Gerard Van Hoven

Stability of a diffuse linear pinch with axial boundaries

A formulation of the stability behavior of a finite‐length pinch is presented. A general initial perturbation is expressed as a uniformly convergent sum over a complete discrete k set. A variational calculation is then performed, based on the energy principle, in which the end‐boundary conditions appear as constraints. The requisite Lagrange multipliers mutually couple the elemental periodic excitations. The resulting extended form of δW still admits a proper second‐variation treatment so that the minimization and stability considerations of Newcomb remain applicable. Comparison theorems are discussed as is the relevance of this end‐effect model to the stability of solar coronal loops.

Solar flares and plasma instabilities: Observations, mechanisms and experiments

In this review the plasma-physics basis for the solar flare phenomenon is treated from three different perspectives. The discussion begins at the sun with a brief enumeration of the plasma-relevant observations and what they indicate about ambient physical conditions and possible flare mechanisms. Next, theoretical descriptions are presented of several models which have been suggested to explain these characteristics, with particular emphasis given to those processes involving magnetic field reconnection. In this context resistive tearing, the most pervasive slow magnetohydrodynamic instability, is treated at some length, and its time-scale and energy-output properties are described. Finally, the discussion ends in the laboratory, with a review of the progress of a number of experiments designed to simulate solar flares.

Behavior of the sideband instability

The mechanism of the trapped−electron instability of a large−amplitude wave is revealed by the following experimental observations: Sideband waves exhibit an initial enhanced damping (examined by the use of linear test excitations) for a distance ∼λb′ the large−wave oscillation length. Beyond this point, the unstable waves grow with a rate linearly proportional to the main−wave electric potential. Measurements show that the instability growth depends on the initial amplitude of the large wave and can persist after this wave field has decayed by tens of decibels. This implication that the driving force of the instability resides in the particles is substantiated by direct measurements of the electron distribution function which, in the presence of a large wave, is found to develop a ’’bump−on−the−tail’’ of sufficient magnitude to account for the observed sideband growth.

Resistive magnetic tearing in a finite length pinch

The effects of axial boundary conditions on the tearing mode of a cylindrical pinch are described. A flexible inertial ’’line‐tying’’ model is used to restrict the available perturbations of a force‐free current‐channel equilibrium, similar to that in a reversed‐field pinch. The resistively unstable mode is found to be azimuthally symmetric (m = 0), and the external (ideal) and internal (resistive) solutions are detailed, the latter being found by a unique numerical procedure. The solutions can be either ’’constant‐ψ’’ or fast growing, depending on the width of the current channel. Threshold behavior and subsequent growth rates are calculated. Finally, an application of this reconnection mechanism to the flare instability of a narrow solar coronal loop is described.

Observations of harmonic dispersion and sideband coupling in a plasma

Experiments with large−amplitude electron−wave signals demonstrate the existence of nonlinear Floquet−Bloch harmonics and of a passive four−wave coupling interaction. Propagation of the first spatial−temporal harmonic is verified by direct dispersion measurements. The parametric process acts to couple test−wave excitations at nearby frequencies symmetric about a high−level pump. Several possible models for this effect are examined, and it is shown that a four−wave mode−coupling process provides the only consistent explanation. The observed passive interaction operates at spatial positions and at pump−wave levels preceding the turn−on of the trapped−electron sideband instability, and also in the presence of detrapping interference. These results indicate the indifference of the four−wave mechanism to particle trapping, and lead to the inference that the unstable electron sidebands must also be coupled by this competing nonlinear process. Implications of this conclusion for studies of the sideband instabili...

Hydromagnetic stability of coronal arcade structures The effects of photospheric line tying

A model is given of the magnetic-field equilibrium and possible dynamic excitations of a solar coronal arcade. Such structures are well observed in the spectral range from Hα to X-rays and often give rise to two-ribbon flares. However, the preflare state must be stable to ideal magnetohydrodynamic disturbances, and we treat this problem with particular attention to the necessary foot-point boundary conditions. Having devised a reasonably general perturbation set, we use an energy-principle analysis to show the strong stabilizing influence of inertial field-line tying at the photosphere.

Simulations of coronal disconnection events

The lack of evidence for magnetic disconnection of coronal mass ejections (CMEs) from the Sun has long been a puzzle, as it implies a buildup of the interplanetary magnetic field (IMF) magnitude over time. Such a buildup is ruled out by observations. Magnetic reconnection above helmet streamer configurations could provide a mechanism for maintaining the observed relative constancy of the IMF [McComas et al., 1989]; McComas et al. [1991] showed observational evidence of reconnection above a streamer. We investigate this interpretation using time-dependent MHD simulations. We model the opening of new magnetic flux on the Sun (as might occur in a CME or other transient event) as an increase in magnetic flux at the poles of a simulated corona. We find that this perturbation can in fact cause reconnection above an equatorial helmet streamer, and the resultant density signature is similar to the observations of McComas et al. [1991].

High conductivity magnetic tearing instability

The field‐reconnection instability of a magnetic neutral sheet is studied using magnetohydrodynamic theory, including the electron‐inertia term in Ohm’s law. The behavior is described for the full range of the Coulomb‐resistivity vs collisionless skin‐depth parameter ζ=1020.3B T1.5/lnΛ) a2.5 n2.3 (cgs), describing the field reversal. Such long‐wavelength tearing can occur over a wide span of physical conditions from those of solar active regions (ζ≪1) to those in the geomagnetic tail (ζ≫1). In particular, the growth rate of the infinite‐conductivity instability may be expressed as ω≈1020.9B/a2.5n1.3, for a hydrogen plasma. In this limit, the time scale of auroral development is found to be 103.2 sec, a value close to that observed. The regime of applicability of this formulation is also discussed, and the results are compared with those obtained by other methods, including the Vlasov equation.

Direct nonlinear coupling of electromagnetic waves and electrostatic waves in a plasma: Theory

Nonlinear coupling among small amplitude electromagnetic and electrostatic waves in a cylindrical plasma‐column waveguide is analyzed theoretically. The warm plasma equations of motion, in the displacement/polarization format, are combined with the wave equation for guided transverse magnetic waves to derive the system dispersion relation and the coupled‐mode equations for this configuration. The coupling coefficients predict the strength of a given multiwave interaction from the intrinsic properties of the plasma waveguide. When the frequency selection rule is satisfied, for wave numbers consistent with the system dispersion relation, off‐resonance excitation will occur if the interaction is confined to a finite length of the waveguide. Typical interaction resonances are illustrated on the system dispersion diagram by an experimentally useful graphical construction. Numerical estimates of the coupling strengths of selected three‐wave “scattering” and “radiation” interactions are made from data obtained w...

RESISTIVE INSTABILITY OF THE SHEET PINCH.

An investigation of the linear “tearing mode” instability of the sheet pinch with uniform resistivity is described. A first integral of the coupled perturbation equations for magnetic fields and fluid velocities is used to find constraints on the growth rate which detail the possible regimes of instability. The existence of pure exponential growth for long wavelengths is shown explicitly in two examples.