Index of content:
Volume 5, Issue 12, December 1993

Numerical calculation of axisymmetric non‐neutral plasma equilibria
View Description Hide DescriptionEfficient techniques for computing axisymmetric non‐neutral plasma equilibria are described. These equilibria may be obtained either by requiring global thermal equilibrium, by specifying the midplane radial density profile, or by specifying the radial profile of ∫n dz. Both splines and finite‐differences are used, and the accuracy of the two is compared by using a new characterization of the thermal equilibrium density profile which gives a simple formula for estimating the radial and axial gradient scale lengths of thermal equilibria. It is found that for global thermal equilibrium 1% accuracy is achieved with splines if the distance between neighboring splines is about two Debye lengths while finite differences require a grid spacing of about one‐half Debye length to achieve the same accuracy.

Coupled tearing modes in plasmas with differential rotation
View Description Hide DescriptionThe global asymptotic matching equations for multiple coupled resistive modes of arbitrary parity in a cylindrical plasma are derived. Three different variational principles are given for the outer region matching data, while the inner region analysis features a careful treatment of the symmetry‐breaking effect of a gradient in the equilibrium current for a zero‐β slab model. It is concluded that the usual constant‐ψ result remains valid and constrains the matrix matching formalism. The dispersion relation is compared with initial value calculations of a double tearing mode when there are small relative rotation velocities between the rational surfaces. In treating differential rotation within the asymptotic matching formalism, flow is ignored in the outer region and is assumed to affect the inner response solely through a Doppler shift. It is shown that the relative rotation can have a strong stabilizing effect by making all but one rational surface effectively ideal.

Imploding cylindrical shock in a perfectly conducting and radiating gas
View Description Hide DescriptionSimilarity solutions to a problem in radiative magnetogasdynamics with strong shocks are presented. Group theoretic methods are used to obtain a condition on the shock Cowling number, and to characterize the state dependent form of the gas absorption coefficient for which the self‐similar solutions are admitted. Numerical calculations have been performed to determine the value of the self‐similar exponent and the profiles of the flow variables, which enable one to assess the influence of thermal radiation, the magnetic field strength, and the adiabatic heat exponent on the flow pattern.

A limitation to the analogy between pure electron plasmas and two‐dimensional inviscid fluids
View Description Hide DescriptionThermal corrections to E×B drifts cause small structures in pure electron plasmas to smear. This smearing breaks the strict analogy between the behavior of pure electron plasmas and the behavior of two‐dimensional inviscid fluids. The causes and consequences of this smearing are discussed, a criterion for the validity of the plasma/fluid analogy is constructed, and experimental examples of the failure of the analogy are presented. The criterion indicates that fluid‐like behavior can persist to scale lengths far smaller than the normal ‘‘collective’’ behavior limit.

Scattering of ordinary‐mode electromagnetic waves by density fluctuations in tokamaks
View Description Hide DescriptionDiscussion and applications are presented for two approaches for estimating the effects of scattering of electromagnetic waves by turbulent density fluctuations in tokamaks. Ordinary‐mode waves propagating nearly perpendicular to the equilibrium magnetic field are considered. The multiple‐scattering approach provides analytic results for the angular and spatial spreading of a microwave beam by the turbulence. The single‐scattering approach yields numerical results and is derived by a compact technique involving Wigner functions. Both approaches are applied to idealized tokamaks to clarify relationships between the approaches and to test limits of applicability of the multiple‐scattering approach.

Study of the diffusion across a magnetic field in a beam–plasma interaction using a drift‐kinetic Vlasov code
View Description Hide DescriptionA drift‐kinetic Eulerian Vlasov code, with fluid equations for the ions, is developed to study the problem of the injection of an electron beam into a two‐dimensional magnetized plasma, often referred to as direct current (dc) helicity injection. The diffusion of electrons across a magnetic field in the presence of a beam–plasma instability is studied. The case of a magnetic field tilted with respect to the beam direction is considered. The competition between the velocity shear Kelvin–Helmholtz (KH) and the beam–plasma (BP) instabilities is investigated in order to analyze the plasma heating and current drive mechanism induced by the beam injection. The KH instability generates low‐frequency plasma convection motion associated with c E×B/B ^{2} drift. In particular, the diffusion coefficients D _{ y } and D _{ v } _{∥} describing, respectively, the anomalous diffusion process induced in space across the magnetic field by the KH instability, and the velocity diffusion process due to the kinetic effects induced in velocity space along the magnetic field by the BP instability, are computed using test‐particle diagnostics. In the present Cartesian model, it is found that D _{ y } = D _{ v ∥ tan2 θ/ω ce } ^{2} where θ is the angle between the magnetic field and the x axis. This relation which links the electron dynamics in the x‐y real space and in the x‐v _{∥} phase space is verified by the numerical code. The Vlasov code provides a powerful tool to study particle diffusion in space and in phase space, especially in the low‐density regions of the distribution function.

On the fast penetration of magnetic field into plasma
View Description Hide DescriptionThe fast penetration of a strong magnetic field into a plasma, caused by the Hall effect, is studied. The phenomenon is likely to govern the early evolution of the magnetic field not only in two‐dimensional geometry, to which previous studies were restricted, but also in three dimensions. This penetration mechanism is suppressed, if both the plasma and electrodes are collisionless, v _{Ae }τ_{ e }≳a, where v _{Ae } is the electron Alfvén velocity, τ_{ e } ^{−1} the collision frequency, and a the characteristic space‐scale. However, the collisionless penetration can occur in the case of a resistive cathode. The self‐consistent effect of ion motion is shown to be of importance only in a very special geometry. Then the penetration speed is limited by the value V _{A}(aω_{ pi }/c)^{−1/3}, where V _{A} is the Alfvén velocity and c/ω_{ pi } the ion skin depth.

Revisiting the validity of quasilinear theory
View Description Hide DescriptionThe weak turbulence theory of Langmuir waves in a one‐dimensional, one‐species plasma is discussed. Analytic calculations using the theory of two‐point correlations show that in the weak turbulence regime, τ_{ ac }≪min(τ_{tr},γ^{−1} _{ k }) (where τ_{ ac } is the field autocorrelation time and τ_{tr} is the particle decorrelation time), the nonlinear enhancement of the mode growth rate γ_{ k } beyond the linear, Landau growth rate γ_{ k } ^{L} is small, additive, and higher order in the weak turbulence expansion parameter. This result thus supports the validity of the quasilinear theory for Langmuir wave turbulence, and disagrees with the predictions of Adam, Laval, and Pesme [Phys. Rev. Lett. 43, 1671 (1979)], which indicate a non‐negligible, multiplicative enhancement in the regime τ_{ ac }≪τ_{tr}≪γ^{−1} _{ k }. Analysis shows that their result comes from the use of an invalid source term for the fluctuations.

Ion‐temperature‐gradient instability driven transport and its parametric scaling
View Description Hide DescriptionExperiments are reported on the ion thermal transport due to the ion‐temperature‐ gradient‐driven instability (ITG mode) and its transport scaling properties with respect to instability parameters like fluctuation level ñ/n _{ i } and linear growth rate as well as the drive parameter η_{ i }(=∂ ln[T _{ i }]/∂ ln[n _{ i }]) in the Columbia Linear Machine [Phys. Fluids 26, 1044 (1983)]. The measured local ion thermal conductivity χ_{⊥}(r) is highly anomalous and strongly correlated with the radial profile of the ITG mode. The linear scaling of the averaged thermal conductivity 〈χ_{⊥}(r)〉 with the averaged mode fluctuation level 〈ñ/n _{ i }〉 and linear growth rate indicates strong turbulence‐type scaling. The scaling of χ_{⊥} with the drive parameter η_{ i } is offset linear.

On nonlinear effects in electron‐cyclotron resonance plasma heating by microwave radiation
View Description Hide DescriptionPossible nonlinear effects in electron‐cyclotron plasma production and heating by microwave radiation are analyzed. They include nonlinear regimes of electron acceleration in strong microwave fields under cyclotron resonance conditions, nonstationary regimes of microwave beam self‐focusing, and some parametric processes. Presented results may be of importance for predictions of plasma response to electron‐cyclotron resonance (ECR) heating or preionization by powerful radiation.

Neoclassical viscosity of a tokamak plasma with large mass flow
View Description Hide DescriptionNeoclassical ion viscosity of a steady tokamak plasma with large mass flow is calculated in a general geometry. In addition to the usual ‘‘resonant’’ contribution, the ‘‘nonresonant’’ contribution has been evaluated. It is found that the nonresonant contribution is not small compared to the resonant contribution when the poloidal rotation speed is large. The viscosity evaluation has been reduced to one‐dimensional integrals. Furthermore, simple analytic formula for the viscosity coefficients are suggested. The velocity strain, which is the source of the viscosity, is also analyzed in detail.

Stability of field‐reversed configurations in the large s experiment (LSX)
View Description Hide DescriptionData from several diagnostics employed on the Large s Experiment (LSX) field‐reversed theta pinch were analyzed to seek correlation between plasma distortions and the confinement properties of the field‐reversed configurations (FRC’s) formed. In particular, an array of B _{θ} probes was used to determine separatrix movement, which might indicate the existence of low‐order modes, such as a tilt instability. No correlation between the quality of confinement and signal was observed. The parameter s, equal to the average number of ion gyroradii inside the separatrix, has been postulated as a measure of FRC stability with values above 2, leading to instability and loss of confinement. However, the confinement observed in experiments conducted over a large range of s (1<s<8) appeared to correlate more with the shape of the equilibrium radial density profile produced during formation rather than s. Flatter profiles correlated with poorer confinement.

Filamentation, current profiles, and transport in a tokamak
View Description Hide DescriptionA tokamak with slightly imperfect magnetic surfaces should have a microscopically filamented current structure. If so, its equilibrium has an analog in the dynamics of interacting charged rods. Then there will be a natural current profile, analogous to thermal equilibrium of the rods (and the natural profile can be calculated by conventional statistical mechanics). This would account for the phenomenon of profile consistency or resilience in tokamaks. In addition to the natural profiles, this filamentary model also predicts an anomalous inward flux of both heat and particles in a tokamak, as well as an anomalous diffusion. These ‘‘inward‐pinch’’ components are related to the current gradient.

An experimental study of magnetic islands as Hamiltonian systems
View Description Hide DescriptionMagnetic islands play an important role in determining plasma transport in toroidal magnetic confinement systems. The magnetic error fields and the associated islands can be theoretically described by a Hamiltonian approach. Experiments have been conducted on the Compact Auburn Torsatron [Fusion Technol. 18, 281 (1990)] to test the applicability and limits of the first‐order Hamiltonian theory to magnetic islands. A novel set of helical trim coils with the same spatial periodicity as an ι– = 1/2 magnetic island were used to create a perturbation field of variable magnitude and phase. Extensive experimental parametric studies of the magnetic island were conducted and compared with theory. It was found that the first‐order Hamiltonian theory is applicable for the complete range of experimental error fields.

Statistical theory of wave propagation and multipass absorption for current drive in tokamaks
View Description Hide DescriptionIn this work the effect of ray stochasticity on the multipass absorption of lower‐hybrid waves, used to drive current in tokamaks, is considered. In toroidal geometry, stochasticity arises as an intrinsic property of the Hamiltonian ray trajectories for lower‐hybrid waves. Based on the wave kinetic equation, a diffusion equation is derived, with damping and sources, for the wave energy density in the stochastic layer. This equation is solved simultaneously with the electron Fokker–Planck equation to describe the quasilinear flattening of the electron distribution function and the subsequent modification of the wave damping. Steady‐state solutions of this system (obtained numerically) indicate that the spectral gap is filled in a self‐regulating manner, so that the boundaries of the diffused wave spectrum are independent of the level of ray stochastic diffusion. This allows the development of a simple (semianalytic) model for the self‐consistent wave spectrum and the radial profile of absorbed power.

Investigations of diffusional effects in applied‐B ion diodes
View Description Hide DescriptionIn this article, a general study of diffusional effects is made numerically as well as theoretically with the aim to reproduce not only the current scaling of ion diodes but also the divergence of the ion beam and physical features such as virtual cathode movement due to the diamagnetic effect. It has been observed experimentally that the ion current exceeds that quantity which would be expected in the presence of a strong magnetic field. It is demonstrated that with the introduction of a diffusional field E _{θ} into the stationary 21/2‐dimensional particle‐in‐cell code based on boundary‐fitted coordinates [T. Westermann, Nucl. Instrum. Methods A 263, 271 (1988)] the simulation results agree well with experiment. This ad hoc model is supported theoretically by linear stability analysis of the stationary state.

Characterization of laser‐produced plasma density profiles using grid image refractometry
View Description Hide DescriptionGrid image refractometry (GIR) is proposed as a technique for determining the two‐dimensional density profiles of long scale‐length laser‐produced plasmas. Its distinctive feature is that an optical probe beam is broken up into ‘‘rays’’ by being passed through a grid before traversing the plasma. The refraction angles of the rays are measured by imaging the plasma at two or more object planes and are integrated to yield the phase front. For cylindrically symmetric plasmas the density profile is then determined using Abel inversion. The feasibility of GIR is illustrated by an experiment in which a thick CH target was irradiated with ∼100 J of 527 nm radiation and diagnosed with a 20 ps, 263 nm probe. The resulting density profile is substantially larger than any that have previously been reported using interferometry and compares quite closely with hydrodynamic simulations.

Cumulative hose instabilities of a magnetically self‐focused slab electron beam
View Description Hide DescriptionTransverse instabilities are investigated for the slab analog of the Bennett equilibrium of a magnetically self‐focused relativistic electron beam propagating through a plasma. Two kinds of plasma are considered: a channel matched to the beam and a broad uniform plasma. The high‐frequency electrostatic transverse two‐stream instability and the lower‐frequency resistive‐hose instability are treated analytically with a distributed tune (‘‘mass’’) model. Asymptotic growth is computed for each instability in various regimes, and analytic results are benchmarked against numerical solutions of the linearized system and particle‐in‐cell simulations. It is found that in the limit of large collisionless skin depth the electrostatic hose is the more virulent mode of beam breakup. Numerical examples are discussed for parameters in the range considered for plasma focusing of the asymmetric beams of interest in high‐energy physics.

Modulational instabilities in strongly pumped systems
View Description Hide DescriptionIn this paper, results of a set of numerical simulations applicable to the problem of particle acceleration by the beating of high‐energy laser waves are presented. The simulations have periodic or open‐ended boundary conditions. The growth rates of the parametric instabilities that are present in both situations are identical. In all cases they yield a destruction of the large amplitude plasma wave in a very short time. The amplitude of the saturation level is shown to be strongly dependent on initial conditions. Finally, some results in the term of the evolution of the distribution function of the background plasma in the context of strong turbulence are shown.

Dynamics of Ne‐like populations in the germanium x‐ray laser
View Description Hide DescriptionTime‐ and two‐dimensional (2‐D) space‐resolved monochromatic imaging is used to study the dynamics of Ne‐like populations in the electron collisionally excited germanium x‐ray laser. Large‐scale variations in the n=3 level population, specifically the upper level of the 2s2p ^{6}3d‐2s2p ^{6}3p laser transition, are observed in plasmas created in uniform and nonuniform irradiation conditions, and the degree of homogeneity along the amplification axis is related to the x‐ray gain. The influence of inhomogeneities on the core‐excited 3d‐3p x‐ray lasers is discussed.