Uniform heating of materials into the warm dense matter regime with laser-driven quasimonoenergetic ion beams

In a recent experiment at the Trident laser facility, a laser-driven beam of quasimonoenergetic aluminum ions was used to heat solid gold and diamond foils isochorically to 5.5 and 1.7 eV, respectively. Here theoretical calculations are presented that suggest the gold and diamond were heated uniformly by these laser-driven ion beams. According to calculations and SESAME equation-of-state tables, laser-driven aluminum ion beams achievable at Trident, with a finite energy spread of Δ$E/E\sim 20\%$, are expected to heat the targets more uniformly than a beam of 140-MeV aluminum ions with zero energy spread. The robustness of the expected heating uniformity relative to the changes in the incident ion energy spectra is evaluated, and expected plasma temperatures of various target materials achievable with the current experimental platform are presented.

Figure 1

Schematic layout of the target (not to scale). A laser-driven beam of quasimonoenergetic aluminum ions is incident on the target at 45°. The diamond and gold foils are heated isochorically by the energetic aluminum ions, and become WDM. The ions that pass through the vacuum gap between the two foils are recorded by a magnetic ion spectrometer. On some shots, a Thomson parabola ion spectrometer replaced the magnetic ion spectrometer.

Figure 2

Energy spectrum of the incident aluminum ions at 0° (black bars) measured from Ref. [54] along with the calculated ion energy spectra after penetrating through a 10-µm gold foil (red bars) or a 15-µm diamond foil (blue bars). The measured ion energy spectrum (indicated as black bars) was used as input data in our srim calculations.

Figure 3

(a) The average stopping power of gold for laser-driven aluminum ions (solid red circles) is shown as a function of target depth. The stopping power of gold for a perfectly monoenergetic 140-MeV aluminum ion is also shown (hollow black triangles) to emphasize the heating uniformity expected from the laser-driven ion beam. (b) Similar calculations of the average stopping power of diamond for laser-driven aluminum ions (solid blue triangles) and for a 140-MeV aluminum ion (hollow black triangles) are shown as functions of the target depth.

Figure 4

An example scenario illustrates how we calculate the heating per atom. Ten aluminum ions with an average kinetic energy of 140 MeV are incident on a target. In this example, the target consists of ten million atoms, and the aluminum ions exit the target with an average kinetic energy loss of 40 MeV per ion.

Figure 5

Expected plasma temperatures of gold and diamond are shown as functions of the heating per atom. SESAME EOS Tables No. 2700 (solid red line) and No. 2705 (dashed red line) are used for gold, and SESAME EOS Tables No. 7830 (dashed blue line) and No. 7834 (solid blue line) are used for diamond.

Figure 6

(a) Expected plasma temperature of a 10-µm-thick gold foil heated by the quasimonoenergetic aluminum ion beam is shown as a function of the target depth. SESAME EOS Tables No. 2700 (hollow black circles) and No. 2705 (solid red circles) were used. (b) Expected plasma temperature of a 15-µm-thick diamond foil heated by the quasimonoenergetic aluminum ion beam is shown as a function of the target depth. SESAME EOS Tables No. 7830 (hollow red triangles) and No. 7834 (solid blue triangles) were used. (c) Expected plasma temperature of a gold foil heated by a monoenergetic 140-MeV aluminum ion beam is shown as a function of the target depth. SESAME EOS Tables No. 2700 (hollow black squares) and No. 2705 (solid red squares) were used. (d) Expected plasma temperature of a diamond foil heated by a monoenergetic 140-MeV aluminum ion beam is shown as a function of the target depth. SESAME EOS Tables No. 7830 (hollow red squares) and No. 7834 (solid blue squares) were used. The error bars in (a,b) were calculated assuming a shot-to-shot variation of ±30% in the incident aluminum ion fluence.

Figure 7

(a) Calculated heating uniformity in the gold foil for three different input energy spectra of the aluminum ions. Solid red circles show the expected heating uniformity within the gold foil using the measured energy spectrum of the incident aluminum ions in srim. Hollow blue triangles show the resulting temperatures of gold vs target depth assuming each aluminum ion had 10% more kinetic energy than the measured energy, while hollow black squares show the temperatures assuming 10% less kinetic energy for each ion. (b) Calculated temperatures of diamond are shown as functions of the target depth using three different energy spectra. Solid blue triangles indicate the temperatures obtained from the measured spectrum, while hollow red circles indicate the results using the ions with 10% more kinetic energy and hollow black squares indicate the results using the ions with 10% less kinetic energy. SESAME Table No. 2705 is used for gold and Table No. 7834 is used for diamond.

Figure 8

(a) Heating per atom as a function of the atomic number. The expected heating per atom calculations with the quasimonoenergetic aluminum ion beams are shown for various target materials to serve as a reference for future experiments. The heating per atom increases with the atomic number. (b) Expected plasma temperatures of various target materials are shown as a function of the atomic number. The temperatures determined by the measured expansion speeds in Ref. [37] are shown together with the calculated plasma temperatures of various target materials using the heating per atom calculations and their corresponding SESAME EOS tables. Error bars of ±15% are shown in the above figures.

Figure 9

(a) The average stopping power of gold for the laser-driven aluminum ion beam (solid red circles) is shown as a function of the target depth. Hollow black triangles indicate the stopping power of gold for a monoenergetic 140-MeV aluminum ion beam. (b) The average stopping power of diamond for the laser-driven ion beam is indicated as solid blue triangles, and the stopping power of diamond for a monoenergetic140-MeV aluminum ion beam is shown as hollow black triangles. (c) Heating nonuniformity within a gold foil is shown as a function of the foil thickness for the laser-driven ion beam case (solid red circles) and for the monoenergetic ion beam case (hollow black triangles). (d) Heating nonuniformity within a diamond foil is shown as a function of the foil thickness for the laser-driven ion beam case (solid blue triangles) and for the monoenergetic ion beam case (hollow black triangles).

Figure 10

Solid red circles indicate the expected temperature of gold heated by a laser-driven aluminum ion beam with an average kinetic energy of 140 MeV, while hollow blue triangles show the expected temperature of gold heated by a more energetic ion beam with an average kinetic energy of 280 MeV. The latter ion beam was produced using an $f/1.5$ off-axis parabola in Ref. [54].