Influence of laser-induced Au-plasma plume collision on the efficiency of x-ray radiations and the energy-transport process relevant to ICF

Experiments and simulations have been carried out to study the colliding process by two lasers irradiating a gold half-hohlraum. Via analyzing the evolutionary x-ray images, radiation fluxes and self-emission spectrum of tracers, influence on the x-ray conversion efficiency and the local plasma temperature Te,i from two gold-plasma plumes have been investigated deeply, which is similar as the configuration in Inertial Confinement Fusion (ICF). Experimental results confirm a region with high electron and ion temperatures Te,i are induced, satisfying the strong collision condition of λi<ΔL , where λ i and ΔL are respectively the ion mean-free path and the gradient length of Te . It leads to almost 30% increasing of M-band component compared to that from a single laser-irradiation case. Meanwhile ion temperature in this region increases more rapidly than electrons, reaching about Ti≈(16±4)  keV ( Te≈(2±0.2)  keV). Thus, our studies provide the experimental evidence of quantitative x-ray enhancement and a non-equilibrium evolution simultaneously due to the plasma collision for the first time. Besides, two-dimensional simulation results reveal that this process can not be precisely described by the traditional shock-heating model by dissipating the shock energy only to ions. But by distributing the viscous heating between both electrons and ions as theoretically discussed by Miller (2020 Comput. Fluids 210 104672), numerical results can match experiments better. This discovery will be of great importance to improve the precision of prediction for ICF.

In fact, high-Z plasma-plume colliding is a complex process which can cause a series of problems for ICF physics.Firstly, shocks are induced during the strong collision and propagate in an ionized plasma.It can compress a stagnation layer and further form a rapidly moved outflow/jet [8,34].When the outflows from the inner ring spruit towards the capsule, it may cause the asymmetric compression.Secondly, during the collision of plasma plumes, it scatters or induces amounts of high-energy particles, such as M-band/hard x-ray emissions and hot electrons.These particles have a much higher ablation depth, which may preheat the capsule and further destroy the symmetric implosion.Besides, the nonuniform density or temperature profiles of plasma states in the hohlraum also induce self-generated electric and magnetic fields [31,40].In these situations, some kinetic effects and the ion-thermal conductivity can not be ignored as well [38,41].Therefore, on the one hand, the strong plasma collision process produces high-energy particles and these particles, i.e Mband x-ray, electrons with energy >1 keV, are destructive for the symmetric implosion.On the other hand, it can also induce the gradient evolutions of plasma temperature or density in the hohlraum, which brings challenge for the accurate description of the self-generated field evolution and energy transport as well.
Additionally, when we theoretically deal with the energy transport process during the strong plasma-plume collision, the different ways to address the shock heating will seriously affect the variation of plasma states, such as temperatures of ions and electrons.In the previous work of 1950s-1960s [42][43][44][45], this process was widely described by distributing the kinetic energy of plasma shocks (plasma plumes) into the thermal energy of plasmas of only ions but ignoring the contribution of electrons.Actually a low-Z plasma was implicitly assumed in their model, predominantly fully ionized deuterium or DT plasma with constant ion charge Z = 1.This traditional shock heating model is even widely-used in a series of radiation-hydrodynamic simulations today.Afterwards in the more recent analysis [46], who generalizes the old results specifically for arbitrary Z, the devotion of electron viscosity was still neglected.However, a new model was proposed by Velikovich et al [47] that they distribute the viscous heating of shock between both ion and electron plasmas by splitting it proportionally to the local values of two physical viscosity coefficients.Subsequently Miller [48] follows this model to explore the differences between the traditional approach theoretically.It found that the viscous heating by the electron component can be non-negligible and may even become dominant for high-Z plasmas.If the contribution of electron viscosity is ignored, namely only dissipating the shock energy to ions, electron temperature comes into equilibration with the ion temperature on a much longer time-scale in the strong collision case.Unfortunately, their work [47,48] lacks experimental evidences to check the accuracy of the new model for high-Z materials.
In total, it is of great importance for the ICF project to integrally investigate the influence of high-Z gold plasma-plume collision on the plasma evolution, x-ray conversion efficiency and on how the energy transport among the shocks, ions and electrons.
In this paper, we have carried out both experiments and simulations to investigate the evolution of two plasma-plumecolliding by using a gold half-hohlraum.Through analyzing the evolutionary x-ray images, fluxes and the spatialresolved spectrum of tracers, x-ray amount and distribution, the in site plasma parameters of electron and ion temperature T e,i , have been simultaneously provided for the first time.Results indicate that a bright x-ray emission region has been formed during the plasma colliding and its M-band component reaches ∼30% of that in a single laser-irradiation case.The plasma parameters, T e ≈ (2 ± 0.2) keV, N e ≈ (6 ± 3) × 10 20 cm −3 and T i ≈ (16 ± 4) keV, show that they increase much higher than the surrounding plasma region.Based on the parameter analysis, the strong collision of λ i ⩽ ∆L x-ray,Te has also been confirmed, where λ i , ∆L x-ray and ∆L Te are respectively the ion mean free path, the scaling length of radiation intensity and the scaling of the electron-temperature gradient.Additionally, our experiments find that non-equilibrium evolution of plasmas (T i ≫ T e ) occurs due to the strong collision.Our two-dimensional radiative-hydrodynamic simulations indicates that the traditional description could not match the experimental results since it uses the shock heating model which ignores the energy transport from the shock to electrons.Our work provides the experimental evidence for the first time to confirm the accuracy of the new model, theoretically discussed by Douglas S. Miller, that it distributes the heating of shock between both ion and electron plasmas by splitting it proportionally to the local values of two physical viscosity coefficients.These discoveries should catch more attention for both ICF and HEDP, especially when we attempt to accurately predict the x-ray conversion efficiency and plasma parameters.

Experimental design
The experiments were performed on Shenguang-III(SG-III) prototype laser facility (tens-of-thousand-joule) in Mianyang, China.Its setup was shown in figure 1(a).Two main laser beams, with a separation of 850 mm, symmetrically irradiated on the interior surface of a half-hohlraum target.The laser pulses both have a super-Gaussian profile at the energy of 800 J, duration of 1 ns and wavelength of 351 nm.Each beam indicates from ±45 • degree to x-axis.Continuous Phase Plates (CPP) were used to provide a 500 µm spatial-smoothed focal spot.Here we define the horizontal plane as x-z plane and the longitudinal direction along the center of cylinder as y-axis.The half-hohlraum was dug by using a rectangular base.A gold (Au) layer with a thickness of 20 µm was overlapped on the interior surface of the hohlraum.The diameter and length of the hohlraum were 1.2 mm and 6 mm, respectively.To detect the temperature evolution, Ti was chosen as the tracer material and it was plated as a mixture together with Au at 1:1 atomic ratio (Ti:Au = 1:1) and a thickness of 0.2 µm upon the 20 µm Au layer.Three typical regions could be formed during the laser-plasma interaction and were marked out in figure 1, i.e. the strong collision region (I), the focal spot (II) and the region between them (III).

Diagnostics
Multiple sets of diagnoses in the experiment were shown in figure 1(b).A spatial-resolved Crystal Spectrometer (CS) along y direction was applied to detect the self-emissions of Ti tracer from 4.4-5.7 keV.The spectra and spatial resolutions respectively reach E/∆E ⩾ 500 and 60 µm.The space resolution was realized by using a 100 µm slit in front of the CS and a 1.2 mm × 0.4 mm diaphragm adhered to the half-hohlraum target was used to confine the size of emission source and the spatial region.Here the chosen region was also marked out with a blue-dashed box in figure 1(a).
An X-ray Framing Camera (XFC) was installed along the opposite direction of CS to monitor the spatial emissions from two plasma plumes and the collision region at several discrete moments.Its spatial and temporal resolutions were ∼30 µm and ∼ 50ps.A 50 µm beryllium foil as a filter was used in the XFC to allow the x-rays whose energy are above 1 keV to pass.

X-ray images
Figure 2 shows the x-ray images from 100 to 1600 ps measured by XFC.The green-dashed line in each image marks out the initial outline of the internal wall of the half-hohlraum.Images in figures 2(a)-(c) show the evolutionary process that the two plasma plumes gradually expand and become brighter and brighter at the preliminary stage of the laser ablation.Images in figures 2(d)-( f ) indicate that the central region of the two plumes begins to emit x-ray radiations at about 650 ps and becomes brighter than the laser spot regions at about 850 ps.Images in figures 2(g)-(i) show that the brightness of radiations decrease rapidly after the laser pulse ends, but radiations in the central collision region still keep brighter compared to those in the two laser spot regions.It means that the temperature or density in the collision region decreases more slowly in the later stage after the lasers end.

X-ray conversion efficiency
X-ray image at 850 ps in figure 2( f ) can been divided into three parts (I, II and II ′ ) with red-dashed rectangles, and it is separately shown in figure 3(a).The spatial-integrated intensity from the three parts indicate that the value from the region I is ∼60% of that from the laser spots at II or II ′ .Besides, the one-dimensional intensity profile along x-axis at y = −300 µm is plotted in figure 3(b).It shows that the length of region II, which is characterized by the half maximum intensity at the full width, reaches ∆L x-ray ≈ 150 µm.Since the x-ray emissions in the central collision region was primarily observed at about 650 ps in our experiment and if we take the uncertainty of the time monitor of ±50 ps into consideration, the averaged expanding speed of plasma plumes can be estimated as ∆x/∆t = (600 µm/ cos 45 • )/(650 ± 50 ps) ≈ 600-700 km s −1 .
As high-energy x-ray photons can cause the preheating of capsule in ICF configuration, it is of great importance to make clear the proportion and spectral feature of x-ray emissions from the colliding region as well.
Figures 4(a)-(c) show the histories of the total, M-band and hard x-ray fluxes measured by the three types of XRDs at 20 • , 30 • and 45 • up to z axis, respectively.The cases with a single laser irradiation have been added for comparison with the double ones.Temporal evolutions of fluxes have been also demonstrated to be repeatable by different shots with the same experimental condition.Results show that radiation fluxes at 0.1-5 keV, 1.6-4 keV and 5-9 keV from the double-laser case are respectively ×2.1, ×2.3 and ×2.1 times of that in the single-laser case.Because the double laser case should be ×2 of the single one without the influence of the plasma-plume colliding process, it reveals that the colliding process leads to the increasing of ∼10% of the single one at 0.1-5 keV and 5-9 keV, but ∼30% of M-band x-ray flux at 1.6-4 keV.
It is worthy noting that the drive lasers only have 1 ns duration in our work.It means that the heavily strong colliding process only lasts a short period (<300 ps).Thus the whole M-band fraction is only 30% compared to that from the single laser spot.As discussed in section 3.1, the image of x-ray emissions (>1 keV) at 850 ps verifies that emissions from region I can even reach about 60% at the strong collision moment.To consider that if the pulse duration of the drive lasers gets longer, such as ⩾3 ns in most ICF experiments rather than 1 ns using here, the plasma colliding process will be persistent to further increase the M-band components.Yet M-band photons can bring the potential risk of 'preheating' before the shock reaches the ice layer of capsule.It also decreases the compression synchrotron or the imposed neutron amount.Therefore,  more attentions lead to pay for the flux value and the x-ray conversion efficiency caused by the strong collision effect in the indirect-drive ICF project.There are three intensity peaks in the spatial resolution for all of the four typical emission lines.They correspond to the two focal spots (III in figure 1(a)) and the central collision region (I), respectively.Two low-lying regions were exactly relative to II.Consistently, the high temperature region was formed due to the plume collision.To compare the divergencies of T e in the three regions, a collision-radiative model with steady-state approximation is used to calculate the theoretical spectrum of Ti emissions in different plasma conditions and it is called RateQ [49] here, in which the population distribution of the atomic levels was obtained by solving the rate equation for an atomic level through the Flexible Atomic Code (FAC) [50].Because both the ratio between Ly-α at about 4977 eV and He-α w at about 4750 eV emissions and the ratio between He-α j,k,l (∼4710 eV) and He-α w emissions are both the function of electron temperature and density but they are sensitive to the temperature variation in the region from 500 to 3000 eV and quite insensitive to the electron density lower than 10 22 cm −3 [51].Meanwhile the rate of He-α w and He-α y (∼4726 eV) is sensitive to electron density because electron collisions also cause a transition from the upper level of 3p state of 'y' to 1p state of 'w' with the increasing of N e .Here the theoretical spectra lines in arbitrary states of temperature T e and density N e can be calculated by using our code.Thus, the optimal T and N e in different positions can be obtained by comparing the theoretical spectrum to the measured spectrum in figure 5(a).lines with the most possible T e and N e .The errors include about 10% uncertainty of the spectrometer calibration, tracer material stoichiometry and the 95% confidence interval in the most likely T e and N e .Results indicate that the electron temperature at x 1 are 2.0 ± 0.3 keV (N e ≈ (6 ± 3) × 10 20 cm −3 ), which is close to the values at x 3 and x ′ 3 (T e = 2.6 and 1.9 keV with N e ≈ (1 ± 0.5) × 10 21 cm −3 ).T e at x 2 between the central collision region and the laser spots is smaller (T e = (1.6 ± 0.2) keV).Figure 6(e) shows the spatial distribution of T e according to the spectra in figure 5(a).The profile also exhibits a structure of three peaks, each at the center and the laser spot regions, and two bottoms between them.If we define the spatial scaling of the collision region by the measured T e with the standard of T e ⩾ 1 2 (T e,max + T e,min ) in the central region.The characteristic length can be expressed as ∆L Te ≈ 200 µm.

Plasma states of electron and ion temperatures
Since the colliding mean-free-path λ αβ between two species can be expressed as where α and β respectively present two particle species (ions or electrons).n β is the density of particle β, A α,β and Z α,β respectively present the mass and charge ionization numbers, v flow is the velocity of plasma flow.lnΛ αβ is the Coulomb logarithm and it can be calculated with parameters of electron temperature T e , density n e and the charge of ionization Z.Based on equation (1), we can use the experimental values obtained above to simply estimate the ionion mean-free-path from two plasma plumes.When T e = 2.0 keV, N e = 6.0 × 10 20 cm −3 , v flow = (700 • cos 45 • ) km s −1 relative to the average velocity along x-axis and Z = 50 at T e ≈ 2-3 keV as that in [52] are chosen, λ i ∼ 50 µm can be obtained.It satisfies λ i < ∆L x-ray,Te .Therefore, our experimental parameters reveal that the strong collision condition reaches and it will lead to the situation of two strong shocks propagating from the central region into the ionized high-Z gold plasma plumes.

Ion temperature based on the spectra broadening
Next let us discuss the ion temperature according to the analysis of the spectra broadening caused by the Doppler effect.Actually, the broadening of self-emission lines are mainly caused by two parts.The first one is relative to the spectrometer caused by the size of emission source, the swag angle of TAM crystal and the resolution of the recorder.The second part is relative to the physical effects such as Doppler and stark broadening effects.Since stark broadening works only when N e and T e are both high, especially N e achieving 10 24 cm −3 above.But in our situation N e ⊆ 10 19 − 10 21 cm −3 based on the spectra fitting.Thus stark broadening can be neglected.However, Doppler broadening is always caused by the thermal movement of ion plasmas.And it can be simply expressed as △λ/λ = ± vs c , where v s is the thermal velocity.Thus, the relation between the spectra Doppler broadening △λ 1/2 and the ion temperature T i can be expressed as in which λ and m i respectively present the central wavelength and ion mass.Due to the strong collision effect, the Doppler broadening is particularly obvious in the central region I. Figures 7(a)-(c) respectively show the spectra broadening of Ti He-α emission lines at x 1,2,3 .It is clearly seen that the Full Maximum at Half Width (FMHW) of He intensity at the central collision region ((16 ± 4) eV at x 1 ) is about ×1 larger than that at the laser spot region II ((8 ± 1) eV at x 3 ).Even lines from the weak collision region III ((11 ± 2) eV at x 2 ) is also higher compared to that at x 3 .
Based on equations ( 1) and (2), ion temperature T i at x 1,2,3 can be estimated out.They are almost T i ≈ (16 ± 4) keV at x 1 , (10 ± 4) keV at x 2 and T i ≈ 2 keV at x 3 .Notedly, T i at x 1 satisfies T i (16 keV) ≫ T e (2 keV), and it is about ×7 higher than that at x 3 where T i ≈ T e .It further reveals that the strong collision process occurs between the two plasma plumes.Not only a high T e region has been performed, but nonequilibrium plasma evolution is also induced due to plasmaplume collision.As discussed in section 3.1, figures 2(g)-( f ) indicate that x-ray images become brighter in the strong collision region than the laser spots after the laser ends.It can be understandable as that since the temperature almost satisfies dynamic equilibrium (T i ≈ T e ) for the plasma plumes in the laser-irradiation region.When no external driven energy imports (laser ends), the plasma cools rapidly due to the electron thermal conductivity.However, in the strong collision region, ions carry a large part of kinetic energy (T i ≫ T e ), ions could scatter energy to electrons during the electron diffusion.Therefore, the stagnation region can keep bright emissions for a longer time.During this process, the energy transport from ions to electrons becomes of particular importance.
In all, by analyzing the x-ray images, radiation fluxes and the spectrum of Ti tracer in our experiments, we find that strong plasma-plume collision occurs in the central region between two laser spots and it satisfies the strong collision condition of λ i < ∆L x-ray,Te .Though the strong collision process lasts a very short period (only 300 ps for 1 ns laser pulses), it results in almost 30% increasing of M-band components when compared to that from a single laser-irradiation case.Even it once reaches about 60% at 850 ps.Besides, the temperature analysis shows that electron and ion temperatures of the collision region both increase rapidly, achieving T e ≈ (2 ± 0.2) keV and T i ≈ (16 ± 4) keV.It induces a quite nonequilibrium evolution of temperatures (T i ≫ T e ).Thus, for the first time our studies provide the experimental evidence of quantitative x-ray enhancement and a non-equilibrium evolution simultaneously due to the plasma collision.

Simulation discussion
Strong shock can be induced during the strong colliding process in ICF, which dissipates the kinetic energy of the plasma into the thermal energy of electrons and ions through the viscosity.This dissipation process is commonly known as the shock heating and can significantly modify the plasma states, especially the temperature.However, the most widely used shock heating model discussed by Zel'dovich and Raizer [45] and implemented in a series of radiative-hydrodynamic codes, fails to calculate the shock heating and further mistakenly predicts the temperature of electrons and ions for high-Z species like Au.For example, in FLASH code we used [53], the shock heating and its effects on the plasma are reflected in the energy equation: where Q e,i are the heating of electrons and ions by the shock and ρ, v, ε and P are respectively the mass density, velocity vector, specific energy and pressure.The subscripts e, i represent electron and ion elements.Since the total energy for the shock heating Q = Q e + Q i can be easily obtained by the Rankine-Hugoniot relations at the shock front, the exact distribution of the heating energy on electrons and ions is divergent.In the traditional model, the shock heating is only applied to the ions, in which Q = Q i with and Q e = 0.It implicitly presents that it is only applicable for low-Z species that the electron viscous forces can be negligible.Nevertheless, for arbitrary Z materials including high-Z species, the electron and ion viscosities can be expressed as where the electron viscosity coefficient η 0 (Z) satisfies η 0 (Z) = 1.81Z(Z 2 +2.82Z+1.343)Z 3 +4.434Z 2 +5.534Z+1.78[47,48].We can see it satisfies η e ∝ Z −1 but η i ∝ Z −4 .Therefore, when the ion charge Z is sufficiently high, the electron viscosity can be non-negligible or even can be dominant during the shock heating when compared to the ion viscosity.Actually, the most ideal way to deal with the correct viscous heating for simulations should calculate the ion and electron viscosities automatically.However, the density and pressure discontinuity in plasma shock structure is not resolved physically in most codes, instead, it is approximated numerically using artificial viscosity.Then, the correct way to distribute the artificial viscous heating between the two plasma components is to split it at each step proportionally to the local values of ion and electron viscosity coefficients.Thus, we add the new model to our code by defining the 'viscosity factor' as f q = η i /(η i + η e ) and addressing the heating energies for electrons and ions respectively as Q e = Q(1 − f q ) and Q i = Qf q .It is the same as [48] and it becomes more physical to distribute the energy of the shock heating to electrons and ions according to the contribution of their viscosity.In this way, we can get a more physical state of plasma evolutions.
To further compare the influence on the plasma evolutions of the traditional and new shock heating models, simulations were carried out by using them in our improved radiationhydrodynamic code to respectively match the experimental results.Here the Equation of State (EOS) and opacity parameters of Au in our simulations are calculated with codes BADGER [54] and IONMIX [55] respectively and benchmarked by the characteristic parameters T e , v flow and x-ray flux from experiments above.
Figure 8(a) shows the T i distribution at t = 0.8 ns from the case with the traditional model and it indicates that in the central collision region, T i reaches about 150 keV, which is much higher than the experimental result of (16 ± 4) keV in figure 7(a).Meanwhile, it almost keeps a much higher value even after the laser heating ends at 1.2 ns (50 keV), which can be clearly seen by comparing the one-dimensional profiles along y = −300 µm in figure 8(b).It reveals that the traditional model mismatches with the experimental results since it dumps too much energy into the ions during the strong collision.
To check the efficiency of the new model and its influence on the plasma evolution, the T i , T e and N e distributions from the two cases are compared in figure 9(a).In the new model, the shock energy is split to both ions and electrons based on the value of ion and electron viscosity, which is relevant to the ionized-charge parameter Z. Figures 9(a) and (c) indicate that, compared to the high T i from the numerical case of the  Though T e increases from about 2.3 keV to 2.8 keV due to the redistribution of energy from shock to electrons, a little bit higher than 2 ± 0.2 keV in experiments, it still seems convincing because T e from our experiment is a time-intergraded result and should be a lower value compared to the time-resolved result during the strongest colliding period (0.8-1.0 ns).The scale length of the temperature gradient in figure 9  temperature >1 keV than that in the laser spot region at 1.2 ns (Solid-red line in figure 10(b)).It reveals that the nonequilibrium plasma evolution caused by the strong collision process will affect x-ray emissions in a longer time.It also agrees the experimental evidence shown in figures 2(g)-(i).
Besides, it is worthy noting that equations ( 4) and ( 5) do not suit the situation where a strong magnetic field exists.Especially for the case of multi-specie collisions in the magnetized plasmas, the anisotropy of electron thermal conductivity should be considered by choosing of Simakov's electron viscosity coefficients [56].Of cause, they are the same in our case where the isotropic condition satisfies.
In total, by comparing the two simulation cases with experimental results, we are for the first time to provide the experimental evidence indicating that the traditional description of shock energy transport does not provide the convincing T i compared to the experiment in the strong collision situation.However, the new model theoretically proposed by Velikovich et al [47] and also discussed by Miller [48] shows a more precise description of plasma parameter evolutions by splitting the shock to both ions and electrons based on their viscosity values.Besides, the influence of x-ray emissions from the strong collision center on the temperature evolution after lasers end has also been confirmed by simulations.

Conclusions
In summary, we have comprehensively investigated the influence of the colliding process between two Au-plasma plumes on the conversion of x-ray radiations and the evolution of the in site plasma state by experiments.The temporal and spatial evolution of x-ray radiations measured by XFC reveals that bright x-ray emissions are formed due to the strong plasma colliding.And x-ray fluxes measured by XRDs in different spectra indicates that the conversion efficiency in M-band region (1.6-4 keV) are particularly high (∼30%) when compared to the component from the single-laser shot in 1 drive duration.Meanwhile, according to the distribution, spatial-resolved T e and T i as well as the plasma parameters of v x-ray and ∆L x-ray,Te have been estimated.Based on the analysis of the characteristic plasma parameters, we find the condition λ i ⩽ ∆L x-ray,Te always satisfies and it demonstrates that strong collision effect dominates in the central collision region.Additionally, The discovery of T i ≫ T e which is totally different from the laser-ablation region of T i ≈ T e verifies that non-equilibrium process occurs during the plasma collision.Furthermore, our two-dimensional radiative-hydrodynamic simulation studies confirm that the usual description of the shock heating model could not describe the ion temperature evolution well when the strong colliding process dominates.Because it ignores the energy transfer from shock to electrons.Here our experimental evidence demonstrate the new model theoretically discussed by A. L. Velikovich and Douglas S. Miller provide more matched results for the first time.Therefore, it calls for more attention on the influence of plasma plume collisions in ICF and HEDP physics, especially the influence on the M-band x-ray conversion and the plasma evolution of non-equilibrium process.
of China Academy of Engineering Physics under Grant No. CX2019023.

Figure 1 .
Figure 1.Experimental setup and diagnostics: (a) 1 ns super-Gaussian laser pulses each with an intensity of ∼5.5 × 10 14 W cm −2 irradiate on the interior surface of a 600(R) 2 π/2 × 6000 µm 3 Au half-hohlraum.The half-hohlraum was dug by using an 850 × 1400 × 6000 µm 3 cuboid.Two laser beams respectively incident from the ±45 • degree to z-axis.The blue-dashed region was chosen to distinguish the spatial-resolved spectrum from three typical regions I(central collision), II (laser spot) and III (weak collision region between I and II).(b) Schematic of three typical diagnostics: (1) the crystal spectrometer (CS) records the x-ray signals with a spatial-resolved along x axis and spectra-resolved along z axis from the selected rectangle (blue-dashed box in (a)).(2) the x-ray framing camera (XFC) respectively record the x-ray images >1 keV with spatial and temporal resolutions of ∼30 µm and ∼50ps.(3) Three types of x-ray diodes (XRDs), respectively measuring the total x-rays from 0.1-5 keV, M-band fraction from 1.6-4 keV and the hard x-ray fraction from 5-9 keV, are located at 20 • , 30 • and 45 • to z-axis upon the chamber.

Figure 2 .
Figure 2. X-ray images from 100-1600 ps.(a)-(c) how the evolution of two plasma plumes at 100, 300 and 500 ps.(d)-( f ) show the occurrence and varieties of x-ray emissions in the central collision region at 650, 750 and 850 ps.(g)-(i) compare the brightness of x rays from the central and two laser spot regions after lasers end at 1200, 1400 and 1600 ps.The brighter emissions in the center reveal that plasmas get cold more slowly in the colliding region.

Figure 5 (
Figure5(a) shows the space-resolved spectrum from 4.4-5.7 keV taking by the CS.Since the tracer material of Ti plasmas expands and moves with gold-plasma plumes during the laser ablating the interior surface, the temperature and density of the in site plasmas in space can be characterized by analyzing the self-emission lines of Ti at different positions.As we see, three bright parts of emissions in space can be clearly distinguished that one corresponds to the collision region (x = 0 or I in figure1(a)) and the other two are the laser spot regions (x = ±500 µm or III in 1(a)).The emissions in the spectra resolution are consistent of three components, the self-line-emission of Au, Ti tracer plasma and the continuous background of x-ray emission noise.After deducting the Au and the continuous emissions, Ly-α and He-α jkl/y/w intensity distributions of Ti are shown in figure5(b).There are three intensity peaks in the spatial resolution for all of the four typical emission lines.They correspond to the two focal spots (III in figure1(a)) and the central collision region (I), respectively.Two low-lying regions were exactly relative to II.Consistently, the high temperature region was formed due to the plume collision.To compare the divergencies of T e in the three regions, a collision-radiative model with steady-state approximation is used to calculate the theoretical spectrum of Ti emissions in different plasma conditions and

Figure 5 .
Figure 5. (a) Spatial-resolved spectrum from 4.4-5.7 keV along x-axis.(b) Ti self-emission intensity lines of Ly-αy and He-α ( jkl,y,w) after detecting Au self-emission and the continuous emission noise.It shows three peaks corresponding to the central collision region (I in figure 1(a)) and the laser spot regions (III), and two low-lying regions between them (II).

Figure 8 .
Figure 8. Ion temperature results with the traditional shock heating model: (a) T i (x, y) at t = 0.8 ns and (b) the one-dimensional T i (x, y = −300 µm) profiles at 0.4, 0.8 and 1.2 ns.

Figure 9 .
Figure 9. Simulation results: (a)-(c) T i , (d)-( f ) Te and (g)-(i) Ne distribution at t = 0.8 ns for the traditional and the new shock heating models respectively.The one-dimensional profiles in (c), ( f ) and (i) correspond to the T i , Te and Ne distributions along y = −300 µm.
( f ) is about 120 µm for both cases.When considering the spatial resolution of 20 µm for XFC and 100 µm for CS detectors, it is about 121 µm and 156 µm.If taking the temporal resolution and some other unideal situations into consideration, it can be regarded as matching the experimental value of ∆L x-ray ≈ 150 µm from figure 3(b) and ∆L Te ≈ 200 µm from figure 6(e) as well.In fact, since x-ray radiations are more determined by the area-density (N e L 2 ), ∆L x-ray should be closer to the scale of density gradient length ∆L Ne rather than ∆L Te .Figure 9(i) plots the density profiles from two cases.It indicates that ∆L Ne decreases from 120 µm to 90 µm in the new model case, which is different from ∆L Ne = ∆L Te (both 120 µm) in the traditional case.Since ∆L x-ray shows a smaller value than ∆L Te in experiments, the smaller ∆L Ne from the new model case seems match the experiments better.Of course, as this divergency is not too large, both time-and space-resolved density detections with a higher resolution is necessary to further confirm this point.Spatial distributions of electron temperature T e from the case with the new shock heating model at 0.4 ns and 1.2 ns are shown in figures 10(a) and (b) and the one-dimensional profiles along y = −300 µm are plotted in figure 10(c).It is clearly seen that T e in the laser focal spot at 0.4 ns (figure 10(a)) increases to >1 keV during the laser heating but decreases rapidly to even 0.2-0.3keV at 1.2 ns after the lasers end (figure 10(c)).Differently, T e in the strong region increases from 0 at 0.4 ns (Dashed-black line in figure 10(b)) to about 2.8 keV (figure 9(c)), and it also keeps a much higher

Figure 10 .
Figure 10.Te spatial distribution from the case with the new shock heating model respectively at (a) 0.4 ns and (b) 1.2 ns and along (c) y = −300 µm.