. Accordingly, no effects such as two-plasmon-decay, reflection at critical density, or enhanced absorption are expected.

2.4. Experimental Methods

All of the experiments that have been evaluated for this study have been performed in the Pecos target area within the Z-Backlighter facility of Sandia National Laboratories. The Z-Beamlet laser [Reference Rambo, Smith and Porter15] was used to heat a gas volume in a cylindrical target through a laser entrance hole that was covered with a thin polymer foil. A bird’s eye view of the target area is depicted in Figure 1. Some experiments included additional diagnostics pictured in the figure, but this article will focus on the near-beam backscatter imaging and shadowgraphy diagnostics.

FIGURE 1: Bird’s eye view rendering of the Pecos target area. Z-Beamlet (bright green) is entering from the left (north). A probe laser (soft green) is propagating through the target and analysed on an optical table to the right (south) of the target chamber.

The targets were cylindrical polycarbonate cells with a polyimide laser entrance window of 3 mm diameter and 1.7 μm thickness, assembled at Sandia by General Atomics [Reference Paguio, Smith and Taylor16]. The targets typically had four diagnostic ports. Two opposing ports with antireflective coated acrylic windows allowed the propagation of a probe beam for optical diagnostics, and two more ports enabled X-ray diagnostics via narrow slits. These slits were covered with 13 μm of polyester or polyimide to contain the fill gas. Figure 2 shows a rendering of the target cells. To protect optics and instruments inside of the target chamber, the gas cells were enclosed in a metal debris box, allowing only for the minimum required access to X-ray diagnostics. The optical diagnostic path was protected by secondary debris windows made from Duraplex™, an impact-hardened variant of polyacrylate [17].

FIGURE 2: (a) Exploded rendering of the target with the main body and mounting base (A1, A2), LEH, optical windows (B), X-ray diagnostic slits (C), and gas inlet nipple (D). (b) Debris enclosure with main body and base (X1, X2), and Duraplex™ debris windows (Y).

2.5. LPI Diagnostics

The primary instruments for the observation of SBS in this paper are a photodiode filtered around the incident laser wavelength (526.6 nm) and a camera recording backscattered light with a similar filter. Both instruments measure the light that is reflected off a square polytetrafluoroethylene (PTFE) screen at the laser entrance wall of the experimental chamber, which has a central aperture that is just large enough to allow unimpeded propagation for the incident laser, as shown in Figure 3. Details for this setup without the diode, the near beam imager (NBI), were recently published by Geissel et al. [Reference Slutz, Herrmann and Vesey3] along with the calibration procedure. PTFE is commonly referred to by DuPont Corporation’s product name Teflon™. With a thickness of a few millimeters, PTFE is an ideal diffuse reflector (scatterer) with an albedo in excess of 98% throughout the visible spectrum and more than 93% when including the near-infrared spectrum (up to λ∼2.5 µm) [Reference Wiley18].

FIGURE 3: Setup of the SBS and SRS near-beam imaging diagnostics. (a) The Z-Beamlet laser enters the chamber through a hole in the PTFE screen (A). Backscattered SBS or SRS light illuminated the screen and recorded via filtered diodes and cameras in the NBI backscatter box (B). (b) Arrangement of instruments inside the NBI backscatter box.

We observe SRS backscatter in a similar setup to SBS but with two differently filtered diodes (long pass filters at 610 nm and 710 nm). Indications of side scatter can be observed on shadowgraphy images of the interaction region as described as follows. Shadowgraphy is the main diagnostic for this observable, using the radial expansion dynamics of the laser-driven blastwave as an indicator for encircled energy density. A detailed description of the measurement and evaluation of deposited laser energy in MagLIF targets has been published recently [Reference Harvey-Thompson, Geissel and Jennings19].

2.6. Shadowgraphy

A pulse train from the Chaco probe laser with a few millijoules at about 500 ps pulse length and 532 nm wavelength was used to image the propagation depth and shape of the laser-induced plasma channel. We will refer to each individual pulse as a frame to emphasize the imaging nature of the diagnostic and to distinguish it from the laser pulses of Z-Beamlet, which were the driver of the experiments. The probe propagation was orthogonal to Z-Beamlet. Two probe paths were used allowing an east-west view of the target in earlier experiments and an up-down view later. The Z-Beamlet laser was polarized horizontally and will, therefore, refer to the later setup as p-polarized view, since the laser polarization was parallel to the imaging plane. Adhering to standard optics terminology, we will refer to the earlier setup as s-polarized view. Figure 4 shows renderings of the p- and s-polarized setups including the two pinhole cameras for side-on and end-on X-ray imaging.

FIGURE 4: (a) Configuration of the target chamber centre for s-polarized view with only one X-ray diagnostic port. (b) Configuration for the p-polarized view. The X-ray diagnostic port opposite to the pinhole camera is used for spectroscopy. Both renderings omitted to debris enclosure for better clarity.

Up to four frames were used, with the late frames carrying blast wave expansion data for the determination of deposited energy. The earliest frame was typically within a few nanoseconds after the end of Z-Beamlet’s main pulse, thus allowing us to determine the laser propagation depth and the overall shape of the heated region in the target. Only the first frame is used in this study. Later frames occurred with 25 ns separation between frames to improve the fidelity of energy deposition measurements as reported by Harvey-Thompson et al. [Reference Harvey-Thompson, Geissel and Jennings19]. The frames were recorded with an ultrafast hybrid CMOS detector developed at Sandia National Laboratories [Reference Claus, Robertson and Fang20].

2.7. Laser Configurations

Z-Beamlet operates at the second harmonic (2ω) of Nd:YLF’s 1053 nm line, which results in a centre wavelength of 526.6 nm. Pulses of 0.3–6 ns width can reach up to 1 TW power with a maximum contained energy of about 4.5 kJ, not accounting for losses in the subsequent beam transport. The laser beam with a square cross section of 31 cm × 31 cm is focused by a 3.2 m lens onto the target with the best focus on the LEH window (with phase plate) or 3.5 mm in front of the LEH window (without phase plate). For the experiments described here, the laser energy was chosen not to exceed a total of 2.5 kJ on target. Three different laser configurations were chosen to reflect parameters that were historically relevant for MagLIF and covered different regimes of LPI generation.

Early experiments were used as a defocused spot on the LEH window without any spot smoothing by distributed phase plates (DPP [Reference Dixit, Nugent, Lawson, Manes and Powell21, Reference Lin, Lawrence and Kessler22]). This scenario also used the highest power and ultimately yielded by far the highest LPI effects as described in detail in Geissel et al. [Reference Geissel, Harvey-Thompson and Awe2]. As laid out in the same publication, two more configurations were employed by using phase plates with 750 µm and 1100 µm diameter for 95% of encircled energy in the spot, which we refer to as DPP750 and DPP1100. These two also used a longer main pulse with lower power to further reduce LPI without sacrificing laser energy. The area characterizing the peak intensity, not including the slopes of the focal spot’s edges, was well described for either phase plate by a circle enclosing 75% of the laser energy [Reference Geissel, Harvey-Thompson and Awe2] at 0.0025 cm² (DPP750) and 0.0053 cm² (DPP1100) but cannot be determined well for cases without phase plate. Acknowledging that concentrated areas with higher and lower intensities exist, we take the area of the smallest rectangle that encloses 75% of the energy as a substitute (0.0013 cm²). All laser configurations used a prepulse to preheat the LEH window and minimize its impact on the main pulse’s energy deposition. The peak of this prepulse was set at 3.5 ns prior to T = 0, which is defined by the half-height point of the rising edge of the main pulse. Table 2 lists a summary of the laser configurations.

TABLE 2: Comparison of laser configurations covered in this study including a plot illustrating the typical laser pulse train. T = 0 is defined as the half-height point of the rising edge of Z-Beamlet’s main pulse. For more details about the focal intensity distribution with or without the two applied phase plates, see Geissel et al. [Reference Slutz, Herrmann and Vesey3].