Index of content:
Volume 11, Issue 1, January 2004
 LETTERS


Discrete Alfvén eigenmodes in highβ toroidal plasmas
View Description Hide DescriptionA new type of highn discrete Alfvén eigenmodes is shown to exist in the largeα second ballooning stable toroidal plasmas. Here, n is the toroidal mode number, q is the safety factor, β is the ratio between plasma and magnetic pressures, and R and r are, respectively, the major and minor radii. These magnetohydrodynamiceigenmodes are bounded by the αinduced potential wells along the magnetic field line and, thus, exist even in absence of the toroidal Alfvén frequency gap. Due to negligible continuum damping via wave energy tunneling, these largeα toroidal Alfvén eigenmodes are quasimarginally stable and, thus, could be readily destabilized by energetic particles.

Laserinduced adiabat shaping by relaxation in inertial fusion implosions
View Description Hide DescriptionThe theory of laserinduced adiabat shaping is carried out for inertial confinement fusion(ICF) capsules. It is shown that a significant improvement of the stability characteristics of ICF implosions can be achieved by shaping the adiabat inside the imploding shell. The optimized adiabat profile has a maximum on the outer ablation surface to lower Rayleigh–Taylor growth rates, and a minimum on the shell inner surface for high compressibility and high neutron yields. Laserinduced adiabat shaping is produced via relaxation using a weak prepulse followed by laser shutoff and the main laser pulse.

 ARTICLES

 Basic Plasma Phenomena, Waves, Instabilities

Physics of nonthermal Penningtrap electron plasma and application to ion trapping
View Description Hide DescriptionA modified Penning–Malmberg trap is used to produce a reflexing beam electron distribution. Positive ions are trapped in the electron space charge within a shaped anode at the center of the beam. Electron reflexing of greater than circuits is observed, with a perveance several times that of earlier single pass devices. Classical slowing of the electron beams is observed. Twostream instability is avoided because the emission limited space charge is subcritical. Trapped ions are observed in two modes of operation; a quiescent mode in which ions are directly counted after destroying the space charge configuration, and a rf mode in which the ion resonance instability is active. Ion inventory up to quasineutral conditions is implied for the quiescent trappingmode.

Diaceleric structures in magnetized plasmas
View Description Hide DescriptionThe existence of novel confinement configurations in magnetized plasmas, coined diaceleric structures, is predicted. The conditions for these configurations to emerge are derived and shown to depend on the functional relation between the sodefined material flux fraction and central velocity pitch. The analysis is based upon the application of the coercive criterion, followed by the adjustment procedure, developed by other authors, to a variational method approach. A complete description of Lagrange multipliers and Beltrami eigenvalues in terms of strictly physical parameters is presented. The model recovers the diamagnetic and reversed field pinch structures, investigated by those authors, leading to a comprehensive classification of the relaxed states in magnetized plasmas.

Eigenmode of ion acoustic instability in the presence of sheared parallel flow
View Description Hide DescriptionIn this paper, results of kinetic, nonlocal analysis of the current driven electrostatic ion acoustic instability in the presence of nonuniform shear flow are presented. The nonlocal behavior is examined by taking the scale length of shear layer as a control parameter. The growth rate and the threshold current are evaluated numerically and compared with those recently found in the local analysis [V. V. Gavrishchaka et al., Phys. Rev. Lett. 80, 728 (1998)].
 Nonlinear Phenomena, Turbulence, Transport

Unstable continuous spectra of transonic axisymmetric plasmas
View Description Hide DescriptionIn transonically rotating toroidalplasmas a new class of local magnetohydrodynamicinstabilities is found, called transslow Alfvén continuum modes, that are due to poloidal flows exceeding the critical slow magnetosonic speed. When this condition is satisfied, virtually the whole plasma becomes unstable with modes localized at, or close to, rational surfaces with approximately the same growth rates. The instabilities are studied from a general point of view, treating magnetically dominated plasmas(tokamaks) and gravitationally dominated plasmas (accretion disks) on an equal footing. In the first kind of plasmas, rotating overstable modes are found with growth rates that are a fraction of the Alfvén frequency, determined by the poloidal Alfvén Mach number. When the mass of the central object is increased, these modes lock to become explosively unstable with growth rates that may exceed the Alfvén frequency. The instabilities are localized on the magnetic/flow surfaces to which the flows and magnetic fields are confined as long as no anomalously large dissipation mechanism is present. It is suggested that the transslow Alfvén continuum modes may generate the necessary turbulence to break this confinement so that accretion could take place and jets could emerge. This theory features: (1) a new effective toroidal scaling of the transonic equilibrium equations, (2) a new compact formulation of the equations for the transonic continuous spectrum, and (3) a completely explicit analytical as well as numerical investigation of the poloidal mode couplings involved in the instabilities.

The Hall instability in accelerated plasma channels
View Description Hide DescriptionThe Hall instability of a perfectly conducting plasma is studied. The twodimensional magnetohydrodynamic equations for systems with large Larmor radius for a twofluid model in which the Hall term is taken into account in Faraday’s law, are investigated. By using a linearized theory it is shown, that the plasma may become unstable under small perturbations. This instability is driven by the plasma acceleration in channel. The most unstable perturbations propagate in the direction where the wave vector is orthogonal to the magnetic field.

Magnetic reconnection with space and time varying reconnection rates in a compressible plasma
View Description Hide DescriptionFast magnetic reconnection of Petschektype including moving shockwaves and discontinuities in a compressible plasma is studied. Magnetic flux tubes of finite size are reconnected by a localized dissipative electric field pulse. This process generates nonlinear perturbations propagating along the initial current surface. The linear wave problem in the outer regions is solved analytically in terms of the reconnection induced sources which move in different directions and with different speeds along the surface. The timecoordinate representation of the solution is given in form of convolution integrals over the reconnection initializing electric field. As an example, reconnection of flux tubes in a sheared magnetic field geometry is analyzed.

Inhomogeneous plasma parametric decay instability driven by frequency modulated pump
View Description Hide DescriptionThe inhomogeneous plasma parametric decay instability (PDI) is studied in the present paper both experimentally and theoretically for different types of pump wavefrequency modulation. It is shown that the theory conclusion on weak sensitivity of inhomogeneous plasma PDI to the pump frequency modulation holds only for modulation faster than the decay wave transient time. In the case of slower modulation, both harmonic and stochastic, the PDI resonant enhancement may take place instead. The expression for amplification in the resonance is derived and several mechanisms of the singularity saturation are studied.

Electron velocity distributions during beam–plasma interaction
View Description Hide DescriptionIt is well known that lowfrequency Alfvén waves can be excited due to an ion/ion instability when a tenuous ion beam streams through a background plasma along a magnetic field. In this article, using a onedimensional particleincell code, the consequence of this beam–plasma interaction process is investigated. Emphasis is placed on the nonlinear effects of enhanced Alfvén waves on beam electrons. In the simulation, the speed between the beam plasma and ambient plasma is considered to be (where is the Alfvén speed), the ratio of beam–plasma density to background plasma density is and are the beam and total plasma densities). For the case being the ratio of kinetic pressure of the ions to magnetic pressure), the Alfvén waves begin to grow exponentially at about and they saturate at about The excited waves are nearly monochromatic, which satisfies the resonant condition, and the perpendicular velocity (the velocity component whose direction is perpendicular to the ambient magnetic field) distribution of the beam electrons peaks away from its origin with a maximum radius about at the saturation stage. Then, the amplitude of the excited waves decreases and the higherfrequency waves are also excited. A quasiequilibrium stage is reached at about and the radius of the ring in the perpendicular velocity distribution is about For the case the situation is similar except that the radius of the ring in the perpendicular velocity distribution of the beam electrons is smaller, and the ring almost disappears at the quasiequilibrium stage. Another point is that both the beam and background electrons can be heated by the excited Alfvén waves. The heating effect is more significant for the beam electrons than the background electrons, and their final thermal speeds are anticorrelated with the parameter

A drift ordered short mean free path description for magnetized plasma allowing strong spatial anisotropy
View Description Hide DescriptionShort mean free path descriptions of magnetized plasmas have existed for almost 50 years so it is surprising to find that further modifications are necessary. The earliest work adopted an ordering in which the flow velocity is assumed to be comparable to the ion thermal speed. Later, less wellknown studies extended the short mean free path treatment to the normally more interesting drift ordering in which the pressure times the mean flow velocity is comparable to the diamagnetic heat flow. Such an ordering is required to properly retain the temperature gradient terms in the viscosity that arise from the gyrophase dependent and independent portions of the distribution function. The treatment herein corrects the expressions for the parallel and perpendicular collisional ion viscosities found in these later treatments which use an approximate truncated polynomial expression for the distribution function and neglect the nonlinear piece of the collision operator due to its bilinear form. The modified parallel and perpendicular ion viscosities contain additional terms quadratic in the heat flux. In addition, the electron parallel and gyroviscosities, which were not considered by previous drift ordered treatments, are evaluated. As in all drift orderings, the collision frequency is assumed small compared to the cyclotron frequency. However, the perpendicular scale lengths are permitted to be much less than (as well as comparable to) the parallel ones; as is the case in many magnetic confinement applications. As a result, the description is valid for turbulent and collisional transport, and also allows stronger poloidal density, temperature, and electrostatic potential variation in a tokamak than the standard Pfirsch–Schlüter ordering.

Confining turbulence in plasmas
View Description Hide DescriptionThe transport properties of electrostaticturbulence in plasmas are investigated by using testparticle simulations. In particular, the possibility of control of the transport in a given synthetic turbulent field, which evolves both in space and time, is explored. The fluctuations are built up taking into account observations of real turbulence in laboratory plasmas, that is, by allowing the field to contain structures lying on all dynamically interesting scales. It is shown that, inside a given region of space, the transport can be reduced when phases of the field are randomized, that is, when correlations of the field, which are responsible for the generation of structures, are annihilated. This means that a barrier for the transport can be achieved in a plasma even without actually suppressing turbulence. When the barrier is active, a flux of particles toward the center of the simulation box is present inside the region where the barrier has been located.
 Magnetically Confined Plasmas, Heating, Confinement

Robust feedback systems for resistive wall modes
View Description Hide DescriptionThe feedback stabilization of magnetohydrodynamic instabilities that grow on the resistive time scale of the chamber walls is an important issue for steadystate tokamaks. Constraints are derived on the inductance coefficients of the feedback system that will ensure that fixed amplification coefficients can be used to provide stability over the entire region in which feedback is in principle possible. Such feedback systems are called robust. Successful feedback is possible for systems that do not satisfy these constraints, but then the signs of the feedback coefficients will depend on the level of plasma instability.

Characterization of electrostatic turbulent fluxes in tokamak edge plasmas
View Description Hide DescriptionA parametrization is presented for the transport from electrostaticturbulence in tokamak edge plasmas. Employing a nonlinear drift waveturbulence simulation,transport coefficients are obtained as functions of a density gradient, temperature gradients, and an external shear parameter. An external radial electric field, is passed to the turbulencemodel as a background shear flow which suppresses the radial flux together with the Reynolds stress induced electric fields. In a multidimensional parameter space, the transport coefficients exhibit a nonmonotonic dependence on the density and temperature gradients that is unique to the low to high confinement transition.

Effects of local features of the equilibrium current density profile on linear tearing modes
View Description Hide DescriptionIt is shown that local features of the equilibrium current density profile, i.e., its gradient and curvature evaluated at the resonant magnetic surface, can modify considerably the linear behavior of tearing modes. These features can become particularly important in cylindrical geometry, at moderate values of the electrical resistivity and of the tearing stability parameter, A new analytic dispersion relation is derived, which takes into account in a consistent way these new terms and which agrees very well with numerically computed growth rates.

The effect of asymmetric gas puffing on toroidal flow in the edge of tokamak plasma
View Description Hide DescriptionThe neoclassical theory of toroidal plasma rotation in the presence of an asymmetric neutral gas source in the edge of tokamak is examined. The poloidal dependence of momentum damping and ion energy loss due to chargeexchange processes are included. It is shown that the toroidalflow velocity increases significantly if the gas is fueled from the inboard side of the tokamak; the radial electric field and its shear are modified accordingly. It is also shown that for a fixed gasfueling rate, the asymmetric fueling has a smaller role in TEXTOR [G. Mank et al., Phys. Rev. Lett. 85, 2312 (2000)] than in COMPASSD [M. Valovi et al., Plasma Phys. Controlled Fusion 44, A175 (2002)]. The role of asymmetric gas injection is therefore effectively stronger in COMPASSD.

Numerical modeling of nonlinear growth and saturation of neoclassical tearing modes
View Description Hide DescriptionNumerical modeling results of the nonlinear growth and saturation of neoclassical tearing modes are presented and compared with analytical theories. The saturated magnetic island width obtained numerically in most cases approximately agrees with that derived from generalized Rutherford equation. For a high bootstrap current density fraction and/or a small magnetic shear at the rational surface, however, the change of the local magnetic shear due to the loss of the bootstrap current inside the island should be taken into account in calculating the saturated island width. At island saturation the tearing mode stability index, Δ^{′}, is found to approximately agree with that found from the linear outer region equation of the tearing mode and to linearly decrease with the saturated island width. During the growth of the island, however, the value of Δ^{′} depends not only on the island width but also on other parameters which affect the plasmacurrent density profile.

Selforganization towards helical states in the Toroidal Pinch Experiment reversedfield pinch
View Description Hide DescriptionIn this paper results of an experimental study of magnetic fluctuations in the Toroidal Pinch Experiment (TPE–RX) [Y. Yagi, S. Sekine, H. Sakakita et al., Fus. Eng. Design 45, 409 (1999)] are reported. This study has permitted the identification of the experimental conditions under which the usually turbulent spectrum of magnetic fluctuations in TPE–RX turns into a single tearing mode, in the socalled quasisingle helicity (QSH) state. The large data set has allowed us to provide a complete two dimensional map of QSH probability in the current plane, being Two main basins of high QSH probability have been found. The first one, at high current and low confirms previous results on QSH in other machines; the second one is completely new, and is found at low current and high These studies show that QSH is a robust, deviceindependent phenomenon, and a significant step towards a laminar type of dynamo in the reversedfield pinch configuration.

Interplay of energetic ions and Alfvén modes in helical plasmas
View Description Hide DescriptionAlfvén eigenmodes and their destabilization by energetic ions in stellarators, mainly, in the Large Helical Device(LHD) [M. Fujiwara, K. Kawahata, N. Ohyabu et al., Nucl. Fusion41, 1355 (2001)] plasmas, are considered. A general expression for the instability growth rate is derived, which generalizes that obtained by Ya. I. Kolesnichenko et al. [Phys. Plasmas 9, 517 (2002)] by taking into account the finite magnitude of the perturbed longitudinal magnetic field. The structures of the Alfvén continuum and Alfvén eigenmodes, as well as the resonances of the wave–particle interaction, are studied. A numerical simulation of the destabilization of Alfvén waves with low mode numbers during neutralbeam injection in a particular LHD shot is carried out. The obtained solutions represent even and odd corelocalized toroidicityinduced Alfvén eigenmodes, the calculated frequencies and the mode numbers being in agreement with experimental data. The growth rates of the instabilities are calculated.

Numerical studies of a steady state axisymmetric coaxial helicity injection plasma
View Description Hide DescriptionSteady state current profile, plasma potential, and plasma flow of an electrostatically driven coaxial helicity injection (CHI) plasma with axisymmetry are numerically investigated using both an open field line Grad–Shafranov equilibrium model and selfconsistent initial value magnetohydrodynamic(MHD) simulations. For CHI plasmas, the Grad–Shafranov model ignores plasma inertia but not a perpendicular, or Grad–Shafranov, flow. The Grad–Shafranov flow is the result of the gradient of Grad–Shafranov potential across magnetic field lines, and is responsible for toroidalcurrent drive. Numerical Grad–Shafranov solutions show that as the characteristic CHI discharge parameter, the normalized voltage becomes order of unity, CHI plasma develops kinkunstable hollow current profile. Here V is the imposed voltage, η the plasma resistivity, the toroidal and injector poloidal flux ratio, and a nominal poloidal field defined by the injector poloidal flux plasma minor radius a, and plasma elongation When a small plasma inertia is included in the equation of motion, such as that in a time dependent MHD calculation, the modification on the perpendicular current is small, but its impact on parallel current distribution and hence the spatial dependence of magnetic flux can be great through the Pfirsch–Schlüterlike effects.