Relativistic plasma mode conversion‐tunneling equations at the second and third electron cyclotron harmonics are derived. A finite k∥ is introduced which keeps the coupling between the O‐mode, the X‐mode and the Bernstein wave in the mode conversion problem for the first time. The solutions for these mode conversion problems without absorption are obtained, and the connection formulas between different wave branches are established. The corresponding transmission, reflection and conversion coefficients are also given. A comparison between the coupled equation and the uncoupled equations is also made.
{"title":"Mode conversion at electron cyclotron harmonics with finite k","authors":"J. Hu, D. Swanson","doi":"10.1063/1.860587","DOIUrl":"https://doi.org/10.1063/1.860587","url":null,"abstract":"Relativistic plasma mode conversion‐tunneling equations at the second and third electron cyclotron harmonics are derived. A finite k∥ is introduced which keeps the coupling between the O‐mode, the X‐mode and the Bernstein wave in the mode conversion problem for the first time. The solutions for these mode conversion problems without absorption are obtained, and the connection formulas between different wave branches are established. The corresponding transmission, reflection and conversion coefficients are also given. A comparison between the coupled equation and the uncoupled equations is also made.","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"46 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":"132802764","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}
For the simulation of laser‐created plasmas, hydrodynamic codes need an atomic physics package, for both the equation of state and the optical properties, which does not use the hypothesis of local thermodynamical equilibrium (LTE). However, in x‐ray laser studies, as well as in indirect drive inertial confinement fusion studies, high‐Z materials can be found where radiation trapping can induce a significant departure from the optically thin description. A method is presented in which an existing LTE code can be changed into a non‐LTE code with radiation‐dependent ionization. This method is numerically simple and its cost, in terms of computing time, is low enough to be used in two‐dimensional simulations.
{"title":"Radiation-dependent ionization model for laser-created plasmas","authors":"M. Busquet","doi":"10.1063/1.860586","DOIUrl":"https://doi.org/10.1063/1.860586","url":null,"abstract":"For the simulation of laser‐created plasmas, hydrodynamic codes need an atomic physics package, for both the equation of state and the optical properties, which does not use the hypothesis of local thermodynamical equilibrium (LTE). However, in x‐ray laser studies, as well as in indirect drive inertial confinement fusion studies, high‐Z materials can be found where radiation trapping can induce a significant departure from the optically thin description. A method is presented in which an existing LTE code can be changed into a non‐LTE code with radiation‐dependent ionization. This method is numerically simple and its cost, in terms of computing time, is low enough to be used in two‐dimensional simulations.","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"21 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":"132859673","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 hydromagnetic equation system for the interplanetary collisionless solar wind is used to derive a set of conservation laws for that medium. It is found that every equation of the original system, including the closure relation, is related to one conservation law. The set that has been derived does not only include the traditional laws, but also a new one for the magnetic moment of the electrons. The conservation set is then used to obtain the space constants for the solar coronal expansion. The new law yields a constant that has not been predicted by other models.
{"title":"A closed set of conservation laws and the evolution of the electron magnetic moment in the collisionless solar wind","authors":"P. Alexander","doi":"10.1063/1.860581","DOIUrl":"https://doi.org/10.1063/1.860581","url":null,"abstract":"A hydromagnetic equation system for the interplanetary collisionless solar wind is used to derive a set of conservation laws for that medium. It is found that every equation of the original system, including the closure relation, is related to one conservation law. The set that has been derived does not only include the traditional laws, but also a new one for the magnetic moment of the electrons. The conservation set is then used to obtain the space constants for the solar coronal expansion. The new law yields a constant that has not been predicted by other models.","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"19 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":"115378198","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}
P. G. Matthews, David L. T. Anderson, F. Anderson, J. Shohet, J. Talmadge
Probe measurements over the two‐dimensional plasma cross section of the average and fluctuating density, electron temperature, and potential, as well as the Reynolds stress, have been made in the Interchangeable Module Stellarator (IMS) [D. T. Anderson, J. A. Derr, and J. L. Shohet, IEEE Trans. Plasma Sci. PS‐9, 212 (1981)]. These measurements were performed at two magnetic field strengths, and also when a positively biased electrode induces a poloidal plasma flow. The data shows the fluctuation‐induced transport to be poloidally asymmetric and dependent upon the location of the electron cyclotron resonance position, and upon the electrode biasing. The induced poloidal plasma flow changes the nominally outward fluctuation‐induced particle transport to be inward (negative radial transport) by changing the phase relationship of the density and potential oscillations. The amplitude of the density and potential fluctuations are, in general, not reduced by the sheared poloidal flow. Calculations are presented comparing the computed Reynolds stress induced poloidal plasma flows with the flow calculated from momentum balance.
在可互换模块仿星器(IMS)上对二维等离子体横截面的平均和波动密度、电子温度、电势以及雷诺应力进行了探针测量[D]。T. Anderson, J. A. Derr, J. L. Shohet, IEEE译。等离子体科学。[j].生物工程学报，2012(1)。这些测量是在两种磁场强度下进行的，也是在正偏置电极诱导极向等离子体流时进行的。数据表明，波动诱导的输运是极性不对称的，并且依赖于电子回旋共振位置的位置和电极偏置。诱导极向等离子体流通过改变密度和势振荡的相位关系，将名义上的向外波动诱导的粒子输运转变为向内(负径向输运)。一般来说，密度和电位波动的振幅不会因剪切的极向流而减小。将计算得到的雷诺应力诱导的极向等离子体流与动量平衡计算得到的极向等离子体流进行了比较。
{"title":"Fluctuation-induced transport and poloidal rotation in the interchangeable module stellarator","authors":"P. G. Matthews, David L. T. Anderson, F. Anderson, J. Shohet, J. Talmadge","doi":"10.1063/1.860574","DOIUrl":"https://doi.org/10.1063/1.860574","url":null,"abstract":"Probe measurements over the two‐dimensional plasma cross section of the average and fluctuating density, electron temperature, and potential, as well as the Reynolds stress, have been made in the Interchangeable Module Stellarator (IMS) [D. T. Anderson, J. A. Derr, and J. L. Shohet, IEEE Trans. Plasma Sci. PS‐9, 212 (1981)]. These measurements were performed at two magnetic field strengths, and also when a positively biased electrode induces a poloidal plasma flow. The data shows the fluctuation‐induced transport to be poloidally asymmetric and dependent upon the location of the electron cyclotron resonance position, and upon the electrode biasing. The induced poloidal plasma flow changes the nominally outward fluctuation‐induced particle transport to be inward (negative radial transport) by changing the phase relationship of the density and potential oscillations. The amplitude of the density and potential fluctuations are, in general, not reduced by the sheared poloidal flow. Calculations are presented comparing the computed Reynolds stress induced poloidal plasma flows with the flow calculated from momentum balance.","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"49 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":"116181535","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 theory of toroidicity‐induced Alfven eigenmodes (TAE) and kinetic TAE (KTAE) is generalized to arbitrary mode numbers for a large aspect ratio low‐beta circular tokamak. The interaction between nearest neighbors is described by a three‐term recursion relation that combines elements from an outer region, described by the ideal magnetohydrodynamic equations of a cylinder, and an inner region, which includes the toroidicity and the nonideal effects of finite ion Larmor radius, electron inertia, and collisions. By the use of quadratic forms, it is proven that the roots of the recursion relation are stable and it is shown how perturbation theory can be applied to include frequency shifts due to other kinetic effects. Analytic forms are derived which display the competition between the resistive and radiative damping, where the radiation is carried by kinetic Alfven waves. When the nonideal parameter is small, the KTAE modes appear in pairs. When this parameter is large, previously found scaling for the single gap case is reproduced analytically.
{"title":"Arbitrary mode number boundary‐layer theory for nonideal toroidal Alfvén modes","authors":"H. Berk, R. Mett, D. Lindberg","doi":"10.1063/1.860617","DOIUrl":"https://doi.org/10.1063/1.860617","url":null,"abstract":"The theory of toroidicity‐induced Alfven eigenmodes (TAE) and kinetic TAE (KTAE) is generalized to arbitrary mode numbers for a large aspect ratio low‐beta circular tokamak. The interaction between nearest neighbors is described by a three‐term recursion relation that combines elements from an outer region, described by the ideal magnetohydrodynamic equations of a cylinder, and an inner region, which includes the toroidicity and the nonideal effects of finite ion Larmor radius, electron inertia, and collisions. By the use of quadratic forms, it is proven that the roots of the recursion relation are stable and it is shown how perturbation theory can be applied to include frequency shifts due to other kinetic effects. Analytic forms are derived which display the competition between the resistive and radiative damping, where the radiation is carried by kinetic Alfven waves. When the nonideal parameter is small, the KTAE modes appear in pairs. When this parameter is large, previously found scaling for the single gap case is reproduced analytically.","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"46 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114040319","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 purpose of this work is to determine ion temperature profiles in spheromaks [Nucl. Fusion 19, 489 (1979)] for the first time. Knowledge of the ion temperature profile is necessary in the correct calculation of plasma confinement parameters. The work herein details the calculation of ion temperature profiles for the Compact Torus Experiment (CTX) [Nucl. Fusion 28, 1555 (1988)] and S‐1 [Phys. Rev. Lett. 46, 188 (1981)] spheromaks. Data from single chord Doppler ion temperature measurements in these devices have been analyzed with the aid of a one‐dimensional equilibrium charge state transport code. Using electron temperature and density profiles from Thomson scattering, and estimates for transport rates, a most probable position for the emission of line radiation can be determined and correlated with the measured Doppler ion temperature, thus generating an ion temperature profile. From this ion temperature profile determination, plasma confinement parameters for the small solid flux conserver CTX [Phys....
这项工作的目的是确定球形标记[核]中的离子温度分布。聚变19,489(1979)]第一次。了解离子温度分布是正确计算等离子体约束参数的必要条件。本文详细介绍了紧凑环面实验(CTX)离子温度分布的计算[核]。[j] .核聚变学报，2008,32(1):1 - 2。Rev. Lett. 46, 188(1981)]。利用一维平衡电荷态输运码对这些装置中单弦多普勒离子温度测量数据进行了分析。利用汤姆逊散射的电子温度和密度分布，以及对输运速率的估计，可以确定线辐射发射的最可能位置，并将其与测量的多普勒离子温度相关联，从而产生离子温度分布。从离子温度分布的测定，等离子体约束参数为小型固体通量守恒器CTX[物理....]
{"title":"Ion temperature profile deconvolution and corrections to confinement parameters in spheromaks","authors":"R. M. Mayo, D. J. Hurlburt, Juan C Fernández","doi":"10.1063/1.860619","DOIUrl":"https://doi.org/10.1063/1.860619","url":null,"abstract":"The purpose of this work is to determine ion temperature profiles in spheromaks [Nucl. Fusion 19, 489 (1979)] for the first time. Knowledge of the ion temperature profile is necessary in the correct calculation of plasma confinement parameters. The work herein details the calculation of ion temperature profiles for the Compact Torus Experiment (CTX) [Nucl. Fusion 28, 1555 (1988)] and S‐1 [Phys. Rev. Lett. 46, 188 (1981)] spheromaks. Data from single chord Doppler ion temperature measurements in these devices have been analyzed with the aid of a one‐dimensional equilibrium charge state transport code. Using electron temperature and density profiles from Thomson scattering, and estimates for transport rates, a most probable position for the emission of line radiation can be determined and correlated with the measured Doppler ion temperature, thus generating an ion temperature profile. From this ion temperature profile determination, plasma confinement parameters for the small solid flux conserver CTX [Phys....","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"10 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":"122362538","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}
An analysis of the radial structure of the ion‐temperature‐gradient‐driven mode is presented and the dependence of the radial correlation length Lr on parameters such as magnetic shear is discussed. It is found that Lr decreases algebraically with increasing shear for moderate to large shear values, and it decreases exponentially with decreasing shear for low shear values. These results seem in qualitative agreement with several experiments which observe strong reduction of the transport coefficients close to the magnetic axis.
{"title":"The radial structure of the ion‐temperature‐gradient‐driven mode","authors":"F. Romanelli, F. Zonca","doi":"10.1063/1.860576","DOIUrl":"https://doi.org/10.1063/1.860576","url":null,"abstract":"An analysis of the radial structure of the ion‐temperature‐gradient‐driven mode is presented and the dependence of the radial correlation length Lr on parameters such as magnetic shear is discussed. It is found that Lr decreases algebraically with increasing shear for moderate to large shear values, and it decreases exponentially with decreasing shear for low shear values. These results seem in qualitative agreement with several experiments which observe strong reduction of the transport coefficients close to the magnetic axis.","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"36 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":"116655053","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 particle simulation with plasma source is carried out on plasma structures generated by an electron emissive electrode floated in a collisionless plasma. When low‐temperature, high‐density thermal electrons are emitted, there appears a negative potential dip in front of the electrode, which is always accompanied by a low‐frequency oscillation. On the other hand, three regimes of plasma structures appear for an electron beam injection. When a high‐flux electron beam is injected, an electron sheath is generated in front of the electrode. The sheath reflects ions flowing to the electrode, providing an increase in the plasma density. When a low‐flux electron beam is injected, no electron sheath is generated. When an intermediate‐flux beam is injected, the electron sheath structure appears periodically in time. The lifetime of the sheath is proportional to the system length. These results of beam injection are almost consistent with those of a Q‐machine experiment.
{"title":"Plasma structures in front of a floated emissive electrode","authors":"S. Ishiguro, N. Sato","doi":"10.1063/1.860589","DOIUrl":"https://doi.org/10.1063/1.860589","url":null,"abstract":"A particle simulation with plasma source is carried out on plasma structures generated by an electron emissive electrode floated in a collisionless plasma. When low‐temperature, high‐density thermal electrons are emitted, there appears a negative potential dip in front of the electrode, which is always accompanied by a low‐frequency oscillation. On the other hand, three regimes of plasma structures appear for an electron beam injection. When a high‐flux electron beam is injected, an electron sheath is generated in front of the electrode. The sheath reflects ions flowing to the electrode, providing an increase in the plasma density. When a low‐flux electron beam is injected, no electron sheath is generated. When an intermediate‐flux beam is injected, the electron sheath structure appears periodically in time. The lifetime of the sheath is proportional to the system length. These results of beam injection are almost consistent with those of a Q‐machine experiment.","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"452 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":"123635653","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 purpose of this paper is to formulate the transport problem for a multispecies rotating toroidal magnetoplasma in the so‐called runaway regime, which is defined by an appropriate ordering of relevant characteristic frequencies, in particular, the Larmor frequency, the characteristic acceleration frequency due to the applied electric field and the effective collision frequency, all evaluated at some characteristic speed v0. A suitable form of the gyrokinetic equation is obtained to describe the time‐dependent, multispecies plasma response to an applied electric field, in toroidal geometry and for a strongly rotating, quiescent, and collisional plasma. Its moment equations are proven to imply the reduction of the energy equation to Joule’s law, as well as consequences on the form of Ohm’s law and of the Grad–Shafranov equation. To construct an approximate solution of the gyrokinetic equation and to evaluate all relevant fluxes, appearing in the moment equations, a general variational solution method is ...
{"title":"Theory of runaway collisional transport","authors":"M. Tessarotto, R. White","doi":"10.1063/1.860615","DOIUrl":"https://doi.org/10.1063/1.860615","url":null,"abstract":"The purpose of this paper is to formulate the transport problem for a multispecies rotating toroidal magnetoplasma in the so‐called runaway regime, which is defined by an appropriate ordering of relevant characteristic frequencies, in particular, the Larmor frequency, the characteristic acceleration frequency due to the applied electric field and the effective collision frequency, all evaluated at some characteristic speed v0. A suitable form of the gyrokinetic equation is obtained to describe the time‐dependent, multispecies plasma response to an applied electric field, in toroidal geometry and for a strongly rotating, quiescent, and collisional plasma. Its moment equations are proven to imply the reduction of the energy equation to Joule’s law, as well as consequences on the form of Ohm’s law and of the Grad–Shafranov equation. To construct an approximate solution of the gyrokinetic equation and to evaluate all relevant fluxes, appearing in the moment equations, a general variational solution method is ...","PeriodicalId":113346,"journal":{"name":"Physics of fluids. B, Plasma physics","volume":"97 6 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":"128000193","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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