The three‐dimensional shapes of azimuthally asymmetric non‐neutral plasmas are investigated numerically, and a simple theory is developed that predicts these shapes in many circumstances.
{"title":"Three‐dimensional non‐neutral plasma shapes","authors":"A. J. Peurrung, J. Fajans","doi":"10.1063/1.860591","DOIUrl":"https://doi.org/10.1063/1.860591","url":null,"abstract":"The three‐dimensional shapes of azimuthally asymmetric non‐neutral plasmas are investigated numerically, and a simple theory is developed that predicts these shapes in many circumstances.","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":"129725545","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}
Electromagnetic wave scattering in a plasma half‐space from a propagating ion acoustic wave density perturbation with a transverse conducting boundary condition is analyzed. The analysis shows that there are two different types of scattered waves. One propagates only in the region where the plasma density is perturbed, its frequency and wave vector satisfies the conditions for a three‐wave interaction process. The other propagates as an unperturbed electron cyclotron mode with either an upshifted or downshifted frequency. Experiments are performed to examine electron cyclotron wave scattering by an ion acoustic wave excited by means of a grid along the magnetic field line in a mirror machine. The backscattered waves propagating away from the density perturbation region are measured and their dependence on the ion acoustic wavelength is examined. The scattered wave in the region of ion acoustic wave propagation is examined by measuring the scattered wave field pattern when the ion acoustic wave number is m...
{"title":"Electron cyclotron wave scattering by a probe launched ion acoustic wave","authors":"Y. S. Zhang, J. Scharer, B. Chapman","doi":"10.1063/1.860611","DOIUrl":"https://doi.org/10.1063/1.860611","url":null,"abstract":"Electromagnetic wave scattering in a plasma half‐space from a propagating ion acoustic wave density perturbation with a transverse conducting boundary condition is analyzed. The analysis shows that there are two different types of scattered waves. One propagates only in the region where the plasma density is perturbed, its frequency and wave vector satisfies the conditions for a three‐wave interaction process. The other propagates as an unperturbed electron cyclotron mode with either an upshifted or downshifted frequency. Experiments are performed to examine electron cyclotron wave scattering by an ion acoustic wave excited by means of a grid along the magnetic field line in a mirror machine. The backscattered waves propagating away from the density perturbation region are measured and their dependence on the ion acoustic wavelength is examined. The scattered wave in the region of ion acoustic wave propagation is examined by measuring the scattered wave field pattern when the ion acoustic wave number is m...","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":"128215650","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 evolution of tearing modes with multiple rational surfaces is discussed. It is demonstrated that, in the presence of small differential rotation, the nonlinear growth might be faster than exponential. This growth occurs as the rotation frequencies of the plasma at the different rational surfaces equilibrate.
{"title":"Nonlinear self‐reinforced growth of tearing modes with multiple rational surfaces","authors":"M. Persson, R. Dewar, E. Maschke","doi":"10.1063/1.860606","DOIUrl":"https://doi.org/10.1063/1.860606","url":null,"abstract":"The nonlinear evolution of tearing modes with multiple rational surfaces is discussed. It is demonstrated that, in the presence of small differential rotation, the nonlinear growth might be faster than exponential. This growth occurs as the rotation frequencies of the plasma at the different rational surfaces equilibrate.","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"39 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":"124794038","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}
Measurements of the radiative power loss are performed on the Extrap‐T1 reversed‐field pinch [Phys. Scr. 44, 358 (1991)] using an absolutely calibrated vacuum ultraviolet spectrometer in the wavelength range between 100 and 1700 A. The contributions to the radiative power loss from deuterium, carbon, nitrogen, oxygen, and chlorine are measured. These partial radiative power losses are further divided into contributions from different ionization stages of these impurities. The additional contribution to the cooling rate due to ionization processes is estimated. Impurities are found to be a main contributor to the power loss in the initial phase of the discharge. Toward the end of the discharge, radiative power loss amounts to less than 10% of the input power, due to the decrease of the electron density. Because of the short particle confinement time and high recycling of impurities, specifically oxygen, the rate coefficient for radiative power loss per ion is only slightly reduced by the increase of the te...
{"title":"Total and partial radiative power loss at high impurity recycling studied in the Extrap‐T1 reversed‐field pinch experiment","authors":"K. Zastrow, J. Brzozowski","doi":"10.1063/1.860578","DOIUrl":"https://doi.org/10.1063/1.860578","url":null,"abstract":"Measurements of the radiative power loss are performed on the Extrap‐T1 reversed‐field pinch [Phys. Scr. 44, 358 (1991)] using an absolutely calibrated vacuum ultraviolet spectrometer in the wavelength range between 100 and 1700 A. The contributions to the radiative power loss from deuterium, carbon, nitrogen, oxygen, and chlorine are measured. These partial radiative power losses are further divided into contributions from different ionization stages of these impurities. The additional contribution to the cooling rate due to ionization processes is estimated. Impurities are found to be a main contributor to the power loss in the initial phase of the discharge. Toward the end of the discharge, radiative power loss amounts to less than 10% of the input power, due to the decrease of the electron density. Because of the short particle confinement time and high recycling of impurities, specifically oxygen, the rate coefficient for radiative power loss per ion is only slightly reduced by the increase of the te...","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"12 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":"124140871","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 mode conversion‐tunneling equation with weakly relativistic absorption at 3ωce has been solved by using the Green function method. The numerical results show that the reflection and conversion coefficients are dramatically reduced when relativistic absorption is included, while the transmission coefficients and the conversion coefficient from the X‐mode on the high field side to the O‐mode on the low field side are independent of absorption. The reduction of these coefficients leads to the reduction of the asymmetry in the absorption between different wave branches. The numerical results also show that the relativistic effect is important even for a relatively low temperature plasma. An important relationship between solutions is expressed by the reciprocity relations which have been proved for any harmonic number. These analyses modify the interpretation of electron cyclotron emission (ECE).
{"title":"Synchrotron radiation and absorption at 3ωce with X‐mode–O‐mode coupling","authors":"J. Hu, D. Swanson","doi":"10.1063/1.860588","DOIUrl":"https://doi.org/10.1063/1.860588","url":null,"abstract":"The mode conversion‐tunneling equation with weakly relativistic absorption at 3ωce has been solved by using the Green function method. The numerical results show that the reflection and conversion coefficients are dramatically reduced when relativistic absorption is included, while the transmission coefficients and the conversion coefficient from the X‐mode on the high field side to the O‐mode on the low field side are independent of absorption. The reduction of these coefficients leads to the reduction of the asymmetry in the absorption between different wave branches. The numerical results also show that the relativistic effect is important even for a relatively low temperature plasma. An important relationship between solutions is expressed by the reciprocity relations which have been proved for any harmonic number. These analyses modify the interpretation of electron cyclotron emission (ECE).","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"13 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":"114065007","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 magnetohydrodynamic stability of a low‐pressure plasma confined along the magnetic field by the end walls that are perfectly reflecting the impinging particles is considered. It is shown that, if the magnetic field lines do not intersect the walls along the normal, a fast instability can develop. An explicit expression for the growth rate has been derived, and an analogy with the usual flute instability has been traced. The instability can play some role in the scrape‐off layers of tokamaks with poloidal limiter.
{"title":"Flute instability in a plasma confined by perfectly reflecting end walls","authors":"D. Farina, R. Pozzoli, D. Ryutov","doi":"10.1063/1.860573","DOIUrl":"https://doi.org/10.1063/1.860573","url":null,"abstract":"The magnetohydrodynamic stability of a low‐pressure plasma confined along the magnetic field by the end walls that are perfectly reflecting the impinging particles is considered. It is shown that, if the magnetic field lines do not intersect the walls along the normal, a fast instability can develop. An explicit expression for the growth rate has been derived, and an analogy with the usual flute instability has been traced. The instability can play some role in the scrape‐off layers of tokamaks with poloidal limiter.","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"451 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114096869","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}
Numerical simulations of current sheet formation in a two‐dimensional ideal incompressible magnetohydrodynamic system reveal that sheets evolve self‐similarly with cross‐sheet profiles close to j(ψ)∝exp(−2αψ). This current profile has previously been derived by several authors as the most probable state in a current‐carrying plasma. A critical review of the different theoretical approaches is given.
{"title":"Current sheet profiles in two-dimensional magnetohydrodynamics","authors":"D. Biskamp","doi":"10.1063/1.860612","DOIUrl":"https://doi.org/10.1063/1.860612","url":null,"abstract":"Numerical simulations of current sheet formation in a two‐dimensional ideal incompressible magnetohydrodynamic system reveal that sheets evolve self‐similarly with cross‐sheet profiles close to j(ψ)∝exp(−2αψ). This current profile has previously been derived by several authors as the most probable state in a current‐carrying plasma. A critical review of the different theoretical approaches is given.","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"45 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":"133714127","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 virial for a system of very long, parallel, charged rods is particularly simple. The virial equation (‘‘theorem’’) relates that quantity to the wall virial and to random and organized internal energies of the system. In the case of a long cylinder of pure‐electron plasma, the virial equation contains, as a special case, an equation derived recently by Davidson and Lund on the basis of mean‐field theory. The virial equation may be used to control the computation of thermodynamic functions for the plasma. It also gives insight into the more complicated motions which occur when the central axis of the column moves in a closed orbit.
{"title":"Virial equation for the two‐dimensional pure electron plasma","authors":"N. Corngold","doi":"10.1063/1.860607","DOIUrl":"https://doi.org/10.1063/1.860607","url":null,"abstract":"The virial for a system of very long, parallel, charged rods is particularly simple. The virial equation (‘‘theorem’’) relates that quantity to the wall virial and to random and organized internal energies of the system. In the case of a long cylinder of pure‐electron plasma, the virial equation contains, as a special case, an equation derived recently by Davidson and Lund on the basis of mean‐field theory. The virial equation may be used to control the computation of thermodynamic functions for the plasma. It also gives insight into the more complicated motions which occur when the central axis of the column moves in a closed orbit.","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":"125319930","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 type of eddy‐damped quasinormal Markovian (EDQNM) closure is shown to be potentially nonrealizable in the presence of linear wave phenomena. This statistical closure results from the application of a fluctuation–dissipation (FD) ansatz to the direct‐interaction approximation (DIA); unlike in phenomenological formulations of the EDQNM, both the frequency and the damping rate are renormalized. A violation of realizability can have serious physical consequences, including the prediction of negative or even divergent energies. A new statistical approximation, the realizable Markovian closure (RMC), is proposed as a remedy. An underlying Langevin equation that makes no assumption of white‐noise statistics is exhibited. Even in the wave‐free case the RMC, which is based on a nonstationary version of the FD ansatz, provides a better representation of the true dynamics than does the EDQNM closure. The closure solutions are compared numerically against the exact ensemble dynamics of three interacting waves.
{"title":"The realizable Markovian closure. I. General theory, with application to three‐wave dynamics","authors":"J. Bowman, J. Krommes, M. Ottaviani","doi":"10.1063/1.860829","DOIUrl":"https://doi.org/10.1063/1.860829","url":null,"abstract":"A type of eddy‐damped quasinormal Markovian (EDQNM) closure is shown to be potentially nonrealizable in the presence of linear wave phenomena. This statistical closure results from the application of a fluctuation–dissipation (FD) ansatz to the direct‐interaction approximation (DIA); unlike in phenomenological formulations of the EDQNM, both the frequency and the damping rate are renormalized. A violation of realizability can have serious physical consequences, including the prediction of negative or even divergent energies. A new statistical approximation, the realizable Markovian closure (RMC), is proposed as a remedy. An underlying Langevin equation that makes no assumption of white‐noise statistics is exhibited. Even in the wave‐free case the RMC, which is based on a nonstationary version of the FD ansatz, provides a better representation of the true dynamics than does the EDQNM closure. The closure solutions are compared numerically against the exact ensemble dynamics of three interacting waves.","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125317068","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 the authors describe a perturbation method used to calculate the flow of a compressible magnetized plasma around a sharp corner with a small turning angle. The main purpose for this analysis is the study of the flow in the exit region of a plasma accelerator in the regime of high magnetic Reynolds number. The physical model is based on a one‐fluid resistive magnetohydrodynamic model (continuum model). The analysis predicts the existence of an acoustic expansion fan near the sharp corner, and a magnetoacoustic expansion fan in the far field. The current lines refract across the acoustic fan. Near an anode there is a strong mass depletion downstream of the corner. Along an anode, some of the current lines reattach far downstream, creating a magnetic boundary layer along the electrode. Near a cathode there is a region of high density and high temperature ahead of the corner. Along a cathode most of the current attaches itself ahead of the corner. Finally, the current refraction predicted by t...
{"title":"Linear analysis of a resistive compressible plasma flow around a sharp corner","authors":"J. Chanty, M. Martínez-Sánchez","doi":"10.1063/1.860824","DOIUrl":"https://doi.org/10.1063/1.860824","url":null,"abstract":"In this article the authors describe a perturbation method used to calculate the flow of a compressible magnetized plasma around a sharp corner with a small turning angle. The main purpose for this analysis is the study of the flow in the exit region of a plasma accelerator in the regime of high magnetic Reynolds number. The physical model is based on a one‐fluid resistive magnetohydrodynamic model (continuum model). The analysis predicts the existence of an acoustic expansion fan near the sharp corner, and a magnetoacoustic expansion fan in the far field. The current lines refract across the acoustic fan. Near an anode there is a strong mass depletion downstream of the corner. Along an anode, some of the current lines reattach far downstream, creating a magnetic boundary layer along the electrode. Near a cathode there is a region of high density and high temperature ahead of the corner. Along a cathode most of the current attaches itself ahead of the corner. Finally, the current refraction predicted by t...","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129949006","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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