Marshall N. Rosenbluth

MHD stability of Spheromak

The Spheromak, an optimal force-free spherical plasma configuration, is analysed for its MHD stability properties. It is shown that flattened ellipse (oblimak) with = k (k independent of ) should be stable against all magnetically driven MHD and resistive tearing modes if surrounded by a conducting wall at about rw/r0 = 1.15. βs of at least 2% can be stably confined, equivalent to 20% in tokamaks.

Raman and Brillouin scattering of electromagnetic waves in inhomogeneous plasmas

Raman and Brillouin scattering of an electromagnetic wave in an inhomogeneous, expanding plasma are studied. Application to laser‐pellet irradiation is considered.

Nonlinear properties of the internal m = 1 kink instability in the cylindrical tokamak

An analysis is presented, in a cylindrical approximation, of the nonlinear behavior of the mu2009=u20091 magnetohydrodynamic kink instability that occurs in a tokamak when the “safety factor” q(r)u2009=u2009rBzu2009/u2009RBu2009θ(r) falls below unity on axis. A kinked neighboring equilibrium is found, which is accessible from the initial straight equilibrium in the sense of satisfying the flux‐conservation constraints. Owing to the singular nature of the fundamental, all harmonics are excited in a singular region near where qu2009(r)u2009=u20091. The nonlinear amplitude is moderate. It is shown that growing modes of this type should produce negative voltage spikes and inward shifts in major radius, as are seen in the experiments. The predicted magnitudes of these two effects are, however, much smaller than those observed.

Parametric decay of electromagnetic waves into two plasmons and its consequences

The parametric decay of the laser radiation into two plasma waves at the quarter critical density of an inhomogeneous plasma is analyzed. The growth rate and threshold of the absolute instability are derived. The bound on the saturation level of the plasma waves is obtained from the consideration of the pump depletion. The scattered radiation at 3/2 ω0 due to the beating of the incident wave with the backward plasma wave is calculated and compared with observations.

Parallel velocity shear instabilities in an inhomogeneous plasma with a sheared magnetic field

Injection of fast neutrals with a component of the beam velocity along the magnetic field B0 results in a plasma having a sheared mean velocity along B0. If this parallel velocity shear U′ and the density inhomogeneity scale length Ln are large enough so that Uu2009′|Lnu2009|/(τu2009+u20091)u20091/2υiu2009>u20091 then a parallel Kelvin‐Helmholtz instability is excited, where vi is the ion thermal speed and τ is the electron temperature/ion temperature. Magnetic shear stabilization requires a shear length Ls comparable to or less than |Lnu2009|, namely, τLu2009su2009/3u2009(τu2009+u20091)u2009 u2009172|u2009(Lnu2009/u2009Ls)3/2u2009| provided |Lnu2009/Ls|u2009 u2009600 and Uu2009′u2009/Ωiu2009≪u20091, where ai and Ωi are the ion gyration radius and ...

Transport properties of a toroidal plasma at low‐to‐intermediate collision frequencies

The neoclassical plasma transport coefficients for axisymmetric toroidal magnetic confinement systems are calculated in the regime of low‐to‐intermediate collision frequency. The problem of solving the linearized drift kinetic equations, and calculating the transport coefficients, is formulated as a variational principle. A maximal form of the variational principle, which is valid in the low‐to‐intermediate collision frequency regime, is used in a numerical solution of the finite dfiference equations, to obtain the distribution function at points on a mesh in phase space. A new analytical result is used to check the accuracy of the numerical calculation for small collision frequencies; this is a correction to the asymptotic banana regime result, obtained from a Wiener‐Hopf analysis of the boundary layer in phase space between the trapped and untrapped particle regions. An analytical correction to the plateau regime analtyical result is also obtained. The transport coefficients are found to be monotonic fu...

Numerical studies of nonlinear evolution of kink modes in tokamaks

A set of numerical techniques for investigating the full nonlinear unstable behavior of low‐β kink modes of given helical symmetry in tokamaks is presented. Uniform current density plasmas display complicated deformations including the formation of large vacuum bubbles provided that the safety factor q is sufficiently close to integral. Fairly large m=1 deformations, but not bubble formation, persist for a plasma with a parabolic current density profile (and hence shear). Deformations for m⩾2 are, however, greatly suppressed.

RELAXATION PROCESSES IN PLASMAS WITH MAGNETIC FIELD. TEMPERATURE RELAXATIONS.

The Fokker‐Planck coefficients of a plasma in the magnetic field are calculated in terms of the spectral function of the electric‐field fluctuations and the dielectric response function; the results are used for the investigation of temperature relaxation processes. It is found that the relaxation rate between the electron and ion temperatures contains, in addition to the usual Spitzer rate, an anomalous term which diverges logarithmically as the mass ratio approaches zero. The physical origin of this anomalous term is the strong coupling between the spiral motion of the electrons and the long‐wavelength, low‐frequency fluctuations produced by the ions; its magnitude can become comparable to the Spitzer rate for a strong magnetic field. In the case of the temperature relaxation between the parallel and perpendicular directions to the magnetic field, the screened Coulomb interaction provides the major relaxation mechanism; the effects of the fluctuations associated with the Bernstein modes are negligibly s...

Single‐mode saturation of the bump‐on‐tail instability: Immobile ions

A slightly unstable plasma with only one or a few linear modes unstable is considered. Nonlinear saturation at small amplitudes has been treated by time-asymptotic analysis which is a generalization of the methods of Bogolyubov and co-workers. In this paper the method is applied to instability in a collisionless plasma governed by the vlasov equation. The bump-on-tail instability is considered for a one-dimensional plasma. (MOW)

Plasma transport in a torus of arbitrary aspect ratio

Finite aspect ratio modifications to neoclassical transport theory are considered. In the general case of arbitrary flux surface geometry, a closed set of macroscopic equations is derived. These include the equation which determines the time evolution of the flux surfaces. In the large aspect ratio case, the Ou2009(ru2009/Ru2009) corrections to the order Ou2009(ru2009)1/2)Ru2009(1/2)) transport coefficients, calculated previously, are obtained. In particular, an expression for the electrical conductivity is obtained which may be regarded as exact for all experimentally interesting aspect ratios.