Magneto-Hydrodynamic High-n Ballooning Mode Instability of an Analytic Axi-Symmetric Toroidal Equilibrium with Arbitrary Aspect Ratio

An exact ballooning mode eigen-equation is derived to study stability of axi-symmetric toroidal plasma with arbitrary aspect ratio, including the tokamak, the finite aspect ratio and the spherical torus plasmas. For comparison with the widely used （ s-α） model, an analytic exact equilibrium configuration with circular magnetic surfaces is analysed in detail. It is indicated that the （s - α） model needs to be improved for more realistic configurations.     

Dual equilibrium in a finite aspect ratio tokamak

A new approach to high pressure magnetically-confined plasmas is necessary to design efficient fusion devices. This Letter presents a new sort of equilibrium combining two solutions of the Grad-Shafranov equation, which describes the magnetohydrodynamic equilibrium in toroidal geometry. The outer equilibrium is paramagnetic and confines the inner equilibrium, whose strong diamagnetism permits to balance large pressure gradients. The existence of both equilibria in the same volume yields a dual equilibrium structure. This combination improves free-boundary mode stability.     

Impact of fast vertical and radial plasma movement on type-I ELMs in ASDEX upgrade

For the ITER project it is clear that steps have to be taken in order to avoid or mitigate type-I ELMs when operating in the standard H-mode scenario. Otherwise, divertor power loads induced by intrinsic ELMs will result in an intolerably short divertor life time. Amongst others, “magnetic triggering” based on a fast vertical movement of the plasma column has proven its ability to achieve ELM frequency control and hence mitigation by locking the ELM frequency to the imposed motion. Here, we report on an attempt to widen this approach by applying a cyclic radial plasma shift. Although motional cycle amplitudes sufficient for ELM frequency locking were achieved even easier than in the vertical case, no ELM control was established for the radial case. Analysis of this different behaviour can allow for better insight into underlying ELM release mechanisms and might potentially be a useful tool for mapping out ELM stability boundaries. Presented at the Workshop “Electric Fields, Structures and Relaxation in Edge Plasmas”, Roma, Italy, June 26–27, 2006.     

Multiple polarization of geodesic curvature induced modes

Dispersion relations for geodesic acoustic modes are derived by using the Grad hydrodynamic equations thereby reconciling long known but not previously explained discrepancy between the results of kinetic and fluid calculations. Extended fluid theory allows a simple analysis of mode polarization and coupling. A new type of electromagnetic modes induced by geodesic compressibility is predicted. These modes are related to Alfvén and geodesic acoustic modes. While a standard geodesic acoustic mode involves poloidally and toroidally symmetric perturbations of electrostatic potential (m=n=0) and the first poloidal side-bands of plasma pressure, new modes involve side-bands of the electrostatic and vector potential as well as pressure perturbations at zeroth and second harmonics. It is shown that there exist two different values of the adiabatic constant depending on the mode polarization. Both standard (electrostatic) geodesic acoustic modes and new electromagnetic modes involve finite perturbations of parallel viscosity, which modify an effective adiabatic (compressibility) index for a toroidal plasma.     

First Observation of Neoclassical Tearing Modes in the HL-2A Tokamak

The m/n = 2/1 neoclassical tearing modes are first observed in HL-2A low density, low beta plasma with central electron cyclotron resonance heating. The neoclassical tearing modes （NTMs） are triggered by a sawtooth crash with m/n = 1/1 precursors, which are toroidal coupled with a small scale m/n = 2/1 mode. The time history of the island width is compared with the prediction of the NTM theory, showing a good agreement between theory and experiment.     

Enhancement of the guide field during the current sheet formation in the three-dimensional magnetic configuration with an X line

Results are presented from studies of the formation of current sheets during exciting a current aligned with the X line of the 3D magnetic configuration, in the CS-3D device. Enhancement of the guide field (parallel to the X line) was directly observed for the first time, on the basis of magnetic measurements. After the current sheet formation, the guide field inside the sheet exceeds its initial value, as well as the field outside. It is convincingly demonstrated that an enhancement of the guide field is due to its transportation by plasma flows on the early stage of the sheet formation. The in-plane plasma currents, which produce the excess guide field, are comparable to the total current along the X line that initiates the sheet itself.     

Tomography analysis of the sawtooth crash with post-cursor in LHCD plasma on HT-7 tokamak

Sawtooth oscillations with post-cursor were observed in LHCD plasma on HT-7 tokamak. The mode exists and decays gradually after the crash, which implies that the magnetic reconnection is incomplete and the central safety factor remains below unity after the crash. From results of the singular value decomposition (SVD) and tomographic reconstructions describing the magnetic surface structures in the crash, it was found that the m/n=1/1 mode survives in the crash. It is shown that, the appearance of the preservation of this mode is inconsistent with the secondary reconnection theory, and we conjecture that the evolving of this mode may be understood with the stochastic field model.     

The combined toroidicity,ellipticity and triangularity effects on the energy deposition of Alfvén modes in pre-heated,low aspect ratio tokamaks

The combined plasma non-uniformity effects on the energy deposition of Alfvén waves launched by an external antenna in pre-heated spherical tokamaks are investigated. The following relevant physical processes are here possible: (a) the emergence of gaps in the shear Alfvén continuum spectrum and the generation of discrete global Alfvén eigenmodes with frequencies inside the gaps; (b) multi-wave interactions, interactions of gaps of the same kind (e.g., toroidicity induced) and of different kinds (toroidicity, ellipticity and triangularity induced) as well as of secondary order gaps arising when a pair of modes is coupled to one or more modes through other coupling parameters; (c) basic wave-plasma interactions as propagation, reflection, mode-conversion, tunneling and deposition. Thus, we solved numerically the full 2D wave equations for the vector and scalar potentials, using a quite general two-fluid resistive tensor-operator, without any geometrical limitations. The results obtained indicate the existence of antenna-launched wave characteristics for which the power is most efficiently coupled in outer regions of plasmas, which is of special interest for low aspect ratio tokamaks, e.g., for the generation of non-inductive current drive as well as for turbulence suppression and transport barriers formation.     

Effect of scalar nonlinearity on zonal flow generation by Rossby waves

Effects of scalar nonlinearity on the generation of zonal flow by Rossby waves in shallow rotating fluid are considered. Zonal flows are generated via the action of Reynolds stress due to vector nonlinearity together with the effects of scalar nonlinearity. It is shown that the scalar nonlinearity reduces the amplitude threshold of the zonal flow instability. In addition, it increases the range of wave vectors of unstable modes subjected to the instability. The growth rate of the instability as a function of the spectrum of primary waves is calculated. The spectrum is assumed to be arbitrary with emphasizing the case of two monochromatic waves.     

Relativistic Magnetosonic Soliton in a Negative-Ion-Rich Magnetized Plasma

Two-dimensional (2D) relativistic magnetosonic solitons in the negative-ion-rich plasma consisting of positive ions Ar⁺, negative ions SF₆^- and electrons are investigated in the presence of an applied magnetic field B₀ and can be described by a Kadomtsev--Petviashvili (KP) equation in the weakly relativistic limit. The ratio of positive ion density to negative ion density has a marked influence on the amplitude Φ_m and width W of the steady-state KP soliton. The interaction law of the nontrivial solitons with rich web structure is studied by the Wronskian determinant method.     

Observation of Fishbone-Like Instabilities Excited by Energetic Electrons on the HL-2A Tokamak

Strong burst of an internal kink mode is observed on the HL-2A tokamak. Features of the fishbone-like mode are presented. The fishbone-like instabihties can be driven during electron cyclotron resonance heating （ECRH） and can be excited on the high field side （HFS） by ECRH. It is found for the first time that the modes also present themselves on the low field side （LFS） during ECRH. Experiments show that the energetic electrons with energy of 35-70 keV play a dominant role in the excitation mechanism, and the experimental results are also consistent with our calculation ones.     

Magnetorotational instability in nonmagnetized plasma

It is shown that the magnetorotational instability (MRI) can be driven in nonmagnetized plasma. In this case, in contrast to the case of strongly magnetized plasma, radial derivative of plasma rotation frequency should be positive for such a driving. The characteristic wave lengths of MRI in nonmagnetized plasma are of the same order of magnitude as those for the Weibel instability.     

Excitation of the dust ion-acoustic and dust acoustic-like perturbations by plasma density ripples

It is shown that the dust ion-acoustic (DIA) and dust acoustic (DA)-like perturbations can be excited by the electron density and ion density ripples, respectively. For this purpose, we use the relevant equations for the DIA and DA-like disturbances and derive the standard Mathieu equation. The latter admits unstable solutions, demonstrating that both the DIA and DA-like mode can be driven on account of the free energy in the plasma density ripples.     

Stimulated brillouin scattering of electromagnetic ion cyclotron waves in a plasma

Using the fluid model for the nonlinear response of ions, we have studied the nonlinear scattering of an electromagnetic ion cyclotron wave off the ion acoustic wave in a plasma. The low frequency nonlinearity arises through the parallel ponderomotive force on ions and the high frequency nonlinearity arises through the nonlinear current density of ions. For a typical nonisothermal plasma (T _e/T _i∼10) the threshold for this instability in a uniform plasma is ∼1mW/cm². At power densities ≳10² W/cm², the growth rate for backscatter turns out to be ∼10⁴s⁻¹.     

Numerical Simulation of Solitary Kinetic Alfvén Waves

Using the two-fluid model in the case of α〉〉1 （α= β/2Q, β is the ratio of thermal pressure to magnetic pressure, and Q = me/mi ）, we numerically investigate the interactions between two solitary kinetic Alfvén waves （SKAWs） and between an SKAW and a density discontinuity. The results show that the two SKAWs would remain in their original shapes and propagate at their initiating speeds, which indicates that SKAWs behave just like standard solitons. The simulation also shows that SKAWs will reflect and refract when crossing a discontinuity and propagating into a higher density region. The transmission wave is an SKAW with increasing density, and the reverberation is a disturbance with lower amplitude.     

Energy confinement and high-k turbulence on HT-7 tokamak

A CO₂ collective scattering system has been developed to measure medium and high-k density fluctuation on HT-7 tokamak. Energy confinement and high-k density fluctuation are studied in ohmic discharges. The saturation of confinement was observed at approximately . For kθ=23 cm⁻¹ turbulence, it is found that fluctuation levels have great increase for , and simultaneously a high frequency turbulence feature appear in the frequency spectra. For kθ=14 cm⁻¹ turbulence, it is observed that fluctuation levels have no changes in uncertainties and the spectra are similar at all discharges in this experiment.     

Density Fluctuation Measurements Using FIR Interferometer on HL-2A Tokamak

Density fluctuations were first measured in the core region of HL-2A tokamak plasma using a newly developed multi-channel FIR interferometer system. In divertor ohmic discharges, we measured the radial density fluctuation levels of 5%, which increase to 10-20% during the appearance of MHD activity. Most of the power density in the density fluctuation spectrum is directly associated with m = 2 tearing modes. The fluctuation levels reduce to 1/3 and plasma confinement is improved during off-axis electron-cyclotron-resonance heating （ECRH）.     

On the scarcity of solutions of the equations of magnetohydrodynamic equilibria with flow

While particular analytic solutions to the equations of axisymmetric MHD equilibria with flow are known, it is not clear what possible choosing of the free parameters of the equation of the magnetic flux will yield a solution. The most important of these is the poloidal stream function. We show that for a given flow to be able to yield an equilibrium, the flow itself must satisfy an analogous equation to the generalized Grad-Shafranov one. The problem therefore turns out to be how common are solutions to this type of equations. It is shown that in a natural space of functions, the set of these solutions is contained within a manifold of infinite codimension: extremely small by any criteria. Hence the class of flows for which an equilibrium, even defined only locally and irrespective of boundary conditions, may be found, is highly constrained.