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结合HL-2A 装置的参数,在电子回旋共振加热(ECRH)离(在)轴加热的情况下,研究高能量捕获电子驱动的鱼骨模不稳定性。数值结果表明,高能量电子极向比压βh 大于某一个比压阈值βh,crit 时,鱼骨模会被高能量电子激发,其频率随高能量电子极向比压的增大而缓慢增加且与高能量电子的环向进动频率一致;比压阈值βh,crit 随着高能量电子密度剖面峰化程度的增加而减小,但当密度剖面增大到一定值时比压阈值βh,crit 趋近于一个常数。此外,还分析了箍缩角和扰动能对鱼骨模实频和增长率的影响。发现在箍缩角α0 =1附近增长率有一极小值,表明高能量勉强通行电子对鱼骨模具有稳定作用;而扰动能 δWˆc增大时,鱼骨模表现出实频变大而增长率变小的特征,这表明了本底等离子体对鱼骨模有一定的稳定效果。     

HL-2A 装置中高能量捕获电子鱼骨模不稳定性研究

结合HL-2A 装置的参数,在电子回旋共振加热(ECRH)离(在)轴加热的情况下,研究高能量捕获电子驱动的鱼骨模不稳定性。数值结果表明,高能量电子极向比压β_h 大于某一个比压阈值β_h,crit 时,鱼骨模会被高能量电子激发,其频率随高能量电子极向比压的增大而缓慢增加且与高能量电子的环向进动频率一致;比压阈值β_h,crit 随着高能量电子密度剖面峰化程度的增加而减小,但当密度剖面增大到一定值时比压阈值β_h,crit 趋近于一个常数。此外,还分析了箍缩角和扰动能对鱼骨模实频和增长率的影响。发现在箍缩角α₀ =1附近增长率有一极小值,表明高能量勉强通行电子对鱼骨模具有稳定作用;而扰动能 δWˆ_c增大时,鱼骨模表现出实频变大而增长率变小的特征,这表明了本底等离子体对鱼骨模有一定的稳定效果。     

Effect of trapped energetic particles on the resistive wall mode

A stability analysis for the resistive wall mode is studied in the presence of trapped energetic particles (EPs). When the EPs' beta exceeds a critical value, a fishbonelike bursting mode (FLM) with an external kink eigenstructure can exist. This offers the first analytic interpretation of the experimental observations [Phys. Rev. Lett. 103, 045001 (2009)]. The mode-particle resonances for the FLM and the q=1 fishbone occur in different regimes of the precession frequency of EPs. In certain ranges of the plasma rotation speed and the EPs' beta, a mode conversion can occur between the resistive wall mode and FLM.     

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A general dispersion relation for fishbone mode is obtained when spatial density profile and pitch angle profile are taken into account. The fishbone modes can be driven into the second stable regime by barely passing energetic particles in high β_h region. The nonresonant fishbone mode can be induced by trapped energetic particles. Similar to the resonant fishbone modes, the nonresonant fishbone modes can also be driven into the second stable regime by trapped energetic particles and the real frequency linearly increases with increasing β_h.     

聚变等离子体中高能量粒子驱动的鱼骨模不稳定性研究

在考虑高能量粒子密度的空间分布及箍缩角分布的条件下,建立了研究鱼骨模的色散关系,并作了数值研究。结果表明：当高能量粒子的密度高于某个阈值时,鱼骨模会在高能量粒子密度梯度最大处被激发,其频率与高能量粒子的环向进动频率一致。在高β_h 区间,高能量勉强通行粒子将驱动鱼骨模进入第二稳定区。高能量捕获粒子能激发非共振鱼骨模,与勉强通行粒子激发的鱼骨模类似,在高β_h 区存在第二稳定区。     

环位形下鱼骨模驱动快离子输运的数值模拟研究

考虑包含动理学效应的鱼骨模结构,使用导心轨道程序 ORBIT,在磁面坐标下研究了不同的扰动模 幅度、频率对快离子再分布的影响,并分析了粒子与扰动发生共振的条件。模拟得出,鱼骨模扰动会使快离子在 实空间、相空间中发生再分布,芯部( ψ_p/ψ _w≤0.2 ,ψ_p 为极向磁通,ψ_w 为最后一个闭合磁面的磁通)快离子密 度下降约 20%,中间磁面位置上( ψ_p/ψ _w≥0.2,ψ_p/ψ _w≤ 0.6)的快离子密度增加约 7%;通过扫描频率发现,相空间中快 离子的再分布对模式频率敏感,并分析了快离子与鱼骨模扰动共振的条件。     

Temperature gradient driven Alfvén instability producing inward energy flux in stellarators

Destabilizing influence of plasma inhomogeneity on Alfvén eigenmodes in stellarators is considered. It is found that the diamagnetic frequency can strongly increase due to the resonance interaction of particles and Alfvén eigenmodes. This occurs when the particle resonance velocity exceeds the thermal velocity, in which case the role of superthermal particles enlarges. Then Alfvén eigenmodes can be destabilized even in the absence of the energetic ion population. It is shown that in the case of the temperature distribution with a large gradient at the periphery, the destabilized mode can channel the energy from the peripheral plasma region to the inner region. A stability analysis employing a model temperature profile of the ions was carried out for the Wendelstein 7-X stellarator. It indicates that the considered mechanism could lead to an Alfvén instability accompanied with the inward energy flux in the first W7-X experiments where long-lasting high-frequency oscillations were observed.     

Effects of q-profiles of a weak magnetic shear on energetic ion excited q=1 mode in tokamak plasmas

In this paper, we study the effect of safety factor profiles, particularly with a very weak magnetic shear, on the m/n = 1mode excited by energetic ions in tokamak plasmas. It is found that the profile plays a significant role in the onset of the mode, and the thresholds for the instability are also derived. The numerical results for configurations with conventional or reversed non monotonic magnetic shears are discussed. The effects of radial location of rational surfaces, edge q value, and flatness of q-profile on the energetic ion excited mode are further analyzed in detail.     

Effects of circulating energetic ions on sawtooth oscillations

In contrast to the well-known result that the effects of the trapped energetic ions (TEI) on the internal kink mode are due to the toroidal precession of the TEI, it is found that the effects of the circulating energetic ions (CEI) on sawtooth are due to the toroidal circulation of the CEI. The effects of the CEI on sawtooth oscillations are found to be different from the well-known purely stabilizing effects of the TEI on sawtooth oscillations; the toroidal circulation of the co-CEI provides an additional sink of free energy and stabilizes the mode; the toroidal circulation of the counter-CEI provides an additional source of free energy and destabilizes the mode.     

Fast-ion losses due to high-frequency MHD perturbations in the ASDEX upgrade Tokamak

Time-resolved energy and pitch angle measurements of fast-ion losses correlated in frequency and phase with high-frequency magnetohydrodynamic perturbations have been obtained for the first time in a magnetic fusion device and are presented here. A detailed analysis of fast-ion losses due to toroidal Alfvén eigenmodes has revealed the existence of a new core-localized magnetohydrodynamic perturbation, the sierpes mode. The sierpes mode is a non-Alfvénic instability which dominates the losses of fast ions in ion cyclotron resonance heated discharges, and it is named for its footprint in the spectrograms ("sierpes" means "snake" in Spanish). The sierpes mode has been reconstructed by means of highly resolved multichord soft-x-ray measurements.     

β-induced Alfvén eigenmodes destabilized by energetic electrons in a Tokamak plasma

The β-induced Alfvén eigenmode (BAE) excited by energetic electrons has been identified for the first time both in the Ohmic and electron cyclotron resonance heating plasma in HL-2A. The features of the instability, including its frequency, mode number, and propagation direction, can be observed by magnetic pickup probes. The mode frequency is comparable to that of the continuum accumulation point of the lowest frequency gap induced by the shear Alfvén continuous spectrum due to finite β effect, and it is proportional to Alfvén velocity at thermal ion β held constant. The experimental results show that the BAE is related not only with the population of the energetic electrons, but also their energy and pitch angles. The results indicate that the barely circulating and deeply trapped electrons play an important role in the mode excitation.     

Anomalous exponents at the onset of an instability

Critical exponents are calculated exactly at the onset of an instability, by using asymptotic expansion techniques. When the unstable mode is subject to multiplicative noise whose spectrum at zero frequency vanishes, we show that the critical behavior can be anomalous; i.e., the mode amplitude X scales with departure from onset μ as ∝μ(β) with an exponent β different from its deterministic value. This behavior is observed in a direct numerical simulation of the dynamo instability, and our results provide a possible explanation for recent experimental observations.     

低杂波电流驱动中的雪崩逃逸增强及鱼骨不稳定性

等离子体中存在的一定数量的高能逃逸电子（E≥1MeV)通过大角度库仑散射从等离子体中碰撞出二次电子，二次电子被低杂波有效地加速成为逃逸电子，这些逃逸电子又被正反馈回等离子体，形成雪崩现象。在此过程中，一部分获得较大横向动量的二次电子或由低杂波驱动的高能电子可能被香蕉轨道捕获，这些被捕获在磁岛中的电子与某种模式的磁场扰动共振时，就出现鱼骨不稳定现象。     

Parametric instability of a magnetic junction under modulated spin-polarized current

The stability is analyzed of the magnetic junction collinear configurations against small fluctuations under amplitude-modulated current with current-perpendicular-to-plane mode. High spin injection is assumed. Under parametric resonance conditions, with the modulation frequency twice the precession frequency, instability is possible of one, or another, or both the collinear configurations. When the direct component of the current density exceeds the instability threshold of the antiparallel configuration, the parametric instability is suppressed by nonparametric one which is induced by the direct current. The parametric instability manifests itself as lowering the threshold of the direct current density in the presence of the high-frequency current; such an effect has been observed in experiments repeatedly.     

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研究了电漂移对通行高能离子与新经典撕裂模(NTM)共振相互作用的影响。利用漂移动力论方法,在求解共振相互作用产生的作用在磁岛上的环向力矩的过程中重新考虑了电漂移的作用。结果表明,在与磁岛运动相关的环向动量平衡中v>0的通行高能离子与v<0的通行高能离子作用恰好相反,当磁岛沿电子抗磁漂移方向传播时,前者趋向于使磁岛传播频率减小,后者趋向于使磁岛传播频率增大,通行高能离子产生的总的环向力矩几乎为零。仅将v>0的通行高能离子所产生的环向力矩带入由环向动量平衡方程和修正的卢瑟福方程所组成的方程组中,数值计算结果表明,描述磁岛旋转频率与宽度随时间做非线性振荡的稳定极限环并不存在。     

The effect of negative ions on the dust acoustic wave in dusty electronegative plasma with positively charged dust grains

The effect of negative ions on the modulational instability properties of nonlinear dust acoustic (DA) waves in the electronegative dusty plasmas was investigated by considering Boltzmann-distributed electrons, negative ions, positive ions as well as positively charged dust grain under the ultraviolet irradiation. It is shown that the modulational instability properties of the DA waves were strongly affected by the temperature and proportion of negative ions. The modulational instability can occur only if the proportion of negative ions was smaller than critical value. The instability growth rate has a maximum value when the proportion of negative ions was a critical one in the unstable region. The effect of photoelectron generated by ultraviolet irradiation on the modulational instability of dust acoustic waves was also discussed by numerical method.     

Geodesic mode spectrum modified by the energetic particles in tokamak plasmas

Effect of a minor concentration of the energetic particles on GAM spectrum in a tokamak is analyzed by drift kinetic theory taking into the account the electron current and diamagnetic drift. A novel method of Jacobi functions is applied to solve the drift kinetic equation for the energetic bounce particles in the limit of high bounce frequency in comparison with the GAM frequency. Using the Q-asymptotic of Jacobi function, it is shown that the energetic minority ions can form the continuum minimum/maximum at the NB or ICR power deposition maximum where the geodesic eigenmode may be excited. In this case, the electron current modeled by shifted Maxwell distribution overcomes the ion Landau damping threshold thus resulting in the GAM instability.     

Internal kink instability during off-axis electron cyclotron current drive in the DIII-D tokamak

Experimental evidence is reported of an internal kink instability driven by a new mechanism: barely trapped suprathermal electrons produced by off-axis electron cyclotron heating on the DIII-D tokamak. It occurs in plasmas with an evolving safety factor profile q(r) when q(min) approaches 1. This instability is most active when ECCD is applied on the high field side of the flux surface. It has a bursting behavior with poloidal/toroidal mode number = m/n = 1/1. In positive magnetic shear plasmas, this mode becomes the fishbone instability. This observation can be qualitatively explained by the drift reversal of the barely trapped suprathermal electrons.     

Soft phonon dispersion in BaTiO3

We treat a simple lattice dynamical model for the critical modes in BaTiO₃. The Ti-ions move in an anharmonic single particle potential formed by the frame of Ba- and O-ions that are bound more tightly to their equilibrium positions. The dipole interaction of displaced Ti-ions is enhanced by polarization effects due to all electronic polarizabilities and to an additional ionic polarizability of the oxygen ions. The transverse optical mode of this model is low lying and softening as temperature decreases until its frequency for zero wavevector vanishes. This leads to a ferroelectric instability. The dispersion of this critical mode for small wavevectors was found to be highly anisotropic. So long this prediction has not been tested experimentally.     

Destabilization of TAE modes by particle anisotropy

Plasmas heated by ICRF produce energetic particle distribution functions which are sharply peaked in pitch-angle. At moderate toroidal mode numbers, this anisotropy is the dominant instability drive when compared with the universal instability drive due to the spatial gradient. The universal drive, acting alone, destabilizes only co-propagating waves (i.e., waves propagating in the same toroidal direction as the diamagnetic flow of the energetic particles), but stabilizes counter-propagating waves (i.e., waves propagating in the toroidal direction opposite to that of the diamagnetic flow of the energetic particles). Nonetheless, in a tokamak, it is possible that particle anisotropy can produce a larger linear growth rate for counter-propagating waves, and provide a mechanism for preferred destabilization of the counter-propagating TAE modes that are sometimes experimentally observed.