Momentum Diffusion Coefficient Research Articles

Electron Scattering by Very‐Low‐Frequency and Low‐Frequency Waves From Ground Transmitters in the Earth's Inner Radiation Belt and Slot Region

AbstractThe very‐low frequency (VLF) and low frequency (LF) waves from ground transmitters propagate in the ionospheric waveguide, and a portion of their power leaks to the Earth's inner radiation belt and slot region where it can cause electron precipitation loss. Using Van Allen Probes observations, we perform a survey of the VLF and LF transmitter waves at frequencies from 14 to 200 kHz. The statistical electric and magnetic wave amplitudes and frequency spectra are obtained at 1 < L < 3. Based on a recent study on the propagation of VLF transmitter waves, we divide the total wave power into ducted and unducted portions, and model the wave normal angle of unducted waves with dependences on L shell, magnetic latitude, and wave frequency. At lower frequencies, the unducted waves are launched along the vertical direction and the wave normal angle increases during the propagation until reaching the Gendrin angle; at higher frequencies, the normal angle of unducted waves follows the variation of Gendrin angle. We calculate the bounce‐averaged pitch angle and momentum diffusion coefficients of electrons due to ducted and unducted VLF and LF waves. Unducted and ducted waves cause efficient pitch angle scattering at L = 1.5 and 2.5, respectively. Although the wave power from ground transmitters at frequencies higher than 30 kHz is low, these waves can cause the pitch angle scattering of lower energy (2–200 keV at L = 1.5) electrons, which cannot resonate with the VLF transmitter waves at frequencies below 30 kHz, lightning generated whistlers, or plasmaspheric hiss.

Drag of heavy quarks in an anisotropic QCD medium beyond the static limit

Heavy quark dynamics in an anisotropic QCD medium have been analyzed within the Fokker-Planck approach. Heavy quark drag force and the momentum diffusion tensor have been decomposed by employing a general tensor basis for an anisotropic medium. Depending upon the relative orientation of the direction of the momentum anisotropy of the medium and heavy quark motion, two drag and four diffusion coefficients have been estimated in the anisotropic QCD medium. The relative significance of different components of drag and momentum diffusion coefficients has been explored. The dependence of the angle between the anisotropic vector and heavy quark motion to the drag and diffusion coefficients has also been studied. Furthermore, the energy loss of heavy quarks due to the elastic collisional process in an anisotropic medium has been studied. It is seen that the anisotropic contributions to heavy quark transport coefficients and its collisional energy loss have a strong dependence on the direction and strength of momentum anisotropy in the QCD medium.

Heavy quark dynamics in a strongly magnetized medium

We present a calculation of the heavy quark momentum diffusion coefficients in a strongly magnetized medium, within the Lowest Landau Level (LLL) approximation. In particular, we use the Hard Thermal Loop (HTL) resummed effective gluon propagator, generalized for a hot and magnetized medium. Using this effective HTL gluon propagator along with the LLL quark propagator we analytically derive the full results for the longitudinal and transverse momentum diffusion coefficients for charm and bottom quarks beyond the static limit. Going beyond the static limit of the heavy quark, we also show numerical results for these coefficients in two special cases where the heavy quark is moving either parallel or perpendicular to the external magnetic field.

Spectral reconstruction details of a gradient-flowed color-electric correlator

In a recently published work we provide a proof-of-concept of a novel method to extract the heavy quark momentum diffusion coefficient from color-electric correlators on the lattice using gradient flow. The transport coefficient can be found in the infrared limit of the corresponding spectral function which is reconstructed through perturbative model fits of the correlator data. In this proceedings report we want to give more detailed insights into the systematic uncertainties of this procedure and compare our results with other studies.

Heavy quark transport coefficients in a viscous QCD medium with collisional and radiative processes

The heavy quark drag and momentum diffusion coefficients in the presence of both the collisional and radiative processes have been studied in a hot viscous QCD medium. The thermal medium effects are incorporated by employing the effective fugacity quasiparticle model based on the lattice QCD equation of state. Viscous effects are embedded into the heavy quark transport through the near-equilibrium distribution functions of the constituent medium particles of the quark-gluon plasma. The viscous corrections to the momentum distributions have been estimated from the effective Boltzmann equation. The effect of shear viscous correction to drag and diffusion is investigated by considering the soft gluon radiation by heavy quarks along with the elastic collisional processes of the heavy quark with the light quarks and gluons within the QGP medium. The momentum and temperature dependence of the heavy quark transport coefficients are seen to be sensitive to the viscous coefficient of the QGP for the collisional and radiative processes. The collisional and radiative energy loss of the heavy quark in the viscous quark-gluon plasma has also been explored.

Application of transient transport analysis method for modulation experiment

A transient TRansport Analysis method for Modulation (t-TRAM) has been developed. This method consists of two methods. One is an instantaneous modulation analysis method using the Hilbert transform (HT) with the analytical mode decomposition (AMD). In the modulation experiments, plasma transport can be changed periodically by modulated external input. Profiles of the modulation amplitude and phase change in time due to the change in the plasma transport. The HT with AMD method can evaluate an instantaneous analytic signal in the presence of changes in the modulation amplitude and phase in time. The other is a transport analysis method to evaluate the diffusion coefficient and the convection velocity from the analytic signal. The t-TRAM has enabled us to evaluate a momentum diffusion coefficient and momentum convection velocity in the presence of a momentum source. The t-TRAM is applied to momentum modulation experiments in JT-60U. The evaluation reveals that a normalized momentum flux has a linear dependence on a normalized momentum gradient during a half cycle of the modulation.

Particle diffusion and acceleration in magnetorotational instability turbulence

ABSTRACT Hot accretion flows contain collisionless plasmas that are believed to be capable of accelerating particles to very high energies, as a result of turbulence generated by the magnetorotational instability (MRI). We conduct unstratified shearing-box simulations of the MRI turbulence in ideal magnetohydrodynamic (MHD), and inject energetic relativistic test particles in simulation snapshots to conduct a detailed investigation on particle diffusion and stochastic acceleration. We consider different amount of net vertical magnetic flux, with sufficiently high resolution to resolve the gyro-radii (Rg) of most particles. Particles with large Rg (≳ 0.03 disc scale height H) show spatial diffusion coefficients of ∼30 and ∼5 times Bohm values in the azimuthal and poloidal directions, respectively. We further measure particle momentum diffusion coefficient D(p) by applying the Fokker–Planck equation, finding that contribution from turbulent fluctuations scales as D(p) ∝ p, and shear acceleration takes over when Rg ≳ 0.1H, characterized by D(p) ∝ p3. For particles with smaller Rg (≲ 0.03H), their spatial diffusion coefficients roughly scale as ∼p−1, and show evidence of D(p) ∝ p2 scaling in momentum diffusion but with large uncertainties. We find that multiple effects contribute to stochastic acceleration/deceleration, and the process is likely affected by intermittency in the MRI turbulence. We also discuss the potential of accelerating PeV cosmic rays in hot accretion flows around supermassive black holes.

Evolution of the velocity distribution of atoms under the action of the bichromatic force

We study numerically the evolution of the velocity distribution of atoms under the action of the bichromatic force. The comparison of the time dependencies of the distribution width and the average acceleration of atoms reveal the correlation of these quantities. We show that the estimation of the momentum diffusion coefficient on the basis of the analogy between the interaction of atoms with the counter-propagating bichromatic waves and the interaction of atoms with the counter-propagating sequences of the $\pi$-pulses roughly corresponds to the results of numerical calculations. To separate the influence of the momentum diffusion on the evolution of atomic momentum distribution from the influence of the time-dependent Doppler shift, we study the motion of a ``heavy'' atom, for which the velocity change during the interaction of an atom with the field can be neglected. Provided that the parameters of the atom-field interaction are optimal, we show that the momentum diffusion coefficient is proportional to the intensity of the laser radiation. We used the Monte Carlo wave-function method for the numerical simulation of the atomic motion.

Heavy quark momentum diffusion from the lattice using gradient flow

We apply the gradient flow on a color-electric two-point function that encodes the heavy quark momentum diffusion coefficient. The simulations are done on fine isotropic lattices in the quenched approximation at $1.5{T}_{c}$. The continuum extrapolation is performed at fixed flow time followed by a second extrapolation to zero flow time. Perturbative calculations of this correlation function under Wilson flow are used to enhance the extrapolations of the nonperturbative lattice correlator. The final estimate for the continuum correlator at zero flow time largely agrees with one obtained from a previous study using the multilevel algorithm. We perform a spectral reconstruction based on perturbative model fits to estimate the heavy quark momentum diffusion coefficient. The approach we present here yields high-precision data for the correlator and is also applicable for actions with dynamical fermions.

Heavy quark momentum diffusion coefficient in 3D gluon plasma

We study the heavy-quark momentum diffusion coefficient in far from equilibrium gluon plasma in a self-similar regime using real-time lattice techniques. We use 3 methods for the extraction: an unequal time electric field 2-point correlator integrated over the time difference, a spectral reconstruction (SR) method based on the measured equal time electric field correlator and a kinetic theory (KT) formula. The time-evolution of the momentum diffusion coefficient extracted using all methods is consistent with an approximate t−12 power law. We also study the extracted diffusion coefficient as a function of the upper limit of the time integration and observe that including the infrared enhancement of the equal-time correlation function in the SR calculation improves the agreement with the data for transient time behavior considerably. This is a gauge invariant confirmation of the infrared enhancement previously observed only in gauge fixed correlation functions.

Hydrodynamics of simply spinning black holes & hydrodynamics for spinning quantum fluids

We find hydrodynamic behavior in large simply spinning five-dimensional Anti-de Sitter black holes. These are dual to spinning quantum fluids through the AdS/CFT correspondence constructed from string theory. Due to the spatial anisotropy introduced by the angular momentum, hydrodynamic transport coefficients are split into groups longitudinal or transverse to the angular momentum, and aligned or anti-aligned with it. Analytic expressions are provided for the two shear viscosities, the longitudinal momentum diffusion coefficient, two speeds of sound, and two sound attenuation coefficients. Known relations between these coefficients are generalized to include dependence on angular momentum. The shear viscosity to entropy density ratio varies between zero and 1/(4π) depending on the direction of the shear. These results can be applied to heavy ion collisions, in which the most vortical fluid was reported recently. In passing, we show that large simply spinning five-dimensional Myers-Perry black holes are perturbatively stable for all angular momenta below extremality.

Lattice QCD constraints on the heavy quark diffusion coefficient

We report progress towards computing the heavy quark momentum diffusion coefficient from the correlator of two chromo-electric fields attached to a Polyakov loop in pure SU(3) gauge theory. Using a multilevel algorithm and tree-level improvement, we study the behavior of the diffusion coefficient as a function of temperature in the wide range $1.1 < T / T_c < 10^4$ in order to compare it to perturbative expansions at high temperature. We find that within errors the lattice results are remarkably compatible with the next-to-leading order perturbative result.

Stochastic acceleration in the relativistic jets of BL Lacertae objects

BL Lacertae objects (BL Lacs) constitute a rare class of active galactic nuclei (AGNs) with the extreme observational features attributed to the Doppler-boosted emission from the relativistic jets, closely aligned along our line-of-sight. The spectral energy distribution (SED), extending over 17–19 orders of the frequency from the radio to the TeV energy range, is of nonthermal origin and shows a typical two-component structure. The lower-energy component, which ranges from the radio to the X-ray frequencies, is widely accepted to be a synchrotron radiation emitted by relativistic electrons. The latter can be accelerated and collimated via the Blandford-Znajek mechanism or magneto-hydrodynamic processes in the vicinity of the central super-massive black hole. However, the accelerated particles should loose the energy, sufficient for the emission of the KeV-TeV photons, very quickly and they require an additional acceleration via the mechanisms operating locally in the jet. According to the different studies and simulations, particles can undergo a strong stochastic (second-order Fermi) acceleration due to the resonant scattering of the magnetohydrodynamic waves, representing the turbulent magnetic irregularities. On the other hand, the jet turbulence can be strongly amplified due to the interaction between the shock front and the density inhomogeneities in the pre-shock relativistic jet fluid. Our intense X-ray spectral study of TeV-detected, bright BL Lacs (Mrk 421, 1ES 1959 + 650, Mrk 501) often demonstrate the signatures of the efficient stochastic acceleration (a low spectral curvature and different correlations expected within the stochastic process). We have also detected the cases when these sources show the relation between the synchrotron SED peak location Ep and peak height Sp in the form Sp∝Epα with the values of the exponent close to 0.6. The latter is expected when the momentum-diffusion coefficient and the turbulence spectrum are variable during the stochastic acceleration process: there is a transition from the Kraichnan-type into the hard-sphere turbulence.

Experimental investigation of lower hybrid current drive induced plasma rotation on the experimental advanced superconducting tokamak

Rotation and its shear can reduce the magnetohydrodynamic instabilities and enhance the confinement. The LHCD has been proposed as a possible means of rotation driving on a future fusion reactor. Exploring the mechanisms of LHCD rotation driving on the current tokamaks can provide important reference for future reactors. On EAST, it was previously shown that 2.45 GHz LHCD can drive plasma toroidal rotation and the change of edge plasma rotation leads the co-current core rotation to increase. At higher frequency, 4.6 GHz lower hybrid wave can more effectively drive co-current plasma toroidal rotation. On EAST, at the lower current, the effects of different LHCD power on plasma toroidal rotation are analyzed. Higher power LHCD has a better driving efficiency. The effect of safety factor (&lt;i&gt;q&lt;/i&gt;) profile on toroidal rotation is also presented. The LHCD can change the profile of safety factor due to current drive. It is found that when the power exceeds 1.4MW, the &lt;i&gt;q&lt;/i&gt; profile remains unchanged and the rotation changes only very slightly with LHCD power, suggesting that the current profile is closely related to rotation. In order to further analyze the dynamic process of plasma toroidal rotation driven by lower hybrid current drive on EAST, the toroidal momentum transport due to LHCD is deduced by using the modulated LHCD power injection. Based on the momentum balance equation, the toroidal momentum diffusion coefficient (&lt;i&gt;χ&lt;/i&gt;&lt;i&gt;&lt;sub&gt;φ&lt;/sub&gt;&lt;/i&gt;) and the toroidal momentum pinch coefficient (&lt;i&gt;V&lt;/i&gt;&lt;sub&gt;pinch&lt;/sub&gt;) are obtained by the method of separation of variables and Fourier analysis for the region where the external momentum source can be ignored. It is found that the momentum diffusion coefficient (&lt;i&gt;χ&lt;/i&gt;&lt;sub&gt;&lt;i&gt;φ&lt;/i&gt;&lt;/sub&gt;) and momentum pinch coefficient (&lt;i&gt;V&lt;/i&gt;&lt;sub&gt;pinch&lt;/sub&gt;) tend to increase from the core to the outer region. This is consistent with the characteristic that the toroidal rotation velocity first changes in the outer region and then propagates to the core when the toroidal rotation is driven by LHCD.

Gyrofluid modeling of magnetosphere in feedback instability

Feedback instability occurs in a coupling system of the magnetosphere and the ionosphere, and is a theoretical model explaining spontaneous development of the quiet aurora. In this study, we extend a model of the magnetosphere in the feedback instability to the gyrofluid model. This extension makes it possible to properly discuss kinetic effects, such as the finite Larmor radius effect, the Landau damping, and the mirror force, on the feedback instability in a framework of a fluid model. The derived model is applied to linear stability analysis of the low-frequency feedback instability in the absence of the mirror force. An analytical expression of the parallel electron momentum diffusion coefficient associated with the electron Landau damping is obtained by considering a Landau-fluid closure model. It is found that high-wavenumber modes are strongly affected by the finite ion Larmor radius effect and the electron Landau damping. In particular, a stabilizing effect of the electron Landau damping is dominant and stronger for high-parallel-wavenumber modes. This result indicates that the lowest-parallel-wavenumber mode primarily grows during the spontaneous development of the quiet aurora.

Transport coefficients from in-medium quarkonium dynamics

The in medium dynamics of heavy particles are governed by transport coefficients. The heavy quark momentum diffusion coefficient, $\kappa$, is an object of special interest in the literature, but one which has proven notoriously difficult to estimate, despite the fact that it has been computed by weak-coupling methods at next-to-leading order accuracy, and by lattice simulations of the pure SU(3) gauge theory. Another coefficient, $\gamma$, has been recently identified. It can be understood as the dispersive counterpart of $\kappa$. Little is known about $\gamma$. Both $\kappa$ and $\gamma$ are, however, of foremost importance in heavy quarkonium physics as they entirely determine the in and out of equilibrium dynamics of quarkonium in a medium, if the evolution of the density matrix is Markovian, and the motion, quantum Brownian; the medium could be a strongly or weakly coupled plasma. In this paper, using the relation between $\kappa$, $\gamma$ and the quarkonium in medium width and mass shift respectively, we evaluate the two coefficients from existing 2+1 flavor lattice QCD data. The resulting range for $\kappa$ is consistent with earlier determinations, the one for $\gamma$ is the first non-perturbative determination of this quantity.

Strongly coupled N=4 supersymmetric Yang-Mills plasma on the Coulomb branch. II. Transport coefficients and hard probe parameters

We study $\mathcal{N} = 4$ super Yang-Mills theory on the Coulomb branch (cSYM) by using its Type IIB supergravity dual. We compute the transport coefficients, and hard probe parameters of $\mathcal{N} = 4$ cSYM at finite temperature $T$. We use the rotating black 3-brane solution of Type IIB supergravity with a single non-zero rotation parameter $r_{0}$ after analytically continuing $r_{0}\rightarrow -ir_{0}$, and in an ensemble where the Hawking temperature $T$ and a scalar condensate $<\mathcal{O}>\sim r_{0}^4$ are held fixed. We find that the bulk viscosity to entropy density ratio of the large black hole branch decreases with temperature and has a maxima around the critical temperature $T_{c}$ while, for the small black hole branch, it increases with temperature. The other transport coefficients and parameters of hard probes, such as the conductivity, jet quenching parameter, drag force, and momentum diffusion coefficients of the large black hole branch increase with temperature and asymptote to their conformal value while, for the small black hole branch, they decrease with temperature.

Full O(a) improvement in electrostatic QCD

EQCD is a 3D bosonic theory containing SU(3) and an adjoint scalar, which efficiently describes the infrared, nonperturbative sector of hot QCD and which is highly amenable to lattice study. We improve the matching between lattice and continuum EQCD by determining the final unknown coefficient in the O(a) matching, an additive scalar mass renormalization. We do this numerically by using the symmetry-breaking phase transition point of the theory as a line of constant physics. This prepares the ground for a precision study of the transverse momentum diffusion coefficient C(qperp) within this theory. As a byproduct, we provide an updated version of the EQCD phase diagram.

Rotation braking with n = 1 nonaxisymmetric magnetic perturbation in the EAST tokamak

The toroidal plasma rotation braking effect during the application of n = 1 static resonant magnetic perturbation is studied by momentum transport analysis in the EAST tokamak. The braking torque shows a global profile and two peaks located near the plasma core and the edge, respectively. The effect of momentum diffusion contributes significantly to the calculated torque. Simulation results with the obtained torque and momentum diffusion coefficients well reproduce the observed plasma rotation evolution. Neoclassical toroidal viscosity (NTV) torque is modeled for comparison with the experimental torque. The total integrated NTV torque is around −0.12 Nm, which is comparable to the observed braking torque (around −0.33 Nm). In the plasma edge, there is a peak in the NTV torque profile, which agrees well in amplitude with the obvious peak in the observed torque density profile. An additional peak in the NTV torque profile due to the ion bounce resonance is also located in the core region. However, the magnitude of this peak is much smaller than the observed one near the plasma core.

Quarkonium dissociation in perturbative QCD

For weakly bound quarkonia, we rederive the next-to-leading order cross sections of quarkonium dissociation by partons that include the hard thermal loop (HTL) resummation. Our results calculated with an effective vertex from the Bethe-Salpeter amplitude reduce to those obtained by potential nonrelativistic QCD (pNRQCD) in the relevant kinematical limit, and they can be used in a wide temperature range applicable to heavy quark systems in heavy ion collisions. Based on the lattice computation of the temperature-dependent binding energy, our numerical analysis on $\Upsilon(1S)$ indicates that at high temperature the dominant mechanism for quarkonium dissociation is inelastic parton scattering as expected in the quasifree approximation, while it is the gluo-dissociation at low temperature. By comparing with the momentum diffusion coefficient of a heavy quark, we discuss possible O(g) corrections to the next-to-leading order thermal width.