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Inverse cascading for initial magnetohydrodynamic turbulence spectra between Saffman and Batchelor Saffman和Batchelor之间初始磁流体动力湍流谱的逆级联
IF 2.5 3区 物理与天体物理 Q2 PHYSICS, FLUIDS & PLASMAS Pub Date : 2023-12-01 DOI: 10.1017/s0022377823001253
Axel Brandenburg, Ramkishor Sharma, Tanmay Vachaspati
In decaying magnetohydrodynamic (MHD) turbulence with a strong magnetic field, the spectral magnetic energy density is known to increase with time at small wavenumbers <jats:inline-formula> <jats:alternatives> <jats:tex-math>$k$</jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022377823001253_inline1.png" /> </jats:alternatives> </jats:inline-formula>, provided the spectrum at low <jats:inline-formula> <jats:alternatives> <jats:tex-math>$k$</jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022377823001253_inline2.png" /> </jats:alternatives> </jats:inline-formula> is sufficiently steep. This process is called inverse cascading and occurs for an initial Batchelor spectrum, where the magnetic energy per linear wavenumber interval increases like <jats:inline-formula> <jats:alternatives> <jats:tex-math>$k^4$</jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022377823001253_inline3.png" /> </jats:alternatives> </jats:inline-formula>. For an initial Saffman spectrum that is proportional to <jats:inline-formula> <jats:alternatives> <jats:tex-math>$k^2$</jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022377823001253_inline4.png" /> </jats:alternatives> </jats:inline-formula>, however, inverse cascading has not been found in the past. We study here the case of an intermediate <jats:inline-formula> <jats:alternatives> <jats:tex-math>$k^3$</jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022377823001253_inline5.png" /> </jats:alternatives> </jats:inline-formula> spectrum, which may be relevant for magnetogenesis in the early Universe during the electroweak epoch. This case is not well understood in view of the standard Taylor expansion of the magnetic energy spectrum for small <jats:inline-formula> <jats:alternatives> <jats:tex-math>$k$</jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022377823001253_inline6.png" /> </jats:alternatives> </jats:inline-formula>. Using high resolution MHD simulations, we show that, also in this case, there is inverse cascading with a strength just as expected from the conservation of the Hosking integral, which governs the decay of an initial Batchelor spectrum. Even for shallower <jats:inline-formula> <jats:alternatives> <jats:tex-math>$k^alpha$</jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022377823001253_inline7.png" /> </jats:alternatives> </jats:inline-formula> spectra with spectral index <jats:inline-formula> <jats:alternatives> <jats:tex-math>$alpha >3/2$</jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022377823
在强磁场的衰减磁流体动力学(MHD)湍流中,谱磁能密度已知在小波数$k$时随时间增加,只要谱在低$k$处足够陡峭。这个过程被称为逆级联,发生在初始巴彻勒谱中,其中每个线性波数区间的磁能像k^4一样增加。然而,对于与k^2$成比例的初始Saffman谱,过去没有发现逆级联。我们在这里研究了中间$k^3$谱的情况,这可能与早期宇宙在电弱时期的磁发生有关。考虑到小$k$的磁能谱的标准泰勒展开,这种情况不能很好地理解。使用高分辨率MHD模拟,我们表明,同样在这种情况下,存在逆级联,其强度与霍斯金积分守恒所期望的一样,它控制了初始Batchelor谱的衰减。即使对于光谱指数为$alpha >3/2$的较浅$k^alpha$光谱,我们的模拟表明,随着时间$t$,光谱在小$k$处的增加与$t^{4alpha /9-2/3}$成正比。$alpha =3/2$的临界光谱指数与霍斯金现象学中光谱包络线的斜率有关。我们对$2048^3$网格点的模拟现在表明,即使对于初始的Saffman谱,也是反向级联的。
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引用次数: 0
Complex structure of turbulence across the ASDEX Upgrade pedestal ASDEX升级基座上的复杂湍流结构
IF 2.5 3区 物理与天体物理 Q2 PHYSICS, FLUIDS & PLASMAS Pub Date : 2023-12-01 DOI: 10.1017/s0022377823001101
L.A. Leppin, T. Görler, M. Cavedon, M.G. Dunne, E. Wolfrum, F. Jenko, the ASDEX Upgrade Team

The theoretical investigation of relevant turbulent transport mechanisms in H-mode pedestals is a great scientific and numerical challenge. In this study, we address this challenge by global, nonlinear gyrokinetic simulations of a full pedestal up to the separatrix, supported by a detailed characterisation of gyrokinetic instabilities from just inside the pedestal top to the pedestal centre and foot. We present ASDEX Upgrade pedestal simulations using an upgraded version of the gyrokinetic, Eulerian, delta-f code GENE (genecode.org) that enables stable global simulations at experimental plasma $beta$ values. The turbulent transport is found to exhibit a multi-channel, multi-scale character throughout the pedestal with the dominant contribution transitioning from ion-scale trapped electron modes/micro-tearing modes at the pedestal top to electron-scale electron temperature gradient modes in the steep gradient region. Consequently, the turbulent electron heat flux changes from ion to electron scales and the ion heat flux reduces to almost neoclassic values in the pedestal centre. $Etimes B$ shear is found to strongly reduce heat flux levels in all channels (electron, ion, electrostatic, electromagnetic) and the interplay of magnetic shear and pressure gradient is found to locally stabilise ion-scale instabilities.

h型基座湍流输运机制的理论研究是一项巨大的科学和数值挑战。在本研究中,我们通过对整个基座直至分离矩阵的全局非线性陀螺仪动力学模拟来解决这一挑战,并通过从基座顶部内部到基座中心和基座底部的陀螺仪动力学不稳定性的详细描述来支持。我们展示了ASDEX升级基座模拟,使用升级版本的陀螺动力学,欧拉,delta-f代码GENE (genecode.org),可以在实验等离子体$beta$值下进行稳定的全局模拟。研究发现,湍流输运表现出多通道、多尺度的特征,其主要贡献从基座顶部的离子尺度捕获电子模式/微撕裂模式转变为陡峭梯度区域的电子尺度电子温度梯度模式。因此,湍流电子热流从离子尺度变化到电子尺度,离子热流在基座中心几乎降低到新古典值。发现$E × B$剪切能强烈降低所有通道(电子、离子、静电、电磁)中的热通量水平,并且发现磁剪切和压力梯度的相互作用可以局部稳定离子尺度的不稳定性。
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引用次数: 0
Generalized cross-helicity in non-ideal magnetohydrodynamics 非理想磁流体力学中的广义交叉螺旋度
IF 2.5 3区 物理与天体物理 Q2 PHYSICS, FLUIDS & PLASMAS Pub Date : 2023-12-01 DOI: 10.1017/s002237782300123x
Prachi Sharma, Asher Yahalom
The objective of the present paper is to investigate the constancy of the topological invariant, denoted the non-barotropic generalized cross-helicity in the case of non-ideal magnetohydrodynamics (MHD). Existing work considers only ideal barotropic MHD and ideal non-barotropic MHD. Here, we consider dissipative processes in the form of thermal conduction, finite electrical conductivity and viscosity and the effect of these processes on the cross-helicity conservation. An analytical approach has been adopted to obtain the mathematical expressions for the time derivative of the cross-helicity. Obtained results show that the generalized cross-helicity is not conserved in the non-ideal MHD limit and indicate which processes affect the helicity and which do not. Furthermore, we indicate the configurations in which this topological constant is conserved despite the dissipative processes. Some examples and applications are also given.
本文的目的是研究非理想磁流体力学(MHD)情况下拓扑不变量的恒常性,即非正压广义交叉螺旋度。现有工作只考虑理想正压MHD和理想非正压MHD。在这里,我们考虑了热传导、有限电导率和粘度形式的耗散过程,以及这些过程对交叉螺旋守恒的影响。采用解析的方法得到了交叉螺旋度时间导数的数学表达式。所得结果表明,广义交叉螺旋度在非理想MHD极限下是不守恒的,并指出了哪些过程影响螺旋度,哪些不影响。此外,我们指出了在耗散过程中该拓扑常数守恒的构型。并给出了一些实例和应用。
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引用次数: 0
Guiding-centre orbit-following simulations of charge exchange loss of NBI ions with the finite Larmor radius effect 有限Larmor半径效应下NBI离子电荷交换损失的导向中心轨道跟踪模拟
IF 2.5 3区 物理与天体物理 Q2 PHYSICS, FLUIDS & PLASMAS Pub Date : 2023-11-29 DOI: 10.1017/s0022377823001186
Yingfeng Xu, Fuqiong Wang, Yongliang Li, Fangchuan Zhong
Guiding-centre orbit-following simulations of the charge exchange (CX) loss of neutral beam injection (NBI) ions are presented. The finite Larmor radius (FLR) effect in the fast ion–neutral collision can be included in guiding-centre orbit-following simulations by using the gyroaverage method. It is proved that the neutralization probability of fast ions computed by using the gyroaverage method in the guiding-centre orbit simulation is roughly the same as that computed in the full-orbit simulation when the time step in the guiding-centre simulation is the order of the gyroperiod. The CX losses of NBI fast ions for two NBIs in the EAST tokamak have been simulated by the guiding-centre orbit-following code GYCAVA, and the FLR effect in the fast ion–neutral collision on CX losses has been numerically studied. The CX effect of the fast ion–neutral collision can significantly enhance NBI ion losses on EAST. The FLR effect in the fast ion–neutral collision can enhance the CX loss. Vertical asymmetry of localized heat loads induced by CX losses is found, which is related to the FLR effect of fast ions and the strong radial gradient of the neutral density near the plasma edge. Heat loads induced by CX losses are localized in the regions near the poloidal angle $theta =-60^circ$ , because the likelihood of exchanging charge is the largest at gyrophase $xi ={rm pi}$ , and this leads to fast downwards moving neutrals. Fast ion loss fractions induced by CX increase with the neutral density increasing.
给出了中性束注入离子电荷交换损失的导向中心轨道跟踪模拟。利用陀螺平均方法,可以将快速离子中性碰撞中的有限拉莫尔半径(FLR)效应纳入导向中心轨道跟踪模拟中。证明了当制导中心模拟的时间步长为陀螺周期的阶数时,用陀螺平均法计算的快离子中和概率与全轨道模拟计算的中和概率大致相同。利用GYCAVA导向中心随轨程序模拟了EAST托卡马克中两个NBI快离子的CX损耗,并对快离子中性碰撞中FLR对CX损耗的影响进行了数值研究。快速离子中性碰撞的CX效应显著增加了NBI离子在EAST上的损失。快速离子中性碰撞中的FLR效应会增加CX的损耗。发现CX损耗引起的局部热负荷垂直不对称,这与快离子的FLR效应和等离子体边缘附近中性密度的强径向梯度有关。CX损失引起的热负荷集中在极向角$theta =-60^circ$附近的区域,因为在陀螺相$xi ={rm pi}$交换电荷的可能性最大,这导致了快速向下移动的中性离子。CX诱导的快速离子损失分数随着中性密度的增加而增加。
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引用次数: 0
Generation of energetic electrons by an electron cyclotron wave through stochastic heating in a spherical tokamak 球形托卡马克中电子回旋波通过随机加热产生高能电子
IF 2.5 3区 物理与天体物理 Q2 PHYSICS, FLUIDS & PLASMAS Pub Date : 2023-11-28 DOI: 10.1017/s0022377823001216
Mingyuan Wang, Shikui Cheng, Bing Liu, Shaodong Song, Dong Guo, Yunyang Song, Wenjun Liu, Debabrata Banerjee, Songjian Li, Tiantian Sun, Xiang Gu, Yingying Li, Jiaqi Dong, Yuejiang Shi, Y.-K. Martin Peng, Adi Liu
This study presents novel findings on stochastic electron heating via a random electron cyclotron wave (ECW) in a spherical tokamak. Hard x ray measurements demonstrate the time evolution of hard x ray counts at different energy bands, consistent with predictions from the stochastic heating model. The ECW heating rate shows a positive correlation with applied power, confirming the effectiveness of stochastic heating. Remarkably, the ECW-driven plasma current remains insensitive to ECW incidence angle, consistent with model predictions. The observed stochastic heating of electrons offers potential for exploring innovative non-inductive current drive modes in spherical tokamaks. This research contributes to the understanding of plasma behaviour and motivates the development of new models for non-inductive current drive in fusion devices.
本文提出了在球形托卡马克中利用随机电子回旋波(ECW)加热随机电子的新发现。硬x射线测量证明了硬x射线计数在不同能带上的时间演变,与随机加热模型的预测一致。ECW加热速率与外加功率呈正相关,证实了随机加热的有效性。值得注意的是,ECW驱动的等离子体电流对ECW入射角不敏感,这与模型预测一致。观察到的电子的随机加热为探索球形托卡马克中创新的无感电流驱动模式提供了潜力。这项研究有助于理解等离子体的行为,并推动了核聚变装置中无感电流驱动新模型的发展。
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引用次数: 0
Nonlinear interaction of Alfvénic instabilities and turbulence via the modification of the equilibrium profiles 通过平衡剖面的修改,研究了气动系统的不稳定性与湍流的非线性相互作用
IF 2.5 3区 物理与天体物理 Q2 PHYSICS, FLUIDS & PLASMAS Pub Date : 2023-11-21 DOI: 10.1017/s0022377823001137
A. Biancalani, A. Bottino, D. Del Sarto, M.V. Falessi, T. Hayward-Schneider, P. Lauber, A. Mishchenko, B. Rettino, J.N. Sama, F. Vannini, L. Villard, X. Wang, F. Zonca, the ASDEX Upgrade team

Nonlinear simulations of Alfvén modes (AMs) driven by energetic particles (EPs) in the presence of turbulence are performed with the gyrokinetic particle-in-cell code ORB5. The AMs carry a heat flux, and consequently they nonlinearly modify the plasma temperature profiles. The isolated effect of this modification on the dynamics of turbulence is studied by means of electrostatic simulations. We find that turbulence is reduced when the profiles relaxed by the AM are used, with respect to the simulation where the unperturbed profiles are used. This is an example of indirect interaction of EPs and turbulence. First, an analytic magnetic equilibrium with circular concentric flux surfaces is considered as a simplified example for this study. Then, an application to an experimentally relevant case of ASDEX Upgrade is discussed.

利用胞内粒子的回旋动力学代码ORB5,对湍流条件下高能粒子驱动的alfv模态(AMs)进行了非线性模拟。AMs携带热流,因此它们非线性地改变了等离子体的温度分布。通过静电模拟研究了这种修正对湍流动力学的孤立影响。我们发现,相对于使用无扰动轮廓的模拟,当使用AM放松的轮廓时,湍流减少了。这是EPs与湍流间接相互作用的一个例子。首先,考虑了一个具有圆形同心磁面的解析磁平衡作为本研究的简化例子。然后,讨论了ASDEX升级在一个实验相关案例中的应用。
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引用次数: 0
Using rational surfaces to improve pellet fuelling in stellarators 使用合理的表面来改善仿星器中的颗粒燃料
IF 2.5 3区 物理与天体物理 Q2 PHYSICS, FLUIDS & PLASMAS Pub Date : 2023-11-16 DOI: 10.1017/s0022377823001010
N. Panadero, K. J. McCarthy, B. Pégourié, R. Carrasco, I. García-Cortés, R. García, J. Hernández-Sánchez, F. Köchl, J. Martínez-Fernández, R. Sakamoto, the TJ-II team

Pellet injection is currently the primary candidate for achieving efficient plasma fuelling, one of the key issues for steady-state operation in large fusion devices. In this paper, pellet injection experiments are performed for several magnetic configurations of the TJ-II stellarator. The aim of this study is to increase the understanding of the role played by rational surfaces in plasmoid drift and deposition profiles in stellarators. The analysis of experimentally observed plasmoid drifts is supported by simulations of such cases made with the HPI2 code. Plasmoid drift is found to be significantly reduced, as in tokamaks, in the vicinity of rational surfaces. This is attributed to the fact that plasmoid external charge reconnection lengths are shorter near rational surfaces, resulting in a more effective damping of the plasmoid drift. Although the effect of plasmoid external currents on the drift is expected to be negligible in stellarators, compared with those caused by plasmoid internal currents, the effect observed in TJ-II is clearly measurable. In addition, simulations show that enhanced drift reductions near rational surfaces lead to significantly different deposition profiles for the magnetic configurations included in this study. This implies that it should be possible to select the magnetic configurations to obtain more efficient pellet fuelling.

颗粒注入是目前实现高效等离子体燃料的主要候选方法,这是大型聚变装置稳态运行的关键问题之一。本文对TJ-II仿星器的几种磁性结构进行了球团注入实验。本研究的目的是增加对合理表面在仿星器等离子体漂移和沉积剖面中所起作用的理解。实验观察到的等离子体漂移的分析得到了用HPI2代码模拟这种情况的支持。等离子体漂移被发现显著减少,如在托卡马克中,在有理表面附近。这是由于等离子体外电荷重联长度在有理表面附近较短,从而更有效地抑制了等离子体漂移。虽然在仿星器中,与等离子体内部电流引起的漂移相比,等离子体外部电流对漂移的影响可以忽略不计,但在TJ-II中观察到的影响显然是可以测量的。此外,模拟表明,在合理表面附近,漂移减小的增强导致本研究中包含的磁性配置的沉积剖面显著不同。这意味着,应该有可能选择磁性配置,以获得更有效的颗粒燃料。
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引用次数: 0
Resonant excitation of single Kelvin–Helmholtz high-order waves in a magnetized electron fluid vortex 磁化电子流体涡旋中单开尔文-亥姆霍兹高阶波的共振激发
3区 物理与天体物理 Q2 PHYSICS, FLUIDS & PLASMAS Pub Date : 2023-11-13 DOI: 10.1017/s0022377823001150
G. Maero, N. Panzeri, L. Patricelli, M. Romé
Thanks to the isomorphism between the drift-Poisson and Euler equations, inviscid two-dimensional fluid experiments can be performed in magnetized, single-component plasmas in Penning–Malmberg traps. Within this analogy, a trapped electron plasma column is equivalent to a two-dimensional vortex. Here, we focus our attention on the generation of V-states, i.e. $l$ -fold symmetric rotating vorticity patches where the deformation with respect to the circular cross-section has reached the nonlinear regime. We detail a linear theoretical analysis and devise an experimental routine to generate V-states through the precise excitation of single Kelvin–Helmholtz perturbations in a magnetized electron plasma. This technique makes use of suitable multipolar rotating electric fields, which are shown to be able to select the desired wavemode. In particular, with rotating fields, a hardware limitation in the highest accessible mode is removed and nonlinear Kelvin–Helmholtz waves of generic order $l$ can be attained, which pave the way for further investigations on the evolution and stability properties of V-states. Systematic experimental results for the selective mode growth in the linear and nonlinear regimes up to saturation and collapse are discussed.
由于漂泊松方程和欧拉方程之间的同构性,可以在Penning-Malmberg陷阱中磁化的单组分等离子体中进行无粘二维流体实验。在这个类比中,一个被捕获的电子等离子体柱相当于一个二维涡旋。在这里,我们将注意力集中在v态的产生上,即$l$ -fold对称旋转涡量斑块,其中相对于圆形截面的变形已经达到非线性状态。我们详细介绍了线性理论分析,并设计了一个实验程序,通过在磁化电子等离子体中精确激发单开尔文-亥姆霍兹微扰来产生v态。该技术利用合适的多极旋转电场,可以选择所需的波模。特别是在旋转场中,消除了最高可达模式的硬件限制,可以获得一般阶$l$的非线性开尔文-亥姆霍兹波,这为进一步研究v态的演化和稳定性特性铺平了道路。讨论了在线性和非线性状态下直至饱和和崩溃的选择模式生长的系统实验结果。
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引用次数: 0
On the analytical description of the nonlinear stage of the Weibel instability in collisionless anisotropic plasma 无碰撞各向异性等离子体中维贝尔不稳定性非线性阶段的解析描述
3区 物理与天体物理 Q2 PHYSICS, FLUIDS & PLASMAS Pub Date : 2023-11-08 DOI: 10.1017/s0022377823001198
A.A. Nechaev, A.A. Kuznetsov, Vl.V. Kocharovsky
On the basis of the energy invariants for the Weibel instability in a collisionless non-relativistic plasma, an analytical relation is obtained between the instantaneous values of the space-averaged energy density of the magnetic field, its dominant wavenumber and the average plasma anisotropy parameter. The relation is valid for arbitrary particle velocity distribution functions, including ones that vary with time at the nonlinear stage of instability. It is obtained under the assumption that the plasma is homogeneous along a certain axis, determined, for example, by an external magnetic field, and taking into account only the modes with wavevectors orthogonal to this axis. We give an estimate of the maximum magnetic field energy achievable during the Weibel instability and show that its ratio to the initial longitudinal energy of particles, even for a large initial plasma anisotropy parameter, cannot exceed the value approximately equal to 0.2. The obtained analytical relation is verified using two-dimensional particle-in-cell simulations.
在无碰撞非相对论等离子体Weibel不稳定性能量不变量的基础上,得到了磁场空间平均能量密度瞬时值、主导波数与平均等离子体各向异性参数之间的解析关系。该关系适用于任意粒子速度分布函数,包括非线性不稳定阶段随时间变化的粒子速度分布函数。它是在假设等离子体沿某一轴是均匀的情况下得到的,例如,由外部磁场决定,并且只考虑与该轴正交的波向量的模式。我们给出了在Weibel不稳定性期间所能达到的最大磁场能量的估计,并表明即使初始等离子体各向异性参数很大,其与粒子初始纵向能量的比值也不能超过约等于0.2的值。通过二维细胞内粒子模拟验证了所得到的解析关系。
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引用次数: 0
The available energy of trapped electrons: a nonlinear measure for turbulent transport 捕获电子的可用能量:湍流输运的非线性测量
3区 物理与天体物理 Q2 PHYSICS, FLUIDS & PLASMAS Pub Date : 2023-10-01 DOI: 10.1017/s0022377823001083
R.J.J. Mackenbach, J.H.E. Proll, R. Wakelkamp, P. Helander
A collisionless plasma possesses a certain amount of ‘available energy’, which is that part of the thermal energy that can be converted into kinetic energy of plasma motion and electromagnetic fluctuations. In this paper we present a calculation of the available energy carried by trapped electrons in a slender non-omnigenous flux tube of plasma. This quantity is compared with gyrokinetic simulations of the nonlinear saturated radial energy flux resulting from turbulence driven by collisionless trapped-electron modes in various stellarators and a tokamak. The numerical calculation of available energy is fast and shows a strong correlation with the turbulent energy fluxes found in the gyrokinetic simulations. Indeed, the energy flux is found to be proportional to the available energy to the power of approximately $3/2$ , which is what one would expect from a simple argument. We furthermore investigate how available energy is distributed across different bounce wells, and it is found that deeply trapped electrons typically contribute most to the available energy. Finally, we investigate the dependence of available energy on gradient strength, and we find important differences between weakly and strongly driven regimes for stellarators and tokamaks.
一个无碰撞的等离子体拥有一定量的“可用能量”,这部分热能可以转化为等离子体运动和电磁波动的动能。本文给出了在细长非均匀等离子体通量管中捕获电子所携带的可用能量的计算方法。这一数值与在不同的仿星器和托卡马克中由无碰撞捕获电子模式驱动的非线性饱和径向能量流的陀螺动力学模拟结果进行了比较。有效能量的数值计算速度很快,并且与陀螺动力学模拟中发现的湍流能量通量有很强的相关性。事实上,能量通量被发现与可用能量成正比,大约是3/2美元的幂,这是人们从一个简单的论点中所期望的。我们进一步研究了可用能量如何分布在不同的弹跳井中,发现深度捕获的电子通常对可用能量贡献最大。最后,我们研究了可用能量对梯度强度的依赖性,并发现了仿星器和托卡马克的弱驱动和强驱动机制之间的重要差异。
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引用次数: 3
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