Large Ion Larmor Radius Research Articles

Ion Landau damping and drift tearing modes

Kinetic treatments of drift tearing modes that match an inner, resonant layer solution to an external magnetohydrodynamic (MHD) solution, characterised by $\unicode[STIX]{x1D6E5}^{\prime }$, can fail to match the ideal MHD boundary condition on the parallel electric field, $E_{\Vert }=0$. In this paper we demonstrate how consideration of ion sound and ion Landau damping effects achieves this, placing the theory on a firm footing. These effects are found to modify the effective critical $\unicode[STIX]{x1D6E5}^{\prime }$ for instability of drift tearing modes, in particular for weak electron temperature gradients. The implications for a realistic hot plasma resonant layer model – involving large ion Larmor radius and semi-collisional electron physics (Connor et al., Plasma Phys. Control. Fusion, vol. 54, 2012, 035003) – are determined.

Scaling and stabilization due to the large ion Larmor radius (LLR) effects in plasma focus devices

Empirical and theoretical relationships based on the model developed by S Lee and the scaling laws observed in plasma focus (PF) devices are considered for determining the optimal regime of operation, where the large Larmor radius (LLR) effects would play a significant role in the reduction of the growth rate of the m=0 mode in the pinch column. That is, a range of values for the current of the pinch, the energy of the generator, the anode radius and an average filling pressure. On the other hand, it is found that the PFs in which enhanced stability could be observed, owing to LLR effects, are restricted to devices operating in a range of storage energy that goes from a few hundreds of joules to few kilojoules. Experimental results obtained in a PF with storage energy of the order of 400 J are discussed.

The large-Larmor-radius Rayleigh–Taylor instability

The effect of a large ion Larmor radius on the Rayleigh–Taylor instability is investigated using the Vlasov fluid model. The results are compared with an ideal magnetohydrodynamic model. It is found that this effect reduces the growth rate of the Rayleigh–Taylor instability with respect to the ideal magnetohydrodynamic growth rate.

Attainment of large ion Larmor radius (LLR) conditions in a compressional Z-pinch

A simple model that allows us to find the optimal conditions, regarding stability, for operation of a compressional pinch is presented. The implosion is represented by a snowplough model with a linearly rising current. We conclude that the time for the pinch to reach the compressed state is significantly prolonged if the pinch is operated in the large ion Larmor radius (LLR) regime while the ion Hall parameter is larger than one.

Large Larmor radius stability of the z pinch.

The linear m=0 stability of the z pinch in the collisionless, large ion Larmor radius regime is examined using the Vlasov fluid model. The results reveal a strong equilibrium dependence. The uniform current density equilibrium shows a reduction in growth rate when the average ion Larmor radius is about one-fifth of the pinch radius. However, finite Larmor radius effects cannot in themselves produce a stabilized z pinch.

Sub-Alfvénic plasma expansion

A large ion Larmor radius plasma undergoes a particularly robust form of Rayleigh–Taylor instability when sub-Alfvénically expanding into a magnetic field. Results from an experimental study of this instability are reported and compared with theory, notably a magnetohydrodynamic (MHD) treatment that includes the Hall term, a generalized kinetic lower-hybrid drift theory, and with computer simulations. Many theoretical predictions are confirmed while several features remain unexplained. New and unusual features appear in the development of this instability. In the linear stage there is an onset criterion insensitive to the magnetic field, initial density clumping (versus interchange), linear growth rate much higher than in the ‘‘classic’’ MHD regime, and dominant instability wavelength of order of the plasma density scale length. In the nonlinear limit free-streaming flutes, apparent splitting (bifurcation) of flutes, curling of flutes in the electron cyclotron sense, and a highly asymmetric expansion are found. Also examined is the effect on the instability of the following: an ambient background plasma (that adds collisionality and raises the expansion speed/Alfvén speed ratio), magnetic-field line tying, and expansion asymmetries (that promotes plasma cross-field jetting).

Boundary Larmor radius effect on electrostatic waves

The linearized Vlasov–Poisson equations, which combine to an integrodifferential equation for the perturbed electric potential, are used to investigate the effect of finite plasma size on the stability of electrostatic waves in a homogeneous plasma slab. The distortion of the gyromotion of the particles at the plasma boundary influences wave stability, a phenomenon termed the boundary Larmor radius (BLR) effect. The integrodifferential equation, treated as an eigenvalue problem, is discretized into a matrix dispersion equation by use of the Galerkin method and is then solved numerically. It is found that the ion Bernstein wave, which is undamped in an infinite homogeneous plasma, now becomes damped with a maximum damping rate of 0.35 ωci at rG/L (ion Larmor radius over wall distance)≊0.15. In general, the damping is less pronounced at shorter perpendicular wavelengths. It implies a necessity to take into account the BLR effect in the kinetic stability studies for sufficiently large ion Larmor radius in comparison to the characteristic dimension.

Rayleigh–Taylor instability of a plasma–vacuum boundary in the limit of a large Larmor radius

The Rayleigh–Taylor instability of a plasma–vacuum boundary is studied with the aid of an ideal one-fluid Hall model corresponding to the limit of a large ion Larmor radius. The global Rayleigh–Taylor instability mode, whose growth rate is Γ(k)=(gk)1/2, still exists in this case, but is not necessarily the dominating one. The exact upper bound for the growth rates of all the other instability modes is found in the low-beta limit. For large wave numbers the growth rate of the fastest instability mode is estimated as Γmax(k)=gk/Ωi.

Theory and simulation of the Rayleigh-Taylor instability in the large Larmor radius.

The theory and first nonlinear simulations of the Rayleigh-Taylor instability in the limit of large ion Larmor radius are presented. It is shown that in the limit of large Larmor radius, the Rayleigh-Taylor instability evolves much faster and in a dramatically different manner than in the limit of small Larmor radius.

Large-Larmor-radius interchange instability.

We observe linear and nonlinear features of a strong plasma/magnetic field interchange Rayleigh-Taylor instability in the limit of large ion Larmor radius. The instability undergoes rapid linear growth culminating in free-streaming flute tips.

On the Vlasov fluid stability of the m = 0 mode in a pure Z pinch

The possibility of using the Vlasov fluid model to describe large ion Larmor radius effects in a Z pinch is discussed. It is shown that the Vlasov fluid formulation can be applied to the m = 0 mode, but the comparison theorem which states that systems which are MHD stable are also Vlasov fluid stable, is shown to be inapplicable in this case.

Ion beam formation in an m = 0 unstable Z pinch

It is well known both in early Z-pinch experiments and more recently in plasma focus experiments that highly accelerated ion beams are formed, this being inferred from the axial centre-of-mass motion of the neutrons produced by nuclear reactions. Two acceleration mechanisms are discussed here. The first, proposed in ref. 1, concerns the acceleration of ions across an electrostatic sheath adjacent to the anode, this sheath having a thickness less than an ion Larmor radius but greater than an electron Larmor radius. The electrons in the sheath, being magnetised, have a c E × B/B 2 drift through which the J r B θ force is provided to satisfy momentum conservation. The second is a new mechanism arising from the occurrence of a violent m = 0 instability, and relies on large ion Larmor radius effects. It is shown that the inclusion of the Hall terms and finite ion Larmor radius (FLR) terms in the MHD equations removes the mirror symmetry each side of an m = 0 neck. A detailed consideration of particle orbits during the formation of the highly compressed neck shows that on the cathode side of the neck an energetic ion beam is formed close to the axis, whilst on the anode side an equal and opposite momentum is distributed among a larger number of ions throughout the cross-section.

Corrections to “Flute instability of an axially-symmetric plasma with a finite ion Larmor radius”

Even in the case of a large ion Larmor radius, the first mode of flute perturbations is unstable (for arbitrary distributions of the pressure and density of the plasma).