Charles F. F. Karney, Nathaniel J. Fisch
A theory for the generation of current in a toroidal plasma by radio-frequency waves is presented. The effect of an opposing electric field is included, allowing the case of time varying currents to be studied. The key quantities that characterize this regime are identified and numerically calculated. Circuit equations suitable for use in ray-tracing and transport codes are given.
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Spontaneous spin-up are widely observed in tokamak plasmas, which is crucially important for plasma confinement. A kinetic theory is proposed to show that a toroidal rotation of core plasma is induced by the topological transition of orbits driven by turbulent diffusion in a collisionless tokamak plasma. The theoretical prediction agrees well with the well-known Rice-scaling of intrinsic core plasma flow. This new theory predicts an intrinsic core parallel flow of $\sim 100km/s$ for the International Thermonuclear Experimental Reactor.
Inductively Coupled Plasma Driven by Asymmetric Triangular Current Waveform
采用二维粒子模拟方法，研究非对称三角波形电流驱动的感应耦合等离子体中射频电流波形和频率对等离子体特性、碰撞过程及电子速度分布函数的影响。
We present results of twisted plasma waves driven by twisted ponderomotive force. With beating of two, co-propagating, Laguerre-Gaussian (LG) orbital angular momentum (OAM) laser pulses with different frequencies and also different twist indices, we can get twisted ponderomotive force. Three-dimensional particle-in-cell simulations are used to demonstrate the twisted plasma waves driven by lasers. The twisted plasma waves have an electron density perturbation with a helical rotating structure. Different from the predictions of the linear fluid theory, the simulation results show a nonlinear ro…
The current-driven electrostatic ion-cyclotron (EIC) instability is studied in presence of a transverse dc electric fields in a collisional magnetized dusty plasma. We derive the appropriate charging equation self consistently by using the Vlasov equation.
It is found that the Lorentz force generated by the magnetic drift drives a generic plasma pinch fluxes of particle, energy and momentum through the Stokes-Einstein relation. The proposed theoretical model applies for both electrons and ions, trapped particles and passing particles.
We propose a new approach to high-intensity laser-driven electron acceleration in a plasma. Here, we demonstrate that a plasma wave generated by a stimulated forward-scattering of an incident laser pulse can be in a longest acceleration phase with an incident laser wave. This is why the plasma wave has the maximum amplification coefficient which is determined by the breakdown (overturn) electric field in which the acceleration of injected relativistic beam electrons occurs. We estimate qualitatively the acceleration parameters of relativistic electrons in the field of a plasma wave generated a…
Photon bursts with a wavelength smaller than the plasma inter-particle distance can drive plasma wakes via Compton scattering. We investigate this fundamental process analytically and numerically for different photon frequencies, photon flux, and plasma magnetization. Our results show that Langmuir and extraordinary modes are driven efficiently when the photon energy density lies above a certain threshold. The interaction of photon bursts with magnetized plasmas is of distinguished interest as the generated extraordinary modes can convert into pure electromagnetic waves at the plasma/vacuum bo…
Generation of terahertz electromagnetic radiation due to coalescence of upper-hybrid waves in the long-wavelength region of strong plasma turbulence driven by a high-current relativistic electron beam in a magnetized plasma is investigated. The width of frequency spectrum as well as angular characteristics of this radiation for various values of plasma density and turbulence energy are calculated using the simple theoretical model adequately describing beam-plasma experiments at mirror traps. It is shown that the power density of electromagnetic emission at the second harmonic of plasma freque…
We identify the desired characteristics and parameters of a beta>1 magnetized plasma, possibly with highly tangled, open field lines, that could be a suitable target to be compressed to fusion conditions by a spherically imploding plasma liner [S. C. Hsu et al., IEEE Trans. Plasma Sci. 40, 1287 (2012)] formed by merging hypersonic plasma jets. This concept is known as plasma-jet-driven magneto-inertial fusion (PJMIF). We set requirements on the target and liner such that (a) compressional heating dominates over thermal transport in the target, and (b) magnetic amplification due to compression …
We explore the role of the background plasma ion motion in self-modulated plasma wakefield accelerators. We employ J. Dawson's plasma sheet model to derive expressions for the transverse plasma electric field and ponderomotive force in the narrow bunch limit. We use these results to determine the on-set of the ion dynamics, and demonstrate that the ion motion could occur in self-modulated plasma wakefield accelerators. Simulations show the motion of the plasma ions can lead to the early suppression of the self-modulation instability and of the accelerating fields. The background plasma ion mot…
Runaway particles can be produced in plasmas with large electric fields. Here we address the possibility that such runaway ions and electrons excite Alfvénic instabilities. The magnetic perturbation induced by these modes can enhance the loss of runaways. This may have important implications for the runaway electron beam formation in tokamak disruptions.
Temporal evolution of the inhomogeneous energy density driven instability (IEDDI) is examined in presence of a nonuniform transverse dc electric field in collisional magnetized plasma cylinder. Using experimentally known parameters relevant to IEDDI, we have estimated the growth rate for $ν$=1, 2 and 3 nonlocal eigenmodes.
The Green's function for rf-driven currents in a toroidal plasma is calculated in the long mean-free-path limit.
New unstable temperature gradient driven modes in an inhomogeneous plasma are identified. These modes represent transient $ω\simeq k_{\Vert }v_{th}^{(e,i)}$ sound oscillations in magnetized plasma that are kinetically destabilized via Landau interactions. Electron and ion sound branches are unstable for large values of the Larmor radius parameter $% k_{\bot}ρ_{e,i}\gg 1,$ respectively. The instability occurs due to a specific plasma response that significantly deviates from Boltzmann distribution in the region $k_{\bot}ρ_{i,e}\gg 1$ . Pacs: 52.35 Kt, 52.35 Qz
A long, relativistic charged particle beam propagating in a plasma is subject to the self-modulation instability. This instability is analyzed and the growth rate is calculated, including the phase relation. The phase velocity of the accelerating field is shown to be significantly less than the drive beam velocity. These results indicate that the energy gain of a plasma accelerator driven by a self-modulated beam will be severely limited by dephasing. In the long-beam, strongly-coupled regime, dephasing is reached in less than four e-foldings, independent of beam-plasma parameters.
We advance a theory of quasistatic approximation and investigate the excitation of nonlinear plasma waves by the driving beam of ultrarelativistic electrons using novel electrostatic-like particle- in-cell code. Assuming that the beam occupies an infinitesimally small volume, we find the radius and length of the plasma bubble formed in the wake of the driver for varying values of the beam charge. The mechanism of the bubble formation is explained by developing simple models of the bubble at large charges. Plasma electrons expelled by the driver charge excite secondary plasma waves which compli…
Plasma zone plate for high-power lasers driven by a Laguerre-Gaussian beam
针对高功率激光操控中传统固态光学器件易受损的问题，提出由拉盖尔-高斯光束有质动力驱动的等离子体波带片，通过粒子模拟验证其聚焦功能，为高功率激光操控提供了新方法。
Compton scattering of gamma rays propagating in a pair plasma can drive the formation of a relativistic electron positron beam. This process is scrutinised theoretically and numerically via particle-in-cell simulations. In addition, we determine in which conditions the beam can prompt a beam-plasma instability and convert its kinetic energy into magnetic energy. We argue that such conditions can be met at the photosphere radius of bright Gamma Ray Bursts.
Similarity Theory and Scaling Networks for Electromagnetic Wave-Driven Plasmas
本文提出了一种基于相似性理论的缩放网络，用于研究电磁波驱动等离子体在不同尺度下的行为特性，通过粒子-细胞模拟验证了等离子体均匀性的尺度不变性。
Generation of electromagnetic radiation near the second harmonic of the plasma frequency during the injection of an electron beam into a rippled-density plasma channel is investigated using both analytical theory and particle-in-cell simulations. The generating scheme is based on nonlinear interaction of the most unstable beam-driven potential plasma wave with its satellite arising due to scattering on the longitudinal modulation of plasma density. Resulting superluminal oscillations of electric current in a finite-size plasma channel radiate electromagnetic waves via the same mechanism which …
We present a new mechanism of attosecond extreme-ultraviolet (XUV) pulses generation from a relativistic laser-driven overdense plasma surfaces in the wavebreaking regime. Through particle-in-cell simulations and analysis, we demonstrate that the observed ultrashort XUV emission for the parameters we considered is predominantly due to a strong plasma-density oscillation subsequent to wavebreaking. The coupling of the strong density variation and the transverse fields in the front surface layer gives rise to the transmitted emission with frequencies mainly around the local plasma frequency. Thi…
The structure of the density singularity formed in a relativistically large amplitude plasma wave close to the wavebreaking limit leads to a refraction coefficient which has a coordinate dependence with discontinuous derivatives. This results in a non-exponentially small above-barrier reflection of an electromagnetic wave interacting with the nonlinear plasma wave.
Formation and Study of a Spherical Plasma Liner for Plasma-Jet-Driven Magneto-Inertial Fusion
本文在PLX装置上首次测量了36个脉冲等离子体射流形成的球形氩衬垫，揭示了射流间从动力学贯穿到碰撞主导的转变，并表明改进射流参数可形成更光滑衬垫，为PJMIF聚变研究提供实验基准。
We propose a new approach to high-intensity relativistic laser-driven electron acceleration in a plasma. Here, we demonstrate that a plasma wave generated by a stimulated forward-scattering of an incident laser pulse can be in the longest acceleration phase with injected relativistic beam electrons. This is why the plasma wave has the maximum amplification coefficient which is determined by the acceleration time and the breakdown (overturn) electric field in which the acceleration of the injected beam electrons occurs. We must note that for the longest acceleration phase the relativity of the …
The power of second harmonic electromagnetic emission is calculated for the case when strong plasma turbulence is excited by a powerful electron beam in a magnetized plasma. It is shown that the simple analytical model of strong plasma turbulence with the assumption of a constant pump power is able to explain experimentally observed bursts of electromagnetic radiation as a consequence of separate collapse events. It is also found that the electromagnetic emission power calculated for three-wave interaction processes occurring in the long-wavelength part of turbulent spectrum is in order-of-mag…
First experimental measurements are presented for the kink instability in a linear plasma column which is insulated from an axial boundary by finite sheath resistivity. Instability threshold below the classical Kruskal-Shafranov threshold, axially asymmetric mode structure and rotation are observed. These are accurately reproduced by a recent kink theory, which includes axial plasma flow and one end of the plasma column that is free to move due to a non-line-tied boundary condition.
In this work we investigate a numerical model of a coaxial RF-driven plasma jet operated at atmospheric pressure. Due to the cylindrical symmetry an adequate 2-D representation of the otherwise 3-dimensional structure is used. A helium-oxygen chemistry reaction scheme is applied. We study the effect of secondary electrons emitted at the inner electrode as well as the inserted dielectric tube and discuss their impact on the discharge behavior. We conclude that a proper choice of materials can improve the desired mode of operation of such plasma jets in terms of materials and surface processing.
The nonlinear propagation of small but finite amplitude dust ion-acoustic waves (DIAWs) in an ion-beam driven plasma with Boltzmannian electrons, positive ions and stationary charged dust grains, is studied by using the standard reductive perturbation technique (RPT). It is shown that there exist two critical values $(γ_{c1}$ and $γ_{c2})$ of ion-beam to ion phase speed ratio $(γ)$, beyond which the beam generated solitons are not possible. The effects of the parameters, namely $γ$, the ratio of the ion-beam to plasma ion density $(μ_{i})$, the dust to ion density ratio $(μ_{d})$ as well as th…
The stability theory of the inductively coupled plasma (ICP) is developed for the case when the electron quiver velocity in RF wave is of the order of or is larger than the electron thermal velocity. The theory predicts the existence the instabilities of the ICP which are driven by the current formed in the skin layer by the accelerated electrons, which move relative ions under the action of the ponderomotive force.
Time-Resolved Interferometric Measurements of Plasma Density Evolution in Laser-Driven Capacitor-Coil Targets
研究通过干涉测量揭示了激光驱动电容线圈靶中等离子体密度的演变，发现两种等离子体源对线圈区域的加载，为磁化高能量密度等离子体实验的设计和建模提供定量信息。
The dynamics of nuclear reaction in plasma is a fundamental issue in many high energy density researches, such as the astrophysical reactions and the inertial confinement fusion. The effective reaction cross-sections and ion stopping power in plasma need to be taken into account to analyze the reactivity. In this research, we have experimentally investigated the from D-D reactions from interactions between deuteron beams and deuterated polystyrene (CD) plasma, driven by two laser pulses respectively. The neutron yields, plasma density and deuteron energy loss in plasma have been measured, and …
A dynamic mitigation is presented for sausage and kink instability growths of a z-current driven magnetized plasma column. We have proposed a dynamic mitigation method based on a phase control to smooth plasma non-uniformities and to mitigate the instability growth in perturbed plasma systems. In this paper we found that a wobbling motion of the z-current electron axis induces a phase-controlled perturbation, so that the growths of the sausage and kink instabilities are successfully mitigated. In general, plasma instabilities emerge from perturbations, and the perturbation phase is normally un…
Filamentation due to the growth of a Weibel-type instability was observed in the interaction of a pair of counter-streaming, ablatively-driven plasma flows, in a supersonic, collisionless regime relevant to astrophysical collisionless shocks. The flows were created by irradiating a pair of opposing plastic (CH) foils with 1.8 kJ, 2-ns laser pulses on the OMEGA EP laser system. Ultrafast laser-driven proton radiography was used to image the Weibel-generated electromagnetic fields. The experimental observations are in good agreement with the analytical theory of the Weibel instability and with p…
A new quasi-neutral model describing the Weibel instability of a high-current relativistic beam propagating through a resistive plasma is developed. It treats beam electrons as kinetic particles, and ambient plasma as a non-relativistic fluid. For a finite-temperature beam, a new class of negative energy magneto-sound waves is identified, which can possess negative energy. Their growth due to collisional dissipation in the cold return current destabilizes the beam-plasma system even for high beam temperatures. We perform detailed two- and three-dimensional particle-in-cell (PIC) simulations of…
The effect of small deviations from a Maxwellian equilibrium on turbulent momentum transport in tokamak plasmas is considered. These non-Maxwellian features, arising from diamagnetic effects, introduce a strong dependence of the radial flux of co-current toroidal angular momentum on collisionality: As the plasma goes from nearly collisionless to weakly collisional, the flux reverses direction from radially inward to outward. This indicates a collisionality-dependent transition from peaked to hollow rotation profiles, consistent with experimental observations of intrinsic rotation.
In this paper, we consider the spectral dependences of transverse electromagnetic waves generated in solar plasma at coalescence of Langmuir waves. It is shown that different spectra of Langmuir waves lead to characteristic types of transversal electromagnetic wave spectra, what makes it possible to diagnose the features of the spectra of Langmuir waves generated in solar plasma.
The expansion of a dense plasma through a more rarefied ionised medium is a phenomenon of interest in various physics environments ranging from astrophysics to high energy density laser- matter laboratory experiments. Here this situation is modeled via a 1D Particle-In-Cell simulation; a jump in the plasma density of a factor of 100 is introduced in the middle of an otherwise equally dense electron-proton plasma with an uniform proton and electron temperature of 10eV and 1keV respectively. The diffusion of the dense plasma, through the rarified one, triggers the onset of different nonlinear ph…
The Alfven wave is analyzed in case of one quasineutral plasma propagating with some constant speed $v_0$ through another static quasineutral plasma. A dispersion equation is derived describing the Alfven wave coupled with the flow driven mode $ω= k v_0$ and solutions are discussed analytically and numerically. The usual solutions for two oppositely propagating Alfvén waves are substantially modified due to the flowing plasma. More profound is modification of the solution propagating in the negative direction with respect to the magnetic field and the plasma flow. For a large enough flow speed…
When a relativistically intense linearly polarized laser pulse is incident on an overdense plasma, a dense electron layer is formed on the plasma edge which relativistic motion results in high harmonic generation, ion acceleration and incoherent synchrotron emission of gamma-photons. Here we present a self-consistent analytical model that describes the edge motion and apply it to the problem of incoherent synchrotron emission by ultrarelativistic plasma electrons. The model takes into account both coherent radiation reaction from high harmonics and incoherent radiation reaction in the Landau-L…
Radio frequency driven plasma jets are frequently employed as efficient plasma sources for surface modification and other processes at atmospheric pressure. The radio-frequency driven micro atmospheric pressure plasma jet ($μ$APPJ) is a particular variant of that concept whose geometry allows direct optical access. In this work, the characteristics of the $μ$APPJ operated with a helium-oxygen mixture and its interaction with a helium environment are studied by numerical simulation. The density and temperature of the electrons, as well as the concentration of all reactive species are studied bo…
Rayleigh-Taylor and Buoyancy-driven instabilities are very common instabilities for an inhomogeneous medium. We examine here how these instabilities grow for incompressible viscoelastic fluids like a strongly coupled dusty plasma by using incompressible generalized hydrodynamic (i-GHD) fluid model. Since the dust particles are pretty massive, the gravitational attraction of earth has a significant role in its dynamics. In this paper the acceleration due to gravity g and the role of strong coupling in the context of gravitationally stratified dusty plasma fluid have been considered. We find tha…
Recently a filamentation instability was observed when a laser-generated pair cloud interacted with an ambient plasma. The magnetic field it drove was strong enough to magnetize and accelerate the ambient electrons. It is of interest to determine if and how pair cloud-driven instabilities can accelerate ions in the laboratory or in astrophysical plasma. For this purpose, the expansion of a localized pair cloud with the temperature 400 keV into a cooler ambient electron-proton plasma is studied by means of one-dimensional particle-in-cell (PIC) simulations. The cloud's expansion triggers the fo…
Technical Aspects of Plasma Operational Simulation (POPSIM): A Framework for Data-Driven Simulation and Control
本文介绍了基于JAX构建的数据驱动模拟与控制框架POPSIM，旨在通过结合原理模型与数据驱动模型解决托卡马克运行控制的模拟建模需求，并报告了其解决的关键软件与运行问题。
We present a detailed analysis of electron trajectories within the sheath regions of capacitively coupled plasmas excited by radio-frequency voltage waveforms at low pressures. Complex features inside the sheaths are identified in several physical quantities, which are sculptured by the trajectories of the bouncing electrons under the influence of the spatio-temporally varying electric field. A method is developed to explain the generation of the various features as a function of surface processes and to identify the trajectories of electrons of different origin.
Collective plasma effects of electron-positron pairs in beam-driven QED cascades
本文通过三维QED-PIC模拟研究束流驱动QED级联产生对等离子体，发现高密度与低伽马因子共同导致显著集体效应，并在理想及现有参数下观测到激光频率上移。
The influence of viscosity gradient (due to shear flow) on low frequency collective modes in strongly coupled dusty plasma is analyzed. It is shown that for a well known viscoelastic plasma model, the velocity shear dependent viscosity leads to an instability of the shear mode. The inhomogeneous viscous force and velocity shear coupling supply the free energy for the instability. The combined strength of shear flow and viscosity gradient wins over any stabilizing force and makes the shear mode unstable. Implication of such a novel instability and its applications are briefly outlined.
We consider diffusion caused by a combined influence of the Hall effect and electric currents, and argue that such diffusion forms chemical inhomogeneities in plasma. The considered mechanism can be responsible for the formation of element spots in laboratory and astrophysical plasmas. Such current-driven diffusion can be accompanied by the propagation of a particular type of waves which have not been considered earlier. In these waves, the impurity number density oscillare alone and their frequency is determined by the electric currents and sort of impurity ions. These compositional waves exi…
In plasma wakefield accelerators, the wave excited in the plasma eventually breaks and leaves behind slowly changing fields and currents that perturb the ion density background. We study this process numerically using the example of a FACET experiment where the wave is excited by an electron bunch in the bubble regime in a radially bounded plasma. Four physical effects underlie the dynamics of ions: (1) attraction of ions toward the axis by the fields of the driver and the wave, resulting in formation of a density peak, (2) generation of ion-acoustic solitons following the decay of the density…
It is shown that the interaction of a plasma with thermal radiation leads to the stabilization of both periodic and solitary nonlinear plasma waves. The stabilized periodic nonlinear plasma waves were indeed observed in the experiment carried out by Looney and Brown. There are many branches of radiation-induced solitary waves in plasmas, corresponding in particular to the density waves in hot plasmas of accretion disks.
Data-driven sparse modeling of oscillations in plasma space propulsion
本文提出基于稀疏回归和Pareto前沿分析的算法，用于获取等离子体空间推进系统中振荡现象的数据驱动模型，并在Hall效应推进器中验证了其有效性与物理可解释性。
A one dimensional parameter study of a magneto-inertial fusion (MIF) concept indicates that significant gain may be achievable. This concept uses a dynamically formed plasma shell with inwardly directed momentum to drive a magnetized fuel to ignition, which in turn partially burns an intermediate layer of unmagnetized fuel. The concept is referred to as Plasma Jet MIF or PJMIF. The results of an adaptive mesh refinement (AMR) Eulerian code (Crestone) are compared to those of a Lagrangian code (LASNEX). These are the first published results using the Crestone and LASNEX codes on the PJMIF conce…
Interaction of external monochromatic, linearly polorized plane EM-wave with nonlinear one-dimensional wake wave, generated by relativistic electron bunch moving in cold plasma, is considered. At definite conditions on parameters of plasma and bunch, nonlinear wake wave can have a pronounced spikes, where plasma electron density has its maximum value and plasma electron velocities are nearing wave breaking limit, i.e. velocity of the rigid driving bunch. Presented calculations show, that external EM-wave, propagating through plasma, normal to the bunch velocity, at such a conditions can be amp…
The excitation of electrostatic waves in plasma by laser electromagnetic pulse is important as it provides a scheme by which the power from the laser electromagnetic (EM) field can be transferred into the plasma medium. The paper presents a fundamentally new ponderomotive pressure-driven mechanism of excitation of electrostatic waves in an overdense magnetized plasma by a finite laser pulse. Particle-in-cell (PIC) simulations using the EPOCH-4.17.10 framework have been utilized for the study of a finite laser pulse interacting with a magnetized overdense plasma medium. The external magnetic fi…
Measurement of magnetic cavitation driven by heat flow in a plasma
该研究通过激光加热外加磁场气柱、质子射线照相重建磁场，直接测量了等离子体中热流驱动的磁空腔现象，分离出纳斯特平流效应，揭示了其对高能量密度等离子体动力学及磁化惯性约束聚变的影响。
A semi-analytic model for plasma-jet-driven magneto-inertial fusion is presented. Compressions of a magnetized plasma target by a spherically imploding plasma liner are calculated in one dimension (1D), accounting for compressible hydrodynamics and ionization of the liner material, energy losses due to conduction and radiation, fusion burn and alpha deposition, separate ion and electron temperatures in the target, magnetic pressure, and fuel burn-up. Results show 1D gains of 3-30 at spherical convergence ratio < 15 and 20-40 MJ of liner energy, for cases in which the liner thickness is 1 cm an…
The nonlinear propagation of electromagnetic waves in pair plasmas, in which the electrostatic potential plays a very important but subdominant role of a "binding glue" is investigated. Several mechanisms for structure formation are investigated, in particular, the "asymmetry" in the initial temperatures of the constituent species. It is shown that the temperature asymmetry leads to a (localizing) nonlinearity that is new and qualitatively different from the ones originating in ambient mass or density difference. The temperature asymmetry driven focusing-defocusing nonlinearity supports stable…
Observations of the interaction of an intense λ0 \approx 10 μm laser pulse with near-critical overdense plasmas (ne = 1.8 - 3 nc) are presented. For the first time, transverse optical probing is used to show a recession of the front surface caused by radiation pressure driven hole-boring by the laser pulse with an initial velocity > 10^6 ms-1, and the resulting collisionless shocks. The collisionless shock propagates through the plasma, dissipates into an ion-acoustic solitary wave, and eventually becomes collisional as it slows further. These conclusions are supported by PIC simulations which…
Isotope Effects on TEM-driven Turbulence and Zonal Flows in Helical and Tokamak Plasmas
研究同位素质量对磁镜和托卡马克等离子体中TEM驱动湍流和区流的影响，发现同位素效应导致输运减少，与传统标度相反。
The destabilizing role of neutrino beams on the Trivelpiece-Gould modes is considered, assuming electrostatic perturbations in a magnetized plasma composed by electrons in a neutralizing ionic background, coupled to a neutrino species by means of an effective neutrino force arising from the electro-weak interaction. The magnetic field is found to significantly improve the linear instability growth rate, as calculated for Supernova type II environments. On the formal level, for wave vector parallel or perpendicular to the magnetic field the instability growth rate is found from the unmagnetized…
In this manuscript, a fluid model is utilized to calculate the density of plasma species assuming geometrically symmetric Ar/CF4 Radiofrequency Capacitively Coupled Plasmas. The electrodes are driven by a sinusoidal waefront with an amplitude of 200 V and a frequency of 13.56 MHz. The gap between the electrodes is 5cm. The plasma species density is calculated as a function of the gas pressure, electron temperature, and the gas composition. In a good agreement with recent experimental results, $CF^+_3$ and F are dominant for all considered simulation parameters. The results explain the pathways…
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