The assembling stabilizing effect of the finite Larmor radius (FLR) and the sheared axial flow (SAF) on the Rayleigh-Taylor instability in Z-pinch implosions is studied by means of the incompressible finite Larmor rad...The assembling stabilizing effect of the finite Larmor radius (FLR) and the sheared axial flow (SAF) on the Rayleigh-Taylor instability in Z-pinch implosions is studied by means of the incompressible finite Larmor radius magnetohydrodynamic (MHD) equations. The finite Larmor radius effects are introduced in the momentum equation with the sheared axial flow through an anisotropic ion stress tensor. In this paper a linear mode equation is derived that is valid for arbitrary kL, where k is the wave number and L is the plasma shell thickness. Numerical solutions are presented. The results indicate that the short-wavelength modes of the Rayleigh-Taylor instability are easily stabilized by the individual effect of the finite Larmor radius or the sheared axial flow. The assembling effects of the finite Larmor radius and sheared axial flow can heavily mitigate the Rayleigh-Taylor instability, and the unstable region can be compressed considerably.展开更多
A magnetohydrodynamic (MHD) formulation is derived to investigate and compare the mitigation effects of both the sheared axial flow and finite Larmor radius (FLR) on the Rayleigh-Taylor (RT) instability in Z-pinch imp...A magnetohydrodynamic (MHD) formulation is derived to investigate and compare the mitigation effects of both the sheared axial flow and finite Larmor radius (FLR) on the Rayleigh-Taylor (RT) instability in Z-pinch implosions. The sheared axial flow is introduced into MHD equations in a conventional way and the FLR effect into the equations via /t → -i(w+ik⊥2pi2Ωi,), as proposed in our previous paper [Chin. Phys. Lett. 2002, 19:217] , where k⊥2 pi2 is referred to FLR effect from the general kinetic theory of magnetized plasma. Therefore the linearized continuity and momentum equations for the perturbed mass-density and velocity include both the sheared axial flow and the FLR effect. It is found that the effect of sheared axial flow with a lower peak velocity can mitigate RT instability in the whole wavenumber region and the effect of sheared axial flow with a higher one can mitigate RT instability only in the large wavenumber region (for normalized wavenumber k】2.4); The effect of FLR can mitigate RT instability in the whole wavenumber region and the mitigation effect is stronger than that of the sheared axial flow with a lower peak velocity in the almost whole wavenumber region.展开更多
A big enough transverse magnetic field applied to soft magnetic ferrite toroid can magnetize the ferrite to a saturation level in transverse direction and almost completely suppresses magnetic domain structures in the...A big enough transverse magnetic field applied to soft magnetic ferrite toroid can magnetize the ferrite to a saturation level in transverse direction and almost completely suppresses magnetic domain structures in the ferrite,the response to the longitudinal alternating electromagnetic field changes from the original domain wall displacements and spin rotations to the precession of magnetization around the transverse field,and the hysteresis loss disappears in the ferrites.Both theoretical and experimental results indicate that the permeability and magnetic loss in the ferrite can be controlled by adjusting the transverse magnetic field.A higher Q value with relatively low permeability can be achieved by increasing the transverse field,which ensures that the ferrite can be operated at high frequencies,with magnetic loss being very low.展开更多
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
It is well known that the spin operators of a quantum particle must obey uncertainty relations. We use the uncertainty principle to study the Larmor clock. To avoid breaking the uncertainty principle, Larmor time can ...It is well known that the spin operators of a quantum particle must obey uncertainty relations. We use the uncertainty principle to study the Larmor clock. To avoid breaking the uncertainty principle, Larmor time can be defined as the ratio of the phase difference between a spin-up particle and a spin-down particle to the corresponding Larmor frequency. The connection between the dwell time and the Larmor time has also been confirmed. Moreover, the results show that the behavior of the Larmor time depends on the height and width of the barrier.展开更多
基金The project supported by the National Natural Science Foundation of China (Nos. 10035020 and 40390150)
文摘The assembling stabilizing effect of the finite Larmor radius (FLR) and the sheared axial flow (SAF) on the Rayleigh-Taylor instability in Z-pinch implosions is studied by means of the incompressible finite Larmor radius magnetohydrodynamic (MHD) equations. The finite Larmor radius effects are introduced in the momentum equation with the sheared axial flow through an anisotropic ion stress tensor. In this paper a linear mode equation is derived that is valid for arbitrary kL, where k is the wave number and L is the plasma shell thickness. Numerical solutions are presented. The results indicate that the short-wavelength modes of the Rayleigh-Taylor instability are easily stabilized by the individual effect of the finite Larmor radius or the sheared axial flow. The assembling effects of the finite Larmor radius and sheared axial flow can heavily mitigate the Rayleigh-Taylor instability, and the unstable region can be compressed considerably.
基金This work was supported by the National Natural Science Foundation of China No.10035020.
文摘A magnetohydrodynamic (MHD) formulation is derived to investigate and compare the mitigation effects of both the sheared axial flow and finite Larmor radius (FLR) on the Rayleigh-Taylor (RT) instability in Z-pinch implosions. The sheared axial flow is introduced into MHD equations in a conventional way and the FLR effect into the equations via /t → -i(w+ik⊥2pi2Ωi,), as proposed in our previous paper [Chin. Phys. Lett. 2002, 19:217] , where k⊥2 pi2 is referred to FLR effect from the general kinetic theory of magnetized plasma. Therefore the linearized continuity and momentum equations for the perturbed mass-density and velocity include both the sheared axial flow and the FLR effect. It is found that the effect of sheared axial flow with a lower peak velocity can mitigate RT instability in the whole wavenumber region and the effect of sheared axial flow with a higher one can mitigate RT instability only in the large wavenumber region (for normalized wavenumber k】2.4); The effect of FLR can mitigate RT instability in the whole wavenumber region and the mitigation effect is stronger than that of the sheared axial flow with a lower peak velocity in the almost whole wavenumber region.
基金Project supported by the National Key Research and Development Program of China(Grant Nos.2022YFB3504800 and 2021YFB3502400)the Key Research and Development Plan of Anhui Province,China(Grant No.202003c08020012)the Key Program of Education Department of Anhui Province,China(Grant No.KJ2019ZD03)。
文摘A big enough transverse magnetic field applied to soft magnetic ferrite toroid can magnetize the ferrite to a saturation level in transverse direction and almost completely suppresses magnetic domain structures in the ferrite,the response to the longitudinal alternating electromagnetic field changes from the original domain wall displacements and spin rotations to the precession of magnetization around the transverse field,and the hysteresis loss disappears in the ferrites.Both theoretical and experimental results indicate that the permeability and magnetic loss in the ferrite can be controlled by adjusting the transverse magnetic field.A higher Q value with relatively low permeability can be achieved by increasing the transverse field,which ensures that the ferrite can be operated at high frequencies,with magnetic loss being very low.
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.
基金Supported by National Natural Science Foundation of China (10775068, 10735010, 10975072, 11035001)973 National Major State Basic Research and Development of China (2007CB815004, 2010CB327803)+1 种基金CAS Knowledge Innovation Project (KJCX2-SW-N02)Research Fund of Doctoral Point (RFDP) (20070284016, 20100091110028)
文摘It is well known that the spin operators of a quantum particle must obey uncertainty relations. We use the uncertainty principle to study the Larmor clock. To avoid breaking the uncertainty principle, Larmor time can be defined as the ratio of the phase difference between a spin-up particle and a spin-down particle to the corresponding Larmor frequency. The connection between the dwell time and the Larmor time has also been confirmed. Moreover, the results show that the behavior of the Larmor time depends on the height and width of the barrier.
