Finite Larmor Radius Stabilization Research Articles

Resonant particle effects on finite Larmor radius stabilization

It is shown that the threshold for instability of a one-dimensional Vlasov-fluid screw pinch is identical to that in ideal magnetohydrodynamics, for arbitrary ion gyroradius. That is, there is no absolute finite Larmor radius stabilization, although the growth rates for the Vlasov-fluid model can be much lower. It is the ions in resonance with the real part of the mode frequency which are responsible for maintaining the instability beyond the value of ρi/a for which ’’finite Larmor radius stabilization’’ would have occurred. An analytical expression for the growth rate near the marginal point is derived using the finite Larmor radius expansion. The expression exhibits the expected scaling with β and Larmor radius.

Finite Larmor radius equations in an arbitrary near-theta pinch geometry

A set of fluid-like equations is derived which describes the stability of a diffuse, high β, arbitrary, near-ϑ pinch configuration. The equations simultaneously include geometric effects which drive ideal magnetohydrodynamic instabilities and kinetic effects which give rise to finite Larmor radius stabilization. A simple heuristic procedure is given for determining these equations in addition to a full derivation starting from basic principles.

Electric field driven flute instabilities in a nonuniform collisional plasma

The stability of a magnetically confined nonuniform plasma column with a radial electric field is examined with a linear single-fluid theory including the effects of rotation, ion-neutral collisions and finite Larmor radius stabilization. The transition from the Rayleigh-Taylor instability in the collisionless limit to the Simon neutral-drag instability in the collision-dominated limit, and the effect of collisions on finite Larmor radius stabilization, is studied in detail. A numerical example is given and the application of the theory to experiments is discussed.

Application of Finite Larmor Radius Equations for Collisionless Plasmas to a θ Pinch

Using finite Larmor radius equations developed in an earlier paper the stability of an arbitrary β rotating θ pinch with straight lines of force in equilibrium is worked out in detail. The resulting differential equation together with boundary conditions and the specification of radial density profiles yields an eigenvalue problem which is solved with the aid of a computer. The results obtained show that an m = 1 rotational instability can occur in a θ pinch and that finite Larmor radius stabilization of this mode is present. It is also found that the rotating plasma should be stable to perturbations with an axial wavelength ≲ 1 m. This provides an explanation of why long θ pinches tend to go unstable uniformly along their length. Finite Larmor radius stabilization is critically dependent on the radial density profile, the steeper gradient favoring stability. Results are also presented showing how a large parallel temperature and shear in the axial flow can modify the rotational instability.

Stability of a Bulged Theta Pinch

An experimental and theoretical study has been made of the hydromagnetic instability of an axisymmetric bulged region in the midplane of a theta pinch 8 m long. The bulged region was generated adiabatically after the initial implosion in such a way that it fulfilled most of the assumptions of the theoretical model; in particular, it was free of end effects for the time of observation. At a filling pressure of 20 m Torr D2 and with a peak magnetic field of 20 kG the plasma, which was collision dominated, had values of temperature, density, and beta on the axis of 120 eV, 3 × 1016cm−3, and 0.7 ± 0.2. The predicted m = 1 instability was observed and for a range of bulge amplitudes its measured growth and propagation along the column agreed to within a factor of less than 2 with the theoretical values. It is concluded that the m = 1 instability of such bulged plasmas is well described by ideal hydro-magnetic theory. Modes with m ≥ 2 were not observed during the m = 1 growth and their absence is attributed to finite Larmor radius stabilization.

Stabilization of a Stellarator Plasma by Finite-Larmor-Radius and Ion-Ion-Collision Effects

The magnetic field, Bc, for onset of nonreproducible fluctuations in stellarator afterglows varies with ion mass as mi0.44. For ion viscous stabilization of drift waves Bc ∼ mi⅜; for finite ion Larmor radius or ion cyclotron frequency stabilization, Bc ∼ mi½.

Resistive Overstabilities and Anomalous ``Diffusion''

A physical picture is given of microinstabilities which can occur in plasmas of finite resistivity with or without an effective gravitational field, and of finite Larmor radius stabilization. The drift waves become overstable because of a phase shift between the density and potential fluctuations. Transport of plasma across a magnetic field also arises from this phase shift; this transport does not necessarily resemble a diffusion process. This mechanism may account for the ``anomalous diffusion'' commonly observed in fully ionized plasmas. Particular attention is paid to the real part of the frequency and to the phase correlations, which can easily be measured to test this hypothesis. In regard to stellarator ``pumpout'', it is found that increasing the conductivity will not reduce the part of the loss rate which is due to the ``universal'' resistive overstability.

Theory of the flute instability in mirror machines

The flute instability of a low β and neutral plasma contained in a mirror machine is investigated. The particle motion in a real mirror field is fully taken into account by using a Hamiltonian method for the solution of the Vlasov equation. An eigenvalue equation is obtained for the potential of the flute-like perturbation assuming an arbitrary radial dependence of plasma density and of the electron and ion energies. Using a variational method, the eigenvalue equation has been discussed in detail for a plasma with no energy gradients. The stability condition has been calculated taking into account terms up to second order in Larmor radius. Finite Larmor radius stabilization is effective for the higher-order modes and cold electron plasmas. The lowest mode, k = 1, is practically not stabilized by finite Larmor radius effects. The discussion of the eigenvalue equation with finite energy gradients has been limited to the case of a hot electron plasma surrounded by a sheath of cold plasma. If the density of the cold plasma is an order of magnitude higher than the density of the hot plasma, the system is stable at all densities. The stabilization is due to the high dielectric constant of the cold plasma.

Remarks on the finite larmor radius stabilization theory for mirror machines

Several existing theoretical treatments of the low-frequency drift instability for low β and low-density plasmas in mirror machines are compared. We point out the importance of boundary conditions, and show that finite Larmor radius stabilization is important for the m = 1 mode. The equation for the electrostatic potential for high densities is solved for some ratios a/r0 of the Larmor radius to the plasma radius. It is found that in the Phoenix experiment, under the present operating conditions, a ratio of a/r0 ⩾ 0.5, corresponding to the field of ⩽5 kG is sufficient for stability.

Remarks on the finite Larmor radius stabilization theory for mirror machines

Several existing theoretical treatments of the low-frequency drift instability for low β and low-density plasmas in mirror machines are compared. We point out the importance of boundary conditions, and show that finite Larmor radius stabilization is important for the m = 1 mode. The equation for the electrostatic potential for high densities is solved for some ratios a/r0 of the Larmor radius to the plasma radius. It is found that in the Phoenix experiment, under the present operating conditions, a ratio of a/r0 ≥ 0.5, corresponding to the field of ≤5 kG is sufficient for stability.

Rotational Instability in the Theta Pinch

An experimental study of the rotation and associated instability was made in a theta pinch with a peak field of 85 kG reached in 2.3 μsec. The starting deuterium gas pressure was in the range 50–150 μ Hg, and for operation on the second half-cycle of the sinusoidal driving field the magnetic flux trapped within the plasma varied between ±100 kMx. In most conditions the circular cross section of the plasma became perturbed along its length by the growth of two flutes which rotated at an angular velocity of up to 6 × 107 rad/sec. It is deduced from measurements on the rotation that the plasma acquires its angular momentum at the start of the half-cycle, and the results are interpreted on the basis that the angular momentum is initially in a diamagnetic (azimuthal) ion current. A model is described for establishing this current as a consequence of contact between the plasma and the walls. Results on the time of onset of the instability, and on the growth rate of the flutes, point to the existence of some damping or stabilizing process; it is found that field diffusion, or a rapid axial contraction of the plasma (due to closed reversed field loops), can lead to instability, and when these are reduced the stable time is increased. The possible influence of finite Larmor radius stabilization is discussed. The stability condition, originally derived for low β but recently shown to have more general validity, is in qualitative agreement with the results.

Rotation and instability of plasma in fastBzcompression experiments

The phenomena of rotation and subsequent instability of plasma in fast compression (thetapinch) devices is discussed in the light of present stability theory including finite Larmor radius effects (Rosenbluth et al., 1961). For the rotation to be unstable the plasma must possess an angular momentum exceeding that appropriate to the ion diamagnetic current and it is suggested that this is acquired as a result of a secondary process occurring as the plasma leaves the wall. It is shown that when this process is taken into account the theory is adequate to explain most observed phenomena and suggests others which might be investigated. In the Appendix to this paper the theory of finite Larmor radius stabilization is interpreted in terms of a hydrodynamic picture. This analysis is not rigorous but does suggest that the stability criteria, originally derived for a specific model, might have more general validity.