Index of content:
Volume 1, Issue 5, May 1994

Stability analysis of the ion‐temperature‐gradient‐driven mode in noncircular tokamak geometry
View Description Hide DescriptionThe tokamak shaping effects on the toroidal branch of the ion‐temperature‐gradient‐driven mode in the long wavelength limit (k ^{2} _{χ}ρ^{2} _{ i }≪ε^{1/2} _{ T }) are studied. A model equilibrium with noncircular cross section is employed, where elongation, Shafranov shift, and triangularity are all taken into account. It is shown that each Fourier term in the expansion of the equilibrium magnetic field is associated with a new branch of the dispersion relation.

Guiding‐center equations for electrons in ultraintense laser fields
View Description Hide DescriptionThe guiding‐center equations are derived for electrons in arbitrarily intense laser fields also subject to external fields and ponderomotive forces. Exhibiting the relativistic mass increase of the oscillating electrons, a simple frame‐invariant equation is shown to govern the behavior of the electrons for sufficiently weak background fields and ponderomotive forces. The parameter regime for which such a formulation is valid is made precise, and some predictions of the equation are checked by numerical simulation.

On the interpretation of diamagnetic loop measurements for a current‐carrying plasma column in a conducting chamber
View Description Hide DescriptionAn expression is derived for the signal of a magnetic loop encircling a plasma column inside a conducting chamber with nonuniform current distribution over the plasma cross section. The plasma with radius much smaller than the length of the column is assumed to be in a quasistationary force‐balanced state. The ratio of the paramagnetic component to the diamagnetic component of the signal is shown to be independent of the loop radius. Both components increase as the loop radius decreases from the chamber radius to the plasma radius. From the derived expressions, the paramagnetic component of the signal is calculated numerically for several current distributions including those of interest for the experiments. At a given total current, the paramagnetic component of the signal may vary considerably, which generally has to be taken into account in interpreting experimental data. The results of the calculations are used to process the data obtained in the experiments on the SPIN plasma device [Knyazev et al., ‘‘Characteristics of plasma produced by a linear discharge in the metal chamber of the SPIN device,’’ J. Tech. Phys. 63, 49 (1993) (in Russian)].

The effect of asymmetries on non‐neutral plasma confinement time
View Description Hide DescriptionTheory predicts that perfectly azimuthally symmetric non‐neutral plasma traps should confine plasma forever. Unintentional trap asymmetries are believed to limit plasma confinement times to less than <10^{5} s. Deliberately applied electrostatic fields break the azimuthal symmetry and affect the plasma confinement time. While small, deliberate asymmetries do not significantly reduce the trap’s confinement properties, large asymmetries significantly degrade the plasma confinement. The scaling laws of this degradation are studied herein. The mechanism of plasma loss appears to change when deliberate asymmetries are applied.

A singular perturbation approach to ion and electron confinement in trapping fields
View Description Hide DescriptionThe confinement of ions and electrons by linear and nonlinear fields is studied. It is assumed that both species are perturbed by collisions with a neutral background gas with the resulting energy and momentum transfer between the interacting species. Asymptotic expansions, based on a singular perturbation approach in terms of the momentum exchange during collisions, are used to determine the distribution function of the confined species.

Ion acoustic solitons in a plasma with finite temperature drifting ions: Limit on ion drift velocity
View Description Hide DescriptionPropagation of ion acoustic solitons in a plasma consisting of finite temperature drifting ions and nondrifting electrons has been studied. It is shown that in addition to the electron inertia and weak relativistic effects, the ion temperature also modifies the soliton behavior. By including the finite ion temperature, limit for the ion drift velocityu _{0} for which the ion acoustic solitons are possible, is obtained. The solitons can exist for v _{ Te }≤u _{0}≤‖u _{0 max}‖, where v _{ Te } is the electron thermal velocity and u _{0 max} is the maximum value of the ion drift velocity. The maximum value of this velocity is decided by the ion temperature. Under the limiting conditions, the Korteweg–deVries (KdV) equation is derived for one‐dimensional ion acoustic soliton. Expressions are obtained for the soliton phase velocity, peak soliton amplitude, soliton width, and the soliton energy. The present results correspond to those of the previous investigations under appropriate plasma conditions.

Theory of electric‐field curvature effects on long‐wavelength drift wave turbulence
View Description Hide DescriptionA simple model of long‐wavelength drift waves is used to study the way in which a radial electric‐field profile influences the growth and saturation of turbulence. For a fixed external field, the effect of curvature (∂^{2} E _{ r }/∂r ^{2}) dominates that of shear (∂E _{ r }/∂r). In the linear regime, both affect the average k _{∥} at which ion damping occurs: shear by shifting the eigenmode off the resonant surface and curvature by changing the eigenmode width. Curvature damps more efficiently and also shifts the real frequency of the drift wave, changing the instability drive. In the nonlinear regime, radial trapping at large fluctuation levels limits the ability of an external electric‐field profile to affect the spatial structure. Changes in damping are now less effective than the feedback between frequency shift and drive. The importance of the frequency shift caused by electric‐field curvature in the presence of finite‐amplitude fluctuations has been demonstrated by numerical calculations.

Partition in power transfer and dissipation rate in self‐sustained turbulence
View Description Hide DescriptionPower partition and energy dissipation rates are examined for a self‐sustained stationary turbulence of a high‐nballooning mode in a tokamak plasma. It is found that the power to excite fluctuations is almost equally transferred to perpendicular ion motion and to parallel electron motion. The ratio of the thermalized power, which excites and sustains the turbulence, to the total power lost by energydiffusion is found to be of the order of the broken symmetry parameter, i.e., the inverse aspect ratio, a/R. The dissipation rates of the fluctuations due to the thermal conductivity, the electron viscosity, and the ion viscosity are also calculated separately. The dissipation is dominated by that associated with the thermal conductivity. The relation between the induced global flux and the microscopic dissipation is also derived. It is found that a fractional part of order a/R of the dissipated power is effective in sustaining the turbulent modes.

Nonlinear waves in hot magnetized plasma
View Description Hide DescriptionNonlinear low‐frequency long wavelength waves are studied in the framework of the proposed method of the direct kinetic equationexpansion in the inverse gyrofrequency power series. Nonlinear two‐dimensional equations are found for perpendicular magnetosonic waves with subsequent reduction to the Korteweg–de Vries equation for quasistationary one‐dimensional (QS1D) perpendicular magnetosonic wave. The dispersion is determined by the ion gyroradius ρ_{ i }. Equations for nonlinear QS1D parallel Alfvén waves and QS1D oblique fast magnetosonic waves are found. It is shown that the form of the equations coincides with that one obtained from hydrodynamics but the dispersion lengths and coefficients at nonlinear terms are different. Dispersion of quasiparallel fast waves is positive and determined by the ion inertial length c/ω_{ pi }, while quasiperpendicular waves have negative dispersion determined by the ion gyroradius ρ_{ i }.

Resonance parallel viscosity in the banana regime in poloidally rotating tokamak plasmas
View Description Hide DescriptionParallel viscosity in the banana regime in a poloidally (E×B) rotating tokamak plasma is calculated to include the effects of orbit squeezing and to allow the poloidal E×BMach numberM _{ p } to have a value of order unity. Here, E is the electric field and B is the magnetic field. The effects of orbit squeezing not only modify the size of the particle orbit, but also change the fraction of poloidally trapped particles. Resonance between the particle parallel (to B) speed u and the poloidal component of the E×B velocity can only occur for those particles with energy (v/v _{ t })^{2}≳M ^{2} _{ p } (with v the particle speed and v _{ t } the thermal speed). Thus, the resonance parallel plasma viscosity in the banana regime decreases exponentially with M ^{2} _{ p } when M ^{2} _{ p }≥1, and has a local maximum of M ^{2} _{ p }∼1.

Magnetic and velocity fluctuation measurements in the REPUTE‐1 reversed‐field pinch plasma
View Description Hide DescriptionMagnetic and velocityfluctuations are studied in the REPUTE‐1 [Plasma Phys. Controlled Fusion 28, 805 (1986)] reversed‐field pinch (RFP). The first measurement of velocityfluctuation in an RFP plasma has been done using a Doppler shift of the O v(O^{4+}, 278.1 nm) line. The fluctuation level increases as the radius of the viewing chord increases. Magnetic fluctuationmeasurements by an insertable probe reveal that the radial cross correlation of toroidal field fluctuation changes its sign at the radius slightly inside the reversal surface. The level of magnetohydrodynamic dynamo term is estimated from magnetic fluctuations at the surface correlation changes and oxygen velocityfluctuationsmeasured with the chord distance of 115 mm. The dynamo term and that due to resistivity are the same level. This fact is consistent with Ohm’s law on which magnetohydrodynamic dynamo models are based.

The influence of a radial electric field on neoclassical orbits and ion prompt losses from tokamak edge plasmas
View Description Hide DescriptionThe effect of the radial electric field on neoclassical orbits in a tokamak using the integrals of drift motion is considered. It is shown that for the most interesting case of high radial electric field shear, due to a dramatic change of the particle orbittopology at a distance of the order of one particle orbit width, it is not correct to apply local theory to describe neoclassical transport processes. For step‐like electrostatic potentials typical for the tokamak plasma periphery in the high (H) mode, the trajectories of the particles can be either squeezed or expanded depending on the location of the potential jump with respect to the unperturbed particle trajectories. The widening of the orbits decreases the threshold energy of suprathermal particles which can be promptly lost and enhances the ion prompt losses which might increase the amplitude of the potential step. It is shown that these effects are more pronounced for a diverted tokamak with the X point located at the inner side of the torus. Simultaneous growth of prompt losses and potential magnitude might be the reason for the fast formation of the narrow electrostatic barrier during the ‘‘low’’–‘‘high’’ (L–H) transition. Toroidal plasma rotation induced by the radial electric field can strongly enhance the destabilizing effect of the step‐like potential.

An explanation for experimental observations of harmonic cyclotron emission induced by fast ions
View Description Hide DescriptionAn explanation, supported by numerical simulations and analytical theory, is given for the harmonic cyclotron emission induced by fast ions in tokamak plasmas—in particular, for the emission observed at low harmonics in deuterium–deuterium and deuterium–tritium experiments in the Joint European Torus [e.g., Phys. Rev. Lett. 60, 33 (1988)]. It is shown that the first protonharmonic, whose field energy amplitude scales as the 0.84 power of the proton density, is one of the highest spectral peaks, whereas the first alpha harmonic is weak. The relative spectral amplitudes of different harmonics are compared. The results are consistent with the experimental observations. The simulations verify that the instabilities are caused by a weak relativistic mass effect. Simulation also shows that a nonuniform magnetic field leads to no appreciable change in the growth rate and saturation amplitude of the waves.

Instability due to axial shear and surface impedance
View Description Hide DescriptionThe stability of plasma flow in the scrape‐off layer of a tokamak, taking into account the surface sheath impedance and the axial shear in the E×Bflow is analyzed. An interesting stability problem arises in the limit that end plates are sufficiently far apart, so that stability can be analyzed when the plasma is taken to interact with a single end plate. As parameters are varied, windows of instability are found, and it is shown that growth rates are maximized for an insulating end plate and are also quite sensitive to the ratio of the ion diamagnetic and E×B drift frequencies. Mixing‐length estimates of the diffusivity are comparable to experimentally observed values.

A numerical study of the Alfvén continuum damping of toroidal Alfvén eigenmodes
View Description Hide DescriptionThe Alfvén continuum damping of the toroidal Alfvén eigenmodes is explicitly formulated for a large aspect ratio force‐free tokamak using analytic continuation. A set of jump conditions across the Alfvén singularities are derived which have to be satisfied by the mode amplitudes. The method is then applied to a simple model equilibrium. The characteristics of the modes and their damping are investigated. The method is expected to be generalizable to models with more complete plasma dynamics.

Kinetic investigation of the effect of lower hybrid current drive on tearing mode instability
View Description Hide DescriptionEffect of lower‐hybrid current drive on tearing mode instability is investigated in a drift kinetic formalism. In collisional regime the co‐driven current plays a stabilizing role to tearing mode but a destabilizing role to drift tearing mode. A competitive effect among the gradients of density, temperature and driven current at the rational surface may exist. In semicollisional regime, lower hybrid current drive increases the growth rate of tearing mode and reduces the growth rate of drift tearing mode.

Synchrotron radiation and its relevance on plasma diagnostics in next generation tokamaks
View Description Hide DescriptionPlasma diagnostics using synchrotron radiation in next generation large tokamaks is discussed. Is is first shown that for electron temperature on axis in excess of 20–25 keV, harmonic overlap invalidates the familiar second harmonic emission method for temperature measurements in the central plasma region. Next, it is shown that radiationmeasurements at arbitrary frequencies of the X‐mode normal to the magnetic field in the horizontal and vertical directions yield a set of independent equations for deriving the plasma parameters characterizing the temperature and density profiles. The method and the salient features of the emitted radiation at arbitrary frequencies are illustrated for parameters being considered in the design of tokamak reactors.

Three‐dimensional propagation and absorption of high frequency Gaussian beams in magnetoactive plasmas
View Description Hide DescriptionIn today’s high frequency systems employed for plasma diagnostics, power heating, and current drive the behavior of the wave beams is appreciably affected by the self‐diffraction phenomena due to their narrow collimation. In the present article the three‐dimensional propagation of Gaussian beams in inhomogeneous and anisotropic media is analyzed, starting from a properly formulated dispersion relation. Particular attention is paid, in the case of electromagnetic electron cyclotron (EC) waves, to the toroidal geometry characterizing tokamak plasmas, to the power density evolution on the advancing wave fronts, and to the absorption features occurring when a beam crosses an EC resonant layer.

Spontaneous generation of toroidal currents
View Description Hide DescriptionA loss‐cone mechanism for self‐generation of toroidal currents is examined in toroidal magnetic configurations with a mirror‐like vertical (poloidal) field. The loss cone is found to be asymmetric with respect to the toroidal velocity. Particles that carry a negative toroidal current are better confined than those that carry a positive current, giving rise to a net toroidal current that can be sufficiently large to close magnetic surfaces. This mechanism is found to be dependent on the curvature drift of particles, indicating that a low‐aspect‐ratio toroidal configuration is more favorable for this type of current generation.

Nonlinear destabilization of linearly stable tearing modes with multiple rational surfaces
View Description Hide DescriptionThe stability of finite size magnetic islands is analyzed in configurations with multiple resonant magnetic surfaces. It is demonstrated that there are configurations that are linearly stable which can be unstable to finite size perturbations. Two different examples of single helicity double tearing are given for configurations with two q=2 surfaces. In the first case the destabilization is due to the extension of magnetic separatrices out to regions of destabilizng current gradients. For the second case the modes are linearly stabilized by the suppression of the linear coupling of the rational surfaces by differential plasma rotation, which essentially decouples the perturbations around the different rational surfaces. A finite size magnetic island will interact quasilinearly with initial plasma rotation. The plasma rotation is then equilibrated and the mode destabilized.