Mechanism of stabilization of ballooning modes by toroidal rotation shear in tokamaks

A ballooning perturbation in a toroidally rotating tokamak is expanded by square-integrable eigenfunctions of an eigenvalue problem associated with ballooning modes in a static plasma. Especially a weight function is chosen such that the eigenvalue problem has only the discrete spectrum. The eigenvalues evolve in time owing to toroidal rotation shear, resulting in a countably infinite number of crossings among them. The crossings cause energy transfer from an unstable mode to the infinite number of stable modes; such transfer works as the stabilization mechanism of the ballooning mode.     

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.     

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.     

Active feedback stabilization of toroidal external modes in tokamaks

Active feedback stabilization of pressure-driven modes in tokamaks is investigated by toroidal computations. Typically, the feedback does not strongly modify the plasma-generated magnetic field perturbation. Feedback with modest gain and a single coil array poloidally stabilizes substantially for a range of coil shapes. Optimum design uses narrow sensor coils not too far from the plasma and rather wide feedback coils, which may be outside the resistive wall. Complex gain, which makes the mode rotate, can decrease the gain required for stabilization, but real gain is more robust.     

Neoclassical toroidal plasma viscosity torque in collisionless regimes in tokamaks

Bumpiness in a magnetic field enhances the magnitude of the plasma viscosity and increases the rate of the plasma flow damping. A general solution of the neoclassical toroidal plasma viscosity (NTV) torque induced by nonaxisymmetric magnetic perturbation (NAMP) in the collisionless regimes in tokamaks is obtained in this Letter. The plasma angular momentum can be strongly changed, when there is a small deviation of the toroidal symmetry caused by a NAMP of the order of 0.1% of the toroidal field strength.     

Theory for toroidal momentum pinch and flow reversal in tokamaks

It is demonstrated that besides the well-known toroidal momentum diffusion flux there is a pinchlike flux in the fluctuation-induced toroidal stress. A toroidal flow profile is determined up to a constant, e.g., the value of the flow at the magnetic axis, by balancing these two fluxes. The remaining residual toroidal stress determines the value of the flow at the axis. It is illustrated that the direction of the flow at the axis can change after plasma confinement is improved. The theory is applied to explain the toroidal flow reversal in tokamak experiments.     

Effect of subsonic toroidal flows on plasma poloidal rotation and ion heat conductivity. In collisional plasmas of elongated tokamaks

The ion poloidal rotation and heat conductivity in collisional plasmas of axially-symmetric tokamaks with elongated cross-sections and with subsonic toroidal plasma flows are considered. It is shown that subsonic toroidal plasma flows, induced by neutral beam injection or radio frequency waves, can strongly affect the poloidal plasma velocity and ion heat conductivity in collisional plasmas of tokamaks. The transport coefficients also depend on the tokamak ellipticity parameter which, in combination with the Mach number, allows to operate transport processes at smaller values of the toroidal Mach number. The importance of taking into account the ion-electron heat exchange and electron temperature toroidal perturbations to find ion temperature toroidal perturbations is demonstrated. This work was partially supported by the State University of Rio de Janeiro (UERJ) and the Rio de Janeiro Research Foundation (FAPERJ).     

Transport-driven toroidal rotation in the tokamak edge

The interaction of passing-ion drift orbits with spatially inhomogeneous but purely diffusive radial transport is demonstrated to cause spontaneous toroidal spin-up in a simple model of the tokamak edge. Physically, major-radial orbit shifts cause orbit-averaged diffusivities to depend on v(∥), including its sign, leading to residual stress. The resulting pedestal-top intrinsic rotation scales with T(i)/B(θ), resembling typical experimental scalings. Additionally, an inboard (outboard) X point enhances co- (counter)current rotation.     

Stabilization of the vertical mode in tokamaks by localized nonaxisymmetric fields

Vertical instability of a tokamak plasma can be controlled by nonaxisymmetric magnetic fields localized near the plasma edge at the bottom and top of the torus. The required magnetic fields can be produced by a relatively simple set of parallelogram-shaped coils.     

Investigation of the plasma potential oscillations in the range of geodesic acoustic mode frequencies by heavy ion beam probing in tokamaks

Specific oscillations within a range of 20 kHz (20 kHz-mode) were investigated on the T-10 and TEXT tokamaks using Heavy Ion Beam Probe (HIBP) diagnostic. Regimes with ohmic heating on both machines, and with off-axis ECRH in T-10 were studied. It was shown that 20 kHz-modes are mainly the potential oscillations. The power spectrum of the oscillations has the form of a solitary quasi-monochromatic peak with a contrast range of (3–5). They are the manifestation of torsional plasma oscillations with poloidal wavenumber m = 0, called zonal flows. It was shown that in TEXT the radial electric field oscillations exist in a limited radial range of 0.65 > < 0.95. The frequency of 20 kHz-mode is varied in the region of observation; it diminishes to the plasma edge. In T-10, after ECRH switch-on, the frequency increases, correlating with the growth of the electron temperature T _e. In both machines the frequency of the 20 kHz-mode varies with local T _e: f T _e ^1/2 , which is consistent with theoretical scaling for geodesic acoustic modes (GAM): f _GAM c _s/R T _e ^1/2 , where c _s is the speed of sound. The absolute frequencies are close to GAM values within a factor of unity.Presented at the Workshop Electric Fields Structures and Relaxation in Edge Plasmas, Nice, France, October 26–27, 2004.     

Effect of passive structure and toroidal rotation on resistive wall mode stability in the EAST tokamak

If βN exceeds no-wallβN, the plasma will be unstable because of external kink and resistive wall mode(RWM). In this article, the effect of the passive structure and the toroidal rotation on the RWM stability in the experimental advanced superconducting tokamak(EAST) are simulated with CHEASE and MARS codes. A model using a one-dimensional(1D)surface to present the effect of the passive plate is proved to be credible. The no wall βN limit is about 3li, and the ideal wall βN limit is about 4.5li on EAST. It is found that the rotation near the q = 2 surface and the plasma edge affects the RWM more.     

Zonal flows in tokamak plasmas with toroidal rotation

Zonal flows in tokamak plasmas with toroidal rotation are theoretically investigated. It is found that the low-frequency branch of zonal flows, which is linearly stable in a nonrotating system, becomes linearly unstable in a rotating tokamak, and that the high-frequency branch of zonal flows, the geodesic acoustic mode, can propagate in the poloidal direction with the frequency significantly lower than the frequency of the standing wave geodesic acoustic mode in the nonrotating system.     

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.     

Geodesic mode instability driven by the electron current in tokamak plasmas

Effect of the parallel electron current on Geodesic Acoustic Modes (GAM) in a tokamak is analyzed by kinetic theory taking into the account the ion Landau damping and diamagnetic drifts. It is shown that the electron current modeled by shifted Maxwell distribution may overcome the phase velocity threshold and ion Landau damping thus resulting in the GAM instability when the parallel electron current velocity is larger than the effective parallel GAM phase velocity Rqω. The instability occurs due to its cross term of the current with the ion diamagnetic drift. Possible applications to tokamak experiments are discussed.