The tokamak L–H (low‐mode–high mode) transition theory can be tested in stellarators in a controlled manner by making use of the two or more local maxima in poloidal viscosity in these devices. Depending on the relative magnitudes of the toroidal and helical components of the magnetic‐field spectrum, the local maxima, and thus transition, can occur either at a critical poloidal E×B Mach number Mp of the order of unity, similar to that of a tokamak, or at an Mp of the order of ‖m−nq‖/m, similar to that of a helically symmetric torus. Here, E(B) is the electric (magnetic) field strength, m (n) is the poloidal (toroidal) mode number of the helical component of the ‖B‖ spectrum, and q is the safety factor. Possible limitations on the test due to the effects of the charge‐exchange momentum loss are discussed.
{"title":"Test of tokamak low‐mode–high‐mode transition theory in stellarators","authors":"K. Shaing","doi":"10.1063/1.860605","DOIUrl":"https://doi.org/10.1063/1.860605","url":null,"abstract":"The tokamak L–H (low‐mode–high mode) transition theory can be tested in stellarators in a controlled manner by making use of the two or more local maxima in poloidal viscosity in these devices. Depending on the relative magnitudes of the toroidal and helical components of the magnetic‐field spectrum, the local maxima, and thus transition, can occur either at a critical poloidal E×B Mach number Mp of the order of unity, similar to that of a tokamak, or at an Mp of the order of ‖m−nq‖/m, similar to that of a helically symmetric torus. Here, E(B) is the electric (magnetic) field strength, m (n) is the poloidal (toroidal) mode number of the helical component of the ‖B‖ spectrum, and q is the safety factor. Possible limitations on the test due to the effects of the charge‐exchange momentum loss are discussed.","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125808431","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The nonlinear behavior of the two‐dimensional Benard problem with periodic boundary conditions in the horizontal direction is studied with particular emphasis on the role of self‐consistent chaotic advection. The results show a complex interplay between vortices driven by the Benard (Rayleigh–Taylor) instability and shear flow, which is driven by the vortices [J. Drake et al., Phys. Fluids B 4, 4881 (1992)] and which causes their decay. Chaotic advection occurs in the transition from the low Rayleigh number (Ra) regime to the high Ra regime [J. Finn, Phys. Fluids B 5, 415 (1993)]. For the former, vortex flow and shear flow coexist, possibly with slow relaxation oscillations. In the high Ra regime there are vortices localized near the upper and lower boundaries with a shear flow in between. As Ra is decreased from the high Ra regime, these vortices broaden, eventually overlapping, causing self‐consistent Lagrangian chaos. This onset of chaos is responsible for several properties of the transition state between the low Ra and the high Ra regimes, most notably the damping of the relaxation oscillations involving vortex and shear flow. It is also observed that the Nusselt number Nu has a peak with respect to Ra in this transition regime characterized by Lagrangian chaos. In the low Ra regime, on the other hand, the relaxation oscillations are on a much slower time scale than the eddy turnover time and the Lagrangian behavior is described by separatrix crossing.
{"title":"The role of self‐consistent Lagrangian chaos in Bénard convection in an annulus","authors":"J. Finn, K. Hermiz","doi":"10.1063/1.860613","DOIUrl":"https://doi.org/10.1063/1.860613","url":null,"abstract":"The nonlinear behavior of the two‐dimensional Benard problem with periodic boundary conditions in the horizontal direction is studied with particular emphasis on the role of self‐consistent chaotic advection. The results show a complex interplay between vortices driven by the Benard (Rayleigh–Taylor) instability and shear flow, which is driven by the vortices [J. Drake et al., Phys. Fluids B 4, 4881 (1992)] and which causes their decay. Chaotic advection occurs in the transition from the low Rayleigh number (Ra) regime to the high Ra regime [J. Finn, Phys. Fluids B 5, 415 (1993)]. For the former, vortex flow and shear flow coexist, possibly with slow relaxation oscillations. In the high Ra regime there are vortices localized near the upper and lower boundaries with a shear flow in between. As Ra is decreased from the high Ra regime, these vortices broaden, eventually overlapping, causing self‐consistent Lagrangian chaos. This onset of chaos is responsible for several properties of the transition state between the low Ra and the high Ra regimes, most notably the damping of the relaxation oscillations involving vortex and shear flow. It is also observed that the Nusselt number Nu has a peak with respect to Ra in this transition regime characterized by Lagrangian chaos. In the low Ra regime, on the other hand, the relaxation oscillations are on a much slower time scale than the eddy turnover time and the Lagrangian behavior is described by separatrix crossing.","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132561020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A theoretical description of the spontaneous (Stringer) poloidal spin‐up of tokamak plasmas is given. A set of reduced equations is derived to investigate various aspects of the phenomenon. A simple physical description of the instability mechanism is given. The theory of the instability is extended to show that the spin‐up persists even under conditions where the growth rate is sonic. A nonlinear evolution equation for unstable poloidal rotation is obtained which shows that the instability mechanism loses its efficacy when the poloidal speed exceeds the poloidal sound speed, thus resulting in nonlinear saturation of the rotation at this level.
{"title":"Spontaneous poloidal spin-up of tokamak plasmas: Reduced equations, physical mechanism, and sonic regimes","authors":"A. Hassam, J. Drake","doi":"10.1063/1.860622","DOIUrl":"https://doi.org/10.1063/1.860622","url":null,"abstract":"A theoretical description of the spontaneous (Stringer) poloidal spin‐up of tokamak plasmas is given. A set of reduced equations is derived to investigate various aspects of the phenomenon. A simple physical description of the instability mechanism is given. The theory of the instability is extended to show that the spin‐up persists even under conditions where the growth rate is sonic. A nonlinear evolution equation for unstable poloidal rotation is obtained which shows that the instability mechanism loses its efficacy when the poloidal speed exceeds the poloidal sound speed, thus resulting in nonlinear saturation of the rotation at this level.","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124160078","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The 13 TW pulsed electron beam generated by Hermes III [J. J. Ramirez et al., Digest of Technical Papers, 6th IEEE Pulsed Power Conference (IEEE, New York, 1987), pp. 294] is transported 10.8 m in a low‐pressure gas with 79±1.5±[5]% energy transport efficiency. The uncertainties refer to the rms shot‐to‐shot variation and estimated systematic error, respectively. The high efficiency obtained is accomplished by removing the inward momentum of the beam at injection via an active magnetic lens. The reduced transverse momentum permits self‐magnetic field confinement at low pressures with low inductive and collisional loss. The region of efficient transport lies between regions of instability. Consistent with experiment, the analytic and numerical models developed here predict that the m=1 resistive hose instability degrades transport above 100 Torr and plasma return‐current instabilities disrupt the beam below 1 Torr. Within this pressure ‘‘window’’ of stable propagation, the models explain the mechanisms responsible for maximum transport.
激光脉冲电子束的研究进展[J]。J. Ramirez et .，技术论文文摘，第六届IEEE脉冲功率会议(IEEE, New York, 1987)， pp. 294]在低压气体中传输10.8 m，能量传输效率为79±1.5±[5]%。不确定度分别是指枪弹间的均方根变化和估计的系统误差。通过主动磁透镜去除注入时光束的向内动量，实现了高效率。减少的横向动量允许在低压下以低的感应和碰撞损耗约束自磁场。有效运输区域位于不稳定区域之间。与实验结果一致，本文建立的分析和数值模型预测，m=1电阻软管的不稳定性会降低100 Torr以上的输运，而等离子体回流电流的不稳定性会破坏1 Torr以下的光束。在这个稳定传播的压力“窗口”内，模型解释了导致最大输运的机制。
{"title":"Dynamics of a 19 MeV, 700 kA, 25 nsec electron beam in a long collisional gas cell","authors":"T. Sanford, D. Welch, R. Mock","doi":"10.1063/1.860584","DOIUrl":"https://doi.org/10.1063/1.860584","url":null,"abstract":"The 13 TW pulsed electron beam generated by Hermes III [J. J. Ramirez et al., Digest of Technical Papers, 6th IEEE Pulsed Power Conference (IEEE, New York, 1987), pp. 294] is transported 10.8 m in a low‐pressure gas with 79±1.5±[5]% energy transport efficiency. The uncertainties refer to the rms shot‐to‐shot variation and estimated systematic error, respectively. The high efficiency obtained is accomplished by removing the inward momentum of the beam at injection via an active magnetic lens. The reduced transverse momentum permits self‐magnetic field confinement at low pressures with low inductive and collisional loss. The region of efficient transport lies between regions of instability. Consistent with experiment, the analytic and numerical models developed here predict that the m=1 resistive hose instability degrades transport above 100 Torr and plasma return‐current instabilities disrupt the beam below 1 Torr. Within this pressure ‘‘window’’ of stable propagation, the models explain the mechanisms responsible for maximum transport.","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128959806","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The effects of nonlocal heat transport on stimulated scattering instabilities of electromagnetic waves are investigated employing the recently derived expression for the electron number density perturbations that are driven by the ponderomotive and thermal forces in high Zi collisional plasmas. The growth rates and the threshold conditions for stimulated Brillouin and stimulated Compton scattering, as well as modulational instabilities, are obtained. It is found that the growth rates of the scattering instabilities of electromagnetic waves are considerably enhanced due to nonlocal electron heat conduction in collisional plasmas.
{"title":"Stimulated scattering instabilities of electromagnetic waves in collisional plasmas","authors":"P. Shukla","doi":"10.1063/1.860592","DOIUrl":"https://doi.org/10.1063/1.860592","url":null,"abstract":"The effects of nonlocal heat transport on stimulated scattering instabilities of electromagnetic waves are investigated employing the recently derived expression for the electron number density perturbations that are driven by the ponderomotive and thermal forces in high Zi collisional plasmas. The growth rates and the threshold conditions for stimulated Brillouin and stimulated Compton scattering, as well as modulational instabilities, are obtained. It is found that the growth rates of the scattering instabilities of electromagnetic waves are considerably enhanced due to nonlocal electron heat conduction in collisional plasmas.","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"205 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120970689","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Modification of the magnetic force by a developed small‐scale magnetohydrodynamic (MHD) turbulence can result in the sign reversal of the effective magnetic pressure. It is due to negative contribution of the MHD turbulence, to the large‐scale magnetic force. It can significantly lower the elasticity of the large‐scale magnetic field [ Sov. Phys. JETP 70, 878 (1990)]. This effect excites instabilities of the large‐scale magnetic field due to the energy transfer from the turbulent pulsations to the latter. The nonturbulent stability criteria are modified due to the effective negative magnetic pressure. These instabilities may provide a mechanism of the large‐scale magnetic ropes formation in the solar convective zone and spiral galaxies. In addition, the instabilities can excite the short‐period solar oscillations.
{"title":"Magnetohydrodynamic instabilities in developed small-scale turbulence","authors":"N. Kleeorin, M. Mond, I. Rogachevskii","doi":"10.1063/1.860582","DOIUrl":"https://doi.org/10.1063/1.860582","url":null,"abstract":"Modification of the magnetic force by a developed small‐scale magnetohydrodynamic (MHD) turbulence can result in the sign reversal of the effective magnetic pressure. It is due to negative contribution of the MHD turbulence, to the large‐scale magnetic force. It can significantly lower the elasticity of the large‐scale magnetic field [ Sov. Phys. JETP 70, 878 (1990)]. This effect excites instabilities of the large‐scale magnetic field due to the energy transfer from the turbulent pulsations to the latter. The nonturbulent stability criteria are modified due to the effective negative magnetic pressure. These instabilities may provide a mechanism of the large‐scale magnetic ropes formation in the solar convective zone and spiral galaxies. In addition, the instabilities can excite the short‐period solar oscillations.","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"73 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127025854","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A mean field Ohm’s law valid for collisionless plasmas is derived kinetically. It is shown that contrary to conventional thinking, the resulting hyperresistivity is significantly smaller than its fluid counterpart due to the fact that the turbulent decorrelation rate is linked to the rapid electron ballistic motion rather than the slower nonlinear mixing time. Moreover, the off‐diagonal contributions to the parallel electron momentum flux are shown to result in Ohm’s law renormalizations that dwarf the current diffusivity and break radial parity symmetry.
{"title":"A mean field Ohm's law for collisionless plasmas","authors":"Biglariand P.H, Diamond, H. Biglari","doi":"10.1063/1.860604","DOIUrl":"https://doi.org/10.1063/1.860604","url":null,"abstract":"A mean field Ohm’s law valid for collisionless plasmas is derived kinetically. It is shown that contrary to conventional thinking, the resulting hyperresistivity is significantly smaller than its fluid counterpart due to the fact that the turbulent decorrelation rate is linked to the rapid electron ballistic motion rather than the slower nonlinear mixing time. Moreover, the off‐diagonal contributions to the parallel electron momentum flux are shown to result in Ohm’s law renormalizations that dwarf the current diffusivity and break radial parity symmetry.","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"371 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122922464","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Ochando, M. Pedrosa, R. Balbín, I. García-Cortés, C. Hidalgo
The correlation between edge radiation, electron temperature, and density fluctuations has been studied in the vicinity of the upper poloidal limiter of the TJ‐I tokamak [Phys. Fluids B 4, 4007 (1992)]. When edge impurity radiation is strongly peaked in the proximity of the limiter radius, electron temperature fluctuations are notably higher than density fluctuations. Results suggest that edge turbulence may be driven by radiative instabilities.
{"title":"Edge turbulence and total radiation in the TJ-I tokamak","authors":"M. Ochando, M. Pedrosa, R. Balbín, I. García-Cortés, C. Hidalgo","doi":"10.1063/1.860962","DOIUrl":"https://doi.org/10.1063/1.860962","url":null,"abstract":"The correlation between edge radiation, electron temperature, and density fluctuations has been studied in the vicinity of the upper poloidal limiter of the TJ‐I tokamak [Phys. Fluids B 4, 4007 (1992)]. When edge impurity radiation is strongly peaked in the proximity of the limiter radius, electron temperature fluctuations are notably higher than density fluctuations. Results suggest that edge turbulence may be driven by radiative instabilities.","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117202267","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The effects of thermal trapped particles on the n=1 internal kink mode are studied using drift kinetic theory. Strong modifications of the magnetohydrodynamic (MHD) results are found, and marginal stability generally occurs at nonzero rotation frequency. For equal electron and ion temperatures, the trapped particles increase the marginal poloidal beta at q=1 substantially above the MHD value. For unequal electron and ion temperatures, the drift resonance with the hotter species becomes increasingly destabilizing and for sufficiently unequal temperatures, this leads to instability below the ideal‐MHD threshold. Treatment of trapped thermal particles requires consideration of the effects of an electrostatic potential. The potential is weakly stabilizing for the internal kink mode. Furthermore, finite beta couples unstable, nearly electrostatic, trapped particle modes to the internal kink mode. At high beta, thermal fluctuations of the trapped particle modes can lead to significant internal kink displacements.
{"title":"Influence of trapped thermal particles on internal kink modes in high temperature tokamaks","authors":"T. Antonsen, A. Bondeson","doi":"10.1063/1.860577","DOIUrl":"https://doi.org/10.1063/1.860577","url":null,"abstract":"The effects of thermal trapped particles on the n=1 internal kink mode are studied using drift kinetic theory. Strong modifications of the magnetohydrodynamic (MHD) results are found, and marginal stability generally occurs at nonzero rotation frequency. For equal electron and ion temperatures, the trapped particles increase the marginal poloidal beta at q=1 substantially above the MHD value. For unequal electron and ion temperatures, the drift resonance with the hotter species becomes increasingly destabilizing and for sufficiently unequal temperatures, this leads to instability below the ideal‐MHD threshold. Treatment of trapped thermal particles requires consideration of the effects of an electrostatic potential. The potential is weakly stabilizing for the internal kink mode. Furthermore, finite beta couples unstable, nearly electrostatic, trapped particle modes to the internal kink mode. At high beta, thermal fluctuations of the trapped particle modes can lead to significant internal kink displacements.","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121010398","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A nonlinear theory is developed for the two‐stream interaction of two relativistic annular electron beams propagating through a grounded cylindrical conducting tube. The theory is based on the assumption that the beams experience energy modulation at a cavity before they enter the drift tube. Two coupled integrodifferential equations are derived which describe beam current modulation in terms of time t and propagation distance z. The evolution of the fundamental mode in the current modulation is investigated analytically by making use of these coupled equations. The amplitude of the fundamental mode, which is a function of the propagation distance, is expressed explicitly in terms of the initial energy modulation, the growth rate of the instability, and the beam intensity. It is found that self‐field effects dominate two‐stream effects at the beginning of the propagation. As the beams propagate further, the two‐stream effects start to dominate and then the perturbations grow exponentially. The saturation ...
{"title":"Nonlinear analysis of the two-stream instability for relativistic annular electron beams","authors":"H. Uhm, Chi-ping Chen","doi":"10.1063/1.860963","DOIUrl":"https://doi.org/10.1063/1.860963","url":null,"abstract":"A nonlinear theory is developed for the two‐stream interaction of two relativistic annular electron beams propagating through a grounded cylindrical conducting tube. The theory is based on the assumption that the beams experience energy modulation at a cavity before they enter the drift tube. Two coupled integrodifferential equations are derived which describe beam current modulation in terms of time t and propagation distance z. The evolution of the fundamental mode in the current modulation is investigated analytically by making use of these coupled equations. The amplitude of the fundamental mode, which is a function of the propagation distance, is expressed explicitly in terms of the initial energy modulation, the growth rate of the instability, and the beam intensity. It is found that self‐field effects dominate two‐stream effects at the beginning of the propagation. As the beams propagate further, the two‐stream effects start to dominate and then the perturbations grow exponentially. The saturation ...","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130722336","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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