A. Bondeson

Local Magnetohydrodynamic Instabilities of Cylindrical Plasma with Sheared Equilibrium Flows

The ideal magnetohydrodynamic stability of cylindrical equilibria with mass flows is investigated analytically and numerically. The flows modify the local (Suydam) criterion for instability at the resonant surfaces where k⋅B=0. Sheared flows below the propagation speed for the slow wave are found to be destabilizing for the Suydam modes. At a critical velocity, where the shear of the flow exactly balances the propagation of the slow wave along the sheared magnetic field, and the k⋅B=0 surface is at the edge of a slow wave continuum, there is instability regardless of the pressure gradient. Above the critical velocity, the k⋅B=0 surface is stable, but an infinite sequence of unstable modes still exists with frequencies accumulating toward the edge of the slow wave continuum at nonzero Doppler shifted frequency. The stability of the infinite sequences becomes a nonlocal problem whenever the accumulation frequency overlaps with a continuum at some other radial location.

Resistive toroidal stability of internal kink modes in circular and shaped tokamaks

The linear resistive magnetohydrodynamical stability of the n=1 internal kink mode in tokamaks is studied numerically. The stabilizing influence of small aspect ratio [Holmes et al., Phys. Fluids B 1, 788 (1989)] is confirmed, but it is found that shaping of the cross section influences the internal kink mode significantly. For finite pressure and small resistivity, curvature effects at the q=1 surface make the stability sensitively dependent on shape, and ellipticity is destabilizing. Only a very restricted set of finite pressure equilibria is completely stable for q0 < 1. A typical result is that the resistive kink mode is slowed down by toroidal effects to a weak resistive tearing/interchange mode. It is suggested that weak resistive instabilities are stabilized during the ramp phase of the sawteeth by effects not included in linear resistive magnetohydrodynamics. Possible mechanisms for triggering a sawtooth crash are discussed.

Relaxation toward states of minimum energy in a compact torus

A finite‐difference, resistive, magnetohydrodynamic code is used to follow the long‐time evolution of decaying nonequilibrium states inside a rigid, perfectly conducting cylindrical boundary. The energy‐to‐magnetic helicity ratio decays toward a minimum, in accord with a conjecture of Taylor. The magnetic Reynolds number is considerably higher than the mechanical Reynolds number for the regime considered. The energy, which is mostly magnetic, tends to decay in bursts associated with current filamentation and magnetic reconnection.

Tilting instability of a cylindrical spheromak

The stability of a low‐beta spheromak with a perfectly conducting cylindrical boundary of length L and radius R is analyzed in terms of force‐free fields with J = λB(λ = const). The axisymmetric equilibrium is found unstable to tilting when the elongation L/R is larger than about 1.67. Numerical solutions of the time‐dependent ideal magnetohydrodynamic equations confirm this result.

Experimental measurements on a 100 GHz frequency tunable quasioptical gyrotron

Experiments on a 100 GHz quasioptical (QO) gyrotron operating at the fundamental (ω=Ωce) are described. Powers larger than 90 kW at an efficiency of about 12% were achieved. Depending on the electron beam parameters, the frequency spectrum of the output can be either single moded or multimoded. One of the main advantages of the QO gyrotron over the conventional gyrotron is its continuous frequency tunability. Various techniques to tune the output frequency have been tested, such as changing the mirror separation, the beam voltage, or the main magnetic field. Within the limitations of the present setup, 5% tunability was achieved. The QO gyrotron designed for operation at the fundamental frequency exhibits simultaneous emission at 100 GHz (fundamental) and 200 GHz (second harmonic). For a beam current of 4 A, 20% of the total rf power is emitted at the second harmonic.

Ideal stability of cylindrical plasma in the presence of mass flow

The ideal stability of cylindrical plasma with mass flows is investigated using the guiding center plasma (GCP) model of Grad [Proceedings of the Symposium on Electromagnetic and Fluid Dynamics of Gaseous Plasmas (Polytechnic Inst. of Brooklyn, New York, 1961), p. 37]. For rotating plasmas, the kinetic treatment of the parallel motion in GCP gives significantly different results from the fluid models, where the pressures are obtained from equations of state. In particular, GCP removes the resonance with slow magnetoacoustic waves and the loss of stability that occurs in magnetohydrodynamics (MHD) for near‐sonic flows. Because of the strong kinetic damping of the sound waves in an isothermal plasma, the slow waves have little influence on plasma stability in GCP at low beta. In the large aspect ratio, low‐beta tokamak ordering, Alfvenic flows are needed to change the ideal GCP stability significantly. At lowest order in the inverse aspect ratio, flow can be favorable or unfavorable for stability of local m...

Theory of quasioptical gyrotrons and gyroklystrons operating at higher harmonics of the cyclotron frequency

A multimode, non-linear, time-dependent formulation of the theory of quasioptical electron cyclotron masers operating at high gyrofrequency harmonics is presented. Linear calculations of the starting current and numerical analyses of the efficiency of the devices are performed. It is shown that with suitable contouring of the DC magnetic field, a stable single mode operation at the second harmonic is possible. To improve the efficiency, an alternative configuration, the quasioptical gyroklystron, is also analysed using single mode and multimode dynamics simulations. The gyroklystron operating at the second harmonic is shown to lead to a significant increase in efficiency (approximately 30%).

Multimode theory and simulation of quasioptical gyrotrons and gyroklystrons

Very high power sources for millimeter wavelength radiation are desired for cyclotron heating of magnetic fusion devices. To meet this goal a quasioptical gyrotron has recently been proposed and analysed using a single mode approach. In this work, a more realistic analysis of the quasioptical gyrotron is carried out using multimode time-dependent simulations to study mode competition in a highly overmoded cavity. It is shown that with suitable contouring of the DC magnetic field, single mode operation at 30% or greater efficiency is possible. To further improve on efficiency, an alternative configuration, the quasioptical gyroklystron, is also analysed using multimode dynamic simulations. The gyroklystron is shown to lead to a significant increasing in efficiency (≈xa045%), particularly at moderate values for the high frequency electric field. Similar analyses of the quasioptical gyrotron and gyroklystron operating on the second harmonic have shown promising results ; efficienciesxa0≈xa030% have been obtained f...

Quasiperiodic forcing and the observability of strange nonchaotic attractors

Quasiperiodically forced nonlinear dynamical systems may exhibit strange nonchaotic attractors. We argue that these attractors occur in a Cantor set of positive Lebesque measure in parameter space. Furthermore, we show that strange nonchaotic attractors have a distinctive frequency spectrum thus making them potentially observable in experiments.

Oscillating Magnetic Islands in a Rotating Plasma

The nonlinear evolution of tearing modes in the presence of sheared mass flow is studied as an initial value problem. Under certain conditions, when the mode is driven unstable primarily by the mass flow, the nonlinear evolution leads to a dynamic state in which the size and shape of the magnetic islands are oscillatory.