Fraction Of Ions Research Articles

A xenon collisional-radiative model applicable to electric propulsion devices: III. Determination of the ionization fraction in low-temperature xenon plasma by using ionic and atomic 6p lines

The ionization fraction is a key figure of merit for optimizing the performance of plasma device. This work presents an optical emission spectroscopy (OES) method to determine the ionization fraction in low-temperature xenon plasma. The emission line-ratio of xenon ionic and atomic 6p–6s transitions is used in this method. A comprehensive collisional-radiative model developed in our previous work is employed to describe the relationship between the line-ratios and the plasma parameters. It is found that some special line-ratios have a sensitive relationship to the ionization fraction, e.g. the ratio of the 460.30 nm line and 828.01 nm lines. These line-ratios are selected for the diagnostic method. The method is demonstrated in a magnetized discharge chamber. The axially-resolved emission spectra of the ionization chamber are measured, and from those the ionization fraction along the chamber axis is determined via the OES method. The axially-resolved ionization fraction is found to be dependent on the magnetic field and agrees well with those obtained from a Langmuir probe. In the experiment, the probe is overheated under some conditions, possibly due to the bombardment by energetic particles. In this case, no results can be obtained from the probe, while the OES method can still obtain reasonable results. Combined with optical tomography and spectral imaging technology, the OES method can also provide the spatial distribution of the ionization fraction, which is needed for revealing the discharge mechanisms of plasma devices.

Effects of Cold Plasma on the Mode Conversion From Fast Magnetosonic Wave to Electromagnetic Ion Cyclotron Wave in the Inner Plasmasphere

AbstractPrevious studies show that fast magnetosonic (MS) wave with frequency of tens of Hz may propagate to low L‐shells (L < 2.0) in the inner plasmasphere and mode convert to electromagnetic ion cyclotron (EMIC) wave where its wave frequency is close to the local crossover‐cutoff‐resonance frequency triplet through different propagation paths. In this study, we investigate how this mode conversion process may depend on the ion composition and electron density by full‐wave simulation with various plasma density profiles and initial wave normal angles (WNAs) of incoming MS wave from magnetic equator and a higher latitude of 15°. We find that critical fraction of minority ion (He+ or M/Q = 2 ion − D+ or He++) exists during the mode conversion, over which the conversion from MS wave to H+ band right‐handedly polarized EMIC wave starts to become negligible. This critical fraction decreases with the incident WNA of MS wave from equator. The efficiency of this conversion process also decreases with the electron density. As incoming MS is from higher latitudes off equator, optimal fraction of minority ion exists, with which the efficiency of conversion from MS wave to H+ band left‐handedly polarized EMIC wave reaches a maximum. Moreover, this maximum conversion efficiency varies with the incident WNA and may approach 100% with WNA close to 90° at the magnetic latitude of 15°. We also find that localized wave structure may be formed when the converted H+ band EMIC wave is trapped between local H+ − D+(He++) bi‐ion resonance frequency and D+(He++) − He+ left‐handed polarization cut‐off frequency with a small M/Q = 2 ion fraction and a relatively larger He+ fraction as incoming MS wave is near equator.

Impact of temperature asymmetry and small fraction of static positive ions on the relaxed states of a relativistic hot pair plasma

Abstract The relaxed state of a magnetized relativistic hot plasma composed of inertial electrons and positrons having different relativistic temperatures and a fraction of static positive ions is studied. From the steady-state solutions of vortex dynamics equations and the relation for current density, a non-force-free triple Beltrami (TB) relaxed state equation is derived. The TB state is characterized by three scale parameters that consequently provide three different self-organized structures. The analysis of the relaxed state shows that for specific values of generalized helicities, the disparity in relativistic temperature and the existence of a small fraction of static positive ions in pair plasma can transform the nature of scale parameters. Moreover, an analytical solution of the TB state for an axisymmetric cylindrical geometry with an internal conductor configuration demonstrates that due to asymmetries of temperature and density of plasma species, diamagnetic structures can transform into paramagnetic ones and vice versa. The present study will improve our understanding of pair plasmas in trap-based plasma confinement experiments and astrophysical environments.

Sustainable power generation from salinity gradients by reverse electrodialysis: Influence of divalent ions

The performance of Reverse Electrodialysis (RED) stacks can be significantly degraded by the presence of divalent ions. To gain a deeper understanding of the influence of divalent ions, a RED model based on the Nernst-Planck framework was developed in this study. Using this model, a simulation study was performed when the feed solutions contain a mixture of NaCl and MgCl2. The impact of the divalent ion Mg2+ on RED performance was examined from the perspective of ion transport. The results indicate that divalent counterions decrease membrane permselectivity and membrane potential, while increasing membrane electrical resistance by affecting ion concentrations within the membrane. The uphill transport of divalent ions occurs only when the molar fraction of divalent ions in the feed solutions is relatively low. Specifically, when the feed solution contains only MgCl2 compared to only NaCl, the open-circuit voltage decreases by 36.2%, and the maximum gross power density decreases by 44.8%.

Self-consistent equilibrium models of prominence thin threads heated by Alfvén waves propagating from the photosphere

The fine structure of solar prominences is composed of thin threads that outline the prominence magnetic field lines. Observations have shown that transverse waves of Alfvénic nature are ubiquitous in prominence threads. These waves are driven at the photosphere and propagate to prominences suspended in the corona. Heating due to Alfvén wave dissipation could be a relevant mechanism in the cool and partially ionised prominence plasma. In this work, we explore the construction of 1D equilibrium models of prominence thin threads that satisfy an energy balance condition between radiative losses, thermal conduction, and Alfvén wave heating. We assumed the presence of a broadband driver at the photosphere that launches Alfvén waves towards the prominence. An iterative method was implemented in which the energy balance equation and the Alfvén wave equation are consecutively solved. From the energy balance equation and considering no wave heating initially, we computed the equilibrium profiles along the thread of the temperature, density, ionisation fraction, and other relevant parameters. On these equilibrium profiles, we used the Alfvén wave equation to compute the wave heating rate, which was then put back in the energy balance equation to obtain new equilibrium profiles, and so on. The process was repeated until convergence to a self-consistent thread model heated by Alfvén waves was achieved. We obtained equilibrium models composed of a cold and dense thread, an extremely thin prominence-corona transition region, and an extended coronal region. We found that the length of the cold thread decreases with the temperature at the prominence core and increases with the Alfvén wave energy flux injected at the photosphere. However, computed equilibrium models for large wave energy fluxes are not possible when the wave heating rate inside the cold thread becomes larger than the radiative losses. The maximum value of the wave energy flux that allows for an equilibrium depends on the prominence core temperature. This constrains the existence of thread equilibria in realistic conditions.

Degradation of nuclear fuel debris analog by siderophore-releasing microorganisms

ABSTRACT In damaged Fukushima Daiichi NPP reactors, groundwater microorganisms have continuously seeped into contaminated water. We investigated the effect of a siderophore-releasing microorganism (SB) on fuel debris analogs. Fuel debris analog pellet samples (FDAPS) and powder samples containing CeO2 (an alternative to UO2)-ZrO2 solid solution and metallic iron were formed. FDAPSs were contacted with SB on a membrane filter placed on agar medium for 50 days. With the addition of SB, Fe-containing degradation products were detected by SEM-EDX analyses on FDAPSs, on the filter, and on the agar medium, revealing that some fractions of Fe ions were dissolved and precipitated on FDAPSs, and the rest became detached from FDAPSs and migrated through the filter. The SB-derived degradation differed from those by P. fluorescens and Na-citrate solution. The RBS and ERDA spectrometry analyses identified the degradation products as Fe oxyhydroxides. Although Zr was detected in small amounts in the Fe area by SEM-EDX and by SIMS analyses, the dissolution of Zr may be limited. These results clarify that the presence of SB accelerates the degradation of fuel debris in which Fe metal regions are preferentially degraded, and some fraction of Fe were detached and migrated from the fuel debris analog.

EUV debris mitigation using magnetic nulls

Next generation EUV sources for photolithography use light produced by laser-produced plasmas (LPP) from ablated tin droplets. A major challenge for extending the lifetime of these devices is mitigating damage caused by deposition of tin debris on the sensitive collection mirror. Especially difficult to stop are high energy (up to 10 keV) highly charged tin ions created in the plasma. Existing solutions include the use of stopping gas, electric fields, and magnetic fields. One common configuration consists of a magnetic field perpendicular to the EUV emission direction, but such a system can result in ion populations that are trapped rather than removed. We investigate a previously unconsidered mitigation geometry consisting of a magnetic null by performing full-orbit integration of the ion trajectories in an EUV system with realistic dimensions and optimize the coil locations for the null configuration. The magnetic null prevents a fraction of ions from hitting the mirror comparable to that of the perpendicular field, but does not trap any ions due to the chaotic nature of ion trajectories that pass close to the null. This technology can potentially improve LPP-based EUV photolithography system efficiency and lifetime and may allow for a different, more efficient formulation of buffer gas.

Ion- and temperature-induced 3-dimensional nanoscale patterning in Ti1-xAlxN deposited by High Power Impulse Magnetron Sputtering

We report on surface-driven self-organization in the TiN-AlN binary system during ion-assisted deposition at elevated temperatures. With an Al:Ti ratio slightly above the boundary of stable cubic growth, various morphologies from single-phase films to highly ordered two-phase films with v-shaped and oblique, striped structures were obtained. The high metal ion fractions and high ion energies obtained by High Power Impulse Magnetron Sputtering result in unique morphologies that are not accessible by conventional magnetron sputtering. A comprehensive structural and chemical analysis of the two-phase films is presented to enlighten the mechanism of phase separation and crystallographic orientation evolution.

Polycyclic aromatic hydrocarbon size tracers

ABSTRACT We examine the dependence of polycyclic aromatic hydrocarbon (PAH) band intensity ratios as a function of the average number of carbon atoms and assess their effectiveness as tracers for PAH size, utilizing the data, models, and tools provided by the NASA Ames PAH Infrared Spectroscopic Data base. To achieve this, we used spectra from mixtures of PAHs of different ionization fractions, following a size distribution. Our work, congruent with earlier findings, shows that band ratios that include the 3.3 μm PAH band provide the best PAH size tracers for small-to-intermediate sized PAHs. In addition, we find that band ratios that include the sum of the 15–20 μm PAH features (I$_{\Sigma _{15-20}}$) and the 6.2 or 7.7 μm bands also serve as good tracers for PAH size in the case of small-to-intermediate sized PAHs, for objects under a similar PAH size distribution as with the presented models. For different PAH size distributions, the application of a scaling factor to the I6.2/I$_{\Sigma _{15-20}}$ ratio can provide estimates for the size of the small-to-intermediate PAH population within sources. Employment of the I6.2/I$_{\Sigma _{15-20}}$ and I7.7/I$_{\Sigma _{15-20}}$ ratios can be of particular interest for JWST observations limited only to ∼5–28 μm MIRI(MRS) coverage.

Mean ionic activity coefficient of associative electrolyte solutions: A comparison study

The performance of four implicit solvent models for associative and two models for non-associative electrolyte solutions has been compared and analyzed for the mean ionic activity coefficient (MIAC) of electrolytes in the solution. Two of these models for associative electrolyte solutions are based on a chemical approach (Fisher-Levin-Guillot-Guissani (FLGG) and Ebeling-Grigo (EG)), and one of them is based on the reference cavity approximation (Zhou-Yeh-Stell (ZYS)). The last one is based on the thermodynamic perturbation theory (Binding mean spherical approximation, BiMSA). Models without ion-pairing also consist of hard sphere (HS) contribution in addition to the electrostatic contribution from the Debye-Hückel (HS + DH) and the mean spherical approximation (HS + MSA) theories. To this aim, the models’ predictions are compared with the numerical solution of the Poisson-Boltzmann equation, the Monte Carlo simulations, and the experimental data. We have shown that considering the ion pairing results in a better agreement of the predicted MIAC against both simulations and experimental data of 2:2 electrolytes. We have also adjusted the ionic diameter and the distance between ion pairs to the MIAC experimental data and validated the estimated fractions of free ions with the electrical conductivity measurements. We have shown that the FLGG model captures the physics of the system more accurately compared to other models.

Preparation of sodium alginate gel microspheres catalysts and its high catalytic performance for treatment of ciprofloxacin wastewater

The discharge of the antibiotic wastewater has increased dramatically in our country with the development of medical science and wide application of antibiotic, resulting in serious harm to human body and ecological environment. In this work, ciprofloxacin (CIP) was selected as one of typical antibiotics and heterogeneous Fenton-like catalysts were prepared for the treatment of ciprofloxacin wastewater. The sodium alginate (SA) gel microspheres catalysts were prepared by polymerization method using double metal ions of Fe3+ and Mn2+ as cross-linking agents. Preparation conditions such as metal ions concentration, mass fraction of SA, polymerization temperature and dual-metal ions as crosslinking agent were optimized. Moreover, the effects of operating conditions such as initial concentration of CIP, pH value and catalyst dosage on CIP removal were studied. The kinetic equation showed that the effect of the initial concentration of CIP on the degradation rate was in line with second-order kinetics, and the effects of catalyst dosage and pH value on the degradation rate of CIP were in line with first-order kinetics. The SA gel microspheres catalysts prepared by dual-metal ions exhibited a high CIP removal and showed a good reusability after six recycles. The SA gel microspheres catalysts with an easy recovery performance provided an economical and efficient method for the removal of antibiotics in the future.

Adsorption of Mono- and Divalent Ions onto Dendritic Polyglycerol Sulfate (dPGS) as Studied Using Isothermal Titration Calorimetry.

The effective charge of highly charged polyelectrolytes is significantly lowered by a condensation of counterions. This effect is more pronounced for divalent ions. Here we present a study of the counterion condensation to dendritic polyglycerol sulfate (dPGS) that consists of a hydrophilic dendritic scaffold onto which sulfate groups are appended. The interactions between the dPGS and divalent ions (Mg2+ and Ca2+) were analyzed using isothermal titration calorimetry (ITC) and showed no ion specificity upon binding, but clear competition between the monovalent and divalent ions. Our findings, in line with the latest theoretical studies, demonstrate that a large fraction of the monovalent ions is sequentially replaced with the divalent ions.

Numerical model supplemented by thin-layer analysis for diffusiophoresis of a particle incorporating finite ion size effects

The impact of finite-sized ions on the diffusiophoresis of a charged colloid subjected to a concentration gradient of electrolyte solution consisting monovalent or multivalent ionic species, is studied. In diffusiophoresis, the ion concentration is of O(1M). In this non-dilute electrolyte solutions, the ion–ion steric interaction is important. We have adopted the Boublik–Mansoori–Carnahan–Starling–Leland (BMCSL) model to account for the ion steric interactions and the Batchelor–Green expression for the relative viscosity of suspension. We have solved the standard model numerically considering ions as point charge (PNP-model), the modified Nernst–Planck equations incorporating the ion steric interaction with constant viscosity (MNP-model), and modification of the MNP-model by incorporating the viscosity variation with the ionic volume fraction (MNPV-model). Semi-analytical expressions for mobility based on a linear perturbation technique under a thinner Debye length is presented for PNP- and MNP-models. In the MNP-model, counterion saturation in the Debye layer due to the ion steric interaction enhances the surface potential by attenuating the shielding effect, diminishes the surface conduction, and magnifies the induced electric field. These in combination create a larger mobility at a thinner Debye length compared with the PNP-model. This increment in mobility attenuates when the MNPV-model is considered. The MNPV-model is more appropriate to analyze the finite ion size effects, and it is found to yield the mobility values more close to the experimental data compared with the MNP- and PNP-model. The semi-analytical expressions for mobility based on the PNP- and MNP-models agree with the corresponding exact numerical solutions when the surface potential is in the order of thermal potential. However, a large discrepancy between the simplified expression and the exact numerical results is found for a concentrated electrolyte in which the induced electric field is large.

The Roles of Dust Growth in the Temperature Evolution and Snow Line Migration in Magnetically Accreting Protoplanetary Disks

The temperature structure of protoplanetary disks provides an important constraint on where in the disks rocky planets like our own form. Recent nonideal magnetohydrodynamical (MHD) simulations have shown that the internal Joule heating associated with magnetically driven disk accretion is inefficient at heating the disk midplane. A disk temperature model based on the MHD simulations predicts that in a disk around a solar-mass young star, the water snow line can move inside the current Earth’s orbit within 1 Myr after disk formation. However, the efficiency of the internal Joule heating depends on the disk’s ionization and opacity structures, both of which are governed by dust grains. In this study, we investigate these effects by combining the previous temperature model for magnetically accreting disks with a parameterized model for the grain size and vertical distribution. Grain growth enhances the gas ionization fraction and thereby allows Joule heating to occur closer to the midplane. However, growth beyond 10 μm causes a decrease in the disk opacity, leading to a lower midplane temperature. The combination of these two effects results in the midplane temperature being maximized when the grain size is in the range 10–100 μm. Grain growth to millimeter sizes can also delay the snow line’s migration to the 1 au orbit by up to a few million years. We conclude that accounting for dust growth is essential for accurately modeling the snow line evolution and terrestrial planet formation in magnetically accreting protoplanetary disks.

Mössbauer and Structure-Magnetic Properties Analysis of AyB1-yCxFe2-xO4 (C=Ho,Gd,Al) Ferrite Nanoparticles Optimized by Doping.

AyB1-yCxFe2-xO4 (C=Ho,Gd,Al) ferrite powders have been synthesized by the sol-gel combustion route. The X-ray diffraction of the CoHoxFe2-xO4 (x = 0~0.08) results indicated the compositions of single-phase cubic ferrites. The saturation magnetisation of CoHoxFe2-xO4 decreased by the Ho3+ ions, and the coercivity increased initially and then decreased with the increase of the calcination temperature. The Mössbauer spectra indicated that CoHoxFe2-xO4 displays a ferrimagnetic behaviour with two normal split Zeeman sextets. The magnetic hyperfine field tends to decrease by Ho3+ substitution owing to the decrease of the A-B super-exchange by the paramagnetic rare earth Ho3+ ions. The value of the quadrupole shift was very small in the CoHoxFe2-xO4 specimens, indicating that the symmetry of the electric field around the nucleus is good in the cobalt ferrites. The absorption area of the Mössbauer spectra changed with increasing Ho3+ substitution, indicating that the substitution influences the fraction of iron ions at tetrahedral A and octahedral B sites. The X-ray diffraction of Mg0.5Zn0.5CxFe2-xO4(C=Gd,Al) results confirmed the compositions of single-phase cubic ferrites. The variation of the average crystalline size and lattice constant are related to the doping of gadolinium ions and aluminum ions. With increasing gadolinium ions and aluminum ions, the coercivity increased and the saturation magnetization underwent a significant change. The saturation magnetization of AlMg0.5Zn0.5FeO4 ferrite reached a minimum value (MS= 1.94 mu/g). The sample exhibited ferrimagnetic and paramagnetic character with the replacement with Gd3+ ions, that sample exhibited paramagnetic character with the replacement with Al3+ ions, and the isomer shift values indicated that iron is in the form of Fe3+ ions.

Anti-site disorder driven short-range order and canted antiferromagnetism in inverse spinel LiNiVO4

Frustration driven short-range magnetic correlations/fluctuations in quantum materials usually host exotic ground states like spin glass, low dimensional magnetism and quantum spin liquid. In this context, different members of spinel (both normal and inverse) family have gained enormous interest and an inverse spinel vanadate, LiNiVO4, seems to be an interesting candidate. Structural investigations reveal that unlike usual cation ordering, Ni and Li ions are randomly distributed at octahedral sites and results in reduced magnetic frustration. Further, an additional anti-site disorder is present, as a small fraction of Ni ions occupies tetrahedral sites. Magnetic susceptibility and heat capacity studies show that short-range magnetic correlations develop below 30 K, followed by a canted antiferromagnetism below 2.2 K. Different competing magnetic interactions due to the presence of disorder and reduced magnetic frustration result in the short-range ordering as well as canted antiferromagnetism in LiNiVO4.

Toward nebular spectral modeling of magnetar-powered supernovae

Context. Many energetic supernovae (SNe) are thought to be powered by the rotational energy of a highly magnetized, rapidly rotating neutron star. The emission from the associated luminous pulsar wind nebula (PWN) can photoionize the SN ejecta, leading to a nebular spectrum of the ejecta with signatures that might reveal the PWN. SN 2012au is hypothesized to be one such SN. Aims. We investigate the impact of different ejecta and PWN parameters on the SN nebular spectrum, and test whether any photoionization models are consistent with SN 2012au. We study how constraints from the nebular phase can be linked into modeling of the diffusion phase and the radio emission of the magnetar. Methods. We present a suite of late-time (1–6 yr) spectral simulations of SN ejecta powered by an inner PWN. Over a large grid of one-zone models, we study the behavior of the physical state and line emission of the SN as the PWN luminosity (LPWN), the injected spectral energy distribution (SED) temperature (TPWN), the ejecta mass (Mej), and the composition (pure O or realistic) vary. We discuss the resulting emission in the context of the observed behavior of SN 2012au, a strong candidate for a PWN-powered SN. We used optical light-curve models and broadband PWN models to predict possible radio emission from SN 2012au. Results. The SN nebular spectrum varies as TPWN varies because the ejecta become less ionized as TPWN increases. Ejecta models with low mass and high PWN power obtain runaway ionization for O I, and in extreme cases, also O II, causing a sharp decrease in their ion fraction over a small change in the parameter space. Certain models can reproduce the oxygen line luminosities of SN 2012au reasonably well at individual epochs, but we find no model that fits over the whole time evolution. This is likely due to uncertainties and simplifications in the model setup. Using our derived constraints from the nebular phase, we predict that the magnetar powering SN 2012au had an initial rotation period ~15 ms, and it is expected to be a strong radio source (F > 100 μJy) for decades.

Formation of the Transition Region for the Quiet Sun

We propose a partially ionized collisional two-fluid model of the formation of the transition region between the cool dense chromosphere and hot tenuous corona for the quiet Sun. The chromosphere is treated as an isothermal gravity-bound two-fluid stratified atmosphere without appreciable vertical flow, on average. The different scale heights of the two fluids result in vertical evolution of the ionization state, and the transition region can be defined according to the ionization fraction. The transition region starts at the altitude where the ionization fraction reaches 0.5, the demarcation between the weakly and strongly ionized gas. The upper border of the region is defined as the temperature at which the particles possess enough energy for ionization, i.e., the first ionization potential. Within the transition region is a diffusion process in which the cold chromospheric particles gain energy and ionize through random collisions with hot coronal particles diffusing upward into the corona, whereas, when colliding with cold chromospheric particles, hot coronal particles lose energy, recombine, and fall into the chromosphere. The type II spicules can be generated when and where the local heating rate is so high that the conditions for a stratified chromosphere are not satisfied; upward flow is formed, penetrating the corona where the chromospheric gas in the spicule is ionized and dispersed. The enhanced radiation via those chromospheric neutral particles cools the coronal gas, and more recombination occurs, producing enhanced downward diffusion. The model reproduces key structural features of the transition region from first principles and a minimum of arbitrary parameters.

Light ion dynamics in the topside ionosphere and plasmasphere during geomagnetic storms

Storm-time topside ionosphere plasma composition, especially the light ion fraction, is an important parameter which controls magnetosphere–ionosphere coupling, plays a part in the growth of local instabilities, and provides information about the ring current, ion upflow, movement of ionization and other important physical processes and parameters. Ion composition is difficult to estimate on fine scales as empirical models tend to be parametrized by fixed inputs, ignoring the role of memory in plasma, and to preferentially capture large scales, while ground radars have limited coverage. In particular, ionospheric composition measurements at mid-latitude are lacking. Here we show, using the new Swarm SLIDEM effective ion mass measurement, a superposed epoch analysis of storm-time dayside and nightside effective ion mass changes, demonstrating the extent and timescales of motion of the [O+]/[H+] transition height with the main phase of geomagnetic storms, as well as directly observing evidence for the latitude dependence of these dynamics.Graphical

Support for the standard picture of thermal X-rays in the wind of ζ Puppis from dielectronic recombination of He-like ions

ABSTRACT We use the line ratios of resolved X-ray resonance and satellite line pairs from Si xiii and Mg xi ions to test the widely held assumption that the shocked plasma in the wind of hot stars is in collisional ionization equilibrium. We specifically apply this test to the prototypical O supergiant ζ Puppis, as its line ratios are well resolved in its total 813 ks Chandra observation. This satellite-to-resonance line ratio is known to be a reliable diagnostic of plasma temperature but has yet to be applied to hot stars due to needing a long exposure time to see both lines above the continuum. In testing the assumed plasma state, we also provide evidence against significant ionization and excitation from proton collisions. Since dielectronic recombination (DR) allows somewhat lower energy free electrons to excite resonance lines than by the usual collisional pathways, we also use the DR flux ratios to extend diagnostics of the ionization fraction of the parent ion to lower temperatures than any other method can achieve. Also, the DR ratio supports a concept of an average free electron temperature, for each target ion used, which can constrain heating models.