Time-dependent Electron Temperature Research Articles

Electron temperature gradient driven transport model for tokamak plasmas

A new model for electron temperature gradient (ETG) modes is developed as a component of the multi-mode anomalous transport module [Rafiq et al., Phys Plasmas 20, 032506 (2013)] to predict a time-dependent electron temperature profile in conventional and low aspect ratio tokamaks. This model is based on two-fluid equations that govern the dynamics of low-frequency short- and long-wavelength electromagnetic toroidal ETG driven drift modes. A low collisionality NSTX discharge is used to scan the plasma parameter dependence on the ETG real frequency, growth rate, and electron thermal diffusivity. Electron thermal transport is discovered in the deep core region where modes are more electromagnetic in nature. Several previously reported gyrokinetic trends are reproduced, including the dependencies of density gradients, magnetic shear, β and gradient of β (β′), collisionality, safety factor, and toroidicity, where β is the ratio of the plasma pressure to the magnetic pressure. The electron heat diffusivity associated with the ETG mode is discovered to be on a scale consistent with the experimental diffusivity determined by power balance analysis.

Numerical Study on the Temporal Evolution of a Helicon Discharge

A numerical model is developed to study the temporal evolution of helicon discharge. The initiation of helicon discharge is first presented in terms of time-dependent electron density and temperature, electric and magnetic fields, and power deposition; then, their steady-state values are compared with experimental data and previous simulations for benchmark. It is found that the evolutions of electron density and temperature arrive steady state around 100 and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.5~\mu \text{s}$ </tex-math></inline-formula> , respectively, while electric and magnetic fields become steady prior to 2 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{s}$ </tex-math></inline-formula> . The spatial distributions of power deposition indicate that RF power is absorbed mostly near the edge, similar to those of electron temperature. Parameter studies show that high background pressure, confining magnetic field strength, and RF power are beneficial to obtaining high-density helicon plasma, while the driving frequency has little effect. These findings are interesting for the design and optimization of helicon plasma source.

Enhanced nonlinear optical effects based on strong coupling between epsilon-near-zero mode and gap surface plasmons

Optical nonlinear effect plays an important role in optical communication, optical detection, quantum information and other areas. However, it is constrained by the weakness of the nonlinear optical response of the common materials. The enhancement of the optical nonlinear response on a nanoscale becomes a critical challenge. Over the years, several ways to enhance the optical nonlinear effects have been suggested. In fact, these technologies can slightly enhance the optical nonlinear response. Recently, some research groups focused on the materials with vanished permittivity, which is called epsilon-near-zero (ENZ) material, showing that it can exhibit large optical nonlinearity due to the field enhancement in the material of this type. However, the ENZ material only holds a large optical nonlinear response in a limited spectral range. In order to overcome this limitation, here in this paper we report the ENZ mode which is excited by the ITO film and strongly coupled to the gap surface plasmons excited by the metal-dielectric-metal structure. To acquire the nonlinear refractive index &lt;i&gt;n&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;, we first calculate the ITO permittivity through the Drude-Lorentz model and find the wavelength of the ENZ material. Then we calculate the time-dependent electron temperature and lattice temperature of ITO by the two-temperature model. According to the elevated electron temperature, we can calculate the plasma frequency &lt;inline-formula&gt;&lt;tex-math id="M1"&gt;\begin{document}${\omega _{\rm p}}$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210290_M1.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210290_M1.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;, and by taking it into the Drude-Lorentz model, we can obtain a new permittivity of ITO compared with the initial one. Finally, we can calculate the variation of the refractive index &lt;inline-formula&gt;&lt;tex-math id="M2"&gt;\begin{document}$ \Delta n $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210290_M2.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210290_M2.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;, and the nonlinear refractive index &lt;inline-formula&gt;&lt;tex-math id="M3"&gt;\begin{document}$ {n_2} = \Delta n/{I_0} $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210290_M3.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210290_M3.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;. In this paper, our coupled structure exhibits a broadband (～1000 nm bandwidth) enhancement of the nonlinear optical effect in the near-infrared spectrum, a maximum nonlinear refractive index &lt;i&gt;n&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt; as large as 3.02 cm&lt;sup&gt;2&lt;/sup&gt;·GW&lt;sup&gt;–1&lt;/sup&gt;, which is nearly 3 orders larger than the previously reported nonlinear refractive index of bare ITO film. As a result, it is possible to realize a dramatically large variation of nonlinear refractive index under a low-power optical field. It is expected to be used in the nano photonic devices such as optical storage, all-optical switches, etc.

A novel method to measure ion density in ICF experiments using x-ray spectroscopy of cylindrical tracers

The indirect drive approach to inertial confinement fusion has undergone important advances in the past few years. Improvements in temperature and density diagnostic methods are leading to more accurate measurements of the plasma conditions inside the Hohlraum and therefore to more efficient experimental designs. The implementation of dot spectroscopy has proven to be a versatile approach to extracting space- and time-dependent electron temperatures. In this method, a microdot of a mid-Z material is placed inside the Hohlraum and its K-shell emission spectrum is used to determine the plasma temperature. However, radiation transport of optically thick lines acting within the cylindrical dot geometry influences the outgoing spectral distribution in a manner that depends on the viewing angle. This angular dependence has recently been studied in the high energy density regime at the OMEGA laser facility, which allowed us to design and benchmark appropriate radiative transfer models that can replicate these geometric effects. By combining these models with the measurements from the dot spectroscopy experiments at the National Ignition Facility, we demonstrate here a novel technique that exploits the transport effects to obtain time-resolved measurements of the ion density of the tracer dots, without the need for additional diagnostics. We find excellent agreement between experiment and simulation, opening the possibility of using these geometric effects as a density diagnostic in future experiments.

Vibrational response and motion of carbon monoxide on Cu(100) driven by femtosecond laser pulses: Molecular dynamics with electronic friction

Carbon monoxide on copper surfaces continues to be a fascinating, rich microlab for many questions evolving in surface science. Recently, hot-electron mediated, femtosecond-laser pulse induced dynamics of CO molecules on Cu(100) were the focus of experiments [Inoue et al., Phys. Rev. Lett. 117, 186101 (2016)] and theory [Novko et al., Phys. Rev. Lett. 122, 016806 (2019)], unraveling details of the vibrational nonequilibrium dynamics on ultrashort (subpicoseconds) timescales. In the present work, full-dimensional time-resolved hot-electron driven dynamics are studied by molecular dynamics with electronic friction (MDEF). Dissipation is included by a friction term in a Langevin equation which describes the coupling of molecular degrees of freedom to electron-hole pairs in the copper surface, calculated from gradient-corrected density functional theory (DFT) via a local density friction approximation (LDFA). Relaxation due to surface phonons is included by a generalized Langevin oscillator model. The hot-electron induced excitation is described via a time-dependent electronic temperature, the latter derived from an improved two-temperature model. Our parameter-free simulations on a precomputed potential energy surface allow for excellent statistics, and the observed trends are confirmed by on-the-fly ab initio molecular dynamics with electronic friction (AIMDEF) calculations. By computing time-resolved frequency maps for selected molecular vibrations, instantaneous frequencies, probability distributions, and correlation functions, we gain microscopic insight into hot-electron driven dynamics and we can relate the time evolution of vibrational internal CO stretch-mode frequencies to measured data, notably an observed redshift. Quantitatively, the latter is found to be larger in MDEF than in experiment and possible reasons are discussed for this observation. In our model, in addition we observe the excitation and time evolution of large-amplitude low-frequency modes, lateral CO surface diffusion, and molecular desorption. Effects of surface atom motion and of the laser fluence are also discussed.

Experimental investigation of the compression and heating of an MHD-driven jet impacting a target cloud

Adiabatic compression has been investigated by having an MHD-driven plasma jet impact a gas target cloud. Compression and heating of the jet upon impact were observed and compared to theoretical predictions. Diagnostics for comprehensive measurements included a Thomson scattering system, a fast movie camera, a translatable fiber-coupled interferometer, a monochromator, a visible-light photodiode, and a magnetic probe array. Measurements using these diagnostics provided the time-dependent electron density, electron temperature, continuum emission, line emission, and magnetic field profile. Increases in density and magnetic field and a decrease in jet velocity were observed during the compression. The electron temperature had a complicated time dependence, increasing at first, but then rapidly declining in less than 1 μs which is less than the total compression time. Analysis indicates that this sudden temperature drop is a consequence of radiative loss from hydrogen atoms spontaneously generated via three-body recombination in the high-density compressed plasma. A criterion for how fast compression must be to outrun radiative loss is discussed not only for the Caltech experiment but also for fusion-grade regimes. In addition, the results are analyzed in the context of shocks the effects of which are compared to adiabatic compression.

Femtosecond laser induced desorption of H2,D2 , and HD from Ru(0001): Dynamical promotion and suppression studied with ab initio molecular dynamics with electronic friction

We perform ab initio molecular dynamics simulations to study the femtosecond laser induced desorption of ${\mathrm{H}}_{2},{\mathrm{D}}_{2}$, and HD from a H:D-saturated Ru(0001) surface. To this aim we have extended the ab initio molecular dynamics with electronic friction (AIMDEF) scheme to include a random force that is a function of a time-dependent electronic temperature. The latter characterizes the action of the ultrashort laser pulse according to a two temperature model. This allows us to perform multidimensional, hot-electron driven reaction dynamics and investigate the dependence of the desorption yields on the relative H:D isotope concentration on the surface. Our AIMDEF simulations show that the desorption process takes place in the presence of a heated adsorbate system that clearly influences the desorption dynamics. The heating of the adsorbate system is more (less) pronounced the larger is the concentration of the lighter (heavier) isotope. As a result, we conclude that the presence of H on the surface favors the desorption of molecules, whereas the presence of D hampers it, in agreement with previous experimental observations in which the phenomenon of ``dynamical promotion'' of a surface reaction had been postulated [Denzler et al., Phys. Rev. Lett. 91, 226102 (2003)].

Femtosecond-laser induced dynamics of CO on Ru(0001): Deep insights from a hot-electron friction model including surface motion

A Langevin model accounting for all six molecular degrees of freedom is applied to femtosecond-laser induced, hot-electron driven dynamics of Ru(0001)($2\ifmmode\times\else\texttimes\fi{}2$):CO. In our molecular dynamics with electronic friction approach, a recently developed potential energy surface based on gradient-corrected density functional theory accounting for van der Waals interactions is adopted. Electronic friction due to the coupling of molecular degrees of freedom to electron-hole pairs in the metal are included via a local density friction approximation, and surface phonons by a generalized Langevin oscillator model. The action of ultrashort laser pulses enters through a substrate-mediated, hot-electron mechanism via a time-dependent electronic temperature (derived from a two-temperature model), causing random forces acting on the molecule. The model is applied to laser induced lateral diffusion of CO on the surface, ``hot adsorbate'' formation, and laser induced desorption. Reaction probabilities are strongly enhanced compared to purely thermal processes, both for diffusion and desorption. Reaction yields depend in a characteristic (nonlinear) fashion on the applied laser fluence, as well as branching ratios for various reaction channels. Computed two-pulse correlation traces for desorption and other indicators suggest that aside from electron-hole pairs, phonons play a non-negligible role for laser induced dynamics in this system, acting on a surprisingly short time scale. Our simulations on precomputed potentials allow for good statistics and the treatment of long-time dynamics (300 ps), giving insight into this system which hitherto has not been reached. We find generally good agreement with experimental data where available and make predictions in addition. A recently proposed laser induced population of physisorbed precursor states could not be observed with the present low-coverage model.

High time resolved electron temperature measurements by using the multi-pass Thomson scattering system in GAMMA 10/PDX.

High time resolved electron temperature measurements are useful for fluctuation study. A multi-pass Thomson scattering (MPTS) system is proposed for the improvement of both increasing the TS signal intensity and time resolution. The MPTS system in GAMMA 10/PDX has been constructed for enhancing the Thomson scattered signals for the improvement of measurement accuracy. The MPTS system has a polarization-based configuration with an image relaying system. We optimized the image relaying optics for improving the multi-pass laser confinement and obtaining the stable MPTS signals over ten passing TS signals. The integrated MPTS signals increased about five times larger than that in the single pass system. Finally, time dependent electron temperatures were obtained in MHz sampling.

One-dimensional time-dependent fluid model of a very high density low-pressure inductively coupled plasma

A time-dependent two-fluid model has been developed to understand axial variations in the plasma parameters in a very high density (peak ne≳5×1019 m−3) argon inductively coupled discharge in a long 1.1 cm radius tube. The model equations are written in 1D with radial losses to the tube walls accounted for by the inclusion of effective particle and energy sink terms. The ambipolar diffusion equation and electron energy equation are solved to find the electron density ne(z,t) and temperature Te(z,t), and the populations of the neutral argon 4s metastable, 4s resonant, and 4p excited state manifolds are calculated to determine the stepwise ionization rate and calculate radiative energy losses. The model has been validated through comparisons with Langmuir probe ion saturation current measurements; close agreement between the simulated and measured axial plasma density profiles and the initial density rise rate at each location was obtained at pAr=30−60 mTorr. We present detailed results from calculations at 60 mTorr, including the time-dependent electron temperature, excited state populations, and energy budget within and downstream of the radiofrequency antenna.

Radial Electron Temperature and Density Measurements Using Thomson Scattering System in GAMMA 10/PDX

A Thomson scattering (TS) system in GAMMA 10/PDX has been developed for the measurement of radial profiles of electron temperature and density in a single plasma and laser shot. The TS system has a large solid angle optical collection system and high-sensitivity signal detection system. The TS signals are obtained using four-channel high-speed digital oscilloscopes controlled by a Windows PC. We designed the acquisition program for six oscilloscopes to obtain 10-Hz TS signals in a single plasma shot, following which the time-dependent electron temperatures and densities can be determined. Moreover, in order to obtain larger TS signal intensity in the edge region, we added a second collection mirror. The radial electron temperatures and densities at six radial positions in GAMMA 10/PDX were successfully obtained.

Time-resolved K-shell line spectra measurement of z-pinch plasmas

A Johann-type crystal spectrometer integrated with x-ray PIN diodes has been developed for measuring the time-resolved K-shell line spectra of the imploding Al wire array. In this spectrometer, the PIN diodes are mounted on the Rowland circle of the cylindrical bent crystal with an appointed position to collect the line emissions from z-pinch plasmas. The spectrometer with four typical channels, which are keyed to the Al ion hydrogen-like (Hα, 0.7171nm and Hβ, 0.6052nm) and helium-like (Heα, 0.7757nm and Heβ, 0.6634nm) resonance lines is designed and fabricated. Example data from the experiment on the Yang accelerator are shown and the time-dependent electron temperature is determined from the signal ratios of Al ion Hα line to Heα line using the collisional and radiative model.

Modeling of K-shell Al and Mg radiation from compact single, double planar and cylindrical alloyed Al wire array plasmas produced on the 1 MA Zebra generator at UNR

Radiative emission from alloyed Al single, double and compact cylindrical wire arrays have been studied using the 1 MA Zebra UNR generator. Single planar wire arrays using ten wires and double planar wire arrays and compact cylindrical wire arrays (CCWA) that both had sixteen wires were utilized. The wire composition is Al-5056 (95% of Al and 5% of Mg). We have observed that implosion of these alloyed Al wire loads generated optically thick Al plasmas that can be diagnosed using K-shell Mg lines. In particular, among the considered loads, the K-shell lines of Al from implosions of the double planar wire arrays have the highest optical depth for He-like Al resonance transitions, which occurred near the stagnation phase. X-ray time-gated and time-integrated spectra and pinhole images as well as photoconductive detectors signals were analyzed to provide information on the plasma parameters; electron temperatures and densities, implosion dynamics features and power and yields of the X-ray radiation. Previously developed non-LTE models were applied to model axially-resolved time-integrated, as well as time-gated spatially-integrated, K-shell spectra from Al and Mg. The derived time-dependent electron temperature, density and axial opacity were studied and compared. In addition, the wire ablation dynamics model (WADM) was used to calculate the kinetic energy of the plasma, which with the aid of a Local Thermal Equilibrium (LTE) magneto-hydrodynamics (MHD) simulation, allowed to estimate the precursor and stagnated z-pinch plasma electron temperatures from implosions of wire array loads.

Spatial and temporal variations of electron temperatures and densities from EUV-emitting lithium plasmas

Planar slabs of pure Li were irradiated with 1.064 nm, 6 ns Nd:YAG laser pulses. Determination of plasma densities at both the earliest times of plasma formation and near the target surface was performed using Nomarski interferometry. The plasma parameters at later times were evaluated using optical emission spectroscopy. The space- and time-dependent electron densities and temperatures of the plasma were determined from their Stark broadening and the relative intensities of the spectral lines, respectively. The advantages and disadvantages of both of these techniques are evaluated and discussed.

Plasma expansions with a time-dependent electron temperature

The fundamental of ion acceleration from the laser-solid interactions is the theory for describing plasma expansions into a vacuum. In the time interval of tens of femtoseconds after the laser pulse reaches the target, the plasma reaches local-thermal equilibrium and then hydrodynamic equations are available. However, it cannot reach macro-thermal equilibrium and does not satisfy Boltzmann distribution. The plasma is non-quasi-neutral and a strong charge separation exists. In fact, the electron temperature is time-dependent and the changing law is governed by the energy transfer between electrons and ions. In this Letter, an analytical solution is obtained for plasma expansions into a vacuum to describe the ion acceleration with a time-dependent electron temperature. It is obtained that the dependence of the plasma density on the potential is different from Boltzmann distribution in the time-dependent case. The time-dependent electron temperature also induces the unsteady ablation rate of the ablation plane, which is defined as the interface between the plasma and the solid (or liquid or gas). The electric field is also obtained and discussed in detail. The particular solution is given to show the influence of the time-dependent electron temperature on the laser-ion acceleration in a particular case: the electron temperature is proportional to the square of time. From that, it is concluded that laser-ion acceleration is more efficient in the time-increasing electron-temperature case than that in the isothermal case. The time-dependence of electron temperature comes from the time-dependence of laser intensity and induces the different efficiency of the laser-ion acceleration. At the ablation plane, the electron density and velocity are also predicted and explained reasonably.

Time-dependent delayed electron spectra: a direct measurement of total decay rate as a function of internal energy

We present a general method to measure internal energy dependant decay rate in the case of systems emitting thermal electrons. Our approach is based on the measurement of the time-dependent kinetic energy spectra of delayed electrons using time-resolved velocity map imaging spectrometry. We illustrate this method in the case of C60 molecules. Indeed electron spectra for C60 have been studied in great details in the past few years, allowing a complete analysis of the observed features. Moreover, C60 offers the opportunity to study competing decay mechanisms demonstrating that the technique may have broader applicability to other molecules. Using a model that includes all contributing decay channels relevant in our time delay range (namely delayed ionization and dissociation by C2 emission) we are able to derive quantitative information on the decay channels of the molecule. In the situation considered here, the time-dependent electron temperature extracted from the kinetic energy spectra is used to determine more precisely the rate constant for the dominant process, namely neutral C2 dissociation channel. In other words, the measurement of the cooling of an ensemble of C60 molecules as a function of time delay after heating provides a direct and quantitative access to its decay dynamics. This method may be used to map out the total rate for complex decay mechanisms.

Electronic effects in radiation damage simulations

A methodology for including electronic effects in classical radiation damage simulations is presented. The method is used to calculate the number of residual defects for low energy (10keV) cascades in Fe, as a function of the electron–phonon coupling strength. It was found that strong electron–phonon coupling reduced the number of residual defects by rapidly removing energy from the cascade and reducing the thermal spike. Intermediate coupling increased the number of defects by quenching the thermal spike and reducing defect recombination. Thermostatting the cascade with the local, time dependent electronic temperature, rather than the ambient temperature, reduced the number of residual defects by enhancing defect recombination. Swift heavy ion irradiation in tungsten was modeled using the same methodology. In this case we found that the number of residual defects created by a given electronic stopping power was strongly dependent on the temperature variation of the electronic heat capacity. In contrast to cascade simulations, the interstitials were located closer to the core of the ion track than the vacancies.

Predicting secondary ion formation in molecular dynamics simulations of sputtering

We present a model to incorporate the excitation and ionization of sputtered particles into molecular dynamics simulations of ion bombardment-induced collision cascades in metals. The kinetic excitation of the solid is described by electronic friction experienced by all moving particles and electron promotion in close atomic collisions. Transport of the resulting excitation energy is treated by a nonlinear diffusion equation. The resulting space- and time-dependent electron temperature is then introduced into a rate equation model describing the ionization of ejected particles. This way, secondary ion formation is described by assigning an individual ionization probability to every sputtered atom. Averaging over the entire flux, this allows the prediction of measurable quantities like integral or spectral ionization probabilities as well as velocity spectra of secondary ions.

Recording the time dependence of the electron temperature and absolute yield of continuous and line X-rays from flat Au targets irradiated on the Iskra-5 facility

Two techniques for recording the absolute yield of continuous X rays in the spectral range > 1 keV and M-series line X rays from flat Au targets irradiated with one channel of the Iskra-5 facility are described. In the first and second methods, radiation is detected with a KAP-crystal-based spectrograph and an X-ray streak camera with a 50-ps time resolution, respectively. Both techniques allow obtainment of absolute values of the yields of continuous and line X-ray radiations from laser plasma that coincide within the measurement accuracy. The time-dependent plasma electron temperature is measured with an X-ray streak camera.

Observation of Collective Modes of Ultracold Plasmas

Applying a radio-frequency electric field to an expanding ultracold neutral plasma leads to the observation of as many as six peaks in the emission of electrons from the plasma. These are identified as collective modes of the plasma and are in qualitative agreement with a model of Tonks-Dattner resonances, electron sound waves propagating in a finite-sized, inhomogeneous plasma. Such modes may provide an accurate method to determine the time-dependent electron temperature.