John A. Tataronis

General two-dimensional magnetohydrodynamic equilibria with mass flow

A set of reduced ideal MHD equations is derived to investigate equilibria of plasmas with mass flow in general two-dimensional geometry. These equations provide a means of investigating the effects of flow on self-consistent equilibria in a number of new two-dimensional configurations, such as helically symmetric configurations with helical axis, which are relevant to stellarators, as well as axisymmetric configurations. It is found that, as in the axisymmetric case, general two-dimensional flow equilibria are governed by a second-order quasilinear partial differential equation for a magnetic flux function, which is coupled to a Bernoulli-type equation for the density. The equation for the magnetic flux function becomes hyperbolic at certain critical flow speeds which follow from its characteristic equation. When the equation is hyperbolic, shock phenomena may exist. As a particular example, unidirectional flow along the lines of symmetry is considered. In this case, the equation mentioned above is always elliptic. An exact solution for the case of helically symmetric unidirectional flow is found and studied to determine flow effects on the magnetic topology.

Current drive via magnetohydrodynamic helicity waves in a nonuniform plasma

Fundamentals of low‐frequency current drive produced by a packet of arbitrarily polarized nonlinear Alfven waves in an incompressible plasma with an inhomogeneous equilibrium magnetic field and aligned fluid velocity are explored. Analysis of the equations of magnetohydrodynamics with electrical conductivity and kinematic viscosity using an eikonal formulation yields coupled nonlinear equations for the Alfven wave amplitude and an induced magnetic field and fluid velocity. Introduction of suitable variables allows simplification of the nonlinear system into a system of coupled linear integrodifferential equations. Particular solutions relate the plasma current to the helicity of the Alfven wave. Two separate and distinct agents contribute to the current drive process: (1) wave dissipation, and (2) spatial inhomogeneity of the plasma medium. The plasma inhomogeneities cause a direct transfer of helicity from the applied Alfven wave to the equilibrium magnetic field and are connected to the damping of a sin...

Mode conversion between Alfvén wave eigenmodes in axially inhomogeneous two-ion-species plasmas

The uniform cylindrical plasma model of Litwin and Hershkowitz [Phys. Fluids 30, 1323 (1987)] is shown to predict mode conversion between the lowest radial order m=+1 fast magnetosonic surface and slow ion‐cyclotron global eigenmodes of the Alfven wave at the light‐ion species Alfven resonance of a cold two‐ion plasma. A hydrogen (h)–deuterium (d) plasma is examined in experiments. The fast mode is efficiently excited by a rotating field antenna array at ω∼Ωh in the central cell of the Phaedrus‐B tandem mirror [Phys. Rev. Lett. 51, 1955(1983)]. Radially scanned magnetic probes observe the propagating eigenmode wave fields within a shallow central cell magnetic gradient in which the conversion zone is axially localized according to nd/nh. A low radial‐order slow ion‐cyclotron mode, observed in the vicinity of the conversion zone, gives evidence for the predicted mode conversion.

Transient phase conjugation in Kerr media, photorefractive media, and plasmas: a comparison

A general solution to a linearized transient problem is presented and is shown to be valid for Kerr materials, photorefractive materials, and plasmas. The solution is expressed in terms of a transfer function that relates the complex frequencies of the probe and the conjugate field. Using this solution, the parameters that govern the overall time behavior are identified and compared. These parameters are then used to discuss the distortion characteristics of the conjugate signal for each of the three materials. >

Nonlinear plasma waves with steady-state d.c. current

Using a low-frequency, low-β model of a magnetized plasma, several nonlinear waves are studied. All the waves share the property that they have a self-consistent time-averaged current in the steady state. The first wave is a onedimensional solitary wave that propagates obliquely to a static magnetic field. The wave magnetic field has a kink structure, which results in the production of the time-averaged current. A two-dimensional wave that propagates parallel to the background magnetic field is also discussed. This is a forced wave, requiring an antenna structure to support it in the steady state. The characteristics of the two-dimensional wave are dependent upon the wave speed, which in turn is determined by the speed of the travelling wave on the external antenna

Enhancement of phase-conjugate reflectivity with linear absorption in four-wave mixing systems

We describe the steady-state enhancement of the phase-conjugate reflectivity that occurs with linear absorption near self-oscillation in four-wave mixing systems. Using a simplified general model, we show that this effect can arise in a variety of phase conjugators including those based on photorefractive and Kerr media. A new expression is introduced for the optimal reflectivity condition, which occurs if the transfer of energy from the strong forward pump to the weak probe is maximized at the entrance to the nonlinear medium.

Resonant four-wave mixing of finite-amplitude Alfvén waves

Using the derivative nonlinear Schrodinger equation, resonant four-wave mixing of finite-amplitude Alfven waves is explored in this paper. The evolution equations governing the amplitudes of the interacting waves and the conservation relations are derived from the basic equation. These evolution equations are used to study parametric amplification and oscillation of two small-amplitude Alfven waves due to two large-amplitude pump (Alfven) waves. It is also shown that three pump waves can mix together to generate a low-frequency Alfven wave in a dissipative plasma.

Radial dependence of magnetohydrodynamic continuum modes for an incompressible plasma

The spatial structure of the magnetohydrodynamic shear Alfven and cusp continuum modes in axisymmetric toroidal geometry is analyzed for an incompressible plasma. The normal component ξ ψ of the plasma displacement is found to have an oscillatory type of singularity, ξ ψ ∼ (ψ - ψ 0 ) δ ∼ sin(|δ|ln|ψ - ψ 0 | + const), or, for example, in the case of up/down symmetry, a purely logarithmic behavior. This result was also obtained in the more general case of a compressible plasma (Salat, A. and Tataronis, J. A. 1999 Phys. Plasmas 6, 3207). However, in that work the incompressible limit could not be taken because the continuum equations were written in terms of a variable that becomes ill-defined in the limit. The present ab initio derivation shows that, in general, the incompressible limit in the previous work, γ → ∞, where γ is the ratio of the specific heats, does give the correct spatial dependence. Furthermore, we prove that it is possible to recover the oscillatory type of singularity for the cylindrical screw pinch from the logarithmic singularity of an up/down symmetric torus.

Reflectivity enhancement due to linear absorption in photorefractive phase-conjugate mirrors with depleted pumps

Using numerical simulations of the fully nonlinear equations that describe the steady-state optical fields that develop within photorefractive phase-conjugate mirrors, we have shown that the phase-conjugate reflectivity can be enhanced in the presence of linear absorption. Our investigations focused on the development of the optical fields that arise when the reflectivity is nonmonotonically dependent on the linear absorption both near and away from self-oscillation. We have identified several significant features associated with the enhancement. Near self-oscillation and with strong pumps, an increase in the loss can lead to a more efficient energy transfer to the probe by altering the phase of the coupling, resulting in an increase in the index grating amplitude. Away from self-oscillation and with strong pumps, the loss alters the distribution of the grating within the crystal, and maximum reflectivity is associated with an optimum distribution. Reflectivity enhancement that is due to linear absorption was shown to occur even in the weak-pump case, thus providing unequivocal evidence of the veracity of this phenomenon.

RF current drive and helicity injection

Recent studies suggest that low frequency electromagnetic waves possessing helicity may drive currents in plasmas with greater efficiency than schemes based on linear momentum transfer to charged particles.1,2 A key issue is the transfer of wave helicity into the helicity of the equilibrium magnetic field. Previously we examined the conversion mechanism by following the dynamics of a packet of arbitrarily polarized Alfven waves propagating in an infinite uniformly magnetized plasma.3,4 Analysis of the equations of magnetohydrodynamics with resistivity and viscosity yielded a set of nonlinear equations governing the Alfven wave amplitude and an induced magnetic field. Solutions for the initial value problem4 related the induced plasma current to the helicity of the wave and the difference between the magnetic diffusivity and viscosity. In the present investigation we examine solutions for the boundary value problem.