Fusion Edge Plasmas Research Articles

Investigation of the cross sections for electron collision ionization of complex molecules

AbstractAn accurate and computationally efficient determination of the cross sections for electron collision ionization of molecules has various applications, such as plasma physics and atmospheric science. In the case of large molecules, ab initio calculations are often difficult and time‐consuming. Here, we develop a feed forward neural network to predict the electron impact ionization cross sections of complex molecules. The training (predicting) set in the method consists of a series of theoretical ionization cross sections for small (large) molecules obtained from the combined model, which integrates the Binary‐Encounter‐Bethe and Deutsch‐Märk models. Several complex systems or targets involving electron collision ionization are evaluated, including molecules such as CH, CH, CH, CH, C, CHO, and CHO. The root mean square errors of the trained and predicted cross sections by the neural network (compared to the values from the combined model) are found to be approximately .0086 and .0930 (in 10 cm), respectively, (using the CHO molecule as an example), indicating our results are very high accuracy. The excellent agreement between the predicted values and the actual values indicates that the neural network is a practical and powerful tool for determining the electron collision ionization cross sections of complex molecules and can provide valuable insights into the dynamics process. Apart from its fundamental importance, this study has far‐reaching implications for gas discharge, low‐temperature plasmas, and fusion edge plasmas and so forth.

Characteristics of Density and Temperature Fluctuation in Fusion Edge Plasma and Implication on Scrape off Layer Width

Characteristics of Density and Temperature Fluctuation in Fusion Edge Plasma and Implication on Scrape off Layer Width

Simulations of fusion edge plasmas by linear plasma devices: physics and plasma–material interactions

Simulations of fusion edge plasmas by linear plasma devices: physics and plasma–material interactions

Development of plasma sources and diagnostics for the simulation of fusion edge plasmas

Although the research on divertors and scrape-off layers (SOLs) has been not as focused on as the recent success of the Korean fusion program, a few linear plasma devices have been developed for simulating divertor and SOL plasmas: (1) diversified plasma simulator (DiPS), a versatile linear machine, has been developed for simulations of divertor and space plasmas with various electric probes, such as single, triple, and Mach Probes and gridded energy analyzer. DiPS consists of two major parts: a divertor plasma simulator with a \(\hbox {LaB}_6\) DC plasma source and a space plasma simulator with a helicon RF plasma source, (2) divertor plasma simulator-1 (DiPS-1) is a part of DiPS with only a \(\hbox {LaB}_6\) cathode, where a low-power laser-induced fluorescence (LIF) is added and more electric probe diagnostics are augmented; it is dedicated only for fusion edge and divertor plasmas, (3) Divertor Plasma Simulator-2 (DiPS-2) has been modified from the DiPS-1 by adding a magnetic nozzle with a limiter structure and by removing the helicon source and space chamber. DiPS-2 is a linear plasma device with a 4-inch \(\hbox {LaB}_6\) cathode, the same as DiPS-1, and it is focused on the development of various diagnostics, such as those used for LIF and laser Thomson scattering (LTS) along with various electric probes, on the divertor and scrape-off plasmas and on the plasma-material interaction (PMI) research, such as that of tungsten and graphite as plasma-facing components (PFCs), (4) A Multi-Purpose Plasma (\(\hbox {MP}^2\)) device is a renovation of the Hanbit mirror device [Kwon et al., Nucl. Fusion 43, 686 (2003)] with the installation of two plasma sources: \(\hbox {LaB}_6\) (DC) and helicon (RF) plasma sources. A honeycomb-like large-area \(\hbox {LaB}_6\) (HLA-\(\hbox {LaB}_6\)) cathode has been developed for the divertor plasma simulation to improve the resistance against the thermal shock fragility for large (8-inch) and high density plasma generation, (5) DiPS-2 has been augmented by adding another cylindrical device, called the Dust interaction with Surfaces Chamber (DiSC) for the generation and diagnostics of dusts. This combined system (DiPS-2+DiSC) has added two more diagnostics: Laser Photo-Detachment (LPD) for dust density and laser Mie Scattering (LMS) for dust size. Moreover, dusts or negative ions have been analyzed by using electric probes and capacitive diagram gauges in Transport and Removal of Dusts (TReD) device.

Inducing thermionic emission from lanthanum hexaboride probes in Magnum-PSI

For thermionic emission rates exceeding the incident plasma electron flux, recent theory proposes an inverse sheath regime, with promising properties for future application in fusion edge plasmas. With the aim of inducing thermionic emission in fusion-relevant plasma conditions, several lanthanum hexaboride probes were heated in the linear plasma generator Magnum-PSI. During exposures at low plasma power and additional pulsed laser heating, the probe’s floating potential was reduced by up to 12%, providing a possible indication of thermionic emission. However, these observations coincided with rapid erosion of probe material, attributed to enhanced lanthanum self-sputtering. During follow-up experiments with helium plasmas at electron temperatures around 1 eV, the lanthanum ion impact energy and sputtering yield were reduced, and rapid erosion was avoided, thus confirming the thesis of self-sputtering. A parameter scan of plasma power resulted in LaB 6 surface temperatures up to 2450 °C, exceeding the theoretical inverse sheath threshold temperature by over 300 °C. However, the probe’s floating potential did not deviate from reference measurements using a probe with high electronic work function, indicating absence of strong thermionic emission. This apparent discrepancy is attributed to the effects of probe surface modifications as observed during these experiments: impurity deposition, erosion and cavity formation. These modifications possibly affected the LaB 6 electronic work function, thereby keeping the inverse sheath threshold out of reach. In conclusion, although LaB 6 has one of the lowest work functions available, the inverse sheath threshold conditions could not be reached with the present setup in Magnum-PSI. Surface modifications thus do form a limiting factor for the application of LaB 6 in fusion-relevant plasma conditions. Moreover, the window of stable operation for LaB 6 in dense hydrogen plasmas is limited below ∼ 1.5 eV, and does not overlap with the conditions expected in the edge region of future fusion devices like ITER. • LaB 6 probes were heated up to 2450 °C under fusion-relevant plasma conditions. • Surface modifications limit the effective operation of powder-pressed LaB 6 . • Lanthanum self-sputtering in dense plasma conditions leads to rapid erosion. • The LaB 6 operation window does not overlap with ITER divertor conditions.

Comparative analysis of the plasma parameters of ECR and combined ECR + RF discharges in the TOMAS plasma facility

The toroidal magnetized system (TOMAS) plasma facility aims at complementary research on wall conditioning methods, plasma production and plasma–surface interaction studies. This paper explores for the first time the parameters in helium electron-cyclotron resonance (ECR) plasma and combined ECR + radio-frequency (RF) discharges in TOMAS. The ECR discharge in this work, at 2.45 GHz and 87.6 mT, is the main one for creating and maintaining the plasma, while the addition of RF power at 25 MHz allows to broaden the achievable electron temperature and density at a given gas flow, as evidenced by triple Langmuir probe measurements. This effect of the combined ECR + RF discharge provides flexibility to study particular aspects of wall conditioning techniques relevant to larger devices, or to approach plasma conditions relevant to fusion edge plasmas for particular surface interaction studies.

Total and partial electron impact ionization cross sections of fusion-relevant diatomic molecules.

We report calculations of total (and absolute) electron-impact ionization cross sections (EICSs) for the fusion-relevant diatomic molecular species BeH, BeN, BeO, WH, WBe, WN, WO, O2, and N2 by means of the Deutsch-Märk and the binary-encounter-Bethe methods in the energy range from threshold to 10 keV. In addition, we discuss an empirical scheme to estimate partial cross sections from the total ones based on reaction energetics and empirical threshold laws and explore its accuracy by assessing available experimental data on total and partial EICSs. Finally, we also report parameters obtained by fitting the calculated cross sections to an expression commonly used in fusion edge plasma modeling.

Synthetic helium beam diagnostic and underlying atomic data

We report on synthetic helium beam emission spectroscopy (BES) in fusion edge plasmas, as enabled by the 3D kinetic (neutral particle) transport code EIRENE. We also review and upgrade the underlying atomic helium data base, resorting to the most recent version of the Goto–Fujimoto collisional-radiative code and a recommended and publicly exposed reference cross section data set from an internationally coordinated (IAEA) evaluation activity. On the example of the Wendelstein 7-X (W7-X) stellarator, we use both the upgraded transport code and data base to simulate the penetration of and radiation from thermal helium used for BES in the island divertor region. This allows to evaluate the applicability of the diagnostic in different plasma backgrounds, simulated with the 3D edge plasma Monte Carlo code EMC3-EIRENE, and with different levels of refinement of underlying atomic data. The sensitivity of the diagnostic to the atomic data set—which is crucial for a quantitative determination of electron density and temperature profiles—is investigated and discussed, as well as the effects of p-He beam widening and correlated line-of-sight integration.

Low-energy collisions between electrons and BeD+

Multichannel quantum defect theory is applied in the treatment of the dissociative recombination and vibrational excitation processes for the BeD+ ion in the 24 vibrational levels of its ground electronic state (). Three electronic symmetries of BeD** states (, , and ) are considered in the calculation of cross sections and the corresponding rate coefficients. The incident electron energy range is 10−5–2.7 eV and the electron temperature range is 100–5000 K. The vibrational dependence of these collisional processes is highlighted. The resulting data are useful in magnetic confinement fusion edge plasma modeling and spectroscopy, in devices with beryllium based main chamber materials, such as ITER and JET, and operating with the deuterium–tritium fuel mix. An extensive rate coefficients database is presented in graphical form and also by analytic fit functions whose parameters are tabulated in the supplementary material.

Stark broadening of hydrogen/deuterium spectral lines by a relativistic electron beam: analytical results and possible applications to magnetic fusion edge plasmas

We present a theory of the Stark broadening of hydrogen/deuterium spectral lines by a relativistic electron beam (REB). The theory is developed analytically by using an advanced formalism. We discuss the possible application of these analytical results to magnetic fusion edge plasmas, taking into account also the major outcome of the interaction of a REB with plasmas: the development of strong Langmuir waves.

Isotope effect on blob-statistics in gyrofluid simulations of scrape-off layer turbulence

In this contribution we apply a recently established stochastic model for scrape-off layer fluctuations to long time series obtained from gyrofluid simulations of fusion edge plasma turbulence. Characteristic parameters are estimated for different fusion relevant isotopic compositions (protium, deuterium, tritium and singly charged helium) by means of conditional averaging. It is shown that large amplitude fluctuations associated with radially propagating filaments in the scrape-off layer feature double-exponential wave-forms. We find increased pulse duration and longer waiting times between peaks for heavier ions, while the amplitudes are similar. The associated radial blob velocity is shown to be reduced for heavier ions. A parabolic relation between skewness and kurtosis of density fluctuations seems to be present. Improved particle confinement in terms of reduced mean value close to the outermost radial boundary and blob characteristics for heavier plasmas is presented.

Impact of cross-field motion on ablation of high-Z dust in fusion edge plasmas

The impact of cross-field motion of high-Z dust grains on their shielding by ablation cloud in edge plasmas of tokamaks is analyzed. The modification of the existing high-Z dust shielding theory is developed, which takes the dust motion effects into account. It is shown that the cross-field motion can lead to a large factor increase of the dust ablation rate, as compared to the previous model. It is also shown that the motion effects take place when the dust cross-field velocity exceeds a threshold value. The dependencies of the dust ablation flux on the dust velocity and of the threshold velocity on the dust size and the ambient plasma temperature are obtained.

Perturbing microwave beams by plasma density fluctuations

The propagation of microwaves across a turbulent plasma density layer is investigated with full-wave simulations. To properly represent a fusion edge-plasma, drift-wave turbulence is considered based on the Hasegawa-Wakatani model. Scattering and broadening of a microwave beam whose amplitude distribution is of Gaussian shape is studied in detail as a function of certain turbulence properties. Parameters leading to the strongest deterioration of the microwave beam are identified and implications for existing experiments are given.

Low-energy collisions between electrons and [formula omitted]: Cross sections and rate coefficients for all the vibrational states of the ion

We provide cross sections and Maxwell rate coefficients for reactive collisions of slow electrons with BeH+ ions on all the eighteen vibrational levels (X1Σ+,vi+=0,1,2,…,17) using a Multichannel Quantum Defect Theory (MQDT)—type approach. These data on dissociative recombination, vibrational excitation and vibrational de-excitation are relevant for magnetic confinement fusion edge plasma modeling and spectroscopy, in devices with beryllium based main chamber materials, such as the International Thermonuclear Experimental Reactor (ITER) and the Joint European Torus (JET). Our results are presented in graphical form and as fitted analytical functions, the parameters of which are organized in tables.

A fully non-linear multi-species Fokker–Planck–Landau collision operator for simulation of fusion plasma

Fusion edge plasmas can be far from thermal equilibrium and require the use of a non-linear collision operator for accurate numerical simulations. In this article, the non-linear single-species Fokker–Planck–Landau collision operator developed by Yoon and Chang (2014) [9] is generalized to include multiple particle species. The finite volume discretization used in this work naturally yields exact conservation of mass, momentum, and energy. The implementation of this new non-linear Fokker–Planck–Landau operator in the gyrokinetic particle-in-cell codes XGC1 and XGCa is described and results of a verification study are discussed. Finally, the numerical techniques that make our non-linear collision operator viable on high-performance computing systems are described, including specialized load balancing algorithms and nested OpenMP parallelization. The collision operator's good weak and strong scaling behavior are shown.

On the Runge–Lenz–Pauli vector operator as an aid to the calculation of atomic processes in laboratory and astrophysical plasmas

On the basis of the original definition and analysis of the vector operator by Pauli (1926 Z. Phys. 336–63), and further developments by Flamand (1966 J. Math. Phys. 7 1924–31), and by Becker and Bleuler (1976 Z. Naturforsch. 517–23), we consider the action of the operator on both spherical polar and parabolic basis state wave functions, both with and without direct use of Pauli’s identity (Valent 2003 Am. J. Phys. 71 171–75). Comparison of the results, with the aid of two earlier papers (Hey 2006 J. Phys. B: At. Mol. Opt. Phys. 39 2641–64, Hey 2007 J. Phys. B: At. Mol. Opt. Phys. 4077–96), yields a convenient ladder technique in the form of a recurrence relation for calculating the transformation coefficients between the two sets of basis states, without explicit use of generalized hypergeometric functions. This result is therefore very useful for application to Stark effect and impact broadening calculations applied to high-n radio recombination lines from tenuous space plasmas. We also demonstrate the versatility of the Runge–Lenz–Pauli vector operator as a means of obtaining recurrence relations between expectation values of successive powers of quantum mechanical operators, by using it to provide, as an example, a derivation of the Kramers–Pasternack relation. It is suggested that this operator, whose potential use in Stark- and Zeeman-effect calculations for magnetically confined fusion edge plasmas (Rosato, Marandet and Stamm 2014 J. Phys. B: At. Mol. Opt. Phys. 105702) and tenuous space plasmas ( H II regions) has not been fully explored and exploited, may yet be found to yield a number of valuable results for applications to plasma diagnostic techniques based upon rate calculations of atomic processes.

An experimental set up for studying the fusion edge plasma facing materials using TOF mass spectrometry

A new experimental set up is developed to study the fusion edge plasma facing materials under impact of low-energy (40–10,000eV) atomic and molecular ions. The primary ions are obtained from a low-pressure D.C. gas discharge Colutron ion source. The product ions resulting from the ion–surface interactions involving different processes, for example, surface-induced dissociation (SID), surface-induced reaction (SIR), chemical- and sputtering are detected and identified by using a single-field linear time-of-flight (TOF) mass spectrometer coupled with a time- and position-sensitive dual micro-channel plate detector. The mass spectra of secondary ions are recorded by employing a pulsed extraction and acceleration technique. The experimental set up, experimental technique and data acquisition methodology are presented and discussed. A test experiment is conducted on the developed set up to demonstrate the performance and reliability of the apparatus. For this, a primary beam of 427eV N2+ ions was chosen to interact with a hydrocarbons covered surface of platinum target kept at room temperature. SID of N2+ into N+ and TOF mass spectra of sputtered, reflected and chemically formed ions from the ion–surface interaction are analyzed. A noticeable feature in the spectra is observed which shows that the odd-electron ions of sputtered hydrocarbons are preferentially produced in the interaction in addition to the other product ions. The nominal mass resolution (M/ΔM) of the present tandem mass spectrometer system is estimated to be about 600, while energy and spatial spreads of the primary ion beam are determined to be about 518meV and 2.8±0.3mm respectively. The survival probability of the incident ions is found to be 6.6% suggesting that the major process of ion–surface interaction at the considered impact energy is neutralization.

Reactive collisions involving the BeH molecular system

In the divertor and fusion edge plasma regions reactive collisions involving the BeH molecular system are taking place. Theoretical ab initio quantum studies of electron collisions with BeH+ resulting in either dissociative recombination, vibrational excitation or dissociative excitation are performed for ions in different vibrational states as well for different isotopologues. Furthermore, the mutual neutralization reaction in collisions of H− with Be+ is studied semiclassically.

Stability and control of iterated non-linear transport solvers for fusion edge plasmas

The application of numerical transport solvers for the steady state plasma boundary of magnetic fusion devices is related to the iterative approximation of a fixed-point of a non-linear map. Although 2D (axisymmetric) or even 3D transport solvers are routinely applied for the quantification of steady state plasma flows, unstable behavior can occur under certain conditions. A simple two-point model is applied to demonstrate the generic nature of this kind of unstable behavior which can occur when the fixed-point loses its stability and resulting in a period doubling route to chaos. Furthermore, it is demonstrated that wavelike oscillations can occur at low divertor temperatures. An adaptive relaxation scheme is presented which allows to suppress discrete and wavelike oscillations in order to stabilize the fixed-point iteration.

Landau–Zener studies of mutual neutralization in collisions of and

Semi-classical Landau–Zener studies of mutual neutralization reactions in low-energy H+ + H− and Be+ + H− collisions are performed. Avoided crossings between ionic and covalent states occurring at large internuclear distances are considered, and electronic couplings between these states are estimated using different semi-empirical and ab initio methods and tested on the H+ + H− reaction. The method is then applied to compute the cross sections and final state distributions for mutual neutralization in collisions of H− with Be+. These are reactions that might be important for the modeling of the fusion edge plasma of the divertor of ITER.