Electrostatic Potential Perturbation Research Articles

Statistics of protein electrostatics.

Molecular dynamics simulations of a small redox-active protein plastocyanin address two questions. (i) Do protein electrostatics equilibrate to the Gibbsian ensemble? (ii) Do the electrostatic potential and electric field inside proteins follow the Gaussian distribution? The statistics of electrostatic potential and electric field are probed by applying small charge and dipole perturbations to different sites within the protein. Nonergodic (non-Gibbsian) sampling is detectable through violations of exact statistical rules constraining the first and second statistical moments (fluctuation-dissipation relations) and the linear relation between free-energy surfaces of the collective coordinate representing the Hamiltonian electrostatic perturbation. We find weakly nonergodic statistics of the electrostatic potential (simulation time of 0.4-1.0 μs) and non-Gibbsian and non-Gaussian statistics of the electric field. A small dipolar perturbation of the protein results in structural instabilities of the protein-water interface and multi-modal distributions of the Hamiltonian energy gap. The variance of the electrostatic potential passes through a crossover at the glass transition temperature Ttr ≃ 170 K. The dipolar susceptibility, reflecting the variance of the electric field inside the protein, strongly increases, with lowering temperature, followed by a sharp drop at Ttr. The linear relation between free-energy surfaces can be directly tested by combining absorption and emission spectra of optical dyes. It was found that the statistics of the electrostatic potential perturbation are nearly Gibbsian/Gaussian, with little deviations from the prescribed statistical rules. On the contrary, the (nonergodic) statistics of dipolar perturbations are strongly non-Gibbsian/non-Gaussian due to structural instabilities of the protein hydration shell.

On anomalous transport of multi-species plasma associated with the resistive ballooning and resistive drift waves driven turbulence

Anomalous transport of multi-species plasma related to the resistive ballooning and resistive drift wave turbulence is considered in a “cold” ion approximation. It is found that similar to the resistive drift wave turbulence [see A. R. Knyazev and S. I. Krasheninnikov, Phys. Plasmas 31, 012502 (2024); and S. I. Krasheninnikov and R. D. Smirnov, Phys. Plasmas (to be published)] the addition of the ballooning drive does not change the main features of anomalous transport of the multi-species plasma: (i) The transport of all ion species is described as a transport of the passive scalars in the turbulent field of the electrostatic potential and electron density perturbation; (ii) the density of ion species with a larger ratio of the mass to charge has the tendency to the accumulation/depletion in the vortices of plasma flow; and (iii) the cross-field transport of all plasma species (including electrons and ions) is described by the same anomalous transport coefficient.

Dimits transition in three-dimensional ion-temperature-gradient turbulence

We extend our previous work on the two-dimensional (2-D) Dimits transition in ion-scale turbulence (Ivanov et al., J. Plasma Phys., vol. 86, 2020, 855860502) to include variations along the magnetic field. We consider a three-field fluid model for the perturbations of electrostatic potential, ion temperature, and ion parallel flow in a constant-magnetic-curvature geometry without magnetic shear. It is derived in the cold-ion, long-wavelength asymptotic limit of the gyrokinetic theory. Just as in the 2-D model, a low-transport (Dimits) regime exists and is found to be dominated by a quasistatic staircase-like arrangement of strong zonal flows and zonal temperature. This zonal staircase is formed and maintained by a negative turbulent viscosity for the zonal flows. Unlike the 2-D model, the three-dimensional (3-D) one does not suffer from an unphysical blow up beyond the Dimits threshold where the staircase becomes nonlinearly unstable. Instead, a well-defined finite-amplitude saturated state is established. This qualitative difference between the 2-D and 3-D models is due to the appearance of small-scale ‘parasitic’ modes that exist only if we allow perturbations to vary along the magnetic field lines. These modes extract energy from the large-scale perturbations and provide an effective enhancement of large-scale thermal diffusion, thus aiding the energy transfer from large injection scales to small dissipative ones. We show that in our model, the parasitic modes always favour a zonal-flow-dominated state. In fact, a Dimits state with a zonal staircase is achieved regardless of the strength of the linear drive, provided the system is sufficiently extended along the magnetic field and sufficient parallel resolution is provided.

Nonlinear simulation and energy analysis of the EAST coherent mode

The EAST coherent modes (CMs) during the inter-ELM phase are simulated by the electromagnetic six-field two-fluid module in BOUT++ framework. The fluctuation level of the electrostatic potential, electron pressure and density perturbations are comparable to the experiments, and the simulated electrostatic perturbation is around two orders of magnitude larger than the magnetic one in EAST CM. The frequency and poloidal wave number are consistent with experiments in the simulations of EAST CM equilibriums. The energy transfer between three-wave coupling indicates that the energy tends to transfer from medium-n to low-n modes in the early nonlinear phase, and the modes coupling effect in the nonlinear saturation phase is larger than that in the early nonlinear phase. Both the energy transfer and bispectral analysis show that the Ni fluctuation tends to generate the ‘single-mode’ coupling and Te tends to be ‘multiple-mode’, which indicates that the collapse of the density profile is larger than the electron temperature. The relative phase analysis is applied to evaluate whether the turbulence can extract the energy from density and temperature profiles. The result indicates that the density profile provides much more energy to drive the turbulence than electron temperature. The kinetic and magnetic energy transfer rates are used to understand the instability and turbulence driving mechanisms of the EAST CM. In the linear phase of the nonlinear simulation, the instability is driven by the peeling-ballooning mode and drift-Alfven wave (DAW), and the radial electric field and shear Alfven wave have large suppressing effects. The turbulence of EAST CM is a predominantly electrostatic mode, which corresponds to the Reynolds stress seven times larger than Maxwell stress. In addition, the effect of the electrostatic part in DAW is much larger than the electromagnetic one.

Gyrokinetic study of collisional resonant magnetic perturbation (RMP)-driven plasma density and heat transport in tokamak edge plasma using a magnetohydrodynamic screened RMP field

The total-f gyrokinetic particle-in-cell code XGC is applied to study various aspects of collisional transport in the tokamak edge pedestal in the presence of resonant magnetic perturbations (RMPs) calculated with M3D-C1. Simulations including the separatrix and scrape-off layer are exercised for a model DIII-D H-mode plasma. Neutral particle recycling is modeled by means of ionization and charge exchange with the plasma. A fully nonlinear Fokker–Planck collision operator is utilized to account for non-Maxwellian edge plasma. The study yields kinetic evidence that (i) neglecting the non-axisymmetric component of the RMP-generated electrostatic potential perturbation could yield a fictitiously high particle pump-out rate in the edge pedestal; that (ii) the experimental level of particle pump-out from the pedestal cannot be provided by collisional transport across Kolmogorov–Arnold–Moser surfaces except across the magnetic separatrix where stochastic magnetic field lines exist; that (iii) the H-mode type electron heat barrier is retained in the steep slope area under the M3D-C1 calculated RMPs; and that (iv) the stochastic electron heat-transport rate around the magnetic separatrix surface is much lower than the prediction by Rechester–Rosenbluth (1978 Phys. Rev. Lett. 40 38–41) and is qualitatively consistent with the experimentally observed rate. Detailed kinetic physics analysis on how the transport fluxes, electrostatic potential perturbation, and -well structure respond to onset of RMPs is also reported.

X-point ion orbit physics in scrape-off layer and generation of a localized electrostatic potential perturbation around X-point

It has been well known that the logarithmically vanishing poloidal magnetic field strength Bθ near the magnetic X-point in a tokamak plasma yields the so-called ion X-loss or X-transport of ions when the ion temperature is high enough [Chang et al., Phys. Plasmas 9, 3884 (2002)], which has a notable impact on the physics just inside the magnetic separatrix surface, e.g., most prominently, to force a well-like structure in the global negative radial electric field and hence a pressure pedestal buildup. In this brief communication, we show that a similar effect exists in the scrape-off (SOL) layer near the X-point that can create a localized electrostatic potential structure around the X-point and have a significant impact on the near-SOL physics.

Modelling and measurement of the electrostatic potential perturbation in consideration of the non-adiabatic electron response to trace tungsten concentration in a tokamak

Trace tungsten ions are almost unavoidable in tokamaks with the tungsten as the first wall material. In high performance plasma, tungsten ions are easily concentrated in the core with a finite gradient along the radius. Prevention of the concentration is an important task for long-pulse H-mode operations. In this paper, it is shown that the tungsten concentration generates electrostatic perturbations due to the bulk electron drift with dissipation. That leads to a phase difference between the electron and the tungsten ion density perturbations. The resultant electrostatic potential extends away from the resonant surface of an internal mode which is characterized by the mode frequency chirping down. This work indicates that the electrostatic potential is mainly determined by the electron kinetics as well as the tungsten-bulk ion collisions, and that the impurity ion dynamics is efficiently influenced by the electron perturbations. Modification of the electron kinetics is a candidate to control the tungsten transport in experiments.

Changes at the Surface Electrostatic Activity is Involved in Infectivity and Elimination of Accumulated Prion Proteins

The results obtained during the study of mutations on the gene coding for the human prion protein showed that the only major consequence of mutations is the perturbation of the protein surface electrostatic potential which subsequently is responsible for the convergence of PrPc to PrPsc. Streptomycin interacting with the prion protein induce electric charge changes on the prion protein surface leading to loss of infectivity as well the formation of small aggregates.

Free Energy Landscape of Cellulose as a Driving Factor in the Mobility of Adsorbed Water.

The diffusion coefficient of water adsorbed in hydrophilic porous materials, such as noncrystalline cellulose, depends on water activity. Faster diffusion at higher water concentrations is observed in experimental and modeling studies. In this paper, two asymptotic water concentrations, near-vacuum and fully saturated, are investigated at the surface of crystalline cellulose with molecular dynamics simulations. An increasing water concentration leads to significant changes in the free energy landscape due to perturbation of local electrostatic potential. Smoothening of strong energy minima, corresponding to sorption sites, and formation of layered structure facilitates water transport in the vicinity of cellulose. The determined transition probabilities and hydrogen bond stability reflect the changes in the energy landscape. As a result of a concentration increase, the emerging basins of attraction and spreading out of those existing in the diluted state lead to an increase in water entropy. Thermal fluctuations of cellulose are demonstrated to rearrange the landscape in the diluted limit, increase adsorbed water entropy, and decrease the water-cellulose H-bond lifetime.

Observation of Oscillatory Radial Electric Field Relaxation in a Helical Plasma

Measurements of the relaxation of a zonal electrostatic potential perturbation in a nonaxisymmetric magnetically confined plasma are presented. A sudden perturbation of the plasma equilibrium is induced by the injection of a cryogenic hydrogen pellet in the TJ-II stellarator, which is observed to be followed by a damped oscillation in the electrostatic potential. The waveform of the relaxation is consistent with theoretical calculations of zonal potential relaxation in a nonaxisymmetric magnetic geometry. The turbulent transport properties of a magnetic confinement configuration are expected to depend on the features of the collisionless damping of zonal flows, of which the present Letter is the first direct observation.

Characterisation of coherent rotating modes in a magnetised plasma column using a mono-sensor tomography diagnostic

In this paper, we report on the core plasma evolution during the rotation of coherent modes in a magnetized plasma column. The study makes use of an original tomographic diagnostic based on a single sensor. The experimental observations demonstrate that the mode shape is constant during the plasma rotation, therefore confirming an a priori assumption of single position measurements. The experimental set-up and the numerical inversion method used to interpret the data are presented. The results are then compared to two-dimensional probe measurements to assess their perturbative character and to give further details on the mode characteristics. A π/2 phase shift between the electrostatic potential and density perturbation is evidenced.

Energetic-particle-induced electromagnetic geodesic acoustic mode in tokamak plasmas

Energetic-particle-induced kinetic electromagnetic geodesic acoustic modes (EKEGAMs) are numerically studied in low β (=plasma pressure/magnetic pressure) tokamak plasmas. The parallel component of the perturbed vector potential is considered along with the electrostatic potential perturbation. The effects of finite Larmor radius and finite orbit width of the bulk and energetic ions as well as electron parallel dynamics are all taken into account in the dispersion relation. Systematic harmonic and ordering analysis are performed for frequency and growth rate spectra of the EKEGAMs, assuming (kρi)∼q−3∼β≪1, where q, k, and ρi are the safety factor, radial component of the EKEGAMs wave vector, and the Larmor radius of the ions, respectively. It is found that there exist critical βh/βi values, which depend, in particular, on pitch angle of energetic ions and safety factor, for the mode to be driven unstable. The EKEGAMs may also be unstable for pitch angle λ0B<0.4 in certain parameter regions. Finite β effect of the bulk ions is shown to have damping effect on the EKEGAMs. Modes with higher radial wave vectors have higher growth rates. The damping from electron dynamics is found decreasing with decrease of the temperature ratio Te/Ti. The modes are easily to be driven unstable in low safety factor q region and high temperature ratio Th/Ti region. The harmonic features of the EKEGAMs are discussed as well.

Theoretical investigations on the enhancing effect of the cation-π interaction on the halogen bond in the M∙∙∙HCCX∙∙∙NH₃ (M = Li⁺, Na⁺, Cu⁺, Ag⁺, Au⁺; X = Cl, Br) complexes.

The M∙∙∙HCCX∙∙∙NH₃ (M = Li⁺, Na⁺, Cu⁺, Ag⁺, Au⁺; X = Cl, Br) complexes were designed to study the influence of cation-π interaction on the X∙∙∙N halogen bonds under M05-2X/aug-cc-pVDZ(PP) level. In comparison with the HCCX∙∙∙NH₃ complexes, the bond distances of the halogen bonds have decreased, and the interaction energies become more negative. The results show that the X∙∙∙N halogen bonds have been strengthened by the cation-π interactions. For different cations, the enhancing effect is more intensive in the order of Au⁺ > Cu⁺ > Ag⁺ > Li⁺ > Na⁺, which indicates that transition metal cations can enhance the halogen bond in a stronger manner. Molecular electrostatic potential and second-order perturbation stabilization energy were calculated to deepen the discussion. In addition, atoms in molecules analysis was performed and the electron density shift was studied.

Ion plasma wave and its instability in interpenetrating plasmas

Some essential features of the ion plasma wave in both kinetic and fluid descriptions are presented. The wave develops at wavelengths shorter than the electron Debye radius. Thermal motion of electrons at this scale is such that they overshoot the electrostatic potential perturbation caused by ion bunching, which consequently propagates as an unshielded wave, completely unaffected by electron dynamics. So in the simplest fluid description, the electrons can be taken as a fixed background. However, in the presence of magnetic field and for the electron gyro-radius shorter than the Debye radius, electrons can participate in the wave and can increase its damping rate. This is determined by the ratio of the electron gyro-radius and the Debye radius. In interpenetrating plasmas (when one plasma drifts through another), the ion plasma wave can easily become growing and this growth rate is quantitatively presented for the case of an argon plasma.

Electromagnetic effects of kinetic geodesic acoustic mode in tokamak plasmas

Electromagnetic effects of the kinetic geodesic acoustic modes (KGAMs) are numerically studied in low β(= plasma pressure/magnetic pressure) tokamak plasmas. The parallel component of the perturbed vector potential is considered along with the electrostatic potential perturbation. The finite Larmor radius and finite orbit width of the ions as well as electron parallel dynamics are all taken into account. Systematic harmonic and ordering analysis is performed for collisionless damping of the KGAMs, assuming β~(κρi)2, where κand ρiare the radial component of the KGAM wave vector and the Larmor radius of the ions, respectively. It is found that the electron parallel dynamics enhances the damping of the electrostatic KGAM modes when the safety factor q is high. In addition, the electromagnetic (finite β effect is revealed to enhance and weaken the damping of the modes in plasmas of low and high safety factor q~2.0 and 5.5, respectively. The harmonic features of the KGAMs are discussed as well.

Gyrokinetic Simulations of Slab Ion Temperature Gradient Turbulence with Kinetic Electrons

Ion temperature gradient (ITG) driven turbulence is investigated by means of gyrokinetic simulations which include both kinetic ions and electrons in slab geometry with uniform equilibrium magnetic field. The study confirms that numerical results satisfy the entropy balance equation including both ions and electrons. The entropy variable is transferred from ions to electrons through the perturbation of electrostatic potential, and the transferred fluctuation is diffused by the electron collision dissipation. In the ITG turbulence with kinetic electrons ion heat diffusion is larger than that with adiabatic electrons. The former is close to the latter when the ion mass is comparable to or larger than the hydrogen one. The difference between the transport coefficients does not originate from the suppression of turbulence by zonal flow, but stems from the difference between their spectra. The lowest wavenumber mode dominates the coefficient in the adiabatic electron case, while the transport is caused not only by the the lowest mode but by higher wavenumbers in the kinetic electron cases.

Magnetosheath excursion and the relevant transport process at the magnetopause

Abstract. A large-amplitude excursion of the magnetosheath (MS) in quiet solar wind conditions on 17 March 2004 was recorded simultaneously by the Cluster and TC-1 spacecraft. During this period, the IMF Bz was entirely northward. The coherence between the bow shock motion and magnetopause (MP) motion is revealed and the excursion velocities of the bow shock motion are analyzed. In addition, the relevant plasma transport phenomenon in the form of flux fluctuations below the ion gyrofrequency at the MP is exposed and is interpreted as manifestation of the drift instability. Correlated observations on charge accumulation and electrostatic potential perturbation are recorded by electron measurements in high energy regime, and also the eventual cross-field vortex motion in the nonlinear stage and the consequential mass exchange are exhibited. The present investigation gives some new insight into the MS plasma transport mechanism across the subsolar MP region in quiet solar wind conditions during a period of northward IMF.

Multiple polarization of geodesic curvature induced modes

Dispersion relations for geodesic acoustic modes are derived by using the Grad hydrodynamic equations thereby reconciling long known but not previously explained discrepancy between the results of kinetic and fluid calculations. Extended fluid theory allows a simple analysis of mode polarization and coupling. A new type of electromagnetic modes induced by geodesic compressibility is predicted. These modes are related to Alfvén and geodesic acoustic modes. While a standard geodesic acoustic mode involves poloidally and toroidally symmetric perturbations of electrostatic potential ( m = n = 0 ) and the first poloidal side-bands of plasma pressure, new modes involve side-bands of the electrostatic and vector potential as well as pressure perturbations at zeroth and second harmonics. It is shown that there exist two different values of the adiabatic constant depending on the mode polarization. Both standard (electrostatic) geodesic acoustic modes and new electromagnetic modes involve finite perturbations of parallel viscosity, which modify an effective adiabatic (compressibility) index for a toroidal plasma.

Low frequency electrostatic waves in weakly inhomogeneous magnetoplasma modeled by Lorentzian (kappa) distributions

Linear dispersion relations for electrostatic waves in spatially inhomogeneous, current-carrying anisotropic plasma, where the equilibrium particle velocity distributions are modeled by various Lorentzian (kappa) distributions and by well-known bi-Maxwellian distribution, are presented. Spatial inhomogeneities, assumed to be weak, include density gradients, temperature gradients, and gradients (shear) in the parallel (to the ambient magnetic field) flow velocities associated with the current. In order to illustrate the distinguishing features of the kappa distributions, stability properties of the low frequency (lower than ion cyclotron frequency) and long perpendicular wavelength (longer than ion gyroradius) modes are studied in detail, and the results are contrasted with those for the bi-Maxwellian distribution. Specific attention is given to the drift waves, the current-driven ion-acoustic waves in the presence of velocity shear, the velocity shear-driven ion-acoustic modes, and the ion temperature-gradient driven modes. Growth rates of the drift wave instability and the current-driven ion-acoustic instability are reduced from their values for bi-Maxwellian distribution due to larger ion Landau damping rates associated with the kappa distributions. For the same reason, excitation conditions for these two instabilities are more stringent in the case of the kappa distributions. Growth rates of the velocity shear-driven ion-acoustic instability and the ion temperature-gradient driven instability are reduced from their values for bi-Maxwellian distribution as a consequence of the reduced adiabatic response of the electrons to the electrostatic potential perturbation. Frequencies of the drift waves and the ion-acoustic waves are also reduced in kappa-distribution plasmas due to the reduced adiabatic response of the electrons.

Rotochemical Heating of Neutron Stars: Rigorous Formalism with Electrostatic Potential Perturbations

The electrostatic potential that keeps approximate charge neutrality in neutron star matter is self-consistently introduced into the formalism for "rotochemical heating" presented in a previous paper by Fernández and Reisenegger. Although the new formalism is more rigorous, we show that its observable consequences are indistinguishable from those of the previous one, leaving the conclusions of the previous paper unchanged.