Effective Electron Collision Frequency Research Articles

Momentum transport studies from multi-machine comparisons

A database of toroidal momentum transport on five tokamaks, Alcator C-Mod, DIII-D, JET, NSTX and JT-60U, has been constructed under a wide range of conditions in order to understand the characteristics of toroidal momentum transport coefficients, namely the toroidal momentum diffusivity (χφ) and the pinch velocity (Vpinch). Through an inter-machine comparison, the similarities and differences in the properties of χφ and Vpinch among the machines have been clarified. Parametric dependences of these momentum transport coefficients have been investigated over a wide range of plasma parameters taking advantage of the different operation regimes in machines. The approach offers insights into the parametric dependences as follows. The toroidal momentum diffusivity (χφ) generally increases with increasing heat diffusivity (χi). The correlation is observed over a wide range of χφ, covering roughly two orders of magnitude, and within each of the machines over the whole radius. Through the inter-machine comparison, it is found that χφ becomes larger in the outer region of the plasma. Also observed is a general trend for Vpinch in tokamaks; the inward pinch velocity (−Vpinch) increases with increasing χφ. The results that are commonly observed in machines will support a toroidal rotation prediction in future devices. On the other hand, differences among machines have been observed. The toroidal momentum diffusivity, χφ, is larger than or equal to χi in JET and JT-60U; on the other hand, χφ is smaller than or equal to χi in NSTX, DIII-D and Alcator C-Mod. In DIII-D, the ratio −RVpinch/χφ at r/a = 0.5–0.6 is about 2, which is small compared with that in other tokamaks (−RVpinch/χφ ≈ 5). Based on these different observations, parametric dependences of χφ/χi, RVpinch/χφ and χφ have been investigated in H-mode plasmas. Across the dataset from all machines, the ratio χφ/χi tends to be larger in low at fixed Te/Ti and . An increase in χφ is observed with decreasing ne and/or increasing Te. The pinch number (−RVpinch/χφ) is observed to increase with increasing at both q95 = 5.5–7.2 and q95 = 3.7–4.5. Here , , Te, Ti, and q95 are, respectively, the normalized effective electron collision frequency, the normalized ion poloidal Larmor radius, the electron and ion temperatures, the inverse ratio of density scale length, , to the major radius, R, and the safety factor at the 95% flux surface.

Effects of Coupling Oscillations on the Electron Conductivity of Hall Thrusters

It is known that the static magnetic field of a Hall thruster remains unchanged with the product of coil current and coil turn kept constant. This is called the ampere-turns equivalence principle, which is used in the static magnetic field design of Hall thrusters. It is found that the discharge characteristic is different with the same static magnetic field which is formed by the same ampere-turns but different coil turns. The effects of the fluctuating magnetic field on the static magnetic field are studied experimentally and theoretically, and the effective collision frequency is calculated based on the dispersion relation of coupling oscillations and the estimation of the fluctuating magnetic field. Results indicate that the different coil turns are accompanied by different coupling intensities which lead to different magnetic field fluctuations. The different magnetic field fluctuations cause differences in the effective electron collision frequency and therefore the electron conductivity and the discharge characteristic of Hall thrusters (© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

1‐D Self‐consistent Fluid Modelling of the Pulsed Magnetron Discharge

AbstractA 1‐D fluid code simulation of the region above the racetrack in a magnetron discharge has been developed to yield predictions for the temporal evolution of the axial plasma parameters during pulsed DC operation. To take into account anomalous cross‐field diffusion transport rates, an effective magnetic field profile has been calculated based on the real experimental values, to yield ratios in the effective electron gyro and collision frequencies comparable with Bohm diffusion. Pulse frequencies from 100 to 500 kHz are considered, with gas pressures ranging from 0.25 to 0.65 Pa. The model results for the plasma potential, electron and ion densities, during the pulse cycle agree well with experimental measurements made in the Liverpool magnetron using time‐resolved Langmuir and emissive probes. In the bulk plasma, the predictions for electron temperature are close to the measured values; however, in the sheath region they are artificially high due to the model assumption that only Maxwellian distributed electrons exist in all regions of the discharge. This inadequacy in the model and the methods to improve has been discussed. Results for DC magnetrons are also shown.

Fluid Model of an Electron Cyclotron Wave Resonance Discharge

A fluid model of a planar electron cyclotron wave resonance argon discharge is presented. The results for a 15-mtorr argon discharge are checked against the particle in cell/Monte Carlo (PIC/MC) simulation results by R. Krimke <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al</i> . and are also compared to the analytical theory and experimental data by B. Pfeiffer. The application of a specific boundary condition for the magnetic potential, the use of an effective electron collision frequency that includes plasma nonuniformities, and the coupled solution of the electrostatic field were found to be essential parameters leading to the agreement of the fluid code with both experimental and PIC/MC findings.

Statistical parameters of nonisothermal lower ionospheric plasma in the electrically active mesosphere

The large V/m electric fields inherent in the lower mesosphere play an essential role in lower ionospheric electrodynamics. They must be the cause of large variations in the electron temperature and the electron collision frequency and consequently of the transition of the ionospheric plasma in the lower part of the D region into a nonisothermal state. This study is based on the datasets on large mesospheric electric fields collected with the 2.2-MHz radar of the Institute of Space and Atmospheric Studies, University of Saskatchewan, Canada (52°N geographic latitude, 60.4°N geomagnetic latitude), and with the 2.3-MHz radar of the Kharkiv V. Karazin National University, Ukraine (49.6°N geographic latitude, 45.6°N geomagnetic latitude). The statistical analysis of these data is presented by [Meek, C.E., Manson, A.H., Martynenko, S.I., Rozumenko, V.T., Tyrnov, O.F. Remote sensing of mesospheric electric fields using MF radars. J. Atmos. Solar-Terr. Phys. 66, 881–890, 2004. 10.1016/j.jastp.2004.02.002]. The large mesospheric electric fields in the 60–67-km altitude range are experimentally established to follow a Rayleigh distribution in the 0 < E < 2.5 V/m interval. These data have permitted the resulting differential distributions of relative disturbances in the electron temperature, θ, and the effective electron collision frequency, η, to be determined. The most probable θ and η values are found to be in the 1.4–2.2 interval, and hence the nonstationary state of the lower part of the D region needs to be accounted for in studying processes coupling the electrically active mesosphere and the lower ionospheric plasma.

Remote sensing of mesospheric electric fields using MF radars

Large mesospheric electric fields can play an essential role in middle atmospheric electrodynamics (see, e.g., Goldberg, R. A., Middle Atmospheric Electrodynamics during MAP, Adv. Space Res. 10 (10) (1990) 209). The V/m electric fields of atmospheric origin can be the possible cause of large variations in the electron collision frequency at mesospheric altitudes, and this provides a unique opportunity to take measurements of electric fields in the lower ionosphere by using remote sensing instruments employing radiowave techniques. A technique has been proposed for making estimates of large mesospheric electric field intensities on the lower edge of the ionosphere by using MF radar data and the inherent effective electron collision frequency. To do this, data collected in Canada and Ukraine were utilized. The developed technique permits the changes in mesospheric electric field intensities to be derived from MF radar data in real time. The statistical analysis of data consistent with large mesospheric electric field intensities in the 60– 67 km region resulted in the following inferences. There are at least two mechanisms for the generation of large mesospheric electric fields in the mesosphere. The most likely mechanism, with a probability of 60–70%, is the summation of random fields from a large number of elementary small-scale mesospheric generators, which results in a one-parameter Rayleigh distribution of the total large mesospheric electric field intensity E with a mean value of approximately 0.7– 0.9 V/m in the 60– 67 km altitude region, or in the corresponding one-parameter exponential distribution of the intensity squared E 2 of large mesospheric electric fields. The second mechanism of unknown nature, with 5–15% probability, gives rise to the sporadic appearance of large mesospheric electric field intensities E>2.5 V/m with a mean of 4 V/m . Statistically significant seasonal differences in the averaged large mesospheric electric field parameters have not been revealed. The probability of the absence of local large mesospheric electric fields amounts to approximately 25% for Ukraine and approximately 30% for Canada. A comparison of the Ukrainian and Canadian data indicates the possible existence of a latitudinal dependence in mean large mesospheric electric field features. Hence, the large electric fields are an additional source of electron heating that must be taken into account in studying a disturbed lower ionosphere and radio wave propagation within it.

INTERNATIONAL STANDARD MODEL OF THE EARTH'S INOSPHERE AND PLASMASPHERE

The standard plasmasphere-ionosphere model of the International Standardization Organization is aimed at providing the distributions of the electron density, total electron content, temperature and effective collision frequency of electrons at altitudes of 65-20000 km (or to the plasmapause) over the Earth, geodetic latitudes of 80 N to 80 S, any longitude, day of the year, and indices of solar and geomagnetic activity. It includes the International Reference Ionosphere developed by the Union Radio-Scientifique Internationale and the Committee on Space Research, and the Russian standard model of the ionosphere. Two modes of operation are envisaged: the climatological monthly average prediction and dynamic short-term forecast of space weather parameters. The reliability of results is improved on input of pre-history of observable solar and geophysical parameters. The software of the standard model is available via the Internet.

Numerical Analysis of the Electromagnetic Fields in a Microwave Plasma Source Excited by Azimuthally Symmetric Surface Waves

The propagation of electromagnetic waves has been studied along the plasma-dielectric interfaces in an azimuthally symmetric surface wave-excited plasma (SWP) source, by using a two-dimensional numerical analysis based on the finite-difference time-domain (FDTD) approximation to Maxwell's equations and nonmagnetized cold plasma-electron equations. The simulation was performed for 2.45-GHz microwaves with plasma electron densities ne=1.0 ×1010–1.0×1012 cm-3 and effective electron collision frequencies νeff/ω=0.01-1 which are spatially uniform. The numerical results demonstrated that the electromagnetic waves propagate as volume waves at plasma electron densities below the cut-off value (ne<nc=7.4×1010 cm-3), while they propagate as surface waves along the plasma-dielectric interfaces at plasma densities above a critical value (ne > ncr ≈3.0×1011 cm-3). In the intermediate cases (nc<ne<ncr), the electromagnetic waves consist of both volume and surface waves that are strongly damped in space. Such a transition from volume to surface waves with increasing plasma electron density was consistent with the results of previous experiments. Moreover, the propagation constants and the field amplitudes calculated numerically were shown to be in good agreement with those obtained theoretically from the dispersion relation of guided electromagnetic waves.

Errors of ionospheric parameter diagnostics by vertical sounding method

The problem of RMS error determination in ionospheric parameters measured by the method of vertical HF soundings is considered here. This problem is solved for the case of topside ionospheric soundings when the height distribution of electron density is monotonic. An analytical expression is obtained which relates the variance of deduced parameters to the correlation function of errors in measured characteristics of sounding signals. The computing simulation provides for errors in real height determination, in reconstruction of vertical velocities of plasma motion, and in effective electron collision frequencies for the measurements of virtual heights, Doppler frequency shift, and radio wave absorption, respectively. Their dependencies on signal polarization, working frequency range, and geomagnetic latitude of observation point are determined. The obtained results are useful for planning plasma diagnostics experiments using HF sounding technique.

New possibilities for mesospheric electricity diagnostics

Abstract A possible cause of large variations in the electron collision frequency could be the effect of strong external electric fields of atmospheric origin. This provides a new opportunity to take measurements of electric fields in the lower ionosphere using remote sensing instruments employing radio wave techniques. It has been proposed the technique for making estimates of strong mesospheric electric field intensities on the lower edge of the ionosphere using MF radar data on the effective electron collision frequency, and the data has been presented. The technique described permits a real-time derivation from MF radar data of changes in mesospheric electric field intensities, and estimates of electric current densities. Our results give proof that the source of strong mesospheric electricity is very likely to be a current source.

The resolving power of radio sounding methods for ionospheric parameter reconstruction

The r.m.s. errors in ionospheric parameters studied by the vertical HF-sounding method were determined for a monotonic height distribution of the electron density. Numerical estimates were obtained for errors in real heights, in vertical velocities of plasma motion and in effective electron collision frequencies deduced from experimental measurements of virtual heights, Doppler frequency shift and radio wave absorption respectively. Their dependencies on signal polarisation, working frequency range and geo-magnetic latitude of the observation point were determined.

Measurement of electron density profile in the lower ionosphere during nighttime by rocket observations of MF and VLF radio waves

Measurements are made on the magnetic field strength of MF and VLF radio stations by rocket observations during nighttime, along with measurements made on the Langmuir probe (dc probe) current and Doppler observations of MF. In the E layer, we can observe the standing wave of the VLF magnetic field strength, and also the ordinary and extraordinary components of MF. In order to make the theoretical values by the full-wave calculation coincide with these observed values with reference to the dc probe currents, we adjust the electron density and the distribution of the electron collision frequency with altitude. By these methods, the electron density of the E layer is estimated from the bottom to the top, and we find the existence of multiple weak Es layers. By MF Doppler observation, we successfully estimate the electron density of the upper E layer, and can estimate the effective electron collision frequency near 110 km in altitude from the strength of the upward component of the extraordinary wave. © 1999 Scripta Technica, Electron Comm Jpn Pt 1, 83(2): 20–28, 2000

Measurement of electron density profile in the lower ionosphere during nighttime by rocket observations of MF and VLF radio waves

Measurements are made on the magnetic field strength of MF and VLF radio stations by rocket observations during nighttime, along with measurements made on the Langmuir probe (dc probe) current and Doppler observations of MF. In the E layer, we can observe the standing wave of the VLF magnetic field strength, and also the ordinary and extraordinary components of MF. In order to make the theoretical values by the full-wave calculation coincide with these observed values with reference to the dc probe currents, we adjust the electron density and the distribution of the electron collision frequency with altitude. By these methods, the electron density of the E layer is estimated from the bottom to the top, and we find the existence of multiple weak Es layers. By MF Doppler observation, we successfully estimate the electron density of the upper E layer, and can estimate the effective electron collision frequency near 110 km in altitude from the strength of the upward component of the extraordinary wave. © 1999 Scripta Technica, Electron Comm Jpn Pt 1, 83(2): 20–28, 2000

Effective electron collision frequency and electrical conductivity of radio frequency plasmas

The electron transport collision frequency in a radio frequency (rf) field νen and the effective rf field frequency ωeff have been found as appropriate integrals of the electron energy distribution function measured in an argon inductively coupled plasma (ICP) at 6.78 MHz. Also, the effective electron collision frequency νeff and ωeff have been found from the plasma conductivity measured with a magnetic probe. It is shown that due to the Ramsauer effect and collisionless power absorption in the ICP, νeff and νeff/ωeff vary unexpectedly slowly with gas pressure.

Ionospheric diagnostics using wave field diffraction near the caustic

Results of investigating the spatial and temporal HF field structure near the skip distance are presented. The data were obtained on midlatitude radio paths less than 1000 km in length, using broadcasting stations as sources of the probe signals. The signals reflected by the ionosphere were received and processed with a multichannel coherent receiver and the largest phased array of the decameter radio telescope UTR‐2. The strong dependence of the probe signal parameters on the ionospheric plasma conditions has allowed formulating and solving a number of model inverse problems of ionospheric diagnostics. It proves possible to determine parameters of the parabolic ionospheric layer, and the effective electron collision frequency, to evaluate horizontal gradients of the electron density and some parameters of the medium‐scale‐size ionospheric irregularities. A number of tests made both within the method and by means of comparison of the restored parameters against the data of other diagnostic techniques demonstrate the high potential and accuracy of the approach described in the paper.

Usage of regularization techniques for effective electron collision frequency determination from oblique ionospheric sounding

Abstract. Computer modelling is used to investigate the possibility of determining ionospheric parameters from slightly oblique ionospheric soundings, using absorption data for decametric radio waves of different polarization. It is shown that with mean square measurement errors of 0.5 dB, and using regularization algorithms to solve the inverse problems, electron collision frequency profiles can be obtained for the night F-region with errors of less than 30%. Both temperatures of electrons and neutrals are also determined to within 10%.

Usage of regularization techniques for effective electron collision frequency determination from oblique ionospheric sounding

Usage of regularization techniques for effective electron collision frequency determination from oblique ionospheric sounding

Theory of modulational interactions in collisional plasmas

The modulational instability development of Langmuir and electromagnetic waves is reviewed in highly collisional plasmas where the characteristic frequency Ω of the modulated perturbations is much less than veff, the effective electron collision frequency. All calculations are based on Braginskii's system of hydrodynamic equations in collision-dominated plasmas and use a simple and universal formalism including new methods developed for description of the modulational effects in arbitrary media. It is demonstrated that the modulational instability for the situation considered is mostly determined by collisional effects (differential Joule heating nonlinearity), in contrast to the wellknown modulational instability in collisionless plasmas (where ponderomotive force nonlinearity dominates). Rates and thresholds of the instabilities are found in various limits. Coupled nonlinear Langmuir and sound waves are presented. Theory taking into account combined effect of the differential Joule heating, ponderomotive force and relativistic electron mass variation on the instability of electromagnetic waves is presented. Effects of magnetic fields are briefly discussed.

Electrical characteristics and electron heating mechanism of an inductively coupled argon discharge

The external electrical characteristics of inductively coupled argon RF discharges at 13.56 MHz have been measured over a wide range of power at gas pressures ranging from 3 mTorr to 3 Torr. External parameters, such as coil voltage, current and phase shift, were measured. From these measurements the equivalent discharge resistance and reactance, the power transfer efficiency and the coupling coefficient between the primary coil and the plasma were determined as a function of discharge power and gas pressure. The efficient RF power transfer and the large value of the effective electron collision frequency found here at low gas pressure suggest some collisionless electron heating mechanisms. This mechanism is identified as non-local electron heating in the inhomogeneous RF field due to spatial dispersion of the plasma conductivity.

Effective collision frequency method in the theory of the conductivity of Coulomb systems. II. Strong interion interaction and plasma structure

The effective collision frequency method developed earlier by the authors for Coulomb systems characterized by strong interion interaction is developed further. An explicit expression is obtained for the effective electron collision frequency on the basis of the exact diagram representation obtained in Part I and the use of the model of a one-component plasma as initial approximation. The description of plasma structure in the corresponding approximation is considered.