A new analytical approach is presented for assessing the reflection of linear Alfven waves in smoothly nonuniform media. The general one‐dimensional case in Cartesian coordinates is treated. It is shown that the wave equations, upon transformation into the form of the Klein–Gordon equation, display a local critical frequency (Ωc) for reflection: At any location in the medium, reflection becomes strong as the wave frequency descends past this characteristic frequency set by the local nonuniformity of the medium. This critical frequency is given by the transformation as an explicit function of the Alfven velocity (VA), and its first (V’A) and second (V■A) derivatives, and hence as an explicit spatial function. The transformation thus directly yields, without solution of the wave equations, the location in the medium at which an Alfven wave of any given frequency becomes strongly reflected and has its propagation practically cut off. The local critical frequency is the square root of the larger coefficient o...
{"title":"Klein–Gordon equation and reflection of Alfvén waves in nonuniform media","authors":"Z. Musielak, J. Fontenla, R. Moore","doi":"10.1063/1.860452","DOIUrl":"https://doi.org/10.1063/1.860452","url":null,"abstract":"A new analytical approach is presented for assessing the reflection of linear Alfven waves in smoothly nonuniform media. The general one‐dimensional case in Cartesian coordinates is treated. It is shown that the wave equations, upon transformation into the form of the Klein–Gordon equation, display a local critical frequency (Ωc) for reflection: At any location in the medium, reflection becomes strong as the wave frequency descends past this characteristic frequency set by the local nonuniformity of the medium. This critical frequency is given by the transformation as an explicit function of the Alfven velocity (VA), and its first (V’A) and second (V■A) derivatives, and hence as an explicit spatial function. The transformation thus directly yields, without solution of the wave equations, the location in the medium at which an Alfven wave of any given frequency becomes strongly reflected and has its propagation practically cut off. The local critical frequency is the square root of the larger coefficient o...","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1995-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115846068","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}
In this work the effect of ray stochasticity on the multipass absorption of lower‐hybrid waves, used to drive current in tokamaks, is considered. In toroidal geometry, stochasticity arises as an intrinsic property of the Hamiltonian ray trajectories for lower‐hybrid waves. Based on the wave kinetic equation, a diffusion equation is derived, with damping and sources, for the wave energy density in the stochastic layer. This equation is solved simultaneously with the electron Fokker–Planck equation to describe the quasilinear flattening of the electron distribution function and the subsequent modification of the wave damping. Steady‐state solutions of this system (obtained numerically) indicate that the spectral gap is filled in a self‐regulating manner, so that the boundaries of the diffused wave spectrum are independent of the level of ray stochastic diffusion. This allows the development of a simple (semianalytic) model for the self‐consistent wave spectrum and the radial profile of absorbed power.
{"title":"Statistical theory of wave propagation and multipass absorption for current drive in tokamaks","authors":"K. Kupfer, D. Moreau, X. Litaudon","doi":"10.1063/1.860557","DOIUrl":"https://doi.org/10.1063/1.860557","url":null,"abstract":"In this work the effect of ray stochasticity on the multipass absorption of lower‐hybrid waves, used to drive current in tokamaks, is considered. In toroidal geometry, stochasticity arises as an intrinsic property of the Hamiltonian ray trajectories for lower‐hybrid waves. Based on the wave kinetic equation, a diffusion equation is derived, with damping and sources, for the wave energy density in the stochastic layer. This equation is solved simultaneously with the electron Fokker–Planck equation to describe the quasilinear flattening of the electron distribution function and the subsequent modification of the wave damping. Steady‐state solutions of this system (obtained numerically) indicate that the spectral gap is filled in a self‐regulating manner, so that the boundaries of the diffused wave spectrum are independent of the level of ray stochastic diffusion. This allows the development of a simple (semianalytic) model for the self‐consistent wave spectrum and the radial profile of absorbed power.","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123995635","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}
Present x‐ray laser plasmas are in the intermediate coupling regime (0.1<Γ<4, Γ≡Z2e2/kTa, with a the ion sphere radius), where the binary collision based arguments of low density plasma kinetic theory can be misleading. The difficulty of modeling the spectral output from neonlike lasers at wavelengths near 200 A has led to the suggestion, based on a low density, electron screened, plasma model, that collisional (‘‘Dicke’’) narrowing may be important. Molecular dynamics results, which include ion collisions and screening effects, are presented here. They indicate that the free‐particle Doppler approximation is still quite accurate for λ∼200 A and Γ≲1. Collisional narrowing will become important at somewhat stronger couplings (Γ∼5) and at this wavelength the diffusion approximation is reasonable for Γ≳10. Collisional narrowing is found to be small even for the higher density (Γ≊4) nickel‐like lasers operating near 45 A.
{"title":"Absence of Dicke narrowing in x-ray laser plasmas","authors":"E. L. Pollock, R. London","doi":"10.1063/1.860565","DOIUrl":"https://doi.org/10.1063/1.860565","url":null,"abstract":"Present x‐ray laser plasmas are in the intermediate coupling regime (0.1<Γ<4, Γ≡Z2e2/kTa, with a the ion sphere radius), where the binary collision based arguments of low density plasma kinetic theory can be misleading. The difficulty of modeling the spectral output from neonlike lasers at wavelengths near 200 A has led to the suggestion, based on a low density, electron screened, plasma model, that collisional (‘‘Dicke’’) narrowing may be important. Molecular dynamics results, which include ion collisions and screening effects, are presented here. They indicate that the free‐particle Doppler approximation is still quite accurate for λ∼200 A and Γ≲1. Collisional narrowing will become important at somewhat stronger couplings (Γ∼5) and at this wavelength the diffusion approximation is reasonable for Γ≳10. Collisional narrowing is found to be small even for the higher density (Γ≊4) nickel‐like lasers operating near 45 A.","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"91 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116265332","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. Litvak, A. Sergeev, E. Suvorov, M. Tokman, I. Khazanov
Possible nonlinear effects in electron‐cyclotron plasma production and heating by microwave radiation are analyzed. They include nonlinear regimes of electron acceleration in strong microwave fields under cyclotron resonance conditions, nonstationary regimes of microwave beam self‐focusing, and some parametric processes. Presented results may be of importance for predictions of plasma response to electron‐cyclotron resonance (ECR) heating or preionization by powerful radiation.
{"title":"On nonlinear effects in electron‐cyclotron resonance plasma heating by microwave radiation","authors":"A. Litvak, A. Sergeev, E. Suvorov, M. Tokman, I. Khazanov","doi":"10.1063/1.860552","DOIUrl":"https://doi.org/10.1063/1.860552","url":null,"abstract":"Possible nonlinear effects in electron‐cyclotron plasma production and heating by microwave radiation are analyzed. They include nonlinear regimes of electron acceleration in strong microwave fields under cyclotron resonance conditions, nonstationary regimes of microwave beam self‐focusing, and some parametric processes. Presented results may be of importance for predictions of plasma response to electron‐cyclotron resonance (ECR) heating or preionization by powerful radiation.","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132414595","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. Nantel, J. Kieffer, B. L. Fontaine, H. Pépin, G. Enright, D. Villeneuve, J. Dunn, H. Baldis, O. Peyrusse
Time‐ and two‐dimensional (2‐D) space‐resolved monochromatic imaging is used to study the dynamics of Ne‐like populations in the electron collisionally excited germanium x‐ray laser. Large‐scale variations in the n=3 level population, specifically the upper level of the 2s2p63d‐2s2p63p laser transition, are observed in plasmas created in uniform and nonuniform irradiation conditions, and the degree of homogeneity along the amplification axis is related to the x‐ray gain. The influence of inhomogeneities on the core‐excited 3d‐3p x‐ray lasers is discussed.
{"title":"Dynamics of Ne-like populations in the germanium x-ray laser","authors":"M. Nantel, J. Kieffer, B. L. Fontaine, H. Pépin, G. Enright, D. Villeneuve, J. Dunn, H. Baldis, O. Peyrusse","doi":"10.1063/1.860561","DOIUrl":"https://doi.org/10.1063/1.860561","url":null,"abstract":"Time‐ and two‐dimensional (2‐D) space‐resolved monochromatic imaging is used to study the dynamics of Ne‐like populations in the electron collisionally excited germanium x‐ray laser. Large‐scale variations in the n=3 level population, specifically the upper level of the 2s2p63d‐2s2p63p laser transition, are observed in plasmas created in uniform and nonuniform irradiation conditions, and the degree of homogeneity along the amplification axis is related to the x‐ray gain. The influence of inhomogeneities on the core‐excited 3d‐3p x‐ray lasers is discussed.","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"2014 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127575373","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 two‐dimensional, self‐consistent, nonlinear model is used to determine the growth rate and saturation level of the cyclotron two‐stream instability for two weakly relativistic electron beams copropagating along a uniform magnetic field with an inverted population in the perpendicular momentum. This instability has been proposed recently as the basis for a double‐stream cyclotron maser. Good agreement is found between the dispersion analysis and computer simulations in the linear regime. The effect of axial momentum spread on the instability is investigated. It is shown that the cyclotron two‐stream instability is primarily electrostatic, which calls for further exploration of an effective input and output coupling scheme for the maser.
{"title":"Linear and nonlinear analysis of the cyclotron two-stream instability","authors":"Chi-ping Chen, G. Bekefi, Wen Hu","doi":"10.1063/1.860564","DOIUrl":"https://doi.org/10.1063/1.860564","url":null,"abstract":"A two‐dimensional, self‐consistent, nonlinear model is used to determine the growth rate and saturation level of the cyclotron two‐stream instability for two weakly relativistic electron beams copropagating along a uniform magnetic field with an inverted population in the perpendicular momentum. This instability has been proposed recently as the basis for a double‐stream cyclotron maser. Good agreement is found between the dispersion analysis and computer simulations in the linear regime. The effect of axial momentum spread on the instability is investigated. It is shown that the cyclotron two‐stream instability is primarily electrostatic, which calls for further exploration of an effective input and output coupling scheme for the maser.","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114884800","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 fast penetration of a strong magnetic field into a plasma, caused by the Hall effect, is studied. The phenomenon is likely to govern the early evolution of the magnetic field not only in two‐dimensional geometry, to which previous studies were restricted, but also in three dimensions. This penetration mechanism is suppressed, if both the plasma and electrodes are collisionless, vAeτe≳a, where vAe is the electron Alfven velocity, τe−1 the collision frequency, and a the characteristic space‐scale. However, the collisionless penetration can occur in the case of a resistive cathode. The self‐consistent effect of ion motion is shown to be of importance only in a very special geometry. Then the penetration speed is limited by the value VA(aωpi/c)−1/3, where VA is the Alfven velocity and c/ωpi the ion skin depth.
{"title":"On the fast penetration of magnetic field into plasma","authors":"J. Kalda","doi":"10.1063/1.860549","DOIUrl":"https://doi.org/10.1063/1.860549","url":null,"abstract":"The fast penetration of a strong magnetic field into a plasma, caused by the Hall effect, is studied. The phenomenon is likely to govern the early evolution of the magnetic field not only in two‐dimensional geometry, to which previous studies were restricted, but also in three dimensions. This penetration mechanism is suppressed, if both the plasma and electrodes are collisionless, vAeτe≳a, where vAe is the electron Alfven velocity, τe−1 the collision frequency, and a the characteristic space‐scale. However, the collisionless penetration can occur in the case of a resistive cathode. The self‐consistent effect of ion motion is shown to be of importance only in a very special geometry. Then the penetration speed is limited by the value VA(aωpi/c)−1/3, where VA is the Alfven velocity and c/ωpi the ion skin depth.","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130212079","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 tokamak with slightly imperfect magnetic surfaces should have a microscopically filamented current structure. If so, its equilibrium has an analog in the dynamics of interacting charged rods. Then there will be a natural current profile, analogous to thermal equilibrium of the rods (and the natural profile can be calculated by conventional statistical mechanics). This would account for the phenomenon of profile consistency or resilience in tokamaks. In addition to the natural profiles, this filamentary model also predicts an anomalous inward flux of both heat and particles in a tokamak, as well as an anomalous diffusion. These ‘‘inward‐pinch’’ components are related to the current gradient.
{"title":"Filamentation, current profiles, and transport in a tokamak","authors":"J. Taylor","doi":"10.1063/1.860555","DOIUrl":"https://doi.org/10.1063/1.860555","url":null,"abstract":"A tokamak with slightly imperfect magnetic surfaces should have a microscopically filamented current structure. If so, its equilibrium has an analog in the dynamics of interacting charged rods. Then there will be a natural current profile, analogous to thermal equilibrium of the rods (and the natural profile can be calculated by conventional statistical mechanics). This would account for the phenomenon of profile consistency or resilience in tokamaks. In addition to the natural profiles, this filamentary model also predicts an anomalous inward flux of both heat and particles in a tokamak, as well as an anomalous diffusion. These ‘‘inward‐pinch’’ components are related to the current gradient.","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124191888","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}
Experiments are reported on the ion thermal transport due to the ion‐temperature‐ gradient‐driven instability (ITG mode) and its transport scaling properties with respect to instability parameters like fluctuation level n/ni and linear growth rate as well as the drive parameter ηi(=∂ ln[Ti]/∂ ln[ni]) in the Columbia Linear Machine [Phys. Fluids 26, 1044 (1983)]. The measured local ion thermal conductivity χ⊥(r) is highly anomalous and strongly correlated with the radial profile of the ITG mode. The linear scaling of the averaged thermal conductivity 〈χ⊥(r)〉 with the averaged mode fluctuation level 〈n/ni〉 and linear growth rate indicates strong turbulence‐type scaling. The scaling of χ⊥ with the drive parameter ηi is offset linear.
{"title":"Ion‐temperature‐gradient instability driven transport and its parametric scaling","authors":"B. Song, A. Sen, P. Tham","doi":"10.1063/1.860551","DOIUrl":"https://doi.org/10.1063/1.860551","url":null,"abstract":"Experiments are reported on the ion thermal transport due to the ion‐temperature‐ gradient‐driven instability (ITG mode) and its transport scaling properties with respect to instability parameters like fluctuation level n/ni and linear growth rate as well as the drive parameter ηi(=∂ ln[Ti]/∂ ln[ni]) in the Columbia Linear Machine [Phys. Fluids 26, 1044 (1983)]. The measured local ion thermal conductivity χ⊥(r) is highly anomalous and strongly correlated with the radial profile of the ITG mode. The linear scaling of the averaged thermal conductivity 〈χ⊥(r)〉 with the averaged mode fluctuation level 〈n/ni〉 and linear growth rate indicates strong turbulence‐type scaling. The scaling of χ⊥ with the drive parameter ηi is offset linear.","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115964195","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}
Thermal corrections to E×B drifts cause small structures in pure electron plasmas to smear. This smearing breaks the strict analogy between the behavior of pure electron plasmas and the behavior of two‐dimensional inviscid fluids. The causes and consequences of this smearing are discussed, a criterion for the validity of the plasma/fluid analogy is constructed, and experimental examples of the failure of the analogy are presented. The criterion indicates that fluid‐like behavior can persist to scale lengths far smaller than the normal ‘‘collective’’ behavior limit.
{"title":"A limitation to the analogy between pure electron plasmas and two‐dimensional inviscid fluids","authors":"A. J. Peurrung, J. Fajans","doi":"10.1063/1.860546","DOIUrl":"https://doi.org/10.1063/1.860546","url":null,"abstract":"Thermal corrections to E×B drifts cause small structures in pure electron plasmas to smear. This smearing breaks the strict analogy between the behavior of pure electron plasmas and the behavior of two‐dimensional inviscid fluids. The causes and consequences of this smearing are discussed, a criterion for the validity of the plasma/fluid analogy is constructed, and experimental examples of the failure of the analogy are presented. The criterion indicates that fluid‐like behavior can persist to scale lengths far smaller than the normal ‘‘collective’’ behavior limit.","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122418192","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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