Numerical Study of Nonequilibrium Seed-Free Argon Plasma Magnetohydrodynamic Generator Using Collisional-Radiative Model

Collisional-radiative models for excited rare-gas atoms in low-temperature plasmas are a widely investigated topic. When these plasmas are optically thick, an ‘escape factor’ is introduced into the models to account for the reabsorption of photons (so-called radiation trapping process). This factor is usually obtained assuming a uniform density profile of the excited species; however, such an assumption is often not satisfied in a bounded plasma. This article reports for the first time a self-consistent collisional-radiative model without using an ad hoc ‘escape factor’ for excited Ar atoms in the 2p states (in Paschen’s notation). Rather, the rate balance equations—i.e. the radiation transfer equations—of the 2p states are numerically solved to yield the actual density profiles. The predictions of this self-consistent model and a model based on the escape factor concept are compared with spatially-resolved emission measurements in a low-pressure inductive Ar plasma. The self-consistent model agrees well with the experiment but the ‘escape factor’ model shows considerable deviations. By the comparative analysis the limitations and shortcomings of the escape factor concept as adopted in a significant number of works are revealed.

A collisional radiative (CR) model has been developed for the diagnostics of Ne–Ar mixture plasma. The 40 fine‐structure resolved energy levels of neon corresponding 2p53s, 2p53p, 2p53d, 2p54s, and 2p54p along with ground state (2p6) and ion state (2p5) have been considered. All the essential population and de‐population channels viz. electron impact excitation‐de‐excitation, ionization, two/three‐body recombination, radiative decay, self‐absorption correction, diffusion, etc., have been considered in the model. The quenching of relatively higher lifetime states 2p53s due to interaction with Ar atoms through associative and Penning ionization is also included in the model. The applicability of the CR model is demonstrated by performing the optical diagnostic of rf induced inductively coupled Ne–Ar mixture plasma. The plasma parameters viz. electron temperature, electron density, and population distribution of levels at various mixture conditions are extracted by coupling the present CR model predictions with emission and absorption measurements by Boffard et al. [J. Phys. D: Appl. Phys., 45, 382001 (2012) and private communication]. The results are also compared with earlier optical models and Langmuir probe measurements. The self‐absorption correction (escape) factors and electron impact excitation rates at various Ne–Ar mixture concentrations are also presented.

To control the H(0) atom production profile in the H(-) ion sources is one of the important issues for the efficient and uniform surface H(-) production. The purpose of this study is to construct a collisional radiative (CR) model to calculate the effective production rate of H(0) atoms from H2 molecules in the model geometry of the radio-frequency (RF) H(-) ion source for Linac4 accelerator. In order to validate the CR model by comparison with the experimental results from the optical emission spectroscopy, it is also necessary for the model to calculate Balmer photon emission rate in the source. As a basic test of the model, the time evolutions of H(0) production and the Balmer Hα photon emission rate are calculated for given electron energy distribution functions in the Linac4 RF H(-) ion source. Reasonable test results are obtained and basis for the detailed comparisons with experimental results have been established.

We show that for the study of emission from weakly ionized low temperature hydrogen plasmas, the processes A+ + A → A+ + A + ħω and A+ + A → A+2 + ħω (where A denotes a neutral atom in ground state and, A+ and A+2 atomic and molecular ions) must be treaded as a source of continual electro–magnetic radiation from low temperature plasma. Both reaction channels are treated separately and the corresponding total and separate spectral intensities are determined for hydrogen plasma at T < 10000K. The obtained results have been also compared with the corresponding spectral intensities for electron–ion bremsstrahlung and electron–ion photorecombination.

To understand the essentiality of the electron energy distribution function in a low-pressure discharge plasma, an experimental study is carried out on the diagnostics of microwave discharge hydrogen plasma with its discharge pressure ~1 torr in a cylindrical quartz tube. The electron kinetic temperature and density are measured by a Langmuir double probe. Number densities of electronically excited states of hydrogen atoms are experimentally examined by an optical emission spectroscopic (OES) measurement of line intensities of the Balmer series. The rotational and vibrational temperatures are observed for the Fulcher-α band spectrum of hydrogen molecule to understand the approximate value to the neutral gas temperature. The number density of the ground state of hydrogen atom is also experimentally estimated from the actinometry measurement. The electron energy probabilistic function (EEPF) is numerically calculated as a solution to the Boltzmann equation. Number densities of excited hydrogen atoms are calculated with the collisional-radiative (CR) model with experimentally measured data as input parameters. It is found that the population densities of excited states of hydrogen atoms become about one order or much larger than those determined by OES measurement if we assume Maxwellian EEPF. The CR model with the EEPF as a solution to the Boltzmann equation theoretically reproduce the experimentally measured values very well.

An algorithm for diagnosing the electron density and temperature of helium plasma at atmospheric pressure has been developed based on a revised helium collisional-radiative (CR) model. Atomic collision processes are included, and part of the atomic data of electron collision processes in the conventional CR model has been updated to expand its valid pressure. The algorithm uses eight emission lines in the visible-wavelength range as inputs to determine the electron density, electron temperature, and number density of the two metastable states by fitting the number density of the states corresponding to the emission lines. The algorithm has a considerably small theoretical error. In the microwave-discharged low-pressure helium plasma experiment, the results obtained with the algorithm agreed well with the results obtained with the probe method. The electron density and temperature of the atmospheric-pressure helium plasma obtained with the algorithm agreed well with the results of the continuum spectrum analysis.

Collisional-radiative modeling with multitemperature thermodynamic models

The motion-induced dephasing is a severe problem that limits the accuracy of a quantum control process by using external laser fields in neutral Rydberg atoms. This dephasing is a major issue that limits the realizable fidelity of a quantum entangling gate with neutral atoms when there is a {\it gap} time for the Rydberg atom to drift freely. We find that such a dephasing can be largely suppressed by using a transition in a `V'-type dual-rail configuration. The left~(right) arm of this `V' represents a transition to a Rydberg state $|r_{1(2)}\rangle$ with a Rabi frequency $\Omega e^{ikz}~(\Omega e^{-ikz})$, where $z$ is frozen without atomic drift, but changes linearly in each experimental cycle. Such a configuration is equivalent to a transition between the ground state and a hybrid and time-dependent Rydberg state with a Rabi frequency $\sqrt2\Omega$, such that there is no phase error whenever the state returns to the ground state. We study two applications of this method. First, it is possible to faithfully transfer the atomic state between a hyperfine ground state $|1\rangle$ and Rydberg states $|r_{1(2)}\rangle$ with no {\it gap} time between the excitation and deexcitation. Second, by adding infrared laser fields to induce transition between $|r_{1(2)}\rangle$ and a nearby Rydberg state $|r_3\rangle$ via a largely detuned low-lying intermediate state in the {\it gap} time, the atom can keep its internal state in the Rydberg level as well as adjust the population branching in $|r_{1(2)}\rangle$ during the {\it gap} time. This allows an almost perfect Rydberg deexcitation after the {\it gap} time, making it possible to recover a high fidelity in the Rydberg blockade gate. The theory paves the way for high-fidelity quantum control over neutral Rydberg atoms without cooling qubits to the motional ground states in optical traps.

A complex 0D collisional-radiative model (CRM) experimentally validated was used to describe in details the time evolution of the densities of all the species present in a non-equilibrium plasma generated in a background gas mixture composed by 64%H + 31%O + 5%C. This initial CRM involving 1050 reactions and 79 species is gradually reduced in term of number of reactions and species in order to be easily implemented in LSP particle-in-cell (PIC) simulations and to optimize the characteristics of an electron beam generated by a surface flashover on a velvet cathode. The reduction was done using comparisons between the electron densities calculated with the complete initial set of reactions and species. The reduction was successfully performed in three steps leading to a first reduced CRM (99 reactions and 26 species) followed by a second reduced CRM (nine reactions and eight species) and a third CRM (seven reactions and four species). The latter is obtained by lumping all the hydrogen excited states in a single fictitious sate, the spontaneous emission frequencies of these excited states in a single fictitious frequency and the three atoms of the gas mixture onto one single fictitious atom. The electron density evolution is well reproduced even with the most reduced CRM (third CRM) that leads to a mean relative error of about 3% without never exceeding 11%.

The effect of radiation trapping is included in the standard collisional-radiative model for atomic hydrogen under a typical condition of divertor plasmas The population of the first excited level of the ionizing plasma component is strongly enhanced by the absorption of resonance line photons produced by the recombining plasma component, and the effective ionization rate coefficient is also strongly enhanced.

One-electron capture and target-ionization in He +-neutral-atom collisions

In a magnetically insulated diode, collision-free electrons return to the cathode and no electron current is present at the anode. Electron transport to the anode is studied in this paper. Steady-state space-charge-limited flow is assumed initially. Breakdown of ion flow occurs when static neutral atoms at the anode undergo charge exchange, which results in neutral atoms drifting across the diode. These are subsequently ionized by reflexing ions producing electrons trapped in Larmor orbits throughout the diode. These electrons drift to the anode via ionization and inelastic collisions with other neutral atoms. Model calculations compare the effects of foil and mesh cathodes. Steady-state space-charge-limited ion current densities are calculated. The neutral atom density at the cathode is determined as a function of time. The shorting time of the diode is scaled versus the electrode separation d, the diode potential V/sub 0/, the magnetic field, and the initial concentration of static neutron atoms.

At long distances interactions between neutral ground state atoms can be described by the Van der Waals potential V(r) =-C6/r^6-C8/r^8 - ... . In the ultra-cold regime atom-atom scattering is dominated by s-waves phase shifts given by an effective range expansion p cot d0 (p) = -1/a0 + r0 p^2/2 + ... in terms of the scattering length a0 and the effective range r0. We show that while for these potentials the scattering length cannot be predicted, the effective range is given by the universal low energy theorem r0 = A + B/a0+ C/a0^2 where A,B and C depend on the dispersion coefficients Cn and the reduced di-atom mass. We confront this formula to about a hundred determinations of r0 and a0 and show why the result is dominated by the leading dispersion coefficient C6. Universality and scaling extends much beyond naive dimensional analysis estimates.

A kinetic model is proposed, allowing us to describe the kineticsof the electronic components of a non-equilibrium low-temperature argonplasma over a wide range of values of the degrees of the ionization. Themodel incorporates a large number of electronic states of argon atoms (upto n~30) and takes into account the processes of electron elasticscattering from neutral argon atoms and ions, electronic excitation anddeexcitation by electron impact, the processes of ionization of atoms incollisions with electrons and unexcited atoms and mutually reverseprocesses of electron-ion recombination, reactions of dissociativerecombination and electron-impact dissociation of molecular ions. Theresults of calculations performed in the framework of the proposed modelhave shown that the electron energy distribution in a high-pressure plasmamay conserve a non-Maxwellian character up to rather high values of thedegree of ionization (ne/N~3×10-3), principally followingthe ionization and recombination processes initiated by atomic impact.

Collisional-radiative (CR) models describe the atomic processes in a plasma by tracking the population density in the ground and excited states for each charge state of the atom/ion. These models predict important plasma properties such as charge state distributions and radiative emissivity and opacity. Accurate descriptions of the CR balance of the plasma are essential in fusion whole device modeling, especially when significant impurities are introduced into the plasmas. In an integrated fusion plasma and CR simulation, a CR model, which is a high-dimensional stiff ODE, needs to be solved on each grid point in the configuration space, and can overwhelm the overall computational cost. In this work, we propose a machine-learning-based method that discovers a latent space and learns its corresponding latent dynamics, which can capture the essential physics to make accurate predictions at much lower online computational cost. The proposed approach is physics-assisted, due to its combination of a physical latent space and a data-driven latent space. It has been demonstrated that the proposed architecture can predict both the full-order CR dynamics and a physical quantity of interest accurately.