Transverse instabilities are investigated for the slab analog of the Bennett equilibrium of a magnetically self‐focused relativistic electron beam propagating through a plasma. Two kinds of plasma are considered: a channel matched to the beam and a broad uniform plasma. The high‐frequency electrostatic transverse two‐stream instability and the lower‐frequency resistive‐hose instability are treated analytically with a distributed tune (‘‘mass’’) model. Asymptotic growth is computed for each instability in various regimes, and analytic results are benchmarked against numerical solutions of the linearized system and particle‐in‐cell simulations. It is found that in the limit of large collisionless skin depth the electrostatic hose is the more virulent mode of beam breakup. Numerical examples are discussed for parameters in the range considered for plasma focusing of the asymmetric beams of interest in high‐energy physics.
{"title":"Cumulative hose instabilities of a magnetically self-focused slab electron beam","authors":"D. Whittum","doi":"10.1063/1.860559","DOIUrl":"https://doi.org/10.1063/1.860559","url":null,"abstract":"Transverse instabilities are investigated for the slab analog of the Bennett equilibrium of a magnetically self‐focused relativistic electron beam propagating through a plasma. Two kinds of plasma are considered: a channel matched to the beam and a broad uniform plasma. The high‐frequency electrostatic transverse two‐stream instability and the lower‐frequency resistive‐hose instability are treated analytically with a distributed tune (‘‘mass’’) model. Asymptotic growth is computed for each instability in various regimes, and analytic results are benchmarked against numerical solutions of the linearized system and particle‐in‐cell simulations. It is found that in the limit of large collisionless skin depth the electrostatic hose is the more virulent mode of beam breakup. Numerical examples are discussed for parameters in the range considered for plasma focusing of the asymmetric beams of interest in high‐energy physics.","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"8 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":"117172897","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}
G. Smith, D. R. Cook, A. Kaufman, A. Kritz, S. W. Mcdonald
Discussion and applications are presented for two approaches for estimating the effects of scattering of electromagnetic waves by turbulent density fluctuations in tokamaks. Ordinary‐mode waves propagating nearly perpendicular to the equilibrium magnetic field are considered. The multiple‐scattering approach provides analytic results for the angular and spatial spreading of a microwave beam by the turbulence. The single‐scattering approach yields numerical results and is derived by a compact technique involving Wigner functions. Both approaches are applied to idealized tokamaks to clarify relationships between the approaches and to test limits of applicability of the multiple‐scattering approach.
{"title":"Scattering of ordinary‐mode electromagnetic waves by density fluctuations in tokamaks","authors":"G. Smith, D. R. Cook, A. Kaufman, A. Kritz, S. W. Mcdonald","doi":"10.1063/1.860547","DOIUrl":"https://doi.org/10.1063/1.860547","url":null,"abstract":"Discussion and applications are presented for two approaches for estimating the effects of scattering of electromagnetic waves by turbulent density fluctuations in tokamaks. Ordinary‐mode waves propagating nearly perpendicular to the equilibrium magnetic field are considered. The multiple‐scattering approach provides analytic results for the angular and spatial spreading of a microwave beam by the turbulence. The single‐scattering approach yields numerical results and is derived by a compact technique involving Wigner functions. Both approaches are applied to idealized tokamaks to clarify relationships between the approaches and to test limits of applicability of the multiple‐scattering approach.","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":"127159964","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}
Data from several diagnostics employed on the Large s Experiment (LSX) field‐reversed theta pinch were analyzed to seek correlation between plasma distortions and the confinement properties of the field‐reversed configurations (FRC’s) formed. In particular, an array of Bθ probes was used to determine separatrix movement, which might indicate the existence of low‐order modes, such as a tilt instability. No correlation between the quality of confinement and signal was observed. The parameter s, equal to the average number of ion gyroradii inside the separatrix, has been postulated as a measure of FRC stability with values above 2, leading to instability and loss of confinement. However, the confinement observed in experiments conducted over a large range of s (1
{"title":"Stability of field-reversed configurations in the large s experiment (LSX)","authors":"J. Slough, A. Hoffman","doi":"10.1063/1.860554","DOIUrl":"https://doi.org/10.1063/1.860554","url":null,"abstract":"Data from several diagnostics employed on the Large s Experiment (LSX) field‐reversed theta pinch were analyzed to seek correlation between plasma distortions and the confinement properties of the field‐reversed configurations (FRC’s) formed. In particular, an array of Bθ probes was used to determine separatrix movement, which might indicate the existence of low‐order modes, such as a tilt instability. No correlation between the quality of confinement and signal was observed. The parameter s, equal to the average number of ion gyroradii inside the separatrix, has been postulated as a measure of FRC stability with values above 2, leading to instability and loss of confinement. However, the confinement observed in experiments conducted over a large range of s (1<s<8) appeared to correlate more with the shape of the equilibrium radial density profile produced during formation rather than s. Flatter profiles correlated with poorer confinement.","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"75 1 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":"128056487","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}
Efficient techniques for computing axisymmetric non‐neutral plasma equilibria are described. These equilibria may be obtained either by requiring global thermal equilibrium, by specifying the midplane radial density profile, or by specifying the radial profile of ∫n dz. Both splines and finite‐differences are used, and the accuracy of the two is compared by using a new characterization of the thermal equilibrium density profile which gives a simple formula for estimating the radial and axial gradient scale lengths of thermal equilibria. It is found that for global thermal equilibrium 1% accuracy is achieved with splines if the distance between neighboring splines is about two Debye lengths while finite differences require a grid spacing of about one‐half Debye length to achieve the same accuracy.
{"title":"Numerical calculation of axisymmetric non‐neutral plasma equilibria","authors":"R. Spencer, S. N. Rasband, R. Vanfleet","doi":"10.1063/1.860594","DOIUrl":"https://doi.org/10.1063/1.860594","url":null,"abstract":"Efficient techniques for computing axisymmetric non‐neutral plasma equilibria are described. These equilibria may be obtained either by requiring global thermal equilibrium, by specifying the midplane radial density profile, or by specifying the radial profile of ∫n dz. Both splines and finite‐differences are used, and the accuracy of the two is compared by using a new characterization of the thermal equilibrium density profile which gives a simple formula for estimating the radial and axial gradient scale lengths of thermal equilibria. It is found that for global thermal equilibrium 1% accuracy is achieved with splines if the distance between neighboring splines is about two Debye lengths while finite differences require a grid spacing of about one‐half Debye length to achieve the same accuracy.","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"12 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":"128473195","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. Ghizzo, P. Bertrand, M. Shoucri, E. Fijalkow, M. Feix
A drift‐kinetic Eulerian Vlasov code, with fluid equations for the ions, is developed to study the problem of the injection of an electron beam into a two‐dimensional magnetized plasma, often referred to as direct current (dc) helicity injection. The diffusion of electrons across a magnetic field in the presence of a beam–plasma instability is studied. The case of a magnetic field tilted with respect to the beam direction is considered. The competition between the velocity shear Kelvin–Helmholtz (KH) and the beam–plasma (BP) instabilities is investigated in order to analyze the plasma heating and current drive mechanism induced by the beam injection. The KH instability generates low‐frequency plasma convection motion associated with cE×B/B2 drift. In particular, the diffusion coefficients Dy and Dv ∥ describing, respectively, the anomalous diffusion process induced in space across the magnetic field by the KH instability, and the velocity diffusion process due to the kinetic effects induced in velocity sp...
{"title":"Study of the diffusion across a magnetic field in a beam–plasma interaction using a drift‐kinetic Vlasov code","authors":"A. Ghizzo, P. Bertrand, M. Shoucri, E. Fijalkow, M. Feix","doi":"10.1063/1.860548","DOIUrl":"https://doi.org/10.1063/1.860548","url":null,"abstract":"A drift‐kinetic Eulerian Vlasov code, with fluid equations for the ions, is developed to study the problem of the injection of an electron beam into a two‐dimensional magnetized plasma, often referred to as direct current (dc) helicity injection. The diffusion of electrons across a magnetic field in the presence of a beam–plasma instability is studied. The case of a magnetic field tilted with respect to the beam direction is considered. The competition between the velocity shear Kelvin–Helmholtz (KH) and the beam–plasma (BP) instabilities is investigated in order to analyze the plasma heating and current drive mechanism induced by the beam injection. The KH instability generates low‐frequency plasma convection motion associated with cE×B/B2 drift. In particular, the diffusion coefficients Dy and Dv ∥ describing, respectively, the anomalous diffusion process induced in space across the magnetic field by the KH instability, and the velocity diffusion process due to the kinetic effects induced in velocity sp...","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":"134364645","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 weak turbulence theory of Langmuir waves in a one‐dimensional, one‐species plasma is discussed. Analytic calculations using the theory of two‐point correlations show that in the weak turbulence regime, τac≪min(τtr,γ−1k) (where τac is the field autocorrelation time and τtr is the particle decorrelation time), the nonlinear enhancement of the mode growth rate γk beyond the linear, Landau growth rate γkL is small, additive, and higher order in the weak turbulence expansion parameter. This result thus supports the validity of the quasilinear theory for Langmuir wave turbulence, and disagrees with the predictions of Adam, Laval, and Pesme [Phys. Rev. Lett. 43, 1671 (1979)], which indicate a non‐negligible, multiplicative enhancement in the regime τac≪τtr≪γ−1k. Analysis shows that their result comes from the use of an invalid source term for the fluctuations.
{"title":"Revisiting the validity of quasilinear theory","authors":"Y.‐M. Liang, P. Diamond","doi":"10.1063/1.860550","DOIUrl":"https://doi.org/10.1063/1.860550","url":null,"abstract":"The weak turbulence theory of Langmuir waves in a one‐dimensional, one‐species plasma is discussed. Analytic calculations using the theory of two‐point correlations show that in the weak turbulence regime, τac≪min(τtr,γ−1k) (where τac is the field autocorrelation time and τtr is the particle decorrelation time), the nonlinear enhancement of the mode growth rate γk beyond the linear, Landau growth rate γkL is small, additive, and higher order in the weak turbulence expansion parameter. This result thus supports the validity of the quasilinear theory for Langmuir wave turbulence, and disagrees with the predictions of Adam, Laval, and Pesme [Phys. Rev. Lett. 43, 1671 (1979)], which indicate a non‐negligible, multiplicative enhancement in the regime τac≪τtr≪γ−1k. Analysis shows that their result comes from the use of an invalid source term for the fluctuations.","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"19 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":"134302950","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}
Neoclassical ion viscosity of a steady tokamak plasma with large mass flow is calculated in a general geometry. In addition to the usual ‘‘resonant’’ contribution, the ‘‘nonresonant’’ contribution has been evaluated. It is found that the nonresonant contribution is not small compared to the resonant contribution when the poloidal rotation speed is large. The viscosity evaluation has been reduced to one‐dimensional integrals. Furthermore, simple analytic formula for the viscosity coefficients are suggested. The velocity strain, which is the source of the viscosity, is also analyzed in detail.
{"title":"Neoclassical viscosity of a tokamak plasma with large mass flow","authors":"C. Chang","doi":"10.1063/1.860553","DOIUrl":"https://doi.org/10.1063/1.860553","url":null,"abstract":"Neoclassical ion viscosity of a steady tokamak plasma with large mass flow is calculated in a general geometry. In addition to the usual ‘‘resonant’’ contribution, the ‘‘nonresonant’’ contribution has been evaluated. It is found that the nonresonant contribution is not small compared to the resonant contribution when the poloidal rotation speed is large. The viscosity evaluation has been reduced to one‐dimensional integrals. Furthermore, simple analytic formula for the viscosity coefficients are suggested. The velocity strain, which is the source of the viscosity, is also analyzed in detail.","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"25 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":"124992842","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 article, a general study of diffusional effects is made numerically as well as theoretically with the aim to reproduce not only the current scaling of ion diodes but also the divergence of the ion beam and physical features such as virtual cathode movement due to the diamagnetic effect. It has been observed experimentally that the ion current exceeds that quantity which would be expected in the presence of a strong magnetic field. It is demonstrated that with the introduction of a diffusional field Eθ into the stationary 21/2‐dimensional particle‐in‐cell code based on boundary‐fitted coordinates [T. Westermann, Nucl. Instrum. Methods A 263, 271 (1988)] the simulation results agree well with experiment. This ad hoc model is supported theoretically by linear stability analysis of the stationary state.
{"title":"Investigations of diffusional effects in applied‐B ion diodes","authors":"T. Westermann, R. Schuldt","doi":"10.1063/1.860956","DOIUrl":"https://doi.org/10.1063/1.860956","url":null,"abstract":"In this article, a general study of diffusional effects is made numerically as well as theoretically with the aim to reproduce not only the current scaling of ion diodes but also the divergence of the ion beam and physical features such as virtual cathode movement due to the diamagnetic effect. It has been observed experimentally that the ion current exceeds that quantity which would be expected in the presence of a strong magnetic field. It is demonstrated that with the introduction of a diffusional field Eθ into the stationary 21/2‐dimensional particle‐in‐cell code based on boundary‐fitted coordinates [T. Westermann, Nucl. Instrum. Methods A 263, 271 (1988)] the simulation results agree well with experiment. This ad hoc model is supported theoretically by linear stability analysis of the stationary state.","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"36 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":"114681705","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}
Similarity solutions to a problem in radiative magnetogasdynamics with strong shocks are presented. Group theoretic methods are used to obtain a condition on the shock Cowling number, and to characterize the state dependent form of the gas absorption coefficient for which the self‐similar solutions are admitted. Numerical calculations have been performed to determine the value of the self‐similar exponent and the profiles of the flow variables, which enable one to assess the influence of thermal radiation, the magnetic field strength, and the adiabatic heat exponent on the flow pattern.
{"title":"IMPLODING CYLINDRICAL SHOCK IN A PERFECTLY CONDUCTING AND RADIATING GAS","authors":"C. Radha, V. Sharma","doi":"10.1063/1.860596","DOIUrl":"https://doi.org/10.1063/1.860596","url":null,"abstract":"Similarity solutions to a problem in radiative magnetogasdynamics with strong shocks are presented. Group theoretic methods are used to obtain a condition on the shock Cowling number, and to characterize the state dependent form of the gas absorption coefficient for which the self‐similar solutions are admitted. Numerical calculations have been performed to determine the value of the self‐similar exponent and the profiles of the flow variables, which enable one to assess the influence of thermal radiation, the magnetic field strength, and the adiabatic heat exponent on the flow pattern.","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"41 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":"114304554","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}
Surface electron acoustic waves on a two‐electron component plasma in a semi‐infinite half‐space are investigated. The dispersion relation of these waves differs considerably from that of the surface electron plasma waves.
{"title":"Electron acoustic surface waves in a two‐electron component plasma","authors":"R. Bharuthram, S. S. Misthry, M. Yu","doi":"10.1063/1.860567","DOIUrl":"https://doi.org/10.1063/1.860567","url":null,"abstract":"Surface electron acoustic waves on a two‐electron component plasma in a semi‐infinite half‐space are investigated. The dispersion relation of these waves differs considerably from that of the surface electron plasma waves.","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"14 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":"130667954","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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