Density Gradient Scale Length Research Articles

Overtaking interactions in a strongly coupled inhomogeneous dusty plasma: the role of polarization force

The nonlinear propagation of dust-acoustic waves (DAWs) is considered in a collisionless, inhomogeneous, weakly and strongly coupled dusty plasma composed of negatively charged dust, electrons, and ions. The reductive perturbation method is used to derive a Korteweg–de Vries equation (KdV). It is found that the KdV solitons are affected by the plasma parameters, whereas only rarefactive DAWs are obtained. Hirota’s bilinear approach is used to investigate the overtaking collision of two and three-soliton solutions. Physical parameters such as polarization, and the ions and electrons density gradient scale lengths have a significant impact and cause alterations in the behaviour of the solitons. Notably, as the polarization and ion density gradient scale length increase, the amplitude and width of the solitons decrease. Furthermore, the system parameters also affect the phase shifts of the solitons. The findings presented here have potential applications in the study of acoustic waves in compact astrophysical systems, where quantum polarization and inhomogeneity effects cannot be ignored, as well as in laboratory plasmas.

Relationships between ionospheric parameters derived from ionosonde observations and characteristics of post-sunset GHz scintillation during high solar activities (2012−2013) at Sanya (18.3°N, 109.6°E), China

In this study, we presented the characteristics of post-sunset GHz scintillation occurrence and ionospheric parameters derived from ionosonde observations, including the critical frequency of F2-layer (foF2), peak height of F2-layer (hmF2), minimum virtual height of F-layer (h’F), scale height around the F2-layer peak (Hm), virtual height (h’F5) and true height (hF5) measured at 5 MHz, in high solar activity years (2012-2013) of solar cycle 24 at Sanya (18.3°N, 109.6°E; dip lat.: 12.8°N), China. Furthermore, we investigated the relationships between the equinoctial asymmetry of scintillation and these ionospheric parameters. In addition, the growth rates of Rayleigh-Taylor instability were calculated on the basis of the ionosonde measurements and models, respectively. The results showed that the equinoctial asymmetry of scintillation onset time would be associated with the scale length of vertical electron density gradient (L), which affects the growth of Rayleigh-Taylor instability at the bottom of F-layer. The seasonal variations of foF2, Hm and scale length of vertical electron density gradient would be the reason to cause the seasonal variations of scintillation occurrence, and the equinoctial asymmetry of scintillation occurrence rate over low latitude can be related to the background electron density and the vertical drifts around sunset in F-layer. The correlations between the scintillation strength represented by the daily maximum S4 and the daily maximum values of foF2, hmF2, h’F, Hm, and also the drifts over low latitudes were weak, which need to be further studied.

Impact of impurities on drift wave instabilities in reversed-field pinch plasmas.

The drift wave in the presence of impurity ions was investigated numerically in reversed-field pinch plasmas, using the gyrokinetic integral eigenmode equation. By comparing the results of regular and hollow plasma density profiles, it was found that the ion temperature gradient mode for the hollow density profile case is much harder to excite. For the impurity effects, when the impurity density gradient is opposite to the electrons, namely when L_{ez} (L_{ez}=L_{ne}/L_{nz} with 1/L_{n} being the density gradient scale length, and the subscript "e" and "z" indicates electrons and impurity ions, respectively) is negative, the impurities can enhance the instability. On the contrary, when L_{ez} is positive, the instability is stabilized. Regarding the trapped electron mode (TEM), the growth rate for plasmas with a hollow density profile remains smaller than that of the standard density gradient. There exists a threshold in L_{ez}. When L_{ez} is less than this value, the impurities destabilize the TEMs, while when L_{ez} is greater than this value, the impurities stabilize the TEMs. In addition, the influence of the collisionality on the TEMs was also studied.

Correlation of fast electron ejections, terahertz waves, and harmonics emitted from plasma mirrors driven by sub-relativistic ultrashort laser pulse

When an ultrashort laser pulse incidents onto a plasma mirror, there exist fast electron ejections, terahertz (THz) radiation, and harmonic generation simultaneously. We investigated the correlation of these three emission phenomena at a preplasma density gradient scale length of (0.05–1)λ and sub-relativistic laser intensity (a0 = 0.4) via particle-in-cell simulation. It is shown that THz radiation is positively correlated with fast electron ejections. As the gradient scale length increases, both enhance first, reach a maximum at 0.4λ, and then degrade at a longer scale length. Harmonic generation, on the other hand, presents the strongest radiation at a sharp surface of 0.05λ and then decays continuously at a softer gradient, indicating that it has an anti-correlation with the fast electron ejections at first (<0.4λ) but turns into a positive correlation at a softer gradient. We find that the laser energy absorption mechanism plays a vital role in the correlation among these emission phenomena. At a sharp boundary of <0.4λ gradient scale length, the Brunel mechanism is dominated, and the absorption rate increases gradually with the increasing gradient scale length. However, at the softer boundary of >0.4λ, the absorption rate decreases continuously according to stochastic heating, and the dependence on laser polarization is eventually lost. The transition of laser absorption mechanisms alters the correlation among fast electrons, THz driven by ejected fast electrons via coherent transition radiation, and harmonics excited by bounded electrons.

Efficient Narrow-Band Terahertz Radiation from Electrostatic Wakefields in Nonuniform Plasmas.

It is shown that electrostatic plasma wakefields can efficiently radiate at harmonics of the plasma frequency when the plasma has a positive density gradient along the propagation direction of a driver. The driver propagating at a subluminal group velocity excites the plasma wakefield with the same phase velocity. However, due to the positive density gradient, the wake phase velocity steadily increases behind the driver. As soon as the phase velocity becomes superluminal, the electrostatic wakefield couples efficiently to radiative electromagnetic modes. The period of time when the phase velocity stays above the speed of light depends on the density gradient scale length. The wake radiates at well-defined harmonics of the plasma frequency in the terahertz band. The angle of emission depends on the gradient scale and the time passed behind the driver. For appropriate plasma and driver parameters, the wake can radiate away nearly all its energy, which potentially results in an efficient, narrow-band, and tunable source of terahertz radiation.

Relationship Between Presunset Wave Structures and Interbubble Spacing: The Seeding Perspective of Equatorial Plasma Bubble

AbstractIn this paper, we study on the precursor seed structures well before the prospective occurrence of equatorial plasma bubble (EPB). We use the scanning mode observations made by the 30‐MHz Gadanki Ionospheric Radar Interferometer for estimating interbubble spacing and high time resolution observations made by a collocated digisonde for inferring horizontal wavelength of wave‐like variations prior to the onset of EPB. Horizontal wavelength of wave‐like variations has been inferred from plasma density variations and height variations of isodensity contours; both show consistent results. Remarkable agreement has been found between the estimated horizontal wavelength and interbubble spacing, which demonstrates the potential of digisonde in providing relevant seed structure for a prospective EPB formation. Further analysis based on observational results and numerical simulation of collisional interchange instability shows that while the eventual formation of EPB has a strong bearing on the height of the F layer and density gradient scale length, the growth perspective of the EPB depends on the seed wavelength. These results are presented and discussed keeping the future prospective of EPB forecasting/nowcasting.

Kappa distributed trapped electrons, drift wave instability and nonlinear structures in O–H plasma of ionosphere

Generation of drift waves by field-aligned shear flow of protons and oxygen ions is investigated in the presence of kappa distributed trapped electrons in upper ionosphere within auroral latitudes. Very low-frequency electrostatic waves having frequencies of the order of a few Hz observed by Freja satellite at altitude 1700 km can be either the ion acoustic waves (IAWs) or the electrostatic drift waves EDW depending up on density uniformity or non-uniformity in the region. Growth rate of drift wave increases in the presence of 0.4 percent hydrogen ions in oxygen plasma. Drift wave is coupled with the four branches of ion acoustic modes in this bi-ion plasma. In nonlinear regime, EDW and IAWs produce electrostatic solitary structures of a few meters width and their amplitude depends up on the density gradient scale length, non-thermality parameter and trapping of electrons.

Hot-electron generation at direct-drive ignition-relevant plasma conditions at the National Ignition Facility

Laser–plasma interaction instabilities can be detrimental for direct-drive inertial confinement fusion by generating high-energy electrons that preheat the target. An experimental platform has been developed and fielded on the National Ignition Facility to investigate hot-electron production from laser–plasma instabilities at direct-drive ignition-relevant conditions. The radiation-hydrodynamic code DRACO has been used to design planar-target experiments that generate plasma and interaction conditions comparable to direct-drive ignition designs: IL ∼ 1015 W/cm2, Te > 3 keV, and density-gradient scale lengths of Ln ∼ 600 μm in the quarter-critical density region. The hot-electron properties were inferred by comparing the experimentally observed hard x-ray spectra to Monte Carlo simulations of hard x-ray emission from hot electrons depositing energy in the target. Hot-electron temperatures of ∼40 keV to 60 keV and the fraction of laser energy converted to hot electrons of ∼0.5% to 5% were inferred in plastic targets for laser intensities at the quarter-critical density surface of (∼4 to 14) × 1014 W/cm2. The use of silicon ablators was found to mitigate the hot-electron preheat by increasing the threshold laser intensity for hot-electron generation from ∼3.5 × 1014 W/cm2 in plastic to ∼6 × 1014 W/cm2 in silicon. The overall hot-electron production is also reduced in silicon ablators when the intensity threshold is exceeded.

Growth of Rayleigh instability in a Hall thruster channel having dust in exit region

In a Hall thruster, the axial movement of ions towards the exit of the chamber and the divergence of ion beam sputter the wall and thus the maximum erosion of wall of the exit region takes place. This way the dust is generated, which is largely confined near the exit of the channel. By considering dust particles with negative charge, we derive and solve the dispersion equation for the growth of Rayleigh instability in the thruster plasma and examine its growth rate for different density, charge, mass and temperature of the dust particles. We also talk about the role of density gradient scale length on the growth of the instability.

Few-cycle laser wakefield acceleration on solid targets with controlled plasma scale length

We measure the emission of energetic electrons from the interaction between relativistic-intensity ultrashort laser pulses and a solid density plasma with a tunable density gradient scale length. We detect an electron beam that only appears with few-cycle pulses (<10 fs) and large plasma scale lengths (L > λ0). Numerical simulations, in agreement with the experiments, reveal that these electrons are accelerated by a laser wakefield. Plasma waves are indeed resonantly excited by the few-cycle laser pulses in the near-critical density region of the plasma. Electrons are then injected by ionization into the plasma waves and accelerated to relativistic energies. In this laser wakefield acceleration regime, the plasma waves are rotated by the plasma density gradient, which results in the electrons not being emitted in the same direction as the driving laser pulse.

Impact of the pulse contrast ratio on molybdenum K\u03b1 generation by ultrahigh intensity femtosecond laser solid interaction

We present an extended experimental study of the absolute yield of Kα x-ray source (17.48 keV) produced by interaction of an ultrahigh intensity femtosecond laser with solid Mo target for temporal contrast ratios in the range of 1.7 × 107–3.3 × 109 and on three decades of intensity 1016–1019 W/cm². We demonstrate that for intensity I ≥ 2 × 1018 W/cm² Kα x-ray emission is independent of the value of contrast ratio. In addition, no saturation of the Kα photon number is measured and a value of ~2 × 1010 photons/sr/s is obtained at 10 Hz and I ~1019 W/cm². Furthermore, Kα energy conversion efficiency reaches the same high plateau equal to ~2 × 10−4 at I = 1019 W/cm² for all the studied contrast ratios. This original result suggests that relativistic J × B heating becomes dominant in these operating conditions which is supposed to be insensitive to the electron density gradient scale length L/λ. Finally, an additional experimental study performed by changing the angle of incidence of the laser beam onto the solid target highlights a clear signature of the interplay between collisionless absorption mechanisms depending on the contrast ratio and intensity.

Properties of ion temperature gradient and trapped electron modes in tokamak plasmas with inverted density profiles

We perform a numerical study of linear stability of the ion temperature gradient (ITG) mode and the trapped electron mode (TEM) in tokamak plasmas with inverted density profiles. A local gyrokinetic integral equation is applied for this study. From comprehensive parametric scans, we obtain stability diagrams for ITG modes and TEMs in terms of density and temperature gradient scale lengths. The results show that, for the inverted density profile, there exists a normalized threshold temperature gradient above which the ITG mode and the TEM are either separately or simultaneously unstable. The instability threshold of the TEM for the inverted density profile is substantially different from that for normal and flat density profiles. In addition, deviations are found on the ITG threshold from an early analytic theory in sheared slab geometry with the adiabatic electron response [T. S. Hahm and W. M. Tang, Phys. Fluids B 1, 1185 (1989)]. A possible implication of this work on particle transport in pellet fueled tokamak plasmas is discussed.

Effect of bromine-dopant on radiation-driven Rayleigh–Taylor instability in plastic foil

Effects of bromine (Br) dopant on the growth of radiation-driven ablative Rayleigh–Taylor instability (RTI) in plastic foils are studied by radiation hydrodynamics simulations and theoretical analysis. It is found that the Br-dopant in plastic foil reduces the seed of ablative RTI. The main reasons of the reduction are attributed to the smaller oscillation amplitude of ablative Richtmyer–Meshkov instability (RMI) induced by the smaller post-shock sound speed, and the smaller oscillation frequency of ablative RMI induced by the smaller ablation velocity and blow-off plasma velocity. The Br-dopant also decreases the linear growth rate of ablative RTI due to the smaller acceleration. Treating the perturbation growth as a function of foil’s displacement, the perturbation growth would increase in Br-doped foil at the phase of ablative RTI, which is attributed to the decrease of the ablation velocity and the density gradient scale length. The results are helpful for further understanding the influence of high-Z dopant on the radiation-driven ablative RTI.

Modeling of 3D magnetic equilibrium effects on edge turbulence stability during RMP ELM suppression in tokamaks

Recent experimental observations have found turbulent fluctuation structures that are non-axisymmetric in a tokamak with applied 3D fields. In this paper, two fluid resistive effects are shown to produce changes relevant to turbulent transport in the modeled 3D magnetohydrodynamic (MHD) equilibrium of tokamak pedestals with these 3D fields applied. Ideal MHD models are insufficient to reproduce the relevant effects. By calculating the ideal 3D equilibrium using the VMEC code, the geometric shaping parameters that determine linear turbulence stability, including the normal curvature and local magnetic shear, are shown to be only weakly modified by applied 3D fields in the DIII-D tokamak. These ideal MHD effects are therefore not sufficient to explain the observed changes to fluctuations and transport. Using the M3D-C1 code to model the 3D equilibrium, density is shown to be redistributed on flux surfaces in the pedestal when resistive two fluid effects are included, while islands are screened by rotation in this region. The redistribution of density results in density and pressure gradient scale lengths that vary within pedestal flux surfaces between different helically localized flux tubes. This would produce different drive terms for trapped electron mode and kinetic ballooning mode turbulence, the latter of which is expected to be the limiting factor for pedestal pressure gradients in DIII-D.

Plasma turbulence in the equatorial electrojet: A two-dimensional Hamiltonian fluid model

A nonlinear unified fluid model that describes the Equatorial Electrojet, including the Farley-Buneman and gradient-drift plasma instabilities, is defined and shown to be a noncanonical Hamiltonian system. Two geometric constants of motion for the model are obtained and shown to be Casimir invariants. A reformulation of the model shows the roles of the density-gradient scale-length (Ln) and the cross-field drift-velocity (υE) in controlling the dynamics of unstable modes in the growing, transition, and saturation phases of a simulation.

Impurity effects on trapped electron mode in tokamak plasmas

The effects of impurity ions on the trapped electron mode (TEM) in tokamak plasmas are numerically investigated with the gyrokinetic integral eigenmode equation. It is shown that in the case of large electron temperature gradient (ηe), the impurity ions have stabilizing effects on the TEM, regardless of peaking directions of their density profiles for all normalized electron density gradient R/Lne. Here, R is the major radius and Lne is the electron density gradient scale length. In the case of intermediate and/or small ηe, the light impurity ions with conventional inwardly (outwardly) peaked density profiles have stabilizing effects on the TEM for large (small) R/Lne, while the light impurity ions with steep inwardly (outwardly) peaked density profiles can destabilize the TEM for small (large) R/Lne. Besides, the TEM driven by density gradient is stabilized (destabilized) by the light carbon or oxygen ions with inwardly (outwardly) peaked density profiles. In particular, for flat and/or moderate R/Lne, two independent unstable modes, corresponding respectively to the TEM and impurity mode, are found to coexist in plasmas with impurity ions of outwardly peaked density profiles. The high Z tungsten impurity ions play a stronger stabilizing role in the TEM than the low Z impurity ions (such as carbon and oxygen) do. In addition, the effects of magnetic shear and collision on the TEM instability are analyzed. It is shown that the collisionality considered in this work weakens the trapped electron response, leading to a more stable TEM instability, and that the stabilizing effects of the negative magnetic shear on the TEM are more significant when the impurity ions with outwardly peaked density profile are taken into account.

Anticorrelated Emission of High Harmonics and Fast Electron Beams From Plasma Mirrors.

We report for the first time on the anticorrelated emission of high-order harmonics and energetic electron beams from a solid-density plasma with a sharp vacuum interface-plasma mirror-driven by an intense ultrashort laser pulse. We highlight the key role played by the nanoscale structure of the plasma surface during the interaction by measuring the spatial and spectral properties of harmonics and electron beams emitted by a plasma mirror. We show that the nanoscale behavior of the plasma mirror can be controlled by tuning the scale length of the electron density gradient, which is measured insitu using spatial-domain interferometry.

An analytic approach for density gradient injection in laser wake field acceleration

In laser wake field acceleration, it is relatively easy to achieve and control electron injection by adopting a plasma density gradient. This scheme of plasma density gradient injection has been studied in recent years both theoretically and experimentally, but thus far theoretical studies have been done mostly by particle-in-cell simulations. In this paper the density gradient injection and acceleration of electrons are studied with a newly developed analytic approach. The energy threshold for electron injection versus plasma density gradient scale length is given. It is shown that in the plasma density gradient region, the energy threshold of electron injection becomes lower at later times after the driving laser pusle or when the gradient becomes sharper. Evolution of plasma wave's phase velocity and motion of the background electrons in the plasma density gradient are worked out in the linear plasma wave regime, i.e. the normalized laser intensity is a0～1. The energy, the location, and the timing of the injected electrons are obtained. Separatrices of test electrons in the gradient region are obtained by Hamiltonian theory. The influence of injection timing in the density gradient region on the succeeding acceleration in the homogeneous plasma density region is also discussed. It is indicated that whether the injected electrons may be accelerated efficiently or not in the homogeneous region depends on both the energy of the electrons and the phase of the plasma wave at the gradient-to-homogeneous turning point. The analytic results are confirmed by particle-in-cell simulations.

Density Gradient Effect on the Non-Linear Spectrum of the Rayleigh–Taylor Instability

Nonlinear spectrum of the deceleration phase Rayleigh–Taylor instability (RTI) has been investigated in the inertial confinement fusion. Growth rate of the deceleration phase RTI has been expressed well in the form of $$ \upgamma_{\text{k}} =\upalpha_{2} \sqrt {\frac{\text{kg}}{{1 + {\text{kL}}_{\text{m}} }}} -\upbeta_{2} {\text{ku}}_{\text{a}} , $$ where α and β are constants. g, k, L m and u a are the target acceleration, the wave number, the finite density gradient scale length and the ablation velocity, respectively (Betti et al. in Phys Plasmas 5:1446, 1998). Analytically obtained results indicate that the mass power spectrum can be described as an inverse power law with an approximate spectral index of 2.3 in the limit of $$ {\text{kL}}_{0} \ll 1 $$ , where k is the wave number and L 0 is the ablation front thickness and we have shown that power-law slope for kL m ≫ 1 is the most that it is changing with k −4. Furthermore, it has been found that nonlinear power spectrum decreases slowly by increasing of the hot spot radius. Our obtained value is in agreement with theoretical findings (Keskinen et al. in Phys. Plasmas 14:012705, 2007).

Impurity effects on short wavelength ion temperature gradient mode in elongated tokamak plasmas

The effects of impurity ions on the short wavelength ion temperature gradient (SWITG) driven instability in elongated tokamak plasmas are numerically investigated with the gyrokinetic integral eigenmode equation. It is found that for a moderate electron density gradient, the SWITG mode is first destabilized and then stabilized with increasing elongation κ, which is different from the conventional long wavelength ITG mode. For a large electron density gradient, the elongation can effectively stabilize the SWITG mode. Moreover, the low Z impurity ions with inwardly (outwardly) peaked density profiles have stabilizing (destabilizing) effects on the SWITG modes in elongated plasmas. Interestingly, the high Z tungsten impurity ions with inwardly peaked density profiles play a stronger stabilizing role in the SWITG modes than the low Z impurity ions (such as carbon and oxygen) do. In particular, the high Z tungsten impurity ions with a weakly outwardly peaked density profile still have a stabilizing effect. Finally, the critical threshold of impurity density gradient scale length for exciting impurity mode is also numerically obtained, indicating that the impurity mode is harder to be excited in elongated plasmas than in circular ones.