In this paper, the effect of finite Larmor radius （FLR） on high n ballooning modes is studied on the basis of FLR magnetohydrodynamic （FLR-MHD） theory. A linear FLR ballooning mode equation is derived in an ＇s^--...In this paper, the effect of finite Larmor radius （FLR） on high n ballooning modes is studied on the basis of FLR magnetohydrodynamic （FLR-MHD） theory. A linear FLR ballooning mode equation is derived in an ＇s^-- α＇ type equilibrium of circular-flux-surfaces, which is reduced to the ideal ballooning mode equation when the FLR effect is neglected. The present model reproduces some basic features of FLR effects on ballooning mode obtained previously by kinetic ballooning mode theories. That is, the FLR introduces a real frequency into ballooning mode and has a stabilising effect on ballooning modes （e.g., in the case of high magnetic shear s^- ≥ 0.8）. In particular, some new properties of FLR effects on ballooning mode are discovered in the present research. Here it is found that in a high magnetic shear region （s^- ≥ 0.8） the critical pressure gradient （αc,FLR） of ballooning mode is larger than the ideal one （αc,IMHD） and becomes larger and larger with the increase of FLR parameter b0. However, in a low magnetic shear region, the FLR ballooning mode is more unstable than the ideal one, and the αc,FLR is much lower than the αc,IMHD. Moreover, the present results indicate that there exist some new weaker instabilities near the second stability boundary （obtained from ideal MHD theory）, which means that the second stable region becomes narrow.展开更多
A hybrid model of MHD and kinetic theory is proposed to investigate the synergetic stabilizing effects of sheared axial flow and finite Larmor radius on the RayleighTaylor instability in Zpinch implosions.In our m...A hybrid model of MHD and kinetic theory is proposed to investigate the synergetic stabilizing effects of sheared axial flow and finite Larmor radius on the RayleighTaylor instability in Zpinch implosions.In our model the MHD plasma is considered to respond to a perturbation with exp at frequency ω+ik2⊥ρ2iΩi instead of frequency ω,where k2⊥ρ2i is the finite Larmor radius effects given from the general kinetic theory of magnetized plasma.Therefore linearized continuity and momentum equations include automatically the finite Larmor radius effects.Dispersion relation is derived,which includes the effects of a density discontinuity and the finite Larmor radius as well as a sheared flow that produces the KelvinHelmholtz instability.The dispersion equation is examined in three cases.The results indicate that the synergetic effect of sheared axial flow and the finite Larmor radius can mitigate both the RayleighTaylor instability and the hybrid RayleighTaylor/KelvinHelmholtz instability.Moreover,the synergetic mitigation effect is stronger than either of them acting separately.展开更多
The synergistic stabilizing effect of gyroviscosity and sheared axial flow on the Rayleigh-Taylor instability in Z-pinch implosions is studied by means of the incompressible viscid magneto-hydrodynamic equations.The g...The synergistic stabilizing effect of gyroviscosity and sheared axial flow on the Rayleigh-Taylor instability in Z-pinch implosions is studied by means of the incompressible viscid magneto-hydrodynamic equations.The gyroviscosity(or finite Larmor radius) effects are introduced in the momentum equation through an anisotropic ion stress tensor.Dispersion relation with the effect of a density discontinuity is derived.The results indicate that the short-wavelength modes of the Rayleigh-Taylor instability are easily stabilized by the gyroviscosity effects.The long wavelength modes are stabilized by the sufficient sheared axial flow.However,the synergistic effects of the finite Larmor radius and sheared axial flow can heavily mitigate the Rayleigh-Taylor instability.This synergistic effect can compress the Rayleigh-Taylor instability to a narrow wave number region.Even with a sufficient gyroviscosity and large enough flow velocity,the synergistic effect can completely suppressed the Rayleigh-Taylor instability in whole wave number region.展开更多
A method for gyrokinetic simulation of low frequency(lower than the cyclotron frequency)magnetic compressional modes in general geometry is presented.The gyrokinetic-Maxwell system of equations is expressed fully in t...A method for gyrokinetic simulation of low frequency(lower than the cyclotron frequency)magnetic compressional modes in general geometry is presented.The gyrokinetic-Maxwell system of equations is expressed fully in terms of the compressional component of the magnetic perturbation,δBk,with finite Larmor radius effects.This introduces a"gyro-surface"averaging ofδBk in the gyrocenter equations of motion,and similarly in the perpendicular Ampere’s law,which takes the form of the perpendicular force balance equation.The resulting system can be numerically implemented by representing the gyro-surface averaging by a discrete sum in the configuration space.For the typical wavelength of interest(on the order of the gyroradius),the gyro-surface averaging can be reduced to averaging along an effective gyro-orbit.The phase space integration in the force balance equation can be approximated by summing over carefully chosen samples in the magnetic moment coordinate,allowing for an efficient numerical implementation.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10775040 and 10775043)
文摘In this paper, the effect of finite Larmor radius （FLR） on high n ballooning modes is studied on the basis of FLR magnetohydrodynamic （FLR-MHD） theory. A linear FLR ballooning mode equation is derived in an ＇s^-- α＇ type equilibrium of circular-flux-surfaces, which is reduced to the ideal ballooning mode equation when the FLR effect is neglected. The present model reproduces some basic features of FLR effects on ballooning mode obtained previously by kinetic ballooning mode theories. That is, the FLR introduces a real frequency into ballooning mode and has a stabilising effect on ballooning modes （e.g., in the case of high magnetic shear s^- ≥ 0.8）. In particular, some new properties of FLR effects on ballooning mode are discovered in the present research. Here it is found that in a high magnetic shear region （s^- ≥ 0.8） the critical pressure gradient （αc,FLR） of ballooning mode is larger than the ideal one （αc,IMHD） and becomes larger and larger with the increase of FLR parameter b0. However, in a low magnetic shear region, the FLR ballooning mode is more unstable than the ideal one, and the αc,FLR is much lower than the αc,IMHD. Moreover, the present results indicate that there exist some new weaker instabilities near the second stability boundary （obtained from ideal MHD theory）, which means that the second stable region becomes narrow.
文摘A hybrid model of MHD and kinetic theory is proposed to investigate the synergetic stabilizing effects of sheared axial flow and finite Larmor radius on the RayleighTaylor instability in Zpinch implosions.In our model the MHD plasma is considered to respond to a perturbation with exp at frequency ω+ik2⊥ρ2iΩi instead of frequency ω,where k2⊥ρ2i is the finite Larmor radius effects given from the general kinetic theory of magnetized plasma.Therefore linearized continuity and momentum equations include automatically the finite Larmor radius effects.Dispersion relation is derived,which includes the effects of a density discontinuity and the finite Larmor radius as well as a sheared flow that produces the KelvinHelmholtz instability.The dispersion equation is examined in three cases.The results indicate that the synergetic effect of sheared axial flow and the finite Larmor radius can mitigate both the RayleighTaylor instability and the hybrid RayleighTaylor/KelvinHelmholtz instability.Moreover,the synergetic mitigation effect is stronger than either of them acting separately.
文摘The synergistic stabilizing effect of gyroviscosity and sheared axial flow on the Rayleigh-Taylor instability in Z-pinch implosions is studied by means of the incompressible viscid magneto-hydrodynamic equations.The gyroviscosity(or finite Larmor radius) effects are introduced in the momentum equation through an anisotropic ion stress tensor.Dispersion relation with the effect of a density discontinuity is derived.The results indicate that the short-wavelength modes of the Rayleigh-Taylor instability are easily stabilized by the gyroviscosity effects.The long wavelength modes are stabilized by the sufficient sheared axial flow.However,the synergistic effects of the finite Larmor radius and sheared axial flow can heavily mitigate the Rayleigh-Taylor instability.This synergistic effect can compress the Rayleigh-Taylor instability to a narrow wave number region.Even with a sufficient gyroviscosity and large enough flow velocity,the synergistic effect can completely suppressed the Rayleigh-Taylor instability in whole wave number region.
基金supported by National Science Foundation and U.S.Department of Energy grants.
文摘A method for gyrokinetic simulation of low frequency(lower than the cyclotron frequency)magnetic compressional modes in general geometry is presented.The gyrokinetic-Maxwell system of equations is expressed fully in terms of the compressional component of the magnetic perturbation,δBk,with finite Larmor radius effects.This introduces a"gyro-surface"averaging ofδBk in the gyrocenter equations of motion,and similarly in the perpendicular Ampere’s law,which takes the form of the perpendicular force balance equation.The resulting system can be numerically implemented by representing the gyro-surface averaging by a discrete sum in the configuration space.For the typical wavelength of interest(on the order of the gyroradius),the gyro-surface averaging can be reduced to averaging along an effective gyro-orbit.The phase space integration in the force balance equation can be approximated by summing over carefully chosen samples in the magnetic moment coordinate,allowing for an efficient numerical implementation.
