The accurate definition and powerful evaluation modeling of the various generalized Fermi–Dirac and Bose–Einstein functions remain a challenging problem in various areas of physics. In this study, we develop a general analytical technique for accurately calculating logarithmic and double Fermi–Dirac and Bose–Einstein functions. The obtaining analytical formulae are established by considering the binomial expansion theorem. The obtained expressions are valid in chemical potential values between -∞ <μ <0 and have been designated as explicit form features, high precision, and less computing time. The calculation results are tabularly illustrated to show the consistency of the analytical relations analysis under the effect of parameters. Based on a comprehensive analysis of the results, they are potentially useful in applications to evaluate thermionic emission and astrophysics problems.
{"title":"Accurate analytical evaluation of the generalized logarithmic and double Fermi–Dirac and Bose–Einstein functions","authors":"Bahtiyar A. Mamedov, Duru Özgül","doi":"10.1002/ctpp.202400051","DOIUrl":"10.1002/ctpp.202400051","url":null,"abstract":"<p>The accurate definition and powerful evaluation modeling of the various generalized Fermi–Dirac and Bose–Einstein functions remain a challenging problem in various areas of physics. In this study, we develop a general analytical technique for accurately calculating logarithmic and double Fermi–Dirac and Bose–Einstein functions. The obtaining analytical formulae are established by considering the binomial expansion theorem. The obtained expressions are valid in chemical potential values between -∞ <μ <0 and have been designated as explicit form features, high precision, and less computing time. The calculation results are tabularly illustrated to show the consistency of the analytical relations analysis under the effect of parameters. Based on a comprehensive analysis of the results, they are potentially useful in applications to evaluate thermionic emission and astrophysics problems.</p>","PeriodicalId":10700,"journal":{"name":"Contributions to Plasma Physics","volume":"65 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141271588","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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}
A computational study is presented on laser wakefield acceleration (LWFA) in bubble regime with the use of ultrashort laser pulse propagating in an under-dense plasma. The Particle-In-Cell simulations are performed to investigate the bubble wakefield acceleration of electrons realized by the incidence of an intense laser beam on cold, under-dense plasma in two-dimensional geometry. Different simulations are carried out and the results are compared for the beams with trapezoidal and Gaussian temporal pulse profiles having almost equal but slightly different energy contents. Focus is given to plasma density modulation, wakefield strength, electrons self-injection, energy spectrum of accelerated electrons, the effect of an external longitudinal magnetic field and the study of pump depletion length and dephasing length in bubble regime with respect to these laser pulse profiles. Two limiting cases of the trapezoidal pulse, that is, triangular and rectangular pulses, are also discussed for better understanding of the role of steepness and plateau region in the laser pulse profile to the bubble wakefield acceleration. Since down ramp density gradient plays a crucial role for the generation of high-quality electron beam in plasma wakefield acceleration as well as in LWFA, three different adjustments on the down ramp length determining three different density gradients are discussed for uncovering the role of trapezoidal laser pulse in LWFA.
{"title":"Role of ultrashort trapezoidal temporal pulse profile in laser wakefield acceleration in bubble regime","authors":"Sonu Kumar, Dhananjay K. Singh, Hitendra K. Malik","doi":"10.1002/ctpp.202300181","DOIUrl":"10.1002/ctpp.202300181","url":null,"abstract":"<p>A computational study is presented on laser wakefield acceleration (LWFA) in bubble regime with the use of ultrashort laser pulse propagating in an under-dense plasma. The Particle-In-Cell simulations are performed to investigate the bubble wakefield acceleration of electrons realized by the incidence of an intense laser beam on cold, under-dense plasma in two-dimensional geometry. Different simulations are carried out and the results are compared for the beams with trapezoidal and Gaussian temporal pulse profiles having almost equal but slightly different energy contents. Focus is given to plasma density modulation, wakefield strength, electrons self-injection, energy spectrum of accelerated electrons, the effect of an external longitudinal magnetic field and the study of pump depletion length and dephasing length in bubble regime with respect to these laser pulse profiles. Two limiting cases of the trapezoidal pulse, that is, triangular and rectangular pulses, are also discussed for better understanding of the role of steepness and plateau region in the laser pulse profile to the bubble wakefield acceleration. Since down ramp density gradient plays a crucial role for the generation of high-quality electron beam in plasma wakefield acceleration as well as in LWFA, three different adjustments on the down ramp length determining three different density gradients are discussed for uncovering the role of trapezoidal laser pulse in LWFA.</p>","PeriodicalId":10700,"journal":{"name":"Contributions to Plasma Physics","volume":"65 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141198439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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}
Yuchen Xu, Shifeng Mao, Wenjin Chen, Zhiwei Ma, Minyou Ye
Edge localized modes resulted from magnetohydrodynamic (MHD) instabilities in the pedestal region are a significant concern for future tokamaks. In this work, Ci-Liu-Ti (CLT), an MHD code in the three-dimensional toroidal geometry, is applied for the linear simulation of the ideal pedestal MHD instabilities. The simulations are performed for the experimental advanced superconducting tokamak-like elongated divertor configuration with large triangularity, which is generated by the high-accuracy free-boundary equilibrium solver (CLT-EQuilibrium, i.e., CLT-EQ) developed recently. The present work focuses on the influence of the magnetic shear, which is scanned by adjusting the pedestal current with a fixed pedestal pressure profile. As the pedestal current increases, both the local (Slocal) and global (Sglobal) magnetic shear decrease. The ballooning mode is destabilized along with the decrease of Slocal, and stabilized when Slocal is negative for the whole region of bad curvature, which implies the access of the second stable region. Further increase of the pedestal current leads to the destabilization of the kink mode, which is stabilized again until Sglobal is negative at the location of significant gradient of current density. The simulated results are consistent with the findings in Radovanovic et al. Nucl. Fusion 62 (2022) 086004 and C. K. Sun et al. Phys. Plasmas 25 (2018) 082106, which indicates the availability of CLT in the linear simulation of the ideal pedestal instabilities.
基座区域的磁流体动力学(MHD)不稳定性导致的边缘局部模式是未来托卡马克的一个重要问题。在这项工作中,Ci-Liu-Ti(CLT)-- 一种三维环形几何的 MHD 代码-- 被应用于理想基座 MHD 不稳定性的线性模拟。模拟是针对实验性先进超导托卡马克式大三角形细长分流器构型进行的,该构型由最近开发的高精度自由边界平衡求解器(CLT-EQuilibrium,即 CLT-EQ)生成。本研究的重点是磁剪切的影响,在基座压力曲线固定的情况下,通过调整基座电流来扫描磁剪切。随着基座电流的增加,局部(Slocal)和全局(Sglobal)磁切变都会减小。气球模式随着 Slocal 的减小而失稳,当整个曲率不良区域的 Slocal 为负值时,气球模式趋于稳定,这意味着进入了第二个稳定区域。基座电流的进一步增大导致扭结模式失稳,直到 Sglobal 在电流密度显著梯度位置为负值时,扭结模式才再次稳定下来。模拟结果与 Radovanovic 等人在 Nucl.Fusion 62 (2022) 086004 和 C. K. Sun et al. Phys. Plasmas 25 (2018) 082106 的研究结果一致,这表明 CLT 可用于理想基座不稳定性的线性模拟。
{"title":"Study of the influence of magnetic shear on the linear MHD instabilities in the pedestal of elongated divertor configurations using CLT code","authors":"Yuchen Xu, Shifeng Mao, Wenjin Chen, Zhiwei Ma, Minyou Ye","doi":"10.1002/ctpp.202300106","DOIUrl":"10.1002/ctpp.202300106","url":null,"abstract":"<p>Edge localized modes resulted from magnetohydrodynamic (MHD) instabilities in the pedestal region are a significant concern for future tokamaks. In this work, Ci-Liu-Ti (CLT), an MHD code in the three-dimensional toroidal geometry, is applied for the linear simulation of the ideal pedestal MHD instabilities. The simulations are performed for the experimental advanced superconducting tokamak-like elongated divertor configuration with large triangularity, which is generated by the high-accuracy free-boundary equilibrium solver (CLT-EQuilibrium, i.e., CLT-EQ) developed recently. The present work focuses on the influence of the magnetic shear, which is scanned by adjusting the pedestal current with a fixed pedestal pressure profile. As the pedestal current increases, both the local (<i>S</i><sub>local</sub>) and global (<i>S</i><sub>global</sub>) magnetic shear decrease. The ballooning mode is destabilized along with the decrease of <i>S</i><sub>local</sub>, and stabilized when <i>S</i><sub>local</sub> is negative for the whole region of bad curvature, which implies the access of the second stable region. Further increase of the pedestal current leads to the destabilization of the kink mode, which is stabilized again until <i>S</i><sub>global</sub> is negative at the location of significant gradient of current density. The simulated results are consistent with the findings in Radovanovic et al. Nucl. Fusion 62 (2022) 086004 and C. K. Sun et al. Phys. Plasmas 25 (2018) 082106, which indicates the availability of CLT in the linear simulation of the ideal pedestal instabilities.</p>","PeriodicalId":10700,"journal":{"name":"Contributions to Plasma Physics","volume":"64 7-8","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141108018","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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}
We summarize the method of hydrodynamic approximation for weakly ionized plasmas developed with Klimontovich in 1962 and give a generalization to many—component systems using Onsagers matrix theory and including dispersion effects. We develop the conductivity theory of complex plasma and electrolyte mixtures based on the model of charged hard spheres with given non-additive contact distances, including frequency-dependent electric fields. These generalizations are made with the aim to allow applications to complex natural systems as atmospheric plasmas and seawater. Finally, we give as an example a numerical calculation of the single ion conductivities of a six-component seawater model.
{"title":"Kinetic theory of weakly ionized plasma and electrolyte mixtures including Onsager matrix and frequency dispersion effects","authors":"W. Ebeling","doi":"10.1002/ctpp.202300161","DOIUrl":"10.1002/ctpp.202300161","url":null,"abstract":"<p>We summarize the method of hydrodynamic approximation for weakly ionized plasmas developed with Klimontovich in 1962 and give a generalization to many—component systems using Onsagers matrix theory and including dispersion effects. We develop the conductivity theory of complex plasma and electrolyte mixtures based on the model of charged hard spheres with given non-additive contact distances, including frequency-dependent electric fields. These generalizations are made with the aim to allow applications to complex natural systems as atmospheric plasmas and seawater. Finally, we give as an example a numerical calculation of the single ion conductivities of a six-component seawater model.</p>","PeriodicalId":10700,"journal":{"name":"Contributions to Plasma Physics","volume":"64 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/ctpp.202300161","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141122019","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}