Controllable non-ideal plasmas from photoionized compressed gases

Based on a suite of molecular dynamics simulations, we propose a strategy for producing non-ideal plasmas with controllable properties over a wide range of densities between those of ultracold neutral plasmas and those of solid-density plasmas. We simulated the formation of non-equilibrium plasmas from photoionized, cool gases that are spatially precorrelated through neutral–neutral interactions that are important at moderate-to-high pressures. A wide range of physical properties, including Coulomb collisional rates, partial pressures, screening strengths, continuum lowering, interspecies Coulomb coupling, electron degeneracy and ionization states, were characterized across more than an order of magnitude variation in the initial gas pressure. A wide range of plasma properties are also found to vary when the initial pressure of a precorrelated gas is varied. Thus, we propose that non-ideal plasmas with tunable properties can be generated by photo-ionizing a dense, precorrelated gas. We find that the optimal initial density range for the gas is near a Kirkwood/Widom–Fisher line in the neutral-gas phase diagram. This strategy for generating non-ideal plasmas suggests experiments that have significant advantages over both ultracold and solid-density plasma experiments because the collisional, collective and recombination timescales can be tuned across many orders of magnitude, potentially allowing for a wider range of diagnostics. Moreover, the added costs of cooling ultracold plasmas and diagnosing dense matter with x-rays are eliminated.

Given these considerations, it would be useful to have an alternate table-top method that allows for wide and continuous variations in density with independent control over the temperature and ionization state, including 2. Mitigation of DIH: pressure-induced precorrelation Forming plasmas at low densities has numerous advantages, including the ability to control the ionization state, allowing for table-top visible lasers as probes and the relatively slow time scales associated with collisions and collective phenomena. However, DIH limits the Coulomb coupling parameter to an order of unity unless some mechanism for precorrelation is employed [64]. For this reason, cooling a gas to temperatures well below the DIH temperature has limited advantages. Conversely, in the extreme limit of employing a solid or liquid as a target, the ions are highly precorrelated [65,66]; in fact, these systems can be viewed as 'overcorrelated' [67]. Such dense targets can be isochorically heated to various temperatures to achieve a range of plasma conditions. However, because of the high densities and pressures, these plasmas require large facilities for their creation and diagnosis.
To motivate our strategy, we review the process of DIH that occurs following photoionization of a neutral gas. The initial temperature T 0 and the final temperature T f are related to the spatial correlations in the initial and final states by [41] T T  v k  k  S  T  S  T  k  k  k  1  3   d  2 , , , is the Coulomb potential in Fourier space, and ò(k) is the dielectric response function. Because of the very large electron-ion mass ratio, the ion-ion collisions associated with the DIH process are much faster than electronion collisional processes, and this allows us to neglect any changes in the electrons during DIH. As a result, ò(k) is approximately constant during that short time interval (about one ionic plasma period [42]). Thus, to achieve large ion-ion coupling after DIH, an initial state with correlations similar to those of the desired plasma is needed.
Because of the issues mentioned above with ultracold and dense plasma experiments, we have examined DIH for modest temperatures at densities that lie between those of UCNPs and dense plasmas. To mitigate DIH in this intermediate density range, we propose precorrelating the neutral gas through strong neutral-neutral interactions. This is most easily accomplished by increasing the gas pressure to achieve various levels of precorrelation before ionization; photoionization is then used to form a two-temperature plasma. For conciseness, we will refer to a plasma formed through this procedure as a 'pressure-induced precorrelated plasma' (PIPP), and the basic idea is illustrated in figure 1. The ionic and electronic Coulomb couplings are shown in the left and right panels of the figure, respectively, where the mean ionization state has been taken to be Z 1 á ñ = . At very low density, but higher than that typical of UCNPs, neutral-neutral interactions are very weak.
In this low-density regime, DIH leads to a final coupling parameter of order unity [41]; using this fact, we can solve for the DIH temperature (denoted by T DIH ) as a function of density: where n i is the ion density and e is the fundamental charge. T DIH becomes of order room temperature (denoted by T room ) at a density of approximately n 1.4 10 cm For densities in this range and above, there is little advantage to cooling the gas before ionization; this is indicated by a horizontal line at T room , and the critical density n c is shown as a vertical line in the figure. These lines set the lower density and temperature limits of the PIPP regime in figure 1. The contours in the figure are the logarithm of the Coulomb coupling; if there were no correlations, the plasma could evolve through DIH to the contour labeled '0.0', which sets the upper bound for PIPPs, as that state is already achievable with lower-density plasmas. Thus, in the PIPP region, a plasma can be formed from an uncooled gas, and any precorrelation from the modest density is expected to lead to a coupling parameter exceeding unity. The feasibility of producing plasmas in this manner should be addressed: a literature search revealed two experiments, labeled 'UCLA' [60,61] and 'Imperial College' [59] in the figure, that fall near the PIPP regime. We also show a portion of the regime accessible by experiments at the National Ignition Facility (NIF); we note that PIPPs would, in principle, provide a platform for exploring physics relevant to NIF on a smaller scale, as can be seen by the constant coupling contours shared by both the PIPP regime and the NIF regime.
There are two main factors that dictated our choice of the candidate gas: (1) we preferred a gas that was used in one of the recent experiments that have conditions similar to PIPPs; this would favor the feasibility of the PIPP paradigm, (2) the size of the atoms constituting the gas must be such that the average interatomic distance in the Figure 1. Notional region of PIPPs in temperature-density space. The ionic (left panel) and electronic (right panel) coupling parameters denoted by Γ ii and Γ ee , respectively, are shown in a temperature-density plane, taking the mean ionization state to be Z 1 á ñ = . (Here n i and n e denote the ion and electron densities and T i and T e denote the ion and electron temperatures, respectively.) The regime of ultracold neutral plasmas (UCNPs) is shown at the lower left, and the high-temperature regime of plasmas created at the National Ignition Facility (NIF) are shown at the upper right. Our proposed region for PIPPs is shown, as well; we define this region as plasmas that are created from room-temperature gases and that have strong correlations created by the modest densities. We also show where previous experiments have been done, denoted by 'Imperial College' [59] and 'UCLA' [60,61], suggesting the feasibility of PIPP experiments. The contours are log-scale coupling parameters that reveal how the very disparate plasmas probe similar dimensionless properties of the plasmas. neutral gas state is similar to the average separation between the ions in the plasma state; this is an important requirement for DIH mitigation that follows from the discussion on DIH, as described above. The 'UCLA' experiments are some of the recent experiments that have conditions similar to PIPPs; these experiments employed helium, argon and xenon (Xe). Among the choices, Xe offers the largest interatomic separation in its neutral state that is similar to the average separation between Xe ions in the plasma state. For the above reasons, we have chosen to study neutral Xe gas in this work. We consider Xe at a temperature of 300 K, which is above its critical point [68], thereby avoiding liquid droplet formation. In the next section, we will discuss the computational models used for our studies of PIPPs generally, and dense Xe in particular.

Computational methods
Our primary approach is to employ a variety of MD models using effective pair potentials to simulate the process of creating PIPPs over a wide range of densities. Because PIPPs are created out of equilibrium and tend toward a two-temperature state, methods such as path integral Monte Carlo (PIMC) [69] and Kohn-Sham-Mermin density functional theory (DFT) [70] cannot be applied. PIMC is formulated around an equilibrium thermodynamic density matrix, and DFT formulations assume an equilibrium Fermi-Dirac distribution for the electrons; neither approach applies to a wide range of plasma experiments. Moreover, as PIPPs can span the classical to quantum regimes, PIMC and DFT would be extremely inefficient computationally. In this section, we describe computational methods appropriate to PIPPs.
We employ non-equilibrium MD using several interparticle potentials. The different potentials, described in detail below, are needed to model the neutral gas and the plasma state, including potentials needed to explore strong electron-ion coupling. We use a standard MD approach that employs a velocity-Verlet integrator, a Berendsen thermostat and periodic boundary conditions; typically, for each simulation, 10 4 or more particles were used. An equilibration phase was used for equilibrium simulations of the initial gas and for examinations of equation-of-state issues; otherwise, the simulations were non-equilibrium (e.g., entering the plasma state from the neutral state).
In section 3.1, we discuss the range of potentials needed to explore PIPP behavior using this MD approach. Three classes of potentials are needed to describe PIPPs. To examine precorrelation prior to ionization, we require an accurate neutral-neutral potential. Following ionization, we begin with the equilibrated initial state formed by the neutrals and evolve according to an effective ion-ion potential. For studies that involve details of the electronic state of the PIPP, we further require potentials that can be used to evolve the electrons as an independent species. Because the plasma potentials rely on knowledge of the atomic states, we discuss our generalized Saha model in section 3.2.

Interparticle interactions
Precorrelation in the neutral gas can be modeled using MD with an appropriate neutral-neutral potential. While a wide range of potentials exist for this case, such as the commonly used Lennard-Jones potential, we employed a potential chosen specifically for Xe. The neutral Xe-Xe interactions are known to be well described over a range of pressures by the exponential-6 (E6) potential [71][72][73] u r r where r is the distance between two atoms, ε/k B =243.1 K, η=13, and σ=4.37 Å [73]. After equilibration, the gas is photoionized, and the interactions become dominated by Coulomb forces.
We do not directly model the ionization process, but rather assume that each neutral is instantly converted to an ion and that the formation of electronic screening clouds is rapid. The time scales involved are those of laser ionization, electron scattering, and ion equilibration. As the ionization is occurring, the electron subsystem equilibrates on a time scale of inverse electron plasma frequency, forming screening clouds around the ions. Subsequently, the ions respond on a time scale of the inverse ion plasma frequency, which is ∼100-1000 times larger than the electron equilibration time scale. This ordering of the time scales is a valid assumption; however, for further validation, MD coupled with atomic kinetics is required. Further, we have assumed that 100% of the neutrals are ionized. When the ionization is below 100%, neutrals will start playing a role; however, their impact on DIH mitigation is unclear. It is possible that the advantages of precorrelation are minimized by the presence of the neutrals. On the contrary, since the neutrals are much less energetic than the ions, it is also possible that the neutral subsystem serves as a cooling bath for the ions, thereby mitigating DIH even further. In order to examine these different possibilities, it is required to perform MD with explicit ion-neutral and neutral-neutral interactions in addition to ion-ion interactions for different ionization fractions. Such detailed simulations to further examine our assumptions would be the focus of future work. Within the assumptions we have made, we use the (precorrelated) final conditions from the neutral gas simulation as the initial conditions of the plasma simulation and evolve according to a plasma potential relevant for ion-ion interactions at the appropriate ionization level (see the following subsection for a more detailed discussion of our ionization model).
An accurate MD model for ion-ion interactions in this moderately dense regime is the Yukawa potential [41], which is given in Gaussian-cgs units by Here, Z α is the charge number of the αth ion and λ e is the degeneracy-corrected electron-screening length [74] (also referred to as Thomas where T e is the electron temperature (in energy units), and E n m is the electron Fermi energy for electron density n e . We choose Z Z = á ñ a for all ions, where the mean ionization Z á ñ is calculated using a non-ideal Saha equation [75][76][77]; see section 3.2 for details. The Yukawa potential has found wide use in dusty plasmas [78] and UCNPs [79] and has been analyzed in detail recently for dense plasmas [80]. Depending on the PIPP conditions, more development of the ion-ion potential may be called for; for example, as the electronelectron coupling is varied, PIPPs can explore a wider variety of potentials beyond the basic Yukawa potential. The Yukawa potential also neglects ionic core-core interactions beyond the Coulomb interaction; such interactions will be the subject of future work. For these initial studies, we employ the basic Yukawa form (4).
Despite the utility of the E6 and Yukawa potentials, they do not describe dynamic electronic degrees of freedom. For the second set of simulations, we allow for explicit electronic degrees of freedom through the use of quantum-statistical potentials (QSPs) [81][82][83]. In particular, we employ a QSP composed of a diffractive term from Hansen-McDonald [81] and a Pauli exclusion term between electrons derived from the low-density limit of the spin-averaged Lado potential [82,83] ) is the thermal de Broglie wavelength, μ αγ is the reduced mass, and δ αγ is the Kronecker delta. Note that the indices (α, γ) now run over the electrons as well as the ions. Recent comparisons of the QSP model with PIMC predictions for radial distribution functions (RDFs) across a wide range of conditions [84] reveal the accuracy of QSPs for the conditions of PIPPs.

Atomic ionization model
Because we are considering compressed gases that are below solid density, we employ a non-ideal Saha equation rather than an average-atom model [74] to compute ionization levels. The framework of the Saha approach has the additional advantage that it naturally yields the distribution of charge states, not only the average. In its ideal form, the well-known Saha equations [75,76] describing the transitions between N ionization states (in addition to the neutral state) are given by A root solver can be used to solve for Z á ñ, and once Z á ñ is known, the individual species concentrations can be calculated from the following recursion relations: For the specific case of Xe, we need to explore only the first few ionization states because of the limited temperature range of interest. Using the values obtained from [85], we take N=5 and set {E j }={12, 21, 32, 46, 57} eV. We estimate the statistical weights by assuming that Xe, like other noble gases (beyond He), initially ionizes by losing electrons from the outermost p-subshell. Taking values from [77,86], we have {g j }={1, 6, 9, 4, 9, 6}. While the gas in consideration is below solid density, it is still compressed to form Xe-Xe correlations, and this basic Saha model must be extended to its non-ideal form to capture many-body screening effects.
In a dense plasma, the environment surrounding each atom can significantly modify the energy required for ionizing transitions. These modifications are collectively referred to as IPD because they tend to have the effect of lowering ionization energies. To capture the effects of IPD, we employ the standard method of Stewart and Pyatt (SP) [50]. While our choice of IPD model is not unique, we do not expect large deviations from the SP model and other IPD models in this regime. In the SP model, the electrostatic potential about a point ion is calculated using the following two assumptions: • Within the ion-sphere radius (r<a i ), the ion density is zero, and the electron density is constant. (Here, a i is the ion-sphere radius defined as a n 3 4 ) .) • Beyond the ion-sphere radius (r>a i ), the electrons and ions exhibit linear screening in terms of their respective screening lengths.
Solving the associated Poisson equation and enforcing 2  -continuity in the potential results in an electrostatic potential that can be radially expanded about an ion position as u r Z e r E j j 2 , where ΔE j is the IPD energy shift. This energy shift associated with the jth ionization state is given by While it remains unclear which IPD model is most appropriate, we have employed this standard model both to self-consistently predict an accurate ionization state to use in the MD simulations and to illustrate the degree to which IPD physics can be explored with PIPPs. Our goal here is not to develop Saha models beyond this standard description. Future plasma experiments employing dense gases could provide more insights into IPD, and more refined models could then be developed.

Plasma properties in the PIPP regime
Before we examine how plasma properties vary across the PIPP and what this reveals about our knowledge of non-ideal plasmas, we demonstrate some features of precorrelation induced by pressure. Simulations were performed in which we first equilibrated the MD using the E6 potential and computed the RDF. Then, from those initial positions and velocities, we evolved the plasma to equilibrium using the Yukawa potential. Results for four different initial gas pressures P 0 ={50, 62, 143, 1393} atm are shown in figure 3. In the left four panels, we show the initial (gray) neutral-neutral RDFs, g nn (r), and final (colored) ion-ion RDFs, g ii (r). It is evident that higher pressures result in increased correlation in the initial gas, which in turn leads to smaller differences in the RDF between the gas and plasma states. Thus, DIH can be controlled by varying the initial gas pressure, thereby allowing the Coulomb coupling of the resulting PIPP to be controlled.
While it is common to characterize non-ideal plasmas through the bare ionic Coulomb coupling parameter Z e a T ii i i 2 2 G = á ñ , PIPPs are two-temperature electron-ion mixtures that are not well characterized by Γ ii . For this reason, an effective coupling parameter can be used to capture the coupling of the system more accurately. One such effective coupling parameter that approximates the effect of screening is given by e ii s ii where a T i e e k l = ( )is the screening parameter. The time evolution of these coupling parameters is shown in the right panel of figure 3, where Z 2 á ñ = in each case. Over a range of initial gas pressures, the post-DIH Γ ii ranges from roughly 10 to 364, which covers most of the strong-coupling regime. When screening is included via ii s G , effective couplings from roughly 1 to 40 are obtained, with κ varying from 1.7 to 2.2 (see figure 6). Thus,  . Impact of precorrelation. In the left four panels, we show the impact of precorrelating a neutral gas on the DIH process. The gray curves are the MD-predicted neutral-neutral RDFs, g nn (r), for a dense xenon gas (E6 potential) at four different pressures prior to ionization. The colored curves show the ion-ion RDFs, g ii (r), for the now ionized plasma (Yukawa potential) following DIH; note that the g ii (r) curves at high pressures are not substantially different from those at low pressures prior to ionization. For the four different pressures, the right panel shows the impact of precorrelation on the coupling parameter, using two different definitions of the parameter (dashed line, Γ ii and solid line, ii s G ); the colors of the curves in the right panel correspond to the colors of the g ii (r) curves in the left four panels.
PIPPs can be used to create much larger variations in the effective coupling strength than can their UCNP counterparts [62,79].
To better understand why such a steep transition takes place as the initial pressure goes from 50 to 62 atm, we examine the underlying microfields of the plasma after photoionization. We introduce the microfield distribution which represents the distribution of forces F (in units of e a i 2 2 ) on the initial energy landscape of the system immediately after ionization; here N is the number of ions in the system, F 0 j ( ) is the net force on the jth ion at t=0, where t=0 marks the instant of ionization, and áñ denotes the ensemble average. Following the analysis of [42], the early-time temperature evolution can be described as T t T t 0 ò á ñ = ( ). We can process our MD data to obtain microfields immediately after ionization of the correlated gas. Figure 4 shows p(F) for Z 1 á ñ = and initial pressures of 50, 62 and 143 atm; all p(F) were converged using 10 5 particles. As the initial pressure is increased from 50 to 143 atm, the peak of p(F) shifts towards smaller F, and the width of p(F) decreases, thereby decreasing F 2 á ñ from ∼6.6 e a i 2 2 to ∼0.1 e a i 2 2 . This shift in the microfield distribution peak to a lower value of F indicates far more cancellations in the interparticle forces. Further, the most significant changes in p(F) occur from 50 to 62 atm, which could be attributed to a Fisher-Widom or Kirkwood line crossing, as suggested by the change in the RDFs from monotonic to oscillatory in figure 3 3 .
Having established that DIH can be partly mitigated in a controlled manner to achieve a range of coupling strengths, we turn to some of the unique plasma properties that can be measured with PIPPs. For these studies, we include the electronic degrees of freedom explicitly in the MD simulations through the use of QSPs for a more complete exploration of the relevant physics.

Strong electron-ion coupling
We begin by examining the intraspecies correlation functions g ii (r), g ei (r) and g ee (r), which are shown in figure 5 for four different initial gas pressures; the RDFs are at the post-DIH temperature. There are some interesting features in the RDFs that merit a brief discussion. The electron-electron RDF undergoes a Kirkwood-like transition in the region near 50 atm, with its peak at the same location as the ion peak; there are strong correlations in the peak locations of g ei (r) and g ee (r) with those of g ii (r), suggesting that the electrons are highly localized around the ions in these plasmas. Moreover, g 0 1 ee > ( ) for most of the initial gas pressures considered, indicating that an effective attraction between electrons (mediated by the ions) exists. , respectively. All the p(F) were converged using 10 5 particles. 3 While the monotonic-oscillatory crossover is similar in both the Kirkwood and Widom-Fisher cases, [89] gives a precise distinction based on the structure of the poles of the correlation functions. We did not perform such an analysis here and therefore do not know which type of line we have; we leave that analysis for future work.
From these simulations, several simple plasmas properties can be immediately examined. In particular, we can calculate the explicit coupling between the ions and electrons through an interspecies coupling parameter Z Z e a T ) [88], species masses are m α and m γ , the ion-sphere radius is a ii =a i , and the electron-sphere radius is a a a n 3 4 ee ei e e 1 3 p = = = ( ) . We can additionally examine the screening strength κ=a i /λ e and degeneracy parameter Θ=T e /E F . Species couplings Γ αγ are shown in the left panel of figure 6, where we see that the largest variations in the species couplings occur in the 50-100 atm range. The coupling strength and degeneracy are shown in the right panel of figure 6, and while the screening parameter remained approximately constant, the degeneracy varied by a factor of more than three. We have also explored the more complex plasma properties of (1) IPD, (2) transport phenomena, and (3) EOS, which we have described in detail below.

Ionization potential depression
IPD has seen renewed interest recently in the context of dense plasma experiments [53,55]. The energy shifts associated with IPD modify the ionization balance in a plasma, and this balance affects important properties such as opacity, the EOS, and transport coefficients. Further, these modifications to the ionization balance become more pronounced as the coupling increases. Despite the significance of IPD physics, there is a lack of well-established models that describe the phenomenon, as has been shown by recent dense plasma experiments [55]. The widely used SP model of IPD was found to increasingly disagree with measurements in these dense plasma experiments at higher ionization levels (see section 3.2 for a review of the SP model). Instead, the lesserknown Ecker-Kröll model, given by for the jth ionization state [51], offered better agreement with IPD measurements for the same conditions. As shown in figure 7, the significant differences between the SP and Ecker-Kröll predictions of IPD for PIPP conditions are similar to those observed in dense plasma experiments. Thus, the lower energy-density environments of PIPPs (relative to dense plasmas) and their controllability over a range of densities enable these plasmas to provide an optimal platform for validating different IPD models without the complexities associated with dense plasma conditions. Figure 5. Partial radial distribution functions. The functions g ii (r) (blue), g ei (r) (green), and g ee (r) (red) were computed with MD using quantum-statistical potentials for 3×10 4 total particles (10 4 ions and Z 2 á ñ = ). Note the extreme behavior of g ee (r), which exceeds unity near r=0 for sufficiently high pressures, revealing substantial ion-mediated effective interactions as electrons localize near (relatively) isolated ions.
A notable feature in the IPD predictions is the sensitivity to pressure in the 50-62 atm range, a property shared with the other applications discussed below. Re-examining figure 3, we see that the gas RDF undergoes a monotonic-oscillatory transition, which is either a Kirkwood or Fisher-Widom transition [89]; this transition can be seen in particular in the 50-62 atm range (blue and green curves). Thus, establishing the Kirkwood/ Fisher-Widom line for the gas of interest can yield considerable controllability.

Transport phenomena
Turning next to transport phenomena, which are critical to a hydrodynamic description of plasmas, PIPPs can provide a platform for exploring quantities such as transport coefficients (diffusivities, viscosities, conductivities, etc) that are relevant to conditions in ICF experiments [45,57,58,74]. Most transport coefficients tend to be inversely proportional (or proportional) to a scattering cross section, which generally is not a transferable quantity among different transport processes [74]; however, we can explore the qualitative effects of variations in PIPP conditions on these cross sections by employing a Coulomb logarithm (CL) as a proxy. Here, we consider CLs of the form [74] Figure 6. Γ αγ , κ and Θ versus initial gas pressure. The species coupling, Γ αγ , as a function of the initial gas pressure for a xenon plasma. The electron temperature T e ∼6 eV, which corresponds to Z 2 á ñ = . The coupling can be controlled further by varying T e as well. Figure 7. IPD versus initial gas pressure. The energy shifts associated with IPD, ΔE j , as a function of the initial gas pressure for a xenon plasma. The electron temperature T e ∼6 eV, which corresponds to Z 2 á ñ = . The coupling can be controlled further by varying T e as well.

Equation of state
Finally, we examine PIPPs as a platform for investigating multi-temperature EOS models, which are essential to the hydrodynamic description of a plasma [90]. For example, large-scale experiments involving plasmas (e.g., ICF) require an accurate EOS for their design and interpretation [56,57,91,92]. Because electrons and ions are at different temperatures in most laboratory plasmas, it is important to develop an accurate two-temperature EOS. Although theoretical efforts have explored this topic over many years [88,[93][94][95][96], much less experimental work on this subject has been conducted. To understand the role that PIPPs could play in such experimental studies, we calculate final system pressures using MD simulations as the initial pressure of the gas phase is varied.
Here, we present a two-temperature generalization for comparison with MD simulations. The total pressure of a multi-component system can be decomposed as  figure 9 in units of the idealelectron pressure. Here, the electron-ion contribution to the excess pressure is shown to vary the most, and this finding could be of interest for experiments focused on electron-ion interactions. However, the total pressure, which is primarily dominated by the ideal-electron pressure, is of the most interest from a hydrodynamic perspective. Figure 8. Λ αγ versus initial gas pressure. The Coulomb logarithm, Λ αγ , as a function of the initial gas pressure for a xenon plasma. The electron temperature T e ∼6 eV, which corresponds to Z 2 á ñ = . The coupling can be controlled further by varying T e as well. Figure 9. Plasma pressure versus initial gas pressure. Equations of state from MD simulations (left panel) and using a mean-field approximation (right panel) as a function of the initial gas pressure for a xenon plasma. The electron temperature T e ∼6 eV, which corresponds to Z 2 á ñ = . The coupling can be controlled further by varying T e as well.
It should be noted that k 2  is always real; however, the root k 2 -becomes negative for B<0, which leads to an unphysical result for the correlation functions and consequently the pressures. Given our definition of T ij , this spurious range is encountered for the temperature ratios m m T T 1 where we have assumed that m e <m i . However, T e ?T i for our systems of interest, hence this regime will be avoided naturally. Finally, the total pressure is given by In the single-temperature limit, where the temperature ratio is unity, many of the above quantities simplify dramatically. Here, we have β=β e =β i =β ie , and the correlation functions can be expressed as The total excess pressure reduces to which is the standard DH result. Similarly, in the limit T T e i  , the leading-order excess pressure is given by the ion-ion correlations in the form P T 24 The DH results provide useful formulae for estimating various quantities. Moreover, since it is well-known that the DH approximation fails for non-ideal plasmas, we use it to compare with the more accurate models to suggest which experiments are in regions beyond what DH is capable of describing. For example, as shown in the right panel of figure 9, the two methods predict total pressures with the opposite sign and disparate magnitudes. Note that we have reduced both P  and P ii ex D  by a factor of 10 to clearly show the variations in the other partial pressures. A striking observation is that the total pressure predicted by DH is negative in all cases because of the contribution of the ion-ion excess pressure. Moreover, the electron-ion excess pressure has a sign opposite that of its MD analog. These observations lead us to conclude that the DH approximation severely breaks down for the PIPP conditions studied here. Such disparities between the DH and MD predictions call for validation of the different EOS models with experiments.

Summary, conclusion and outlook
In summary, we have proposed a strategy for creating non-ideal plasmas at densities intermediate to UCNPs and dense plasmas. Because these plasmas mitigate DIH through correlations induced by pressure, we refer to them as PIPPs. We have studied PIPPs through a series of MD simulations that simulate the neutral gas before ionization to establish neutral-neutral correlations. From those initial states, we further evolve the system in the plasma state to examine the impact of those correlations. We discovered that there is a narrow pressure range over which there is a transition from weak to strong DIH mitigation, and we have identified that with a Fisher-Widom or Kirkwood line in the neutral gas. We anticipate that PIPPs can exploit this behavior to create a platform that allows for unique variations in plasma properties without some of the complexities of UCNP and dense plasmas, which perhaps allows for diagnostics such as near-visible Thomson scattering and terahertz spectroscopy [100][101][102][103][104] to be developed for non-ideal plasmas. Importantly, this behavior occurs near conditions of previous experiments [60,61].
We have quantified the potential range of coupling parameters that PIPPs might explore, using both bare and screened coupling parameters. We found, as shown in the left panel of figure 6, that the post-DIH Γ ii varies from roughly 10 to 364, which covers most of the strong-coupling regime. When the effect of screening is included, the effective coupling ii s G varies from roughly 1 to 40. These predictions suggest much larger couplings than can be achieved by UCNPs. Through simulation studies with explicit electrons, we have also shown that novel strong coupling behavior among the electrons may be achievable with PIPPs. In particular, our results indicate that an effective attractive interaction between electrons can be created in this intermediate density regime. This attraction, revealed through studies of g ee (r) in which g 0 1 ee > ( ) , is mitigated by strong electronion coupling. Because PIPPs allow for a wide range of electron temperatures, depending on the ionization laser energy, electron attraction is potentially very precisely controllable in PIPPs.
We also examined variations of a number of other quantities, including IPD and transport phenomena (using the CL as a generic proxy). IPD predictions for PIPPs using the SP and EK model (see figure 7) shows differences that are similar to the differences between the predictions of the two models observed in dense plasma experiments. Thus, the lower energy-density environments and their controllability over a range of densities enable these plasmas to provide an optimal platform for validating different IPD models without the complexities associated with dense plasma conditions. Figure 8 shows our predictions for ion-ion, ion-electron and electron-electron CLs; all are near unity or smaller, representing the most theoretically challenging regime of transport in plasmas; in particular, the ion-ion CL shows a three order-of-magnitude variation over the range of initial gas pressures considered.
We performed a careful study of two-temperature EOS using MD with electrons simulated explicitly using QSPs; the MD predictions of two-temperature EOS were then compared with the EOS predicted by a twotemperature DH theory (see figure 9). The EOS predicted by DH theory differs significantly from the MD prediction of EOS, both in magnitude and sign, suggesting not only that PIPPs explore EOS regimes of interest, but also that experimental design studies cannot rely on DH theory. As an aside, our studies have also revealed the drastic failure of the two-temperature DH theory and motivate the need for more theoretical work on twotemperature equations of state.
There are many avenues for future work based on these studies. From a modeling point of view, the potentials could be improved to allow for more accuracy across larger ranges of pressure. Moreover, the models could be extended to elements other than Xe and to mixtures, perhaps involving molecules. With better models, and more species, interesting regimes of PIPPs could be better identified and used to motivate specific experiments. Our results also point to theoretical issues that require further development, such as CLs near zero and two-temperature equations of state. So far, we have not explored non-steady-state properties of PIPPs, or whether they can be sculpted or tagged [34,36]. Most importantly, future work is needed to explore realistic experimental designs, and explore how a wider array of diagnostics might be included in these non-ideal plasma studies.