Pub Date : 2024-01-15DOI: 10.1017/s0022377823001423
C. Albert Johansson, Pavel Aleynikov
Electron-cyclotron resonance heating (ECRH) is the main heating mechanism in the Wendelstein 7-X (W7-X) stellarator. Although second-harmonic ECRH (X2) has been used routinely for plasma startup, startup at third harmonic (X3) is known to be much more difficult. In this work, we investigate the energy gain of particles during nonlinear wave–particle interaction for conditions relevant to second- and third-harmonic startups in W7-X. We take into account both the beam and the ambient magnetic field inhomogeneities. The latter is shown to significantly increase the mean energy gain resulting from a single wave–particle resonant interaction. In W7-X-like conditions, the improvement in maximum gained energy is up to 4 times the analogous uniform magnetic field case. However, this improvement is not enough to ensure X3 startup. The optimal magnetic field inhomogeneity length scale for average energy gain and start up in W7-X-like conditions is found to be in the range of $1$ to $3 {rm km}^{-1}$. A possibility of using multiple beams with neighbouring resonances is also considered. A considerable enhancement of the energy gain is demonstrated.
{"title":"Electron cyclotron resonance during plasma initiation","authors":"C. Albert Johansson, Pavel Aleynikov","doi":"10.1017/s0022377823001423","DOIUrl":"https://doi.org/10.1017/s0022377823001423","url":null,"abstract":"<p>Electron-cyclotron resonance heating (ECRH) is the main heating mechanism in the Wendelstein 7-X (W7-X) stellarator. Although second-harmonic ECRH (X2) has been used routinely for plasma startup, startup at third harmonic (X3) is known to be much more difficult. In this work, we investigate the energy gain of particles during nonlinear wave–particle interaction for conditions relevant to second- and third-harmonic startups in W7-X. We take into account both the beam and the ambient magnetic field inhomogeneities. The latter is shown to significantly increase the mean energy gain resulting from a single wave–particle resonant interaction. In W7-X-like conditions, the improvement in maximum gained energy is up to 4 times the analogous uniform magnetic field case. However, this improvement is not enough to ensure X3 startup. The optimal magnetic field inhomogeneity length scale for average energy gain and start up in W7-X-like conditions is found to be in the range of <span><span><span data-mathjax-type=\"texmath\"><span>$1$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240112135018386-0980:S0022377823001423:S0022377823001423_inline2.png\"/></span></span> to <span><span><span data-mathjax-type=\"texmath\"><span>$3 {rm km}^{-1}$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240112135018386-0980:S0022377823001423:S0022377823001423_inline3.png\"/></span></span>. A possibility of using multiple beams with neighbouring resonances is also considered. A considerable enhancement of the energy gain is demonstrated.</p>","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"12 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139471138","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-01-11DOI: 10.1017/s0022377822000794
Bo Zeng, Zijia Zhao, Xiaohu Yang, Shaowu Yang, Yanyun Ma
Beam–target reactions in fusion plasmas play an important role in both magnetic confinement fusion and inertial confinement fusion in the condition of low-density plasmas with high-velocity interactions. The traditional method for calculating beam–target reaction rate neglects the transport process of incident particles in inhomogeneous plasmas, leading to errors providing that the temperature and density in the transport path of incident particles vary obviously. An improved method considering the transport process is proposed in this paper to eliminate the deficiencies. Then the method is employed in high-speed plasma collision studies. When the initial plasma density and temperature are set to $0.5,{rm g},{rm cm}^{-3}$ and 100 eV, it is found that the beam–target reaction rate calculated by the traditional method is almost identical to that by our method if the collision velocity is less than 600 km s$^{-1}$. However, the traditional method is not suitable for study as the collision velocity gets higher, inducing obvious differences, which can reach 70 % at 1000 km s$^{-1}$. The improved method will make large corrections to evaluate the importance of the non-negligible beam–target reaction for inertial confinement fusion schemes with large implosion velocity such as double-cone ignition and impact ignition, in which the high-speed plasmas collide with each other to realize plasma ignition.
聚变等离子体中的束靶反应在低密度等离子体与高速相互作用的磁约束聚变和惯性约束聚变中都起着重要作用。计算束-靶反应速率的传统方法忽略了入射粒子在不均匀等离子体中的输运过程,导致入射粒子输运路径上的温度和密度变化明显时产生误差。本文提出了一种考虑输运过程的改进方法,以消除这些缺陷。然后将该方法用于高速等离子体碰撞研究。当初始等离子体密度和温度分别设置为$0.5,{rm g},{rm cm}^{-3}$和100 eV时,发现当碰撞速度小于600 km s$^{-1}$时,传统方法计算出的束靶反应速率与我们的方法计算出的反应速率基本一致。但是,随着碰撞速度的增大,传统方法就不适合研究了,会产生明显的差异,在 1000 km s$^{-1}$ 时差异可达 70%。改进后的方法将对内爆速度较大的惯性约束聚变方案(如双锥点火和撞击点火)进行较大的修正,以评估不可忽略的束靶反应的重要性,在这些方案中,高速等离子体相互碰撞实现等离子体点火。
{"title":"Improved numerical simulation model for nuclear reaction rate calculations in high-speed plasma collisions","authors":"Bo Zeng, Zijia Zhao, Xiaohu Yang, Shaowu Yang, Yanyun Ma","doi":"10.1017/s0022377822000794","DOIUrl":"https://doi.org/10.1017/s0022377822000794","url":null,"abstract":"<p>Beam–target reactions in fusion plasmas play an important role in both magnetic confinement fusion and inertial confinement fusion in the condition of low-density plasmas with high-velocity interactions. The traditional method for calculating beam–target reaction rate neglects the transport process of incident particles in inhomogeneous plasmas, leading to errors providing that the temperature and density in the transport path of incident particles vary obviously. An improved method considering the transport process is proposed in this paper to eliminate the deficiencies. Then the method is employed in high-speed plasma collision studies. When the initial plasma density and temperature are set to <span><span><span data-mathjax-type=\"texmath\"><span>$0.5,{rm g},{rm cm}^{-3}$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240110160745098-0021:S0022377822000794:S0022377822000794_inline2.png\"/></span></span> and 100 eV, it is found that the beam–target reaction rate calculated by the traditional method is almost identical to that by our method if the collision velocity is less than 600 km s<span><span><span data-mathjax-type=\"texmath\"><span>$^{-1}$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240110160745098-0021:S0022377822000794:S0022377822000794_inline3.png\"/></span></span>. However, the traditional method is not suitable for study as the collision velocity gets higher, inducing obvious differences, which can reach 70 % at 1000 km s<span><span><span data-mathjax-type=\"texmath\"><span>$^{-1}$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240110160745098-0021:S0022377822000794:S0022377822000794_inline4.png\"/></span></span>. The improved method will make large corrections to evaluate the importance of the non-negligible beam–target reaction for inertial confinement fusion schemes with large implosion velocity such as double-cone ignition and impact ignition, in which the high-speed plasmas collide with each other to realize plasma ignition.</p>","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"13 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139423885","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-01-11DOI: 10.1017/s0022377823001460
W. Ling, C. Jing, J. Wan, A. Mao, Q. Xiao, J. Guan, J. Cheng, C. Liu, P. E
Our earth is immersed in the near-earth space plasma environment, which plays a vital role in protecting our planet against the solar-wind impact and influencing space activities. It is significant to investigate the physical processes dominating the environment, for deepening our scientific understanding of it and improving the ability to forecast the space weather. As a crucial part of the National Major Scientific and Technological Infrastructure–Space Environment Simulation Research Infrastructure (SESRI) in Harbin, the Space Plasma Environment Research Facility (SPERF) builds a system to replicate the near-earth space plasma environment in the laboratory. The system aims to simulate the three-dimensional (3-D) structure and processes of the terrestrial magnetosphere for the first time in the world, providing a unique platform to reveal the physics of the 3-D asymmetric magnetic reconnection relevant to the earth's magnetopause, wave–particle interaction in the earth's radiation belt, particles’ dynamics during the geomagnetic storm, etc. The paper will present the engineering design and construction of the near-earth space plasma simulation system of the SPERF, with a focus on the critical technologies that have been resolved to achieve the scientific goals. Meanwhile, the possible physical issues that can be studied based on the apparatus are sketched briefly. The earth-based system is of great value in understanding the space plasma environment and supporting space exploration.
{"title":"Design and construction of the near-earth space plasma simulation system of the Space Plasma Environment Research Facility","authors":"W. Ling, C. Jing, J. Wan, A. Mao, Q. Xiao, J. Guan, J. Cheng, C. Liu, P. E","doi":"10.1017/s0022377823001460","DOIUrl":"https://doi.org/10.1017/s0022377823001460","url":null,"abstract":"<p>Our earth is immersed in the near-earth space plasma environment, which plays a vital role in protecting our planet against the solar-wind impact and influencing space activities. It is significant to investigate the physical processes dominating the environment, for deepening our scientific understanding of it and improving the ability to forecast the space weather. As a crucial part of the National Major Scientific and Technological Infrastructure–Space Environment Simulation Research Infrastructure (SESRI) in Harbin, the Space Plasma Environment Research Facility (SPERF) builds a system to replicate the near-earth space plasma environment in the laboratory. The system aims to simulate the three-dimensional (3-D) structure and processes of the terrestrial magnetosphere for the first time in the world, providing a unique platform to reveal the physics of the 3-D asymmetric magnetic reconnection relevant to the earth's magnetopause, wave–particle interaction in the earth's radiation belt, particles’ dynamics during the geomagnetic storm, etc. The paper will present the engineering design and construction of the near-earth space plasma simulation system of the SPERF, with a focus on the critical technologies that have been resolved to achieve the scientific goals. Meanwhile, the possible physical issues that can be studied based on the apparatus are sketched briefly. The earth-based system is of great value in understanding the space plasma environment and supporting space exploration.</p>","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"25 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139420562","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-01-05DOI: 10.1017/s002237782300140x
C.J. Nixon, C.C.T. Pringle, J.E. Pringle
<p>Observations, mainly of outbursts in dwarf novae, imply that the anomalous viscosity in highly ionized accretion discs is magnetic in origin and requires that the plasma <span><span><span data-mathjax-type="texmath"><span>${beta sim 1}$</span></span><img data-mimesubtype="png" data-type="" src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240104165850964-0798:S002237782300140X:S002237782300140X_inline1.png"/></span></span>. Until now, most simulations of the magnetic dynamo in accretion discs have used a local approximation (known as the shearing box). While these simulations demonstrate the possibility of a self-sustaining dynamo, the magnetic activity generated in these models saturates at <span><span><span data-mathjax-type="texmath"><span>$beta gg 1$</span></span><img data-mimesubtype="png" data-type="" src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240104165850964-0798:S002237782300140X:S002237782300140X_inline2.png"/></span></span>. This long-standing discrepancy has previously been attributed to the local approximation itself. There have been recent attempts at simulating magnetic activity in global accretion discs with parameters relevant to the dwarf novae. These too find values of <span><span><span data-mathjax-type="texmath"><span>$beta gg 1$</span></span><img data-mimesubtype="png" data-type="" src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240104165850964-0798:S002237782300140X:S002237782300140X_inline3.png"/></span></span>. We speculate that the tension between these models and the observations may be caused by numerical magnetic diffusivity. As a pedagogical example, we present exact time-dependent solutions for the evolution of weak magnetic fields in an incompressible fluid subject to linear shear and magnetic diffusivity. We find that the maximum factor by which the initial magnetic energy can be increased depends on the magnetic Reynolds number as <span><span><span data-mathjax-type="texmath"><span>${mathcal {R}}_{m}^{2/3}$</span></span><img data-mimesubtype="png" data-type="" src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240104165850964-0798:S002237782300140X:S002237782300140X_inline4.png"/></span></span>. We estimate that current global numerical simulations of dwarf nova discs have numerical magnetic Reynolds numbers around six orders of magnitude less than the physical value found in dwarf nova discs of <span><span><span data-mathjax-type="texmath"><span>${mathcal {R}}_{m} sim 10^{10}$</span></span><img data-mimesubtype="png" data-type="" src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240104165850964-0798:S002237782300140X:S002237782300140X_inline5.png"/></span></span>. We suggest that, given the current limitations on computing power, expecting to be able to compute realistic dynamo action in observable accretion discs using numerical MHD is, for the
{"title":"On the role of numerical diffusivity in MHD simulations of global accretion disc dynamos","authors":"C.J. Nixon, C.C.T. Pringle, J.E. Pringle","doi":"10.1017/s002237782300140x","DOIUrl":"https://doi.org/10.1017/s002237782300140x","url":null,"abstract":"<p>Observations, mainly of outbursts in dwarf novae, imply that the anomalous viscosity in highly ionized accretion discs is magnetic in origin and requires that the plasma <span><span><span data-mathjax-type=\"texmath\"><span>${beta sim 1}$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240104165850964-0798:S002237782300140X:S002237782300140X_inline1.png\"/></span></span>. Until now, most simulations of the magnetic dynamo in accretion discs have used a local approximation (known as the shearing box). While these simulations demonstrate the possibility of a self-sustaining dynamo, the magnetic activity generated in these models saturates at <span><span><span data-mathjax-type=\"texmath\"><span>$beta gg 1$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240104165850964-0798:S002237782300140X:S002237782300140X_inline2.png\"/></span></span>. This long-standing discrepancy has previously been attributed to the local approximation itself. There have been recent attempts at simulating magnetic activity in global accretion discs with parameters relevant to the dwarf novae. These too find values of <span><span><span data-mathjax-type=\"texmath\"><span>$beta gg 1$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240104165850964-0798:S002237782300140X:S002237782300140X_inline3.png\"/></span></span>. We speculate that the tension between these models and the observations may be caused by numerical magnetic diffusivity. As a pedagogical example, we present exact time-dependent solutions for the evolution of weak magnetic fields in an incompressible fluid subject to linear shear and magnetic diffusivity. We find that the maximum factor by which the initial magnetic energy can be increased depends on the magnetic Reynolds number as <span><span><span data-mathjax-type=\"texmath\"><span>${mathcal {R}}_{m}^{2/3}$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240104165850964-0798:S002237782300140X:S002237782300140X_inline4.png\"/></span></span>. We estimate that current global numerical simulations of dwarf nova discs have numerical magnetic Reynolds numbers around six orders of magnitude less than the physical value found in dwarf nova discs of <span><span><span data-mathjax-type=\"texmath\"><span>${mathcal {R}}_{m} sim 10^{10}$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240104165850964-0798:S002237782300140X:S002237782300140X_inline5.png\"/></span></span>. We suggest that, given the current limitations on computing power, expecting to be able to compute realistic dynamo action in observable accretion discs using numerical MHD is, for the","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"23 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139102663","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-28DOI: 10.1017/s0022377823001332
J.L. Henares, P. Puyuelo-Valdes, C. Salgado-López, J.I. Apiñaniz, P. Bradford, F. Consoli, D. de Luis, M. Ehret, F. Hannachi, R. Hernández-Martín, A. Huber, L. Lancia, M. Mackeviciute, A. Maitrallain, J.-R. Marquès, J.A. Pérez-Hernández, C. Santos, J.J. Santos, V. Stankevic, M. Tarisien, V. Tomkus, L. Volpe, G. Gatti
The ability to quickly refresh gas-jet targets without cycling the vacuum chamber makes them a promising candidate for laser-accelerated ion experiments at high repetition rate. Here we present results from the first high repetition rate ion acceleration experiment on the VEGA-3 PW-class laser at CLPU. A near-critical density gas-jet target was produced by forcing a 1000 bar H$_2$ and He gas mix through bespoke supersonic shock nozzles. Proton energies up to 2 MeV were measured in the laser forward direction and 2.2 MeV transversally. He$^{2+}$ ions up to 5.8 MeV were also measured in the transverse direction. To help maintain a consistent gas density profile over many shots, nozzles were designed to produce a high-density shock at distances larger than 1 mm from the nozzle exit. We outline a procedure for optimizing the laser–gas interaction by translating the nozzle along the laser axis and using different nozzle materials. Several tens of laser interactions were performed with the same nozzle which demonstrates the potential usefulness of gas-jet targets as high repetition rate particle source.
{"title":"Proton and helium ions acceleration in near-critical density gas targets by short-pulse Ti:Sa PW-class laser","authors":"J.L. Henares, P. Puyuelo-Valdes, C. Salgado-López, J.I. Apiñaniz, P. Bradford, F. Consoli, D. de Luis, M. Ehret, F. Hannachi, R. Hernández-Martín, A. Huber, L. Lancia, M. Mackeviciute, A. Maitrallain, J.-R. Marquès, J.A. Pérez-Hernández, C. Santos, J.J. Santos, V. Stankevic, M. Tarisien, V. Tomkus, L. Volpe, G. Gatti","doi":"10.1017/s0022377823001332","DOIUrl":"https://doi.org/10.1017/s0022377823001332","url":null,"abstract":"<p>The ability to quickly refresh gas-jet targets without cycling the vacuum chamber makes them a promising candidate for laser-accelerated ion experiments at high repetition rate. Here we present results from the first high repetition rate ion acceleration experiment on the VEGA-3 PW-class laser at CLPU. A near-critical density gas-jet target was produced by forcing a 1000 bar H<span><span><span data-mathjax-type=\"texmath\"><span>$_2$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231227162729962-0649:S0022377823001332:S0022377823001332_inline1.png\"/></span></span> and He gas mix through bespoke supersonic shock nozzles. Proton energies up to 2 MeV were measured in the laser forward direction and 2.2 MeV transversally. He<span><span><span data-mathjax-type=\"texmath\"><span>$^{2+}$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231227162729962-0649:S0022377823001332:S0022377823001332_inline2.png\"/></span></span> ions up to 5.8 MeV were also measured in the transverse direction. To help maintain a consistent gas density profile over many shots, nozzles were designed to produce a high-density shock at distances larger than 1 mm from the nozzle exit. We outline a procedure for optimizing the laser–gas interaction by translating the nozzle along the laser axis and using different nozzle materials. Several tens of laser interactions were performed with the same nozzle which demonstrates the potential usefulness of gas-jet targets as high repetition rate particle source.</p>","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"1 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139053358","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-28DOI: 10.1017/s0022377823001307
T. Rubin, J.M. Rax, N.J. Fisch
The Hamiltonian dynamics of a single particle in a rotating plasma column, interacting with an magnetic multipole is perturbatively solved for up to second order, using the method of Lie transformations. First, the exact Hamiltonian is expressed in terms of canonical action-angle variables, and then an approximate integrable Hamiltonian is introduced, using another set of actions and angles, which describe the centre of oscillation for the particle. The perturbation introduces an effective ponderomotive potential, which to leading order is positive. At the second order, the pseudopotential consists of a sum of terms of the Miller form, and can have either sign. Additionally, at second order, the ponderomotive interaction introduces a modification to the particle effective mass, when considering the motion along the column axis. It is found that particles can be axially confined by the ponderomotive potentials, but acquire radial excursions which scale as the confining potential. The radial excursions of the particle along its trajectory are investigated, and a condition for the minimal rotation frequency for which the particle remains radially confined is derived. Last, we comment on the changes to the aforementioned solution to the pseudopotentials and particle trajectory in the case of resonant motion, that is, a motion which has the same periodicity as the perturbation.
{"title":"Guiding centre motion for particles in a ponderomotive magnetostatic end plug","authors":"T. Rubin, J.M. Rax, N.J. Fisch","doi":"10.1017/s0022377823001307","DOIUrl":"https://doi.org/10.1017/s0022377823001307","url":null,"abstract":"<p>The Hamiltonian dynamics of a single particle in a rotating plasma column, interacting with an magnetic multipole is perturbatively solved for up to second order, using the method of Lie transformations. First, the exact Hamiltonian is expressed in terms of canonical action-angle variables, and then an approximate integrable Hamiltonian is introduced, using another set of actions and angles, which describe the centre of oscillation for the particle. The perturbation introduces an effective ponderomotive potential, which to leading order is positive. At the second order, the pseudopotential consists of a sum of terms of the Miller form, and can have either sign. Additionally, at second order, the ponderomotive interaction introduces a modification to the particle effective mass, when considering the motion along the column axis. It is found that particles can be axially confined by the ponderomotive potentials, but acquire radial excursions which scale as the confining potential. The radial excursions of the particle along its trajectory are investigated, and a condition for the minimal rotation frequency for which the particle remains radially confined is derived. Last, we comment on the changes to the aforementioned solution to the pseudopotentials and particle trajectory in the case of resonant motion, that is, a motion which has the same periodicity as the perturbation.</p>","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"70 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139053095","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-28DOI: 10.1017/s0022377823001368
J.-M. Rax, R. Gueroult, N.J. Fisch
Angular momentum coupling between a rotating magnetized plasma and torsional Alfvén waves carrying orbital angular momentum (OAM) is examined. It is demonstrated not only that rotation is the source of Fresnel–Faraday rotation – or orbital Faraday rotation effects – for OAM-carrying Alfvén waves, but also that angular momentum from an OAM-carrying Alfvén wave can be transferred to a rotating plasma through the inverse process. For the direct process, the transverse structure angular rotation frequency is derived by considering the dispersion relation for modes with opposite OAM content. For the inverse process, the torque exerted on the plasma is derived as a function of wave and plasma parameters.
{"title":"Rotating Alfvén waves in rotating plasmas","authors":"J.-M. Rax, R. Gueroult, N.J. Fisch","doi":"10.1017/s0022377823001368","DOIUrl":"https://doi.org/10.1017/s0022377823001368","url":null,"abstract":"<p>Angular momentum coupling between a rotating magnetized plasma and torsional Alfvén waves carrying orbital angular momentum (OAM) is examined. It is demonstrated not only that rotation is the source of Fresnel–Faraday rotation – or orbital Faraday rotation effects – for OAM-carrying Alfvén waves, but also that angular momentum from an OAM-carrying Alfvén wave can be transferred to a rotating plasma through the inverse process. For the direct process, the transverse structure angular rotation frequency is derived by considering the dispersion relation for modes with opposite OAM content. For the inverse process, the torque exerted on the plasma is derived as a function of wave and plasma parameters.</p>","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"165 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139053359","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-28DOI: 10.1017/s0022377823001344
Zhaoyang Liu, Guoyong Fu
Fishbone bursts have been observed to strongly correlate to internal transport barrier (ITB) formation in a number of tokamak devices. A simple model incorporating the fishbone dynamics and ion pressure gradient evolution is proposed in order to investigate the key physics parameters assisting the triggering of ITB. The time evolution of fishbone is described by the well-known predator–prey model. For each burst cycle, the energetic particles (EPs) resonantly interact with fishbone and are radially expelled from inner region leading to a radial current. A compensating bulk plasma return current and, hence, poloidal flow can be induced if the fishbone cycle frequency is greater than the poloidal flow damping rate. When the shear of the poloidal flow exceeds a critical value, the turbulent fluctuations are suppressed and the bulk ion pressure gradient transits to the high-confinement state. It is shown that this process is only sensitive to the deposition rate of the trapped EPs within the $q=1$ surface, but not sensitive to other parameters. A quantitative formula for the shearing rate of poloidal flow induced by fishbone bursts is derived and verified numerically.
在一些托卡马克装置中,已经观察到鱼骨状爆发与内部输运势垒(ITB)的形成密切相关。为了研究有助于触发 ITB 的关键物理参数,我们提出了一个包含鱼骨动力学和离子压力梯度演变的简单模型。鱼刺的时间演化由著名的捕食者-猎物模型描述。在每个迸发周期,高能粒子(EPs)与鱼骨发生共振作用,并从内部区域径向排出,形成径向电流。如果鱼刺循环频率大于极性流阻尼率,就会诱发补偿性的大体等离子体回流,从而产生极性流。当极环流的剪切力超过临界值时,湍流波动被抑制,大块离子压力梯度过渡到高约束状态。研究表明,这一过程只对 $q=1$ 表面内被困 EP 的沉积率敏感,而对其他参数不敏感。推导出了鱼骨爆裂诱导的极性流剪切率定量公式,并进行了数值验证。
{"title":"A simple model for internal transport barrier induced by fishbone in tokamak plasmas","authors":"Zhaoyang Liu, Guoyong Fu","doi":"10.1017/s0022377823001344","DOIUrl":"https://doi.org/10.1017/s0022377823001344","url":null,"abstract":"<p>Fishbone bursts have been observed to strongly correlate to internal transport barrier (ITB) formation in a number of tokamak devices. A simple model incorporating the fishbone dynamics and ion pressure gradient evolution is proposed in order to investigate the key physics parameters assisting the triggering of ITB. The time evolution of fishbone is described by the well-known predator–prey model. For each burst cycle, the energetic particles (EPs) resonantly interact with fishbone and are radially expelled from inner region leading to a radial current. A compensating bulk plasma return current and, hence, poloidal flow can be induced if the fishbone cycle frequency is greater than the poloidal flow damping rate. When the shear of the poloidal flow exceeds a critical value, the turbulent fluctuations are suppressed and the bulk ion pressure gradient transits to the high-confinement state. It is shown that this process is only sensitive to the deposition rate of the trapped EPs within the <span><span><span data-mathjax-type=\"texmath\"><span>$q=1$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231227145526428-0286:S0022377823001344:S0022377823001344_inline1.png\"/></span></span> surface, but not sensitive to other parameters. A quantitative formula for the shearing rate of poloidal flow induced by fishbone bursts is derived and verified numerically.</p>","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"65 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139053363","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-27DOI: 10.1017/s0022377823001277
A. Sladkomedova, I. Cziegler, A.R. Field, A.A. Schekochihin, D. Dunai, P.G. Ivanov, the MAST-U Team and the EUROfusion MST1 Team
The properties of the edge ion-scale turbulence are studied using the beam emission spectroscopy (BES) diagnostic on MAST. Evidence of the formation of large-scale high-amplitude coherent structures, filamentary density blobs and holes, 2–4 cm inside the plasma separatrix is presented. Measurements of radial velocity and skewness of the density fluctuations indicate that density holes propagate radially inwards, with the skewness profile peaking at 7–10 cm inside the separatrix. Poloidal velocities of the density fluctuations measured using cross-correlation time delay estimation (CCTDE) are found to exhibit an intermittent behaviour. Zonal-flow analysis reveals the presence of poloidally symmetric coherent oscillations – low-frequency (LF) zonal flows and geodesic acoustic modes (GAM). Shearing rates of the observed zonal flows are found to be comparable to the turbulence decorrelation rate. The observed bursts in density-fluctuation power are followed by quiescent periods with a transient increase in the power of sheared flows. Three-wave interactions between broadband turbulence and a GAM are illustrated using the autobispectral technique. It is shown that the zonal flows and the density-fluctuation field are nonlinearly coupled and LF zonal flows mediate the energy transfer from high- to low-frequency density fluctuations.
{"title":"Intermittency of density fluctuations and zonal-flow generation in MAST edge plasmas","authors":"A. Sladkomedova, I. Cziegler, A.R. Field, A.A. Schekochihin, D. Dunai, P.G. Ivanov, the MAST-U Team and the EUROfusion MST1 Team","doi":"10.1017/s0022377823001277","DOIUrl":"https://doi.org/10.1017/s0022377823001277","url":null,"abstract":"<p>The properties of the edge ion-scale turbulence are studied using the beam emission spectroscopy (BES) diagnostic on MAST. Evidence of the formation of large-scale high-amplitude coherent structures, filamentary density blobs and holes, 2–4 cm inside the plasma separatrix is presented. Measurements of radial velocity and skewness of the density fluctuations indicate that density holes propagate radially inwards, with the skewness profile peaking at 7–10 cm inside the separatrix. Poloidal velocities of the density fluctuations measured using cross-correlation time delay estimation (CCTDE) are found to exhibit an intermittent behaviour. Zonal-flow analysis reveals the presence of poloidally symmetric coherent oscillations – low-frequency (LF) zonal flows and geodesic acoustic modes (GAM). Shearing rates of the observed zonal flows are found to be comparable to the turbulence decorrelation rate. The observed bursts in density-fluctuation power are followed by quiescent periods with a transient increase in the power of sheared flows. Three-wave interactions between broadband turbulence and a GAM are illustrated using the autobispectral technique. It is shown that the zonal flows and the density-fluctuation field are nonlinearly coupled and LF zonal flows mediate the energy transfer from high- to low-frequency density fluctuations.</p>","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"8 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139053253","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-27DOI: 10.1017/s0022377823001320
A.C.D. Hoffmann, B.J. Frei, P. Ricci
We present a convergence study of the gyromoment (GM) approach, which is based on projecting the gyrokinetic distribution function onto a Hermite–Laguerre polynomial basis, focused on the cyclone base case (CBC) (Lin et al., Phys. Rev. Lett., vol. 83, no. 18, 1999, pp. 3645–3648) and Dimits shift (Dimits et al., Phys. Plasmas, vol. 7, no. 3, 2000, pp. 969–983) as benchmarks. We report that the GM approach converges more rapidly in capturing the nonlinear dynamics of the CBC than the continuum GENE code (Jenko et al., Phys. Plasmas, vol. 7, no. 5, 2000, pp. 1904–1910) when comparing the number of points representing the velocity space. Increasing the velocity dissipation improves the convergence properties of the GM approach, albeit yielding a slightly larger saturated heat flux. By varying the temperature equilibrium gradient, we show that the GM approach successfully reproduces the Dimits shift (Dimits et al., Phys. Plasmas, vol. 7, no. 3, 2000, pp. 969–983) and effectively captures its width, which is in contrast to the gyrofluid framework. In the collisional regime, the convergence properties of the GM approach improve and a good agreement with previous global particle-in-cell results on transport is obtained (Lin et al., Phys. Rev. Lett., vol. 83, no. 18, 1999, pp. 3645–3648). Finally, we report that the choice of collision model has a minimal impact both on the ion temperature gradient growth rate and on the nonlinear saturated heat flux, at tokamak-relevant collisionality.
{"title":"Gyrokinetic moment-based simulations of the Dimits shift","authors":"A.C.D. Hoffmann, B.J. Frei, P. Ricci","doi":"10.1017/s0022377823001320","DOIUrl":"https://doi.org/10.1017/s0022377823001320","url":null,"abstract":"We present a convergence study of the gyromoment (GM) approach, which is based on projecting the gyrokinetic distribution function onto a Hermite–Laguerre polynomial basis, focused on the cyclone base case (CBC) (Lin <jats:italic>et al.</jats:italic>, <jats:italic>Phys. Rev. Lett.</jats:italic>, vol. 83, no. 18, 1999, pp. 3645–3648) and Dimits shift (Dimits <jats:italic>et al.</jats:italic>, <jats:italic>Phys. Plasmas</jats:italic>, vol. 7, no. 3, 2000, pp. 969–983) as benchmarks. We report that the GM approach converges more rapidly in capturing the nonlinear dynamics of the CBC than the continuum GENE code (Jenko <jats:italic>et al.</jats:italic>, <jats:italic>Phys. Plasmas</jats:italic>, vol. 7, no. 5, 2000, pp. 1904–1910) when comparing the number of points representing the velocity space. Increasing the velocity dissipation improves the convergence properties of the GM approach, albeit yielding a slightly larger saturated heat flux. By varying the temperature equilibrium gradient, we show that the GM approach successfully reproduces the Dimits shift (Dimits <jats:italic>et al.</jats:italic>, <jats:italic>Phys. Plasmas</jats:italic>, vol. 7, no. 3, 2000, pp. 969–983) and effectively captures its width, which is in contrast to the gyrofluid framework. In the collisional regime, the convergence properties of the GM approach improve and a good agreement with previous global particle-in-cell results on transport is obtained (Lin <jats:italic>et al.</jats:italic>, <jats:italic>Phys. Rev. Lett.</jats:italic>, vol. 83, no. 18, 1999, pp. 3645–3648). Finally, we report that the choice of collision model has a minimal impact both on the ion temperature gradient growth rate and on the nonlinear saturated heat flux, at tokamak-relevant collisionality.","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"29 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139053409","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}