Proton imaging of high-energy-density laboratory plasmas

Proton imaging has become a key diagnostic for measuring electromagnetic fields in high-energy-density (HED) laboratory plasmas. Compared to other techniques for diagnosing fields, proton imaging is a measurement that can simultaneously offer high spatial and temporal resolution and the ability to distinguish between electric and magnetic fields without the protons perturbing the plasma of interest. Consequently, proton imaging has been used in a wide range of HED experiments, from inertial-confinement fusion to laboratory astrophysics. An overview is provided on the state of the art of proton imaging, including a discussion of experimental considerations like proton sources and detectors, the theory of proton-imaging analysis, and a survey of experimental results demonstrating the breadth of applications. Topics at the frontiers of proton-imaging development are also described, along with an outlook on the future of the field.

Figure 1

Schematic of a proton-imaging setup.

Figure 2

Schematic of the main processes involved in the TNSA mechanism. (a) First, a laser prepulse impinges upon and heats a thin target to form a preplasma. The target contains layers of proton-rich hydrocarbons as common contaminants. (b) Second, the peak of the pulse arrives, efficiently heating electrons to relativistic temperatures. These electrons expand and propagate through the target. (c) Third, the hot electrons emerge into the vacuum and form an electron sheath with a strength of $\sim \mathrm{TV}/\mathrm{m}$. This field ionizes the rear surface such that ions are accelerated to multi-MeV energies. Adapted from [180].

Figure 3

(a) TNSA spectrum obtained on the NOVA Petawatt laser at LLNL, expressed in the number of protons per MeV (left scale). Adapted from [282]. TNSA cutoff energies plotted against (b) laser intensity on target and (c) laser energy. The data are from a select number of experiments where a scan in laser energy was performed. Adapted from [339].

Figure 4

Schematic of an exploding-pusher mode of capsule implosion and fusion in direct-drive inertial-confinement fusion. (a) Multiple laser beams directly and symmetrically illuminate the thin-glass-shell capsule surface. (b) The explosion of the shell caused by laser energy absorption drives a strong spherical shock propagating radially toward the capsule center. (c) The converging shock collapses in the center and bounces back, resulting in an increase of ion temperature and fuel density, and (d) the facilitation of nuclear fusion reactions and burn.

Figure 5

(a) Typical spectra of fusion products generated in a $\mathrm{D}{}^3\mathrm{He}$-filled, thin-glass-shell, laser-driven exploding pusher as implemented for backlighters on the Omega laser facility. (b) DD and (c) $\mathrm{D}{}^3\mathrm{He}$ proton yields as a function of laser energy on the capsule. Adapted from [118].

Figure 6

RCF stack obtained at PHELIX, consisting of seven films of the type HD-810 and five films of the type MD-55. The proton Bragg peak energy is given for each film layer. Adapted from [15].

Figure 7

Proton images using a $\mathrm{D}{}^3\mathrm{He}$ source. (a) Synthetic proton images of the target shown at the top of (c), several nanoseconds after lasers have driven shocks into the gray tube from either end. The top image is of 13 MeV protons, and the bottom image is of 14.7 MeV protons. These are the detected energies from protons born at 14.7 MeV and down scattered in energy by the target, allowing different aspects of the target to be imaged with a monoenergetic source. (b) The same images from the experiment taken from a two-piece stack of CR-39. The top image of down-scattered 13 MeV protons is from the rear side of the first piece of CR-39, while the bottom image of 14.7 MeV protons is from the front side of the second piece of CR-39. The bottom image of (c) shows an enlargement of CR-39. Each dark circle is a particle track, and the faint diagonal line is due to laser light from a microscope’s autofocus mechanism. This image corresponds to about $1.6\times {10}^{-4}{\mathrm{cm}}^2$, which is equivalent to 15% of the area of one pixel in the experimental images. Adapted from [160].

Figure 8

Contour plot of the number of tracks vs the track contrast and diameter for the piece of CR-39 shown in the inset. The four particle species visible are labeled on the plot (compare to the inset image). Intrinsic CR-39 noise appears in the low-contrast low-diameter regime. Contours represent a constant number of tracks per unit contrast and diameter; the values of this quantity corresponding to plotted contours form a geometric series with a ratio of 2. As defined in this review, a high contrast number is a dark track, while a low contrast number is a light track. Adapted from [341].

Figure 9

Diagram illustrating the main components of a proton-imaging diagnostic. Left panels: typical proton sources. TNSA protons are generated using a short-pulse (SP) laser to irritate a thin foil, which emits protons in a beam with a broadband energy profile. $\mathrm{D}{}^3\mathrm{He}$ protons are generated using long-pulse (LP) lasers to drive the implosion on a thin-shell capsule, which isotropically emits monoenergetic DD and $\mathrm{D}{}^3\mathrm{He}$ protons as fusion by-products. Right panels: typical proton detectors. TNSA protons are collected on a stack of RCFs that provides energy resolution. $\mathrm{D}{}^3\mathrm{He}$ protons are collected on CR-39, one for each proton energy. Center diagram: typical proton-imaging setup in a magnified point-source configuration, including source, optional mesh, the plasma under study, and detector (not drawn to scale).

Figure 10

Proton images of a laser-driven, solid $840\mathrm{\mu }\mathrm{m}$ diameter CH sphere, made using a setup similar to Fig. 9. (a) Image recorded with no laser drive on the CH sphere. (b)–(d) Images recorded with laser drive for three different particle types and energies. Adapted from [270].

Figure 11

(a) Bragg peak proton energy vs depth in the RCF stack (solid curve) and corresponding time of flight for three different values of the source-object separation $r_{\mathrm{s}}$ (dotted line, 1 mm; dashed line, 2 mm; dash-dotted line, 3 mm). (b) Normalized energy response curves for an RCF stack made of several layers of HD810 (solid curve). (c) Normalized temporal response curve for the stack configuration in (a) and a source-plasma distance of 3 mm (solid curve). The red dashed curves in (b) and (c) are response curves multiplied by a typical TNSA exponential spectrum with temperature of 2 MeV. Adapted from [243].

Figure 12

Proton probing of the expanding sheath at the rear surface of a laser-irradiated target. (a) Setup of the experiment. A proton beam is used as a transverse probe of the sheath. (b)–(g) Temporal series of proton images in a time-of-flight arrangement. The probing times are relative to the peak of the interaction. (h) Deflectometry image where a mesh is placed between the probe and the sheath plasma for a quantitative measure of proton deflections. Adapted from [238].

Figure 13

Workflow for a typical particle-tracing algorithm. Courtesy of L. Romagnani.

Figure 14

An ellipsoidal blob magnetic field used to illustrate contrast regimes. $(x_0,y_0)$-slice plots of (a) magnetic-field strength $B=|\mathit{B}|$ and (b) MHD current density $j_z$ in the center of the ellipsoidal blob (at $z=z_0$), normalized by the maximum field strength $B_{\max }$ and maximum current density, respectively. The magnetic-field lines and the field’s orientation are shown in white in (a), where ${\ell }_{\mathrm{M}\parallel }={\ell }_{\mathrm{M}\perp }=0.04\mathrm{cm}$. (c),(d) Normalized lineouts of $B_y$ and $j_z$ in $x_0$ (at $y_0=0$) with the values of $B_{\perp }$ and $j_{\parallel }$ line integrated along the trajectories of protons that originate from a source at $(x,y,z)=(0,0,-r_{\mathrm{s}})$ and pass through positions $(x,y,z)=(x_0,y_0,0)$.

Figure 15

Comparison of contrast-parameter ($\mu$) regimes for proton images of the ellipsoidal blob magnetic field described in Fig. 14. Images in the (a) linear, (c) nonlinear injective, and (e) caustic regimes are shown, as are proton-fluence lineouts along $x$ (at $y=0$) in (b), (d), and (f), respectively. Superimposed onto the images is the mapping ${\mathit{d}}_{\perp }={\mathit{d}}_{\perp }({\mathit{x}}_{\perp 0})$ for each case (the solid lines). To generate the images, protons were simulated with $v_0=5.31\times {10}^9\mathrm{cm}/\mathrm{s}$ (corresponding to 14.7 MeV protons), a setup with $r_{\mathrm{s}}=1$ and 30 cm, and a field $B_{\max }=10,200$, and 500 kG for the linear, nonlinear injective, and caustic regime images, respectively. The resolution of the images is $200\times 200\mathrm{pixels}$, with a mean proton density per pixel of 100. Following previous conventions for the ellipsoidal blob ([131]), one can define $\mu$ as $\mu =\sqrt{\pi }e{r}_{\mathrm{s}}{B}_{\max }{\ell }_{\mathrm{M}\parallel }/m_{p}c{v}_0\mathcal{M}{\ell }_{\mathrm{M}\perp }$, where $\mathcal{A}$ is an order-unity constant of proportionality.

Figure 16

Experimental images of TNSA proton deflectometry of a laser-generated plasma shown for geometries in which protons pass first through (a) the plasma (front projection) or (c) target (rear projection). Corresponding synthetic proton images were created with the particle-tracing code ptrace using an idealized magnetic-field torus in (b) front and (d) rear geometries, respectively. Adapted from [34].

Figure 17

Top row: proton images of the fields generated from laser ablation of different target materials at a time of 0.75 ns into a 1 ns, 1025 J interaction. The proton energy is 37.3 MeV for CH, Al, and $\mathrm{Cu}+\mathrm{Al}$, and 30.7 MeV for $\mathrm{Au}+\mathrm{Al}$. Bottom left panel: radial lineouts of the proton fluence ($J$) normalized by the mean inferred reference profile ($J_0$). Bottom right panel: the resulting reconstructed field profiles. For Al and $\mathrm{Cu}+\mathrm{Al}$, the results of double-Gaussian fitting are shown with shaded regions. Adapted from [31].

Figure 18

Schematic of a laser-driven magnetic reconnection geometry. The opposing magnetic fields are driven together in the midplane between the laser focal spots. The fields can be probed at different times to observe the dynamics. Adapted from [197].

Figure 19

Time series for two shots of a high-intensity laser-plasma-driven reconnection experiment in a geometry similar to Fig. 18. Top row: the measured proton fluence at the detector plane. Middle row: the calculated undisturbed beam fluence at the detector plane. Bottom row: the retrieved path-integrated magnetic fields at the interaction plane. The white contours with arrows show the topology of the calculated magnetic fields. Adapted from [209].

Figure 20

Observations of filamentary magnetic-field generation by ion-Weibel instability in laser-generated counterstreaming plasmas. The filamentation scale is on the order of the ion-skin depth. (a) Observations at OMEGA EP using TNSA protons at approximately 5 MeV. Adapted from [74]. (b) Top row: observations at OMEGA using $\mathrm{D}{}^3\mathrm{He}$ protons at 14.7 MeV. Bottom row: synthetic proton images from 3D PIC simulations modeling the experiments from the top row. Adapted from [210].

Figure 21

Data from electrostatic shock experiments in which a dense laser-driven plasma expands into a low-density background plasma. (a) Proton-imaging data taken at the peak of the interaction pulse with 7 MeV TNSA protons. Note the strong modulation associated with the ablating plasma in region I and the modulated pattern ahead of the shock front possibly associated with a reflected ion bunch in region IV. The arrow indicates the laser beam direction. (b)–(c) Details and RCF optical density lineout corresponding to region II, showing modulations associated with a train of solitons. (d)–(k) Details about region III and corresponding lineouts of the probe proton density $\delta n_p/n_{pu}$, the reconstructed electric field $E$, and the reconstructed normalized ion velocity $u_{/}{c}_{ia}$ in the cases of (d)–(g) an ion acoustic soliton and (h)–(k) a collisionless shock wave [the collisionless shock detail corresponds to a different shot (not shown)]. Adapted from [240].

Figure 22

(a) Data from a magnetized shock experiment shown schematically. (b) Proton image taken at 3.75 ns using 14.7 MeV $\mathrm{D}{}^3\mathrm{He}$ protons. The laser is incident from the right and the plasma expands to the right. (c) Proton intensity (red squares) taken from the shaded red region in (b), normalized to the mean intensity, and the associated reconstructed path-integrated magnetic field $\int B_y\mathrm{d}z$ (black solid line). Also shown is the normalized proton intensity (green dashed line) forward modeled from a 2D synthetic magnetic field $B_y(x,z)$, which has the dashed blue profile at $z=0$. The model uncertainties are shown as shaded regions. Adapted from [261].

Figure 23

Proton images of laser-driven magnetized, supersonic jets. For this experiment, 10 kJ of laser energy (20 beams, each with 500 J of energy) was focused over 1 ns into a hollow ring (radius of $800\mathrm{\mu }\mathrm{m}$) to produce the jet. $\mathrm{D}{}^3\mathrm{He}$ 14.7 MeV proton-imaging data were then collected at different times: (a) 1.6, (c) 2.8, and (e) 3.6 ns after the initiation of the drive beams. 3D flash simulations of the experiment were also performed, and (b),(d),(f) synthetic proton images were then generated at these times. In addition, 1D direct inversion analysis was performed on a lineout of the experimental data. The position of the lineout is indicated by the blue line in (e), the lineout itself is shown in (g), and the path-integrated magnetic field is recovered by the inversion shown in (h). Adapted from [87].

Figure 24

Proton images of stochastic magnetic fields amplified by a turbulent laser-plasma dynamo. Left panel: Annotated photograph of the experimental platform used to create the dynamo. The $\mathrm{D}{}^3\mathrm{He}$ 14.7 MeV proton images collected during the experiment are shown in the top middle panels, with corresponding path-integrated magnetic-field maps recovered from these images shown in the bottom middle panels. Estimates of the rms and maximum magnetic-field strengths, as well as the correlation lengths, were then recovered from these maps using statistical methods; see the error bars in the right panel). The results were compared with similar quantities inferred from 3D flash simulations of the experiment (see the triangle markers in the right panel), as well as the same quantities computed directly (the solid lines). Adapted from [23].

Figure 25

TNSA proton images taken during laser irradiation of a $50\mathrm{\mu }\mathrm{m}$ Ta wire (vertical stripe at the center of the images). The frames are three RCF layers from the same shot and refer to different probing times ahead of the peak of the interaction pulse: (a) early time where the proton beam is largely undisturbed ($E_p\sim 8\mathrm{MeV}$, $t\sim -12\mathrm{ps}$); (b),(c) time close to the peak interaction, where the proton beam is modified significantly due to charging of the Ta wire that deflects the protons away from the wire. (b) $E_p\sim 7\mathrm{MeV}$, $t\sim -8\mathrm{ps}$. (c) $E_p\sim 6\mathrm{MeV}$, $t\sim -3\mathrm{ps}$. Adapted from [20].

Figure 26

(a) Schematic of the experimental setup used to image CH foils with 2D seed perturbations using $\mathrm{D}{}^3\mathrm{He}$ proton sources. (b) Expanded view of proton deflections (green arrows) due to RT-induced density, as well as electric-field (blue arrows) and magnetic-field (red symbols) modulations in the target. (c) Path-integrated quantities (arbitrary units) are shown during the linear growth phase. (d) Sample proton-fluence images for flat and modulated foils; scale size is given in the target plane and lineout direction is indicated. Proton fluence is normalized for comparison across different shots. (e) Measured rms fluence variations (red triangles) in proton images. Expected rms variation due to the mass only (green circles) was calculated using density distributions from x-ray data. Adapted from [170]. (f) Face-on proton image of a $15\text{−}\mathrm{\mu }\mathrm{m}$-thick CH foil taken with 25 MeV TNSA protons at 2.12 ns after irradiation. Adapted from [86]. (g) Side-on image using 13 MeV TNSA protons at 2.56 ns after irradiation. Adapted from [84].

Figure 27

(a) 15.1 MeV proton images of imploding capsules at two times: $t=0.8$ and 1.9 ns. In the fluence images, darker shades indicate higher fluence. Comparatively, a fluence peak occurs in the image centers during the early stages of implosion, indicating a “focusing” of imaging protons there, while at later times the fluence is extremely low, or defocused, at the image centers. (b) Radial profiles of the proton-fluence images from (a). (c) Radial electric fields estimated from experimental measurements (open circles) and from lilac simulations (solid circles) vs implosions times. Horizontal error bars represent uncertainties in backlighter burn time. The differences between simulation and data can largely be accounted for by the effects of proton scattering. Adapted from [145].

Figure 28

End-on $\mathrm{D}{}^3\mathrm{He}$ proton images show surpluses in the regions between the pairs of expanding plasma plumes in (a) a gas-filled Au hohlraum but show deficits in (b) a CH-lined, vacuum Au hohlraum. They indicate opposing directions of the self-generated electric fields, as illustrated schematically by the corresponding sketches. Adapted from [148].

Figure 29

Sketch of an advanced proton-imaging detector.