Geodesic acoustic mode induced by toroidal rotation in tokamaks

The effect of toroidal rotation on the geodesic acoustic mode (GAM) in a tokamak is studied. It is shown that, in addition to a small frequency upshift of the ordinary GAM, another GAM, with much lower frequency, is induced by the rotation. The new GAM appears as a consequence of the nonuniform plasma density and pressure created by the centrifugal force on the magnetic surfaces. Both GAMs in a rotating plasma are shown to exist both as continuum modes with finite mode numbers m and n at the rational surfaces q=m/n as well as in the form of axisymmetric modes with m=n=0.     

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采用回旋动理学方程推导得到了环向转动托卡马克等离子体中测地声模的色散关系,分析了环向转动对测地声模、低频模和声波分支的频率以及无碰撞阻尼率的影响.结果表明,测地声模的频率会随着环向转动马赫数而逐渐增大,而其无碰撞阻尼率则会随着环向转动马赫数而迅速减小.此外,低频模和声波分支的频率以及无碰撞阻尼率都会随着环向转动马赫数而逐渐减小,其中环向转动对声波分支的频率以及无碰撞阻尼率的影响非常小,基本上可以忽略.     

托卡马克等离子体环向转动对测地声模的影响

采用回旋动理学方程推导得到了环向转动托卡马克等离子体中测地声模的色散关系,分析了环向转动对测地声模、低频模和声波分支的频率以及无碰撞阻尼率的影响。结果表明,测地声模的频率会随着环向转动马赫数而逐渐增大,而其无碰撞阻尼率则会随着环向转动马赫数而迅速减小。此外,低频模和声波分支的频率以及无碰撞阻尼率都会随着环向转动马赫数而逐渐减小,其中环向转动对声波分支的频率以及无碰撞阻尼率的影响非常小,基本上可以忽略。     

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采用流体模型理论推导了等熵平衡条件下环向转动托卡马克等离子体中带状流的色散关系。从理论上分析了环向转动对测地声模、低频带状流和声波的频率、压力和密度扰动量的影响。结果表明,环向转动对低频带状流的频率没有影响,但会使测地声模的频率逐渐增大。此外,存在环向转动时,低频带状流会具有驻波形式的压力和密度扰动量,且测地声模和声波可以沿着极向传播。而且还发现,等熵平衡可以看成是等温平衡的一种特殊情况。     

托卡马克等熵平衡条件下等离子体环向转动对带状流的影响

采用流体模型理论推导了等熵平衡条件下环向转动托卡马克等离子体中带状流的色散关系。从理论上分析了环向转动对测地声模、低频带状流和声波的频率、压力和密度扰动量的影响。结果表明,环向转动对低频带状流的频率没有影响,但会使测地声模的频率逐渐增大。此外,存在环向转动时,低频带状流会具有驻波形式的压力和密度扰动量,且测地声模和声波可以沿着极向传播。而且还发现,等熵平衡可以看成是等温平衡的一种特殊情况。     

The Brunt–Väisälä frequency of rotating tokamak plasmas

The continuous spectrum of analytical toroidally rotating magnetically confined plasma equilibria is investigated analytically and numerically. In the presence of purely toroidal flow, the ideal magnetohydrodynamic equations leave the freedom to specify which thermodynamic quantity is constant on the magnetic surfaces. Introducing a general parametrization of this quantity, analytical equilibrium solutions are derived that still posses this freedom. These equilibria and their spectral properties are shown to be ideally suited for testing numerical equilibrium and stability codes including toroidal rotation. Analytical expressions are derived for the low-frequency continuous Alfvén spectrum. These expressions still allow one to choose which quantity is constant on the magnetic surfaces of the equilibrium, thereby generalizing previous results. The centrifugal convective effect is shown to modify the lowest Alfvén continuum branch to a buoyancy frequency, or Brunt–Väisälä frequency. A comparison with numerical results for the case that the specific entropy, the temperature, or the density is constant on the magnetic surfaces yields excellent agreement, showing the usefulness of the derived expressions for the validation of numerical codes.     

Numerical study of physical properties of resistive wall modes in tokamaks

The effect of plasma with toroidal rotation on the resistive wall modes in tokamaks is studied numerically. An eigenvalue method is adopted to calculate the growth rate of the modes for changing plasma resistivity and plasma density distribution, as well as the diffusion time of magnetic field through the resistive wall. It is found that the resistive wall mode can be suppressed by the toroidal rotation of the plasma. Also, the growth rate of the resistive wall mode decreases when the edge plasma density is the same as the core plasma density, but it only changes slightly with the plasma resistivity.     

ITER装置中等离子体旋转和反馈控制对电阻壁模影响的数值研究

在托卡马克等离子体中,电阻壁模是非常重要的磁流体不稳定性,特征时间在毫秒量级.对长时间稳态运行下的先进托卡马克,电阻壁模限制着聚变装置的运行参数空间(放电时间和比压),影响经济效益,所以研究电阻壁模稳定性至关重要.本文使用MARS程序,针对ITER装置上9 MA先进运行平衡位形,研究了等离子体旋转和反馈控制对电阻壁模的影响.结果表明,在没有反馈控制时,当比压参数Cβ取0.7,等离子体环向旋转频率达到1.1%的阿尔芬频率时,可以完全稳定电阻壁模;在等离子体环向旋转和反馈控制共同作用时,比压参数Cβ取0.7,反馈增益|G|取0.6时,稳定电阻壁模所需要的等离子体旋转频率为0.2%的阿尔芬频率.可见,单独靠等离子体环向旋转稳定电阻壁模所需的旋转频率较大;而等离子体环向旋转和反馈控制共同作用可以降低稳定电阻壁模的旋转频率临界值,符合先进托卡马克的运行.本文的研究结果对中国聚变工程试验堆CFETR的工程设计和运行具有一定指导意义.     

Observations of an ion-driven instability in non-neutral plasmas confined on magnetic surfaces

The first detailed experimental study of an instability driven by the presence of a finite ion fraction in an electron-rich non-neutral plasma confined on magnetic surfaces is presented. The instability has a poloidal mode number m=1, implying that the parallel force balance of the electron fluid is broken and that the instability involves rotation of the entire plasma, equivalent to ion-resonant instabilities in Penning traps and toroidal field traps. The mode appears when the ion density exceeds approximately 10% of the electron density. The measured frequency decreases with increasing magnetic field strength, and increases with increasing radial electric field, showing that the instability is linked to the E x B flow of the electron plasma. The frequency does not, however, scale exactly with E/B, and it depends on the ion species that is introduced, implying that the instability consists of interacting perturbations of ions and electrons.     

Reduced critical rotation for resistive-wall mode stabilization in a near-axisymmetric configuration

Recent DIII-D experiments with reduced neutral beam torque and minimum nonaxisymmetric perturbations of the magnetic field show a significant reduction of the toroidal plasma rotation required for the stabilization of the resistive-wall mode (RWM) below the threshold values observed in experiments that apply nonaxisymmetric magnetic fields to slow the plasma rotation. A toroidal rotation frequency of less than 10 krad/s at the q=2 surface (measured with charge exchange recombination spectroscopy using C VI) corresponding to 0.3% of the inverse of the toroidal Alfvén time is sufficient to sustain the plasma pressure above the ideal MHD no-wall stability limit. The low-rotation threshold is found to be consistent with predictions by a kinetic model of RWM damping.     

Error field amplification and rotation damping in tokamak plasmas

Toroidal rotation is normally very weakly damped in plasmas that are magnetically confined in the nominally toroidally symmetric tokamak. However, a strong damping of toroidal rotation is observed as such plasmas approach marginal stability for perturbations that produce a kinklike distortion of the plasma. It is shown that the damping of toroidal rotation by very small departures of the magnetic field from toroidal symmetry is greatly enhanced as marginal stability is approached. The response of a plasma to perturbations is studied using a set of electrical circuit elements, which provide an equation for the rotational damping that requires minimal information about the plasma.     

Role of nonlinear coupling and density fluctuations in magnetic-fluctuation-induced particle transport

Three-wave nonlinear coupling among spatial Fourier modes of density and magnetic fluctuations is directly measured in a magnetically confined toroidal plasma. Density fluctuations are observed to gain (lose) energy from (to) either equilibrium or fluctuating fields depending on the mode number. Experiments indicate that nonlinear interactions alter the phase relation between density and magnetic fluctuations, leading to strong particle transport.     

Topology of toroidal helical fields in non-circular cross-sectional tokamaks

The ordinary differential magnetic field line equations are solved numerically; the tokamak magnetic structure is studied on Hefei Tokamak-7 Upgrade （HT-TU） when the equilibrium field with a monotonic q-profile is perturbed by a helical magnetic field. We find that a single mode （m, n） helical perturbation can cause the formation of islands on rational surfaces with q=m/n and q=（m±1,±2,±3,...）/n due to the toroidicity and plasma shape （i.e. elongation and triangularity）, while there are many undestroyed magnetic surfaces called Kolmogorov-Arnold-Moser （KAM） barriers on irrational surfaces. The islands on the same rational surface do not have the same size. When the ratio between the perturbing magnetic field Br（r） and the toroidal magnetic field amplitude Bφ0 is large enough, the magnetic island chains on different rational surfaces will overlap and chaotic orbits appear in the overlapping area, and the magnetic field becomes stochastic. It is remarkable that the stochastic layer appears first in the plasma edge region.     

Rotational stabilization of resistive wall modes by the shear alfvén resonance

It is found that resistive wall modes with a toroidal number n = 1 in tokamaks can be stabilized by plasma rotation at a low Mach number, with the rotation frequency being lower than the ion bounce frequency but larger than the ion and electron precession drift frequencies. The stabilization is the result of the shear-Alfvén resonance, since the thermal resonance effect is negligible in this rotation frequency range. This indicates that tokamaks can operate at normalized pressure values beyond the no-wall stability limit even for low values of plasma rotation, such as those expected in fusion reactor scale devices.     

Self-acceleration of a tokamak plasma during ohmic H mode

Core plasma rotation is observed to change from counter direction to co-current direction during the transition from low (L) to high (H) confinement mode, in Alcator C-Mod plasmas that are heated purely Ohmically and, hence, have no momentum input. The changes of the toroidal velocities, deduced independently from impurity Doppler measurements and from magnetic perturbations associated with sawteeth, agree. The magnitude of the change is consistent with the previously documented scaling for rotation in ion cyclotron rf-heated H modes. The rotation in this Ohmic experiment is obviously not an rf effect but demonstrates unequivocally a transport effect accelerating the plasma.     

Stability of internal transport barriers to ideal MHD ballooning modes

Internal transport barriers (ITB) in tokamaks can form near a minimum in the q profile, q(min), where magnetic shear is weak. We have analyzed their stability to short wavelength (n>1, where n is the toroidal mode number) ideal MHD ballooning modes, by considering the s-alpha model equilibrium. We show that the ballooning transformation fails in regions of low shear but that one can then adopt a complementary approach based on the recurrence relation describing the toroidal coupling of radially localized modes on adjacent rational surfaces. Inclusion of the stabilizing effects of favorable average curvature or finite-n using this technique leads to stable high-pressure ITB configurations. The theory also shows the advantages of operating with low-order rational values of q(min).     

Plasma Response to Resonant Perturbations at Tokamak Edge

In certain circumstances, plasma response suppresses magnetic islands expected at perturbed resonant magnetic surfaces. We investigate the plasma response to the resonant magnetic perturbations in a large aspect ratio tokamak perturbed by external resonant helical windings, considering polar toroidal coordinates for which analytical toroidal equilibrium solutions and perturbing fields are available. We apply an empirical approach to mimic the plasma screening effects by introducing presumed plasma current sheets on the resonance surfaces to cancel the RMP effects. Numerical examples show the effect of plasma response reducing magnetic islands at the plasma edge and also regularizing field lines around the resonant surface. The distribution of connection lengths along the plasma cross section indicates that the plasma response increases the connection lengths since more toroidal turns are performed until a field line reaches the tokamak wall.     

Experimental evidence of momentum transport induced by an up-down asymmetric magnetic equilibrium in toroidal plasmas

The first experimental evidence of parallel momentum transport generated by the up-down asymmetry of a toroidal plasma is reported. The experiments, conducted in the Tokamak à Configuration Variable, were motivated by the recent theoretical discovery of ion-scale turbulent momentum transport induced by an up-down asymmetry in the magnetic equilibrium. The toroidal rotation gradient is observed to depend on the asymmetry in the outer part of the plasma leading to a variation of the central rotation by a factor of 1.5-2. The direction of the effect and its magnitude are in agreement with theoretical predictions for the eight possible combinations of plasma asymmetry, current, and magnetic field.     

Toroidal plasma rotation induced by the dynamic ergodic divertor in the TEXTOR tokamak

The first results of the Dynamic Ergodic Divertor in TEXTOR, when operating in the m/n=3/1 mode configuration, are presented. The deeply penetrating external magnetic field perturbation of this configuration increases the toroidal plasma rotation. Staying below the excitation threshold for the m/n=2/1 tearing mode, this toroidal rotation is always in the direction of the plasma current, even if the toroidal projection of the rotating magnetic field perturbation is in the opposite direction. The observed toroidal rotation direction is consistent with a radial electric field, generated by an enhanced electron transport in the ergodic layers near the resonances of the perturbation. This is an effect different from theoretical predictions, which assume a direct coupling between rotating perturbation and plasma to be the dominant effect of momentum transfer.