Electron-ion Collision Rate Research Articles

Calibrated heating rate measurements using electric-field-induced electron extraction in ultracold neutral plasmas

The heating rate of plasma electrons induced by external fields or other processes can be used as an experimental tool to measure fundamental plasma properties such as electrical conductivity or electron–ion collision rates. We have developed a technique that can measure electron heating rates in ultracold neutral plasmas (UNPs) with $\sim 10\,\%$ precision while simultaneously referencing the measurement to a calibrated amount of heating. This technique uses a sequence of applied electric fields in four sections: to control the ratio of electrons to ions in the UNP; to provide a time for the application of fields that cause electron heating and subsequent thermalization of the electrons after the application of those fields; to extract electrons from the UNP using a method sensitive to electron temperature that allows the measurement of electron heating; and to extract the remaining electrons to measure the total electron (and therefore ion) number. The primary signal used to measure the heating rate is the measurement of the number of electrons that escape in the third section of the experiment as a larger number of escaping electrons indicates a larger amount of heating. We illustrate the use of this technique by measuring electron heating caused by high-frequency radiofrequency (RF) fields. In addition to the main technique, several subtechniques to calibrate the electron temperature, electron density, amount of heating and applied RF field amplitude were developed as well.

Many-body collision contributions to electron momentum damping rates in a plasma influenced by electron strong coupling

Experimental studies of electron-ion collision rates in an ultracold neutral plasma can be conducted through measuring the rate of electron plasma oscillation damping. For sufficiently cold and dense conditions where strong coupling influences are important, the measured damping rate was faster by over 30% as compared to theoretical expectations [Chen et al., Phys. Rev. E 96, 013203 (2017)]. We have conducted a series of numerical simulations to isolate the primary source of this difference. By analyzing the distribution of electron velocity changes due to collisions in a molecular dynamics simulation, examining the trajectory of electrons with a high deflection angle in such simulations, and examining the oscillation damping rate while varying the ratio of two-body to three-body electron-ion collision rates, we have found that the difference is consistent with the effect due to many-body collisions that lead to bound electrons. This has implications for other electron-ion collision related transport properties in addition to electron oscillation damping.

Calculation of the inverse bremsstrahlung absorption in unmagnetized plasmas

AbstractInverse bremsstrahlung is one important way to deliver laser energy to the plasma in inertial confinement fusion. In this article, we study the collisional absorption rate as obtained from the Fokker–Planck treatment of an unmagnetized plasma in harmonic laser field. The electron–ion collision rate is considered in the Krook approximation, and the electron distribution function is considered a Maxwellian function. We evaluate the inverse bremsstrahlung absorption near the irradiated plasma surface in the critical layer. We observe that absorption increases with shorter laser wavelength and lower electron temperatures. When the maximum electron velocity in the limit of q → 1 reaches infinity, the q‐non‐extensive distribution function reduces to the standard Maxwell‐Boltzmann distribution.

The Barkas effect in plasma transport

Molecular dynamics simulations reveal that a fundamental symmetry of the plasma kinetic theory is broken at moderate to strong Coulomb coupling: the collision rate depends on the signs of the colliding charges. This symmetry breaking is analogous to the Barkas effect observed in charged-particle stopping experiments and gives rise to significantly enhanced electron-ion collision rates. It is expected to affect any neutral plasma with moderate to strong Coulomb coupling such as ultracold neutral plasmas (UNPs) and the dense plasmas of inertial confinement fusion and laser-matter interaction experiments. The physical mechanism responsible is the screening of binary collisions by the correlated plasma medium, which causes an asymmetry in the dynamics of large-angle scattering. Because the effect pertains only to close interactions, it is not predicted by traditional transport models based on cut-off Coulomb collisions or linear dielectric response. A model for the effective screened interaction potential is presented which is suitable for the coupling strengths achieved in UNP experiments. Transport calculations based on this potential and the effective potential kinetic theory agree with the simulated relaxation rates and predict that the Barkas effect can cause up to a 70% increase in the electron-ion collision rate at the conditions of present UNP experiments. The influence of the Barkas effect in other transport processes is also considered.

Collisional damping rates for electron plasma waves reassessed.

Collisional damping of electron plasma waves, the primary damping for high phase velocity waves, is proportional to the electron-ion collision rate, ν_{ei,th}. Here, it is shown that the damping rate normalized to ν_{ei,th} depends on the charge state, Z, on the magnitude of ν_{ei,th} and the wave number k in contrast with the commonly used damping rate in plasma wave research. Only for weak collision rates in low-Z plasmas for which the electron self-collision rate is comparable to the electron-ion collision rate is the damping rate given by the commonly accepted value. The result presented here corrects the result presented in textbooks at least as early as 1973. The complete linear theory requires the inclusion of both electron-ion pitch-angle and electron-electron scattering, which itself contains contributions to both pitch-angle scattering and thermalization.

Observation of a strong-coupling effect on electron-ion collisions in ultracold plasmas.

Ultracold plasmas (UCPs) provide a well-controlled system for studying multiple aspects in plasma physics that include collisions and strong-coupling effects. By applying a short electric field pulse to an UCP, a plasma electron center-of-mass oscillation can be initiated. For accessible parameter ranges, the damping rate of this oscillation is determined by the electron-ion collision rate. We performed measurements of the oscillation damping rate with such parameters and compared the measured rates to both a molecular dynamics (MD) simulation that includes strong-coupling effects and a Monte Carlo binary collision simulation designed to predict the damping rate including only weak-coupling considerations. We found agreement between the experimentally measured damping rate and the MD result. This agreement did require including the influence of a previously unreported UCP heating mechanism whereby the presence of a dc electric field during ionization increased the electron temperature, but estimations and simulations indicate that such a heating mechanism should be present for our parameters. The measured damping rate at our coldest electron temperature conditions was much faster than the weak-coupling prediction obtained from the Monte Carlo binary collision simulation, which indicates the presence of a significant strong-coupling influence. The density averaged electron strong-coupling parameter Γ measured at our coldest electron temperature conditions was 0.35(8).

Damping of electron center-of-mass oscillation in ultracold plasmas

Applying a short electric field pulse to an ultracold plasma induces an electron plasma oscillation. This manifests itself as an oscillation of the electron center of mass around the ion center of mass in the ultracold plasma. In general, the oscillation can damp due to either collisionless or collisional mechanisms, or a combination of the both. To investigate the nature of oscillation damping in ultracold plasmas, we developed a molecular dynamics model of the ultracold plasma electrons. Through this model, we found that depending on the neutrality of the ultracold plasma and the size of an applied DC electric field, there are some parameter ranges where the damping is primarily collisional and some primarily collisionless. We conducted experiments to compare the measured damping rate with theory predictions and found them to be in good agreement. Extension of our measurements to different parameter ranges should enable studies for strong-coupling influence on electron-ion collision rates.

Analytical Study of Quantum Magnetic and Ion Viscous Effects on p11B Fusion in Plasma Focus Devices

In this article we studied the feasibility of proton-boron (p11B) fusion in plasmoids produced by plasma pinch devices like plasma focus facility as commercially sources of energy. In plasmoids fusion power for 76 keV < Ti < 1,500 keV exceeds bremsstrahlung loss (W/Pb = 5.39). In such situation gain factor and the ratio of Te to Ti for a typical 150 kJ plasma focus will be 7.8 and 4.8 respectively. Also with considering the ion viscous heating effect W/Pb and Ti/Te will be 2.7 and 6 respectively. Strong magnetic field will reduces ion–electron collision rate due to quantization of electron orbits. While approximately there is no change in electron–ion collision rate, The effect of quantum magnetic field makes ions much hotter than electrons which enhances the fraction of fusion power to bremsstrahlung loss.

Electron-ion collision rates in noble gas clusters irradiated by femtosecond laser pulse

We report a theoretical analysis of electron-ion collision rates in xenon gas clusters irradiated by femtosecond laser pulses. The present analysis is based on the eikonal approximation (EA), the first Born approximation (FBA) and the classical (CL) methods. The calculations are performed using the plasma-screened Rogers potential introduced by Moll et al. [J. Phys. B. 43, 135103 (2010)] as well as the Debye potential for a wide range of experimental parameters. We find that the magnitudes of electron-ion collision frequency obtained in the EA do not fall as rapidly with the kinetic energy of electrons as in the FBA and CL methods for higher charge states of xenon ion (Xe8+ and Xe14+). Furthermore, EA shows that the effect of the inner structure of ion is most dominant for the lowest charge state of xenon ion (Xe1+). In the case of the present effective potential, FBA overestimates the CL results for all three different charge states of xenon, whereas for the Debye potential, both the FBA and CL methods predict collision frequencies which are nearly close to each other.

Electron–ion collision rates in atomic clusters irradiated by femtosecond laser pulses

In atomic clusters irradiated by femtosecond laser pulses, plasmas with high density and high temperature are created. The heating is mainly caused by inverse bremsstrahlung, i.e. determined by electron–ion collisions. In the description of the scattering of electrons on noble gas ions in such plasmas, it is important to account for the inner structure of the ions and the screening by the surrounding plasma medium which can be accomplished by using suitable model potentials. In the wide parameter range met in experiments, the Born approximation is not applicable. Instead, the electron–ion collision frequency is calculated on the basis of classical momentum transport cross sections. Results are presented for xenon, krypton and argon ions in different charge states. A comparison of these results to those for the scattering on Coulomb particles with the same charge shows an enhancement of the collision frequency. The Born approximation, however, leads to an overestimation.

Enhancement of backward Raman scattering by electron-ion collisions

The propagation of light waves in an underdense plasma is studied using one-dimensional Vlasov–Maxwell numerical simulation. It is found that the backward stimulated Raman scattering will be enhanced by electron-ion collisions. With appropriate electron-ion collision rate the Langmuir waves, driven via SRS, can be made to propagate for a long distance.

Theoretical calculation of the relative abundance between He- and Li-like Ti under the coronal condition

This paper provides a theoretical calculation of the relative abundance between He- and Li-like Ti in the electronic temperature range from 0.1 to 20 keV under the coronal conditions. The results show that the abundance of Li-like Ti is <6 percent of He-like Ti as the electronic temperature exceeds 3 keV , and this percentage will further decrease when the photon-ionization is considered. Thus, it is proven that for the Ti plasma it is approximately true that there are only two charge states (H- and He-like) in the plasma when the electronic temperature is beyond 3 keV . The results also show that the abundance of Li-like Ti will reach a maximum in temperatures range from 0.6 to 0.7 keV . In this paper, the Younger formula is used to estimate the electron–ion collision rates and it is shown that this formula is in a good agreement with experiment data and is better than other theoretical methods. Dielectronic recombination of He-like Ti is considered by a full quantum mechanics method and the total electronic recombination rates of He-like Ti will reach the maximum values at the temperature 2.9 keV , which is close to the plasma temperature of 3 keV formed as in Shepard et al. (Phys. Rev. E 53 (1996) 5291).

Coulomb logarithm in femtosecond-laser-matter interaction.

In femtosecond-laser-matter interaction, collisional absorption plays an important role during the early stages of the interaction, when the laser intensity and the plasma temperature still have moderate values. We propose a cutoff impact parameter b(max) for the Coulomb logarithm lambda=ln Lambda in the electron-ion collision rate which takes into account, for an overdense plasma, the crystalline structure of the ion background. Calculations are presented for a bcc lattice and generalized to sc and fcc lattices. The results are applicable for laser intensities I(l)< or =10(17) W cm(-2) and when the Debye theory is valid, that is to say, when the Landau length is distinctly less than the minimum ion distance, and when the Debye screening is unaffected by the electron quiver motion in the laser field. We present the space angle dependence of the cutoff b(max) as also its spatial average, and we discuss the ensuing corrections to the Coulomb logarithm due to the improved values of b(max). Finally, we present the pertinent <lambda> values, averaged over a Maxwellian distribution function, which are needed for applications of the ballistic model for collisions.

Electrical conductivity in tokamaks and extended neoclassical theory

The electrical conductivity measurements reported from various tokamaks (D-III, PLT, TEXT, ASDEX, JT-60, TEXTOR, JET, TFTR) and compared with the usual neoclassical theory are here also compared with the extended neoclassical theory where the electron-electron collision rate is anomalous while the electron-ion collision rate remains Coulombian. It is found that, out of the 14 experiments considered, three are consistent with both the neoclassical and the extended neoclassical theories, four are consistent only with the extended neoclassical theory, and four are consistent with the neoclassical theory and also, within the experimental errors, not inconsistent with the extended neoclassical theory; the remaining three experiments appear to be incompatible with both theories. It is concluded that the extended neoclassical theory is in better agreement with conductivity experiments than the conventional neoclassical theory and, indeed, the extended theory is a serious candidate for explaining tokamak behaviour, since it accommodates naturally an anomalous electron thermal transport, which the conventional neoclassical theory is unable to do

Reflectivity of steep-gradient plasmas in intense subpicosecond laser pulses.

The wave equation for laser light incident on a static, steep-gradient plasma has been solved numerically, with the inclusion of an intensity-dependent electron-ion collision rate, and incorporating spatial dispersion and wave-breaking effects. At moderate intensities (\ensuremath{\sim}${10}^{14}$ W/${\mathrm{cm}}^{2}$), the nonlinearity has little effect on the calculated reflectivity, but at higher intensities the reflectivity is greater than that predicted by a linear model. The discrepancy is small for a steplike plasma (with a density gradient scale length L\ensuremath{\sim}0.01${\ensuremath{\lambda}}_{0}$), but increases for longer scale lengths (L\ensuremath{\sim}${\ensuremath{\lambda}}_{0}$). In the case of p-polarized light, the angular dependence of reflectivity is sharpened at higher intensities, and resonance effects play an important role even for very short scale lengths.

The scaling of absolutely unstable, stimulated Raman scattering from planar, laser-produced plasmas

A study of the scaling of the fraction, fSRS, of the laser energy scattered by stimulated Raman scattering (SRS) is reported. A simple model of SRS as an absolute instability is presented, leading to the hypothesis that fSRS will be determined by the depth of the plasma producing SRS. The results of a number of experiments are used to test this hypothesis. The experiments analyzed used irradiating wavelengths of 1.06, 0.53, and 0.35 μm. In all cases, the plasmas were planar and the electron–ion collision rate was small compared to the homogeneous SRS growth rate. The depth of the plasma, as opposed to the laser intensity or laser wavelength, is found to be the primary determinant of fSRS. In addition, as the depth of the plasma increases, the angular distribution of the scattering is observed to broaden. The implications of these results for analysis of SRS as an absolute instability and for laser fusion are discussed.

A laser-based measurement of electron collision rates for excited states of ionised helium in a plasma

The total de-excitation rate out of the level (n=4) of singly ionised helium was measured using a dye laser to deplete the n=4 population; the rate being inferred from the relative depletion obtained for a given laser power. For the plasma parameters of ne=5*1014 cm-3 and Te=4.3 eV this rate will be dominated by the electron-ion collision rates to n=3 and n=5. The experimental results are compared with those predicted by a ten-level collisional radiative model using the hydrogenic electron-ion collision rate coefficients due to Seaton. Substantial agreement is achieved.

Computer description of the C-stellarator ohmic heating discharges in hydrogen

The behaviour of the ohmic heating discharges of hydrogen in the C-stellarator has been computed for a range of input parameters: ohmic heating currents, confining fields, initial gas densities, and recycling rates. The calculations were performed on a 7094 computer, by solving a set of coupled equations expressing particle densities, temperatures, emission of atomic and molecular light, etc. as functions of time in terms of known rate coefficients for ionization, excitation, dissociation, and charge exchange, and known relationships between electron temperature and the electrical conductivity, the particle loss rate, and the electron-ion collision rate. The calculated quantities are in reasonably good agreement with experimental data over the available range of parameters. The results show, inter alia, that it is immaterial (except for the emitted light) whether the strating gas, or the recycling, consists of 2H or H2; the ion temperatures achieved in the ohmic heating discharges are remarkably independent of the input parameters, and will not exceed similar 30 eV in a plasma of 5-cm radius at 36 kG. Extending the calculations to larger confining fields and discharge radii does not result in very substantial increase in particle temperature, without changing the assumed linear temperature dependence of the loss rate.