Enhanced X-ray emission arising from laser-plasma confinement by a strong transverse magnetic field

Abstract

We analyze, using experiments and 3D MHD numerical simulations, the dynamic and radiative properties of a plasma ablated by a laser (1 ns, 10[Formula: see text]-10[Formula: see text] W/cm[Formula: see text]) from a solid target as it expands into a homogeneous, strong magnetic field (up to 30 T) that is transverse to its main expansion axis. We find that as early as 2 ns after the start of the expansion, the plasma becomes constrained by the magnetic field. As the magnetic field strength is increased, more plasma is confined close to the target and is heated by magnetic compression. We also observe that after [Formula: see text] ns, the plasma is being overall shaped in a slab, with the plasma being compressed perpendicularly to the magnetic field, and being extended along the magnetic field direction. This dense slab rapidly expands into vacuum; however, it contains only [Formula: see text] of the total plasma. As a result of the higher density and increased heating of the plasma confined against the laser-irradiated solid target, there is a net enhancement of the total X-ray emissivity induced by the magnetization.

Figure 1

(a) Setup of the experiment and global plasma morphology resulting from the plasma-magnetic field interaction. A solid (Polytetrafluoroethylene (PTFE), CF${}_2$) target, mimicking an ICF hohlraum wall, is immersed in a large-scale, steady, axial and strong (up to 30 T) magnetic field that is aligned with the target surface (along the z-axis). A long (0.6 ns FWHM) high-power (40 J, 4 × 10¹³ W/cm${}^2$) laser pulse at $\lambda =1$ µm irradiates the wall at normal incidence, inducing plasma heating and expansion. The laser was focused using a 2.2 m focal length lens (f/21) and a random phase plate. (b,c) The images on the right represent the X-ray self-emission images of fluorine He${}_{\beta }$ spectral line obtained by viewing the 3D plasma side-on (i.e. in the XY plane) and from the top (i.e. in the XZ plane) where there was an 20 T applied magnetic field. These images are time-integrated and measured simultaneously on the same shot by two focusing spectrometers with spatial resolution (FSSR) deployed in the experiment (see “Methods” section). The images demonstrate that the global morphology of the plasma corresponds to that sketched in the cartoon (a), i.e. of a plasma that becomes extended in the XZ plane, while it is compressed in the XY plane. The white arrows in the side-view point to the increase in emissivity in the spatial region $\sim 4$ mm (see text).

Figure 2

(a–c) 2D maps of the plasma electron density 40 ns after the laser irradiation on target (located on the left edge of the images at $x=0$), for various strengths of the applied external magnetic field, as indicated. The color scale shown in (a) applies for all images. The images in (b,c) are reconstructed from two different shots with same parameters but obtained by moving the target within the diagnostic field of view, such that we can reconstruct a larger span of the plasma evolution. Patching this way two images obtained on two different shots is possible because the reproducibility of the results is very high, which is due to the external magnetic field generation having less than 1% variation from shot-to-shot. (d) Corresponding radially integrated electron density as a function of the distance from the target, i.e. the 1D densities are obtained from 2D maps as shown in (a–c) and integrated over the axis Y. The lines correspond, respectively, to the case of a free expansion (black, dashed), 10 (thin red) and 30 T (thick blue). The maximum noise level is about $1\times {10}^{16}$ cm${}^{-1}$, i.e. much lower than experimental data.

Figure 3

(a) Relative intensity profile measured by the VSG spectrometer in a wide spectral (integrated over 0.65–1 keV) and spatial range. (b) Relative intensity of the spectral line Ly${}_{\alpha }$ measured by the FSSR spectrometer. (c) Profile of the volumetric electron density inferred in the plasma, and along the axis X, from the FSSR data (see text). (d) Same as (c) for the plasma electron temperature. For all panels, three cases, corresponding to different strengths of the applied magnetic field, are shown: 0 (black, dashed), 20 (red, thin) and 30 T (blue). Note that the values indicated in (c,d) are time-averaged due to time-integrated measurement performed by the FSSR spectrometer. (e) Evolution of the integrated plasma emission intensity (normalized to its value at $B=30$ T), integrated in space (over the domain X = 1–6 mm) and time, and deduced from the intensity profiles shown in (a), as a function of the B-field strength.

Figure 4

(a) Experimental (full) and simulated (dashed) spatial profiles of the X-ray resonance line Ly${}_{\alpha }$ in the free expansion case. The theoretical intensities were normalized by the corresponding experimental points. (b) Same in the case where a transverse magnetic field $B=30$ T is applied. In the simulations, the excitation processes, as well as the recombination ones, were taken into account, as detailed in the “Methods” section. Note that the modelling, for the same velocity of the plasma component, but different densities can result in different slopes for the spectral intensity.

Figure 5

3D MHD simulation results. (a,b) Pseudocolor maps of the relative plasma emission intensity in the XY plane, in logarithm, and for (as indicated) $B=0$ T and $B=30$  T, respectively. Images are normalized to their own respective maximum, which is distinct for each case. (c) Profiles of relative emission intensity, integrated over time (up to 24 ns, which is the maximum time in the simulation) and over the Y and Z-directions, for $B=0$ (black, dashed), 20 (red, thin) and 30 T (blue) (similarly as in Fig. 3a). (d) Profiles of electron density in logarithm scale, integrated over time and over the Y and Z-directions, for $B=0$ (black, dashed), 20 (red, thin) and 30 T (blue). (e) Evolution of the integrated plasma emission intensity (normalized to its value at $B=30$ T), integrated in space and time, as a function of the B-field strength.

Figure 6

(a) Image of the X-ray emission analyzed by the FSSR spectrometer of the laser-induced plasma expansion inside the transverse magnetic field of 30 T strength. What is seen is the spectrally resolved image of the plasma in the XY plane. Arrows demonstrate the increase in emissivity in the spatial region $\sim 4$ mm. (b) FSSR X-ray raw image showing similar spectral range as in (a), but when probing the plasma along a different line of sight, here along the Y-axis of plasma expansion (see Fig. 1). Hence what is seen is the spectrally resolved image of the plasma in the XZ plane. The absence of the Ly${}_{\alpha }$ line here is due to the different target-to-crystal distance that was changed to 214 mm in order to better observe the 2D dynamics (with higher spatial resolution along Z axis and magnification $m=1$ in meridional plane) of the plasma expansion.

Figure 7

Scheme of the mechanisms producing the populations implied in the generation of the spectral resonance lines of multicharged ions. Here are depicted the levels with charges $Z-1$, Z, $Z+1$, each being in its ground states; levels 1 and 2 are excited levels. The red and blue lines correspond to the excitation or recombination population mechanism into the excited level. The further transition of an electron from each excited state (black arrows) leads to the ion emission of the corresponding spectral line.

Figure 8

(a) Relative intensity of the spectral line He${}_{\beta }$ measured by the FSSR spectrometer in the experiment both for a free expansion (black) and for the propagation in the transverse magnetic field with a strength of 20 (red) and 30 T (blue). (b) Experimental and simulated intensity profiles for the resonance line He${}_{\beta }$ in the free expansion case. Theoretical intensities were normalized by the corresponding experimental point. The inferred plasma parameters are indicated. (c) Same as (b) but for the case when the transverse magnetic field $B=30$ T is applied. Our analysis suggests an electron temperature of 54 eV at a density of $2\times {10}^{19}$ ${\text{cm}}^{-3}$ in the shocked region.

Figure 9

(Top) VSG X-ray images (in PSL) for a laser-induced plasma immersed into a magnetic field of different strengths 0–30 T and when the laser intensity is about $2\times {10}^{12}$ W/cm${}^2$ on the target. (bottom) The same but for the laser intensity of $4\times {10}^{13}$ W/cm${}^2$.

Figure 10

(a) Spatial profile of the emitted X-rays as recorded by the VSG and integrated over the 0.65–1 keV spectral range, for a $2\times {10}^{12}$ W/cm${}^2$ laser intensity on target. The plasma was immersed into the magnetic field with strength of 30 T (blue), 20 T (red, thin) or expanded freely in vacuum (black dashed). (b) Same but for the He${}_{\beta }$ spectral line measured by the FSSR spectrometer. (c) Evolution of the integrated plasma emission intensity (normalized to its value at $B=30$ T), integrated in space and time, and deduced from the intensity profiles shown in (a), as a function of the B-field strength.