Landau damping of collective mode in a quasi-two-dimensional repulsive Bose-Einstein condensate

We investigate the Landau damping of the collective mode in a quasi-two-dimension repulsive Bose-Einstein condensate by using the self-consistent time-dependent Hatree-Fock-Bogoliubov approximation and a complete and orthogonal eigenfunction set for the elementary excitation of the system. We calculate the three-mode coupling matrix element between the collective mode and the thermal excited quasi-particles and the Landau damping rate of the collective mode. We discuss the dependence of the Landau damping on temperature, on atom number in the condensate, on transverse trapping frequency and on the length of the condensate. The energy width of the collective mode is taken into account in our calculation. With little approximation, our theoretic calculation results agree well with the experimental ones and are helpful for deducing the damping mechanics and the inter-particle interaction.

Landau damping and frequency-shift of a quadrupole mode in a disc-shaped rubidium Bose–Einstein condensate

The damping and frequency-shift in Landau mechanism of a quadrupole mode in a disc-shaped rubidium Bose-Einstein condensate are investigated by using the Hartree-Fock-Bogoliubov approximation. The practical relaxations of the elementary excitations and the orthometric relation among them are taken into account to obtain advisable calculation formula for damping as well as frequency-shift. The first approximation of Gaussian distribution function is employed for the ground-state wavefunction to suitably eliminate the divergence of the analytic three-mode coupling matrix elements. According to these methods, both Landau damping rate and frequency-shift of the quadrupole mode are analytically calculated. In addition, all the theoretical results agree with the experimental ones.

Landau damping of collective modes in a harmonically trapped Bose-Einstein condensate

This paper proposes a method for calculating the Landau damping of a low-energy collective mode in a harmonically trapped Bose-Einstein condensate. Based on the divergence-free analytical solutions for ground-state wavefunction of the condensate and eigenvalues and eigenfunctions for thermally excited quasiparticles, obtained beyond Thomas-Fermi approximation, this paper calculates the coupling matrix elements describing the interaction between the collective mode and the quasiparticles. With these analytical results this paper evaluates the Landau damping rate of a monopole mode in a spherical trap and discusses its dependence on temperature, particle number and trapping frequency of the system.

Landau damping of longitudinal oscillation in ultra-relativistic plasmas with nonextensive distribution

The generalized dispersion equation for longitudinal oscillation in an unmagnetized, collisionless, isotropic and relativistic plasma is derived in the context of nonextensive q-distribution. An analytical expression for the Landau damping is obtained in an ultra-relativistic regime, which is related to q-parameter. In the limit q →1, the result based on the relativistic Maxwellian distribution is recovered. It is shown that the interactions between the wave and particles are stronger and the waves are more strongly damped for lower values of q-parameter. The results are explained by the increased number of superthermal particles or low velocity particles contained in the plasma with the nonextensive distribution.

Landau damping in a bounded magnetized plasma column

The damping decrement of Landau damping and the effect of thermal velocity on the frequency spectrum of a propagating wave in a bounded plasma column are investigated.The magnetized plasma column partially filling a cylindrical metallic tube is considered to be collisionless and non-degenerate.The Landau damping is due to the thermal motion of charge carriers and appears whenever the phase velocity of the plasma waves exceeds the thermal velocity of carriers.The analysis is based on a self-consistent kinetic theory and the solutions of the wave equation in a cylindrical plasma waveguide are presented using Vlasov and Maxwell equations.The hybrid mode dispersion equation for the cylindrical plasma waveguide is obtained through the application of appropriate boundary conditions to the plasma-vacuum interface.The dependence of Landau damping on plasma parameters and the effects of the metallic tube boundary on the dispersion characteristics of plasma and waveguide modes are investigated in detail through numerical calculations.

Ion Heating from Nonlinear Landau Damping of High Mode Number Toroidal Alfvén Eigenmodes

Bulk ion heating rate from nonlinear Landau damping of high mode number Toroidal Alfven Eigenmodes （TAEs） is calculated in the frame work of weak turbulence theory. The heating rate is lower than the nonlinear spectral transfer rate to more stable modes, but relatively insensitive to the details of linear damping mechanisms.

Effect on Landau damping rates for a non-Maxwellian distribution function consisting of two electron populations

In many physical situations where a laser or electron beam passes through a dense plasma,hot low-density electron populations can be generated,resulting in a particle distribution function consisting of a dense cold population and a small hot population.Presence of such low-density electron distributions can alter the wave damping rate.A kinetic model is employed to study the Landau damping of Langmuir waves when a small hot electron population is present in the dense cold electron population with non-Maxwellian distribution functions.Departure of plasma from Maxwellian distributions significantly alters the damping rates as compared to the Maxwellian plasma.Strong damping is found for highly nonMaxwellian distributions as well as plasmas with a higher density and hot electron population.Existence of weak damping is also established when the distribution contains broadened flat tops at the low energies or tends to be Maxwellian.These results may be applied in both experimental and space physics regimes.

Analysis of Landau damping in radially inhomogeneous plasma column

The Landau damping behavior in a cylindrical inhomogeneous warm magnetized plasma waveguide has been studied.The radial inhomogeneity for different characteristic lengths（L0） with strong spatial dispersion has been taken into account.The analyses have been considered for two limits ωce 〈 ωpe and ωce 〉 ωpe. Due to the radial inhomogeneity of the plasma, all essential equations for studying the Landau damping are calculated in the Bessel–Furrier and differential Bessel–Furrier expansions. The dependence of Landau damping on the inhomogeneity, temperature and external magnetic field for electrostatic modes is scrutinized and described in detail through numerical calculations. The associated numerical results are presented and discussed.

Magnetic-island-induced ion temperature gradient mode： Landau damping, equilibrium magnetic shear and pressure flattening effects

Characteristics of the magnetic-island-induced ion temperature gradient （MITG） mode are studied through gyrofluid simulations in the slab geometry, focusing on the effects of Landau damping, equilibrium magnetic shear （EMS）, and pressure flattening. It is shown that the magnetic island may enhance the Landau damping of the system by inducing the radial magnetic field. Moreover, the radial eigenmode numbers of most MITG poloidal harmonics are increased by the magnetic island so that the MITG mode is destabilized in the low EMS regime. In addition, the pressure profile flattening effect inside a magnetic island hardly affects the growth of the whole MITG mode, while it has different local effects near the O-point and the X-point regions. In comparison with the non-zero-order perturbations, only the quasi-linear flattening effect due to the zonal pressure is the effective component to impact the growth rate of the mode.

Effects of Landau damping and collision on stimulated Raman scattering with various phase-space distributions

Stimulated Raman scattering(SRS)is one of the main instabilities affecting success of fusion ignition.Here,we study the relationship between Raman growth and Landau damping with various distribution functions combining the analytic formulas and Vlasov simulations.The Landau damping obtained by Vlasov-Poisson simulation and Raman growth rate obtained by Vlasov-Maxwell simulation are anti-correlated,which is consistent with our theoretical analysis quantitatively.Maxwellian distribution,flattened distribution,and bi-Maxwellian distribution are studied in detail,which represent three typical stages of SRS.We also demonstrate the effects of plateau width,hot-electron fraction,hot-to-cold electron temperature ratio,and collisional damping on the Landau damping and growth rate.They gives us a deep understanding of SRS and possible ways to mitigate SRS through manipulating distribution functions to a high Landau damping regime.

Landau damping of twisted waves in Cairns distribution with anisotropic temperature

The consideration of orbital angular momentum of an electric field(twisted mode)is applied to the kinetic theory of plasma.The linearized Vlasov–Poisson equation is solved for the anisotropic thermal distributed bi-Maxwellian and Cairns distributions of electrons to obtain the damping rates of twisted waves.The dispersion relation and Landau damping of Langmuir twisted modes are obtained.The presence of twisted modes opens up two more possibilities in Landau damping and dispersion relations.This may generate a mixture with ion sound waves.It seems to play the role of a control parameter of Landau damping.

Nonlinear Landau damping of high frequency waves in non-Maxwellian plasmas

Space plasmas often possess non-Maxwellian distribution functions which have a significant effect on the plasma waves. When a laser or electron beam passes through a dense plasma, hot low density electron populations can be generated to alter the wave damping/growth rate. In this paper, we present theoretical analysis of the nonlinear Landau damping for Langmuir waves in a plasma where two electron populations are found. The results show a marked difference between the Maxwellian and non-Maxwellian instantaneous damping rates when we employ a non-Maxwellian distribution function called the generalized （r, q） distribution function, which is the generalized form of the kappa and Maxwellian distribution functions. In the limiting case of r = 0 and q→∞, it reduces to the classical Maxwellian distribution function, and when r = 0 and q→k ＋1, it reduces to the kappa distribution function.

Landau damping in a dipolar Bose–Fermi mixture in the Bose–Einstein condensation(BEC) limit

By using a mean-field approximation which describes the coupled oscillations of condensate and noncondensate atoms in the collisionless regime, Landau damping in a dilute dipolar Bose-Fermi mixture in the BEC limit where Fermi superfluid is treated as tightly bounded molecules, is investigated. In the case of a uniform quasi-two-dimensional （2D） case, the results for the Landau damping due to the Bose-Fermi interaction are obtained at low and high temperatures. It is shown that at low temperatures, the Landau damping rate is exponentially suppressed. By increasing the strength of dipolar interaction, and the energy of boson quasiparticles, Landau damping is suppressed over a broader temperature range.

Landau Damping of Collective Mode in a Quasi-One-Dimensional Repulsive Bose-Einstein Condensate

We investigate the Landau damping of the collective mode in a quasi-one-dimensional repulsive Bose-Einstein condensate by using the self-consistent time-dependent Hartree-Fock-Bogoliubov approximation.We put forward a new method to calculate the Landau damping rate of the collective mode in the condensate and discuss the dependence of the Landau damping on temperature,on transverse trapping frequency,on atom number in the condensate,and on length of the system.Different from the usual calculation method for the three dimension system,our new calculation method is an interactive one by considering the practical relaxation of the elementary excitation.With little approximation,our theoretical calculation results agree with the experimental ones.Comparing with the usual calculation method,our theory is helpful to deduce the inter-particle interactions in damping phenomenon.

Critical Initial Amplitude of Langmuir Wave Damping

By one-dimensional Vlasov-Poisson simulation, the critical initial state marking the transition between the Landau scenario, in which the electric fields definitively damped to zero and the O＇NEIL scenario, in which the Landau damping is stopped after a certain damping stage, is studied. It is found that the critical initial amplitude e＊ can only exist when the product of the wave number （k~） and the electron thermal velocity （vth） is moderate, that is, 0.2 〈 k^vth 〈 0.7. Otherwise, no critical initial amplitude is found. The value c＊ increases with the increase in km for a fixed Vth, and also increases with the increase in Vth for a fixed kin. When kmVth is fixed, the value s＊ also changes with the wave number and the electron thermal velocity, even though the damping rate and the oscillation frequency are the same in this case.

Simulation Study of IBW Heating in HT-7 Tokamak

Preliminary simulation results obtained with the code developed for ion Bernstein wave （IBW） heating in the HT-7 tokamak are presented. Comparison of the simulation of IBW heating and an HT-7 experiment confirms that using IBW of various frequencies can result in local or global plasma heating. The studies suggest that IBW absorption by ions near the ion cyclotron resonant layer and by electrons via electron Landau damping （ELD） around the maximum of n// offers a possible mechanism of plasma heating.

Relaxation dynamics of Kuramoto model with heterogeneous coupling

The Landau damping which reveals the characteristic of relaxation dynamics for an equilibrium state is a universal concept in the area of complex system. In this paper, we study the Landau damping in the phase oscillator system by considering two types of coupling heterogeneity in the Kuramoto model. We show that the critical coupling strength for phase transition, which can be obtained analytically through the balanced integral equation, has the same formula for both cases. The Landau damping effects are further explained in the framework of Laplace transform, where the order parameters decay to zero in the long time limit.

Conservative Semi-Lagrangian Finite Difference WENO Formulations with Applications to the Vlasov Equation

In this paper,we propose a new conservative semi-Lagrangian(SL)finite difference(FD)WENO scheme for linear advection equations,which can serve as a base scheme for the Vlasov equation by Strang splitting[4].The reconstruction procedure in the proposed SL FD scheme is the same as the one used in the SL finite volume(FV)WENO scheme[3].However,instead of inputting cell averages and approximate the integral form of the equation in a FV scheme,we input point values and approximate the differential form of equation in a FD spirit,yet retaining very high order(fifth order in our experiment)spatial accuracy.The advantage of using point values,rather than cell averages,is to avoid the second order spatial error,due to the shearing in velocity(v)and electrical field(E)over a cell when performing the Strang splitting to the Vlasov equation.As a result,the proposed scheme has very high spatial accuracy,compared with second order spatial accuracy for Strang split SL FV scheme for solving the Vlasov-Poisson(VP)system.We perform numerical experiments on linear advection,rigid body rotation problem;and on the Landau damping and two-stream instabilities by solving the VP system.For comparison,we also apply(1)the conservative SL FD WENO scheme,proposed in[22]for incompressible advection problem,(2)the conservative SL FD WENO scheme proposed in[21]and(3)the non-conservative version of the SL FD WENO scheme in[3]to the same test problems.The performances of different schemes are compared by the error table,solution resolution of sharp interface,and by tracking the conservation of physical norms,energies and entropies,which should be physically preserved.

Photon polarization tensor in a magnetized plasma system

We investigate the photon polarization tensor at finite temperatures in the presence of a static and homogeneous external magnetic field.In our scheme,the summing of the Matsubara frequency is performed after Poisson resummation,which is easily completed and converges quickly.Moreover,the behaviors of finite Landau levels are presented explicitly.It shows a convergence while summing infinite Landau levels.Consequently,there is no necessity to truncate the Landau level in a numerical estimation.At zero temperature,the lowest Landau level(LLL)approximation is analytically satisfied for the vacuum photon polarization tensor.However,we examine that the LLL approximation is not enough for the thermal polarization tensor.The thermal tensor obtains non-trivial contributions from the finite-n Landau levels.And,photon spectra gains a large imaginary contribution in thermal medium,which is the so-called Landau damping.Finally,it is argued that the summation of Matsubara frequency is not commuted with Landau level ones,such conjecture is excluded in our calculations.

Study of Robinson instabilities with a higher-harmonic cavity for the HLS phase Ⅱ project

In the Phase Ⅱ Project at the Hefei Light Source, a fourth-harmonic ＂Landau＂ cavity will be operated in order to suppress the coupled-bunch instabilities and increase the beam lifetime of the Hefei storage ring. Instabilities limit the utility of the higher-harmonic cavity when the storage ring is operated with a small momentum compaction. Analytical modeling and simulations show that the instabilities result from Robinson mode coupling. In the analytic modeling, we operate an algorithm to consider the Robinson instabilities. To study the evolution of unstable behavior, simulations have been performed in which macroparticles are distributed among the buckets. Both the analytic modeling and simulations agree for passive operation of the harmonic cavity.