X-ray Images and Spectrograms with Spatial Resolution: Comparison
Please note this is a comparison between Version 2 by Jason Zhu and Version 1 by Evgeny Filippov.

X-ray imaging diagnostics based on Fresnel lenses are very promising as the field of view is of the order of 1 mm and even higher, and the spatial resolution can reach hundreds of nm. The obvious disadvantage of such diagnostics is the presence of the chromatic effect, which reduces the contrast of the image and leads to the need to use a rather narrow spectral range. The spectrographs with flat or curved crystals used so far have a satisfactory spectral resolution but cannot always provide sufficient luminosity and spatial resolution when it comes to obtaining images of plasma sources. Spectrometers with toroidal schemes do not have these disadvantages, but their surface is much more difficult to fabricate and the resulting schemes are difficult to set up because of the limitation in all six degrees of freedom.

  • X-rays
  • imaging
  • astrophysics
  • laser plasma

1. Introduction

The idea of using lasers to create high-temperature plasma was first publicly pro-posed by N.G. Basov in 1961 at a meeting of the Presidium of the Academy of Sciences of the USSR; it was theoretically substantiated in 1964 [1]. The work [1] caused a worldwide sensation and laid the foundation for a new field, inertial thermonuclear fusion. As part of this field, huge facilities with pulsed high-power lasers were built in the Russian Federation, the USA, Japan, England, France, and Germany.
Although Basov’s research was concerned with the generation of plasma primarily for a controlled thermonuclear reaction, its fundamental and applied significance proved immeasurably more far-reaching. From a fundamental point of view, it generated the possibility of creating a laboratory object with well-controlled parameters and ultra-high energy density to study the physical processes taking place within. From an applied point of view, it led to the creation of powerful sources of coherent (X-ray laser) and thermal radiation that became extremely useful in several scientific fields that are not directly related. One example is X-ray spectroscopy of multiply charged ions, which is both experimentally and theoretically important. For experimentalists, laser plasma has become an object where ions with a very high ionization multiplicity can be obtained relatively easily. The good controllability of the parameters of the plasma also made it possible to perform fairly accurate spectral measurements. The results of these measurements made it possible to benchmark the results of theoretical calculations of the spectra of multiply charged ions, even in situations where relativistic effects, where the significance increases with ion charge, become very important.

2. Application of X-ray Pinhole Camera in Laboratory Astrophysics Experiments

Although the pinhole camera usually has relatively low spatial resolution for high energy density physics, the flexibility of laboratory scaling allows the use of this diagnostic device without obvious limitations due to scaling laws and the use of ~mm scale plasmas in many experiments. In one study [59][2], for example, a four-frame X-ray pinhole camera was used to study the generation of a magnetic field and the magnetization of an astrophysical plasma. For this purpose, a laboratory experiment was conducted at the Prague Asterix Laser System (PALS, Prague, Czech Republic). The laser pulse (~1016 W/cm2) irradiated targets with a special shape in the form of a “snail” to generate a controlled spontaneous magnetic field. This approach is extremely interesting as it allows a high magnetic field strength to be maintained over a long period of time, while the resulting plasma structure is sufficiently stable and equilibrated.
A four-frame pinhole camera with an exposure time of about 1 ns and a delay of 3 ns between frames measured the extreme ultraviolet and soft X-ray region of the laser-induced plasma. The self-emission of the plasma was transferred to a microchannel plate (MCP) connected to a Nikon D600 digital camera at a magnification of ~4. This experimental geometry, including a pinhole diameter of 35 µm, resulted in a spatial resolution of approximately 45 µm. The MCP detector is sensitive to photons in the energy range 10-10,000 eV. The use of a 0.9 µm thick Mylar filter made it possible to cut off photons with an energy of less than 100 eV. The spatial and temporal resolution achieved made it possible to capture the self-emission of hot plasma in the X-ray region inside the ‘snail’ target and to register the moment when the plasma explodes in the center of the target. It was confirmed that the grazing incidence of the laser on a curved surface leads to a continuous reflection of the light along the inner wall of the target.
For the experimental study of plasma jets with astrophysical similarity, the same approach was used in [61][3]. Although the pinhole camera does not provide photon intensity spectra, one of the channels of a fast gated camera can be used to filter a single frame and compare the signal with an unfiltered image. In one study [61][3], this approach was used to measure the electron temperature, which was Te = 50–150 eV in a jet and Te ≈ 150 eV in a copper plasma with shock heating. It should be noted, however, that such a measurement is not very reliable and is more of an estimate of the temperature from below since it is based on a rough estimate of the bremsstrahlung in a rather broad spectral range.
The experiment at the PALS facility used four elliptical pinholes for the X-ray pinhole camera, one of which was covered with 0.2 µm thick Fe foil. The pinhole images were projected onto a four-quadrant detector with a gold-plated microchannel plate (MCP) connected to a phosphor screen and was visualized with a Nikon D1X CCD digital camera. The exposure time was 2 ns and the adjustable intervals between quadrants were configured so that imaging occurred at three different times, two of which measured open and filtered emission simultaneously. The MCP was sensitive to photon energy in the range 10–1000 eV.
The experimental approach was based on a relatively simple method of generating supersonic jets using a defocused laser (3ω = 0.438 µm with a pulse duration of 250 ps and an energy of 100 J) on targets with a high atomic number [62][4]. The jets are produced by the collision of an ablated plasma converging on one axis, which is due to a combination of the annular laser intensity profile on the surface of the target and the radiative cooling [63][5]. X-ray diagnostics with spatial resolution made it possible to determine the parameters of the plasma jet and shock wave and to study their structure and evolution in detail, starting from the initial ionization of the background plasma and the formation of the jet to their subsequent interaction over a period of approximately 15 ns. The result showed a strong shock compression in the copper plasma with a ten-fold increase in density compared to the argon background plasma. The characteristic velocities of the jet and the shock wave were also measured. The X-ray pinhole camera showed that the structure and evolution of the shock wave depend strongly on the density of the neutral gas, both through the properties of the interaction during the formation of the shock wave and through its influence on the initial formation of the jet and its structure. It was concluded that the copper flow was re-oriented, resulting in a narrower and better collimated jet at low gas pressures.
In a similar experiment [64][6], using an X-ray pinhole camera, the interaction of such collimated laser-induced plasma jets with He and Ar gas flows was studied in two irradiation geometries as follows: with a perpendicular laser incidence on the target surface and with an inclination (30 ° relative to the normal of the target) to minimize the heating of the surrounding gas by the laser beam. With the geometry of the inclined interaction, the effect of double shock formation in the surrounding gas was demonstrated. Experiments conducted to test the generation of a plasma jet in this new geometry have clearly shown that even with an inclined case, well-formed plasma jets have parameters that are no worse than those of a normal incidence. The generated plasma structure, registered by an X-ray pinhole camera, is characterized by a sharp, elongated peak of luminosity along the symmetry axis of the laser beam propagation.
In the following studies [65[7][8],66], strong stochastic magnetic fields generated in a turbulent plasma during the collision of two inhomogeneous, asymmetric, weakly magnetized plasma jets were studied at the Omega Laser Facility. The X-ray diagnostics of the experiment visualized the bremsstrahlung in the soft X-ray region in a fully ionized CH plasma using a fast frame X-ray pinhole camera (XRFC) configured with a two-band microchannel plate (MCP) and a CCD camera. The 50-µm array of pinholes was located at 9.14 cm from the center of the target and the main detector at a distance of 27.4 cm, resulting in a 2× magnification of the image. A thin filter consisting of 0.5 µm polypropylene and a 150 nm thick aluminum coating was placed in front of the MCP and removed emission with a photon energy of ≤100 eV. Two temporally integrated images were taken with an interval of 1 ns. The image resolution and the choice of filtering were sufficient to observe the finger-shaped fluctuations of the plasma jets. These fluctuations were explained by density inhomogeneities in the plasma, whose origin can be explained by the effect of turbulent motion. The X-ray images obtained in the work show that the external magnetic field has only a limited influence on the dynamics of the plasma in the experiment, in the case of two individual plasma jets located in an external magnetic field. It was found that for a turbulent laser plasma with supercritical magnetic Reynolds numbers, the magnetic fields enhanced by the dynamo effect are determined by the turbulent dynamics and not by the initial fields or moderate changes in the initial dynamics of the plasma stream, which is consistent with theoretical expectations and modelling. The results suggest the possibility that plasma turbulence caused by strong displacement can generate fields more efficiently than would be expected with the idealized modelling of the magnetohydrodynamics (MHD) of a non-spiral dynamo. This discovery could help explain the large-scale fields obtained from observations of astrophysical systems.
It is worth mentioning that it is not always necessary to use pinhole cameras with multiple channels. Moreover, it can be more interesting to look at the evolution of the process from several lines of observation [67][9]. In the article [60][10], X-ray imaging was used to confirm the effect of magnetic reconnection of lines of force. For this purpose, two synchronized laser beams from the Shenguang (SG) II laser system were focused on one side of the aluminum foil at a distance of 400–600 µm, while the other two laser beams symmetrically irradiated the other side. The target was a loop of aluminum foil and a copper target attached to it. Each beam was focused to a focal spot diameter of 50–100 µm (FWHM), resulting in an incident laser intensity of 5 × 1015 W/cm2. In this experimental approach, X-ray emission was measured from the front, back and side using three X-ray pinhole cameras. The image was taken with a 10-µm pinhole and a 50-µm beryllium filter, resulting in X-rays over ~1 keV being registered on the X-ray film with a higher sensitivity in the range of 1–10 keV.

3. Application of Dispersive X-ray Optics in Alboratory Astrophysics Experiments

3.1. 2D X-ray Imagers Based on Spherically-Bent Crystals at Small Angles of Incidence

To obtain more detailed information about the laser-plasma interaction, methods with a combination of different optics are used. In particular, 2D imagers based on spherically curved crystals at near-normal X-ray incidence are worth mentioning. Image plates or time-resolved X-ray streak cameras are most commonly used as detectors in this case. In contrast to a pinhole camera, this approach allows people to obtain visual information about the emission of ions or hot electrons in a rather narrow, one could say monochromatic, spectral range.
In one study [59][2], a quartz crystal (422) with a bending radius R = 380 mm was used to obtain 2D-resolved images of Cu Kα emission. The use of such a crystal with 2d = 1.5414 Å leads to the registration of the image in the line Ka (λ = 1.54056 Å) at an almost normal angle to the target and to minor distortions due to deviations from the sagittal and meridional planes of the crystal. The disadvantage of this configuration is the small spectral range of the emission, which can be shorter than the width of the Kα line due to the strong heating of the target by the laser. In this case, the absolute measurements of the X-ray yield in Kα line may be inaccurate, especially since the line profile may shift towards higher energies when the temperature changes. However, the spatial and temporal parameters of such a technique are very important for the interpretation of the obtained experimental data. It is also worth noting that visualization in such a narrow range results in a lower signal intensity on the detector than using a pinhole camera.
The image was registered on FUJI BAS MS image plates, which were then scanned using a Fujifilm BAS-1800 scanner with a pixel size of 50 × 50 microns. The system provided a magnification of β=1.73. The measured X-ray data were interpreted in terms of the hot electron generation and the efficiency of conversion of laser energy into hot electrons. This approach made it possible to show a map of the intensity of hot electron generation for a snail target and to demonstrate the formation of a dense hot plasma, similar to a theta-pinch, and the distribution of a large magnetic field penetrating the target.

3.2. 1D and 2D of Spectrometers Based on Spherical Crystals with Spectral Resolution

Optical schemes based on spherical crystals and detectors placed in the sagittal plane of the image make it possible to visualize laser-plasma processes not only with spatial but also with spectral resolution. This is particularly important when a plasma object has a large aspect ratio. In this case, one of the tasks is the ability to investigate the parameters over the entire length of the plasma. For example, in research [29,68,69][11][12][13] conducted at the ELFIE facility (LULI, Polytechnique), a plasma jet with a high aspect ratio was studied for laboratory modelling of Herbig–Haro type astrophysical ejections from young stellar objects (YSOs). A large aspect ratio was achieved using an external magnetic field of 20 T, in which a Teflon target (CF2) was irradiated with a laser pulse with an energy of about ~40 J and a duration of about ~1 ns.
As a result of this approach, important spatial profiles of plasma parameters are given in [68[12][13],69], which are the electronic density and the temperature, as they are of great importance for modelling most physical quantities and for comparisons with astrophysical models. 
As mentioned earlier, this scheme is characterized by a stronger astigmatism and a larger magnification along the jet axis than in the case of the radial direction (i.e., the direction of spectral dispersion). In the sagittal plane, the spatial resolution is determined by the aberrations of the spherical surface in the sagittal plane. In the meridional plane, the spatial resolution is determined by aberrations as well as by the size of the source, the width of the spectral line, and the width of the rocking curve of the crystal. Therefore, it is necessary to correct for spatial distortions for extended sources, otherwise the estimates for the plasma parameters can deviate significantly from the truth due to an incorrect comparison of the relative intensities of the spectral lines.
To illustrate this, Figure 1a shows an X-ray image registered in a laboratory experiment when the collision of two plasma flows was studied in the presence of an external magnetic field and a gas medium (Nitrogen) between two simultaneously laser-irradiated solid CF2 targets. The irradiation parameters and the image registration scheme were identical to those given for a single jet. A focusing spectrometer with spatial resolution based on a spherically-bent mica crystal was used. It is obvious that long wavelengths occupy a shorter spatial extent in the image than shorter wavelengths. This was corrected in Figure 1b using the authors’ anti-distortion code written in Python, which allows the user to graphically select the points of change in magnification while preserving the initial emissivity integral. By correcting the distortions and considering the scaling coefficients on both axes, it is possible to obtain both an X-ray image of a plasma source and spatial profiles of the plasma.
Figure 1. The original (a) and the processed spectrometric image (b) in the experimental campaign. In this case, there are two laser-irradiated targets in the field of view, between which plasma jets interact in an external gas. From left to right, the wavelengths increase. The λc mark corresponds to the position of the central wavelength (part of the spectrum is cut off on the right-hand side because there is no useful information).
Figure 2a shows an example of a 2D X-ray image of a plasma jet for the Heγ fluorine line with equal magnification coefficients in the radial and axial directions in an experiment simulating the collimation of astrophysical flows [70][14]. For this purpose, the scaling coefficients were used (the magnification according to Formulae (6) and (9) was βm = 0.048 in the meridional direction and βs = 0.26 mm in the sagittal direction) and the distortion effect of the optical system was taken into account. Since the magnification factor on one axis was much larger, the averaged values of the neighboring pixels were placed between the stretched points. For the construction, only the (−3:+3) radial neighborhood of the maximum value of the spectral line of each line was used, while the background was completely cut off. In Figure 2a, only the line F He 4p-1s (Heγ
) is shown, while the behavior of the other lines is very similar. The resolution in sagittal and meridional directions was approximately 100 and 500 µm, respectively. The images are composed of several frames (represented by dotted rectangles), each taken for a separate shot with a target at different distances from the diagnostic window of the Helmholtz coil.
Figure 2. (a) X-ray image [70][14] of a plasma jet obtained by a FSSR spectrometer [33][15] along a spectral line with minimal distortion Heγ

(transition in fluorine atom F He 4p-1s, closest to the central wavelength) at 20 T when the inclination of the target was 10 and 20 degrees to the normal. (b) X-ray images of the self-emission of the fluorine Heβ

spectral line obtained by diagnosis of the 3D plasma from the side and from above at a transverse magnetic field of 20 T [34][16]. (c) The analytical approach of the two-component plasma.
In these images, the bending of the expanding plasma can be clearly seen, with two phases being distinguished. First, near the target, both diagnostics show that the propagation of the plasma jet does not depend on the variation of the angle of the magnetic field near the laser-irradiated target surface. Moreover, this propagation is perpendicular to the target surface and is identical to the case where there is no magnetic field. The reason for this behavior is the kinetic gas pressure of the plasma Pdyn, which far exceeds the pressure of the magnetic field Pm in this region, where the electron temperature and density are expected to be above 100 eV and 1 × 1019 cm−3, respectively. The results of the X-ray diagnostics thus helped to establish that the modulation of the jet can be interpreted as a sign of a change in the flow angle or the surrounding field over time, and that a change in the direction of the jet can be a sign of changes in the direction of the surrounding field.
The simultaneous use of multiple spectrometers makes it possible to reconstruct or prove the dynamics of plasma propagation on a 3-dimensional scale. For example, in one study [34][16], two spectrometers were used with an observation line orthogonal to each other and with spatial resolution along the axis of the plasma expansion. Since the spectrometers were installed in a 2D scheme, the experiment (Figure 2b) was able to compare two projections of an X-ray source with a magnetic field perpendicular to the plasma expansion, as occurs in a variety of astrophysical environments, e.g., at the edge of discs surrounding young stars or when coronal mass ejections (CME) [71][17] propagate from the star [72][18]. Note, that images in Figure 2b are integrated over time and measured simultaneously in one shot by two focusing spectrometers with spatial resolution (FSSR) used in the experiment. The white arrows in the side view indicate an increase in the emissivity in the spatial region of ≈ 4 mm.
As a result of this approach, the morphology of the plasma flow was confirmed, which is characterized by expansion in one plane and compression in another. Furthermore, an approach based on the comparison of spatial profiles of the emissivity and the measured electron density and temperature was used to estimate the propagation velocity of the plasma flows. In this way, it was possible to determine the separation of the plasma into two components as follows: dense, slow plasma that is increasingly compressed towards the target as the magnetic field increases, and fast, low-density plasma that is redirected by the magnetic field along the axis. It is noteworthy that the ability of the plasma observed here to propagate against a transverse magnetic field could be of interest for the physics of the edges of the disc, namely to enable the ejections from the disc to cross the gap separating the disc from the star and thus participate in the deceleration of the disc, as postulated in Shakura and Sunyaev [73][19].

3.3. Investigations of Laboratory Astrophysical Plasma by X-ray Spectral Composition

The relative intensities of the spectral lines obtained or the spectral composition itself cannot often be described by only one plasma component. It is concluded that there are additional zones that are not resolved along a particular axis [2,74,75][20][21][22]. This is particularly useful, for example, when the sensitivity of the detector is not sufficient to make reliable measurements with time resolution. In the following studies [2[20][21],74], focusing spectrometers based on spherically curved crystals were used to obtain fluorine ion emission spectra when simulating CTTS accretion columns directed along the magnetic field lines connecting the surrounding material to the star. To study the dynamics of accretion in the laboratory, a collimated narrow (diameter ~1.5 mm) plasma flow was used by superimposing an external (B = 6–30 T) and a homogeneous poloidal magnetic field on an expanding laser-induced plasma (laser duration 0.6 ns, intensity ~1013 W/cm2). The plasma flow propagated with a velocity of vstream=750 km/s parallel to the lines of a large-scale external magnetic field, as in the present picture of mass accretion in CTTS encountering a solid obstacle simulating a high-density region in the stellar chromosphere. In most of the shots, the obstacle was located at 11.7 mm from the main target. The emission spectra were taken with spatial resolution in the direction of laser propagation near the obstacle surface. Since the X-ray images in the experiments were recorded integrally in time, the spectrometer recorded, at each spatial point, the sum of the spectra emitted first by a laser plume expanded freely from the target and then by the plasma generated by the collision of the initial plasma flow and the plasma generated on a solid obstacle. Of course, the plasma parameters at early and late times can be very different, and the resulting spectrograms only give some average values of the plasma parameters. To solve this problem, targets and obstacles with different chemical compositions were used, namely polyvinyl chloride, or PVC (C2H3Cl)n, aluminum, and Teflon (CF2). These materials were used for both the main and obstacle targets so that the plasma of incident and induced flows could be observed separately, registering the spectral lines of fluorine, chlorine, and aluminum, respectively.
The spectra obtained near the obstacle surface have demonstrated that the data obtained cannot be described by a single set of parameters. This is due to the presence of dielectric satellites to the Lyα line (hot plasma with a temperature much higher than 100 eV, exceeding the ionization potential for the L-shell) and to the recombinant nature of the emission of the helium series, where high intensities for high transitions are observed (Figure 2c). The conclusion on the possible presence of an additional plasma component made it possible to use a two-plasma approach, where the parameters of a dense and cold core and a hot and less dense shell were determined. The colder plasma was estimated with a recombination model [76][23], while the parameters of the hot part were measured with the PrismSPECT code [77][24] from the ratio of the intensities of the dielectric satellites to the Lya resonance line. The results on the spatial distribution of the components were then confirmed by optical methods and modelling. Despite the low sensitivity of the system to conduct time-resolved measurements, such an approach was able to detect the formation of a plasma shell, which in the astrophysical case of accretion columns can lead to significant absorption of X-rays.

3.4. Diffraction Gratings

In experiments to study the propagation of plasma flows in a perpendicular magnetic field [34][16], as well as to study the slanted accretion [30][25], a spectrometer based on a diffraction grating with variable line spacing (VSG: variable spatial grating) was used. This VSG spectrometer allows the investigation of a wider spectral range (400–2000 eV) than the FSSR, but with a lower spectral resolution [45][26].
The spectrometer consists of a diffraction grating (average 1200 points per inch), a spectrometer body, and a removable front cone that can accommodate slits for spatial resolution measurements. The image was also captured using an image plate TR. In the experiments, the front part of the spectrometer body was equipped with a vertical slit that allowed spatial resolution of the X-ray emission of the plasma along the horizontal axis, which was one of the expansion points of the plasma. In this case, the grating had its lines in the horizontal direction, resulting in horizontal spatial and vertical spectral resolution on the VSG detector.


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