Volume 20, Issue 5, May 2013

RayleighTaylor (RT) instabilities at interfaces of disparate mass densities have long been known to generate magnetic fields during inertial confinement fusion implosions. An externally applied magnetic field can also be efficiently amplified by RT instabilities. The focus here is on magnetic field generation and amplification at the gasice interface which is RT unstable during the deceleration phase of the implosion. RT instabilities lead to undesirable mix of hot and cold plasmas which enhances thermal energy loss and tends to produce a more massive warmspot instead of a hotspot. Two mechanisms are shown here to mitigate the thermal energy loss from the hotspot. The first mechanism is the reduction of electron thermal conductivity with interfacealigned magnetic fields. This can occur through selfgenerated magnetic fields via the Biermann battery effect as well as through externally applied magnetic fields that undergo an exponential growth via the stretchandfold magnetohydrodynamic dynamo. Selfgenerated magnetic fields during RT evolution can result in a factor of decrease in the electron thermal conductivity at the gasice interface, while externally applied magnetic fields that are compressed to T at the onset of deceleration (corresponding to preimplosion external fields of T) could result in a factor of reduction in electron thermal conductivity at the gasice interface. The second mechanism to mitigate thermal energy loss from the hotspot is to decrease the interface mixing area between the hot and cold plasmas. This is achieved through large external magnetic fields of 1000 T at the onset of deceleration which damp shortwavelength RT modes and longwavelength KelvinHelmholtz modes thus significantly slowing the RT growth and reducing mix.
 ARTICLES

 Basic Plasma Phenomena, Waves, Instabilities

The expansion of a collisionless plasma into a plasma of lower density
View Description Hide DescriptionThis paper considers the asymptotic and numerical solution of a simple model for the expansion of a collisionless plasma into a plasma of lower density. The dependence on the density ratio of qualitative and quantitative features of solutions of the wellknown coldion model is explored. In the coldion limit, we find that a singularity develops in the ion density in finite time unless the density ratio is zero or close to unity. The classical coldion model may cease to be valid when such a singularity occurs and we then regularize the model by the finite iontemperature VlasovPoisson system. Numerical evidence suggests the emergence of a multimodal velocity distribution.

Fivefield simulations of peelingballooning modes using BOUT++ code
View Description Hide DescriptionThe simulations of edge localized modes (ELMs) with a 5field peelingballooning (PB) model using BOUT++ code are reported in this paper. In order to study the particle and energy transport in the pedestal region, the pressure equation is separated into ion density and ion and electron temperature equations. Through the simulations, the length scale Ln of the gradient of equilibrium density is found to destabilize the PB modes in ideal MHD model. With ion diamagnetic effects, the growth rate is inversely proportional to at medium toroidal mode number n. For the nonlinear simulations, the gradient of in the pedestal region can more than double the ELM size. This increasing effect can be suppressed by thermal diffusivities , employing the flux limited expression. Thermal diffusivities are sufficient to suppress the perturbations at the top of pedestal region. These suppressing effects lead to smaller ELM size of PB modes.

Large amplitude inertial compressional Alfvénic shock and solitary waves, and acceleration of ions in magnetohydrodynamic plasmas
View Description Hide DescriptionLarge amplitude inertial compressional Alfvénic shock and solitary waves in magnetohydrodynamic plasmas are investigated. Dispersive effect caused by nonideal electron inertia currents perpendicular to the ambient magnetic field can balance the nonlinear steepening of waves leading to the formation of a soliton. A Sagdeevpotential formalism is employed to derive an energybalance like equation. The range of allowed values of the soliton speed, M (Mach number), plasma β (ratio of the plasma thermal pressure to the pressure in the confining magnetic field), and electron inertia, wherein solitary waves may exist, are determined. Depth of the potential increases with increasing the Mach number and plasma β, however decreases with the increasing electron inertia. The height of soliton increases with increasing in Mach number and decreases with plasma β. And with increasing electron inertial length, the width of soliton increases. The electronion collisional dissipation results a dissipative inertial compressional Alfvén wave, which can produce a shock like structure and can efficiently accelerate ions to the order of the local Alfvén velocity. The shock height increases with the increasing collision frequency, but shock height decreases with increasing plasma β.

Ohmic losses in coaxial resonators with longitudinal innerouter corrugation
View Description Hide DescriptionIn this paper, a coaxial resonator with longitudinal innerouter corrugation is introduced. Its eigenequation and expression of ohmic losses are derived. Ohmic losses in the cavity are investigated. Results show that ohmic losses in the outer and inner conductors share a similar variation trend, while the former is larger than the later. What's more, changes of the inner and outer slot depth and width induce different variations of ohmic losses on the surface of the inner and outer conductors.

Magnetic piston model for higher ion charge and different electron and ion plasma temperatures
View Description Hide DescriptionA new formula for the magnetic piston model, which explicitly describes how the momentum imparted to the ions by the magnetic pressure depends not only on the ion mass but also on the ion charge, as well as, on the plasma electron and ion temperatures, is derived following Rosenbluth's classical particlefield selfconsistent plane approximation analytic calculation. The formula presented in this paper has implications in explaining the experimentally observed separation of the ions of different species and charges by the magnetic field penetrating the plasma and specularly reflecting them.

Linear and nonlinear dynamics of electron temperature gradient mode in nonMaxwellian plasmas
View Description Hide DescriptionThe effect of nonMaxwellian distributed ions on electron temperature gradient mode is investigated. The linear dispersion relation of mode is obtained which shows that the behavior of this mode changes in the presence of superthermal ions. The growth rate of mode driven linear instability is found and is observed to modify due to nonthermal ions. However, it is found that this leaves the electron energy transport coefficient unchanged. In the nonlinear regime, a dipolar vortex solution is derived which indicates that the dynamic behavior of the vortices changes with the inclusion of kappa distributed ions. The importance of present study with respect to space and laboratory plasmas is also pointed out.

Multiwaterbag models of ion temperature gradient instability in cylindrical geometry
View Description Hide DescriptionIon temperature gradient instabilities play a major role in the understanding of anomalous transport in core fusion plasmas. In the considered cylindrical geometry, ion dynamics is described using a driftkinetic multiwaterbag model for the parallel velocity dependency of the ion distribution function. In a first stage, global linear stability analysis is performed. From the obtained normal modes, parametric dependencies of the main spectral characteristics of the instability are then examined. Comparison of the multiwaterbag results with a reference continuous Maxwellian case allows us to evaluate the effects of discrete parallel velocity sampling induced by the MultiWaterBag model. Differences between the global model and local models considered in previous works are discussed. Using results from linear, quasilinear, and nonlinear numerical simulations, an analysis of the first stage saturation dynamics of the instability is proposed, where the divergence between the three models is examined.

Long wavelength gradient drift instability in Hall plasma devices. II. Applications
View Description Hide DescriptionHall plasma devices with electron E × B drift are subject to a class of long wavelength instabilities driven by the electron current, gradients of plasma density, temperature, and magnetic field. In the first companion paper [Frias et al., Phys. Plasmas 19, 072112 (2012)], the theory of these modes was revisited. In this paper, we apply analytical theory to show that modern Hall thrusters exhibit azimuthal and axial oscillations in the frequency spectrum from tens KHz to few MHz, often observed in experiments. The azimuthal phase velocity of these modes is typically one order of magnitude lower than the E × B drift velocity. The growth rate of these modes scales inversely with the square root of the ion mass, . It is shown that several different thruster configurations share the same common feature: the gradient drift instabilities are localized in two separate regions, near the anode and in the plume region, and absent in the acceleration region. Our analytical results show complex interaction of plasma and magnetic field gradients and the E × B drift flow as the sources of the instability. The special role of plasma density gradient is revealed and it is shown that the previous theory is not applicable in the region where the ion flux density is not uniform. This is particularly important for near anode region due to ionization and in the plume region due to diverging ion flux.

Geometrical parameters effects on local electric field enhancement of silverdielectricsilver multilayer nanoshell
View Description Hide DescriptionThe local electric field enhancement at different points of silverdielectricsilver nanoshell is investigated using quasistatic theory. Because of the symmetric and antisymmetric coupling between surface plasmon of inner silver core and outer silver shell, the local electric field spectrum of silverdielectricsilver has two distinct peaks at resonance wavelengths. The silver core size and middle dielectric thickness affect the local electric field enhancement at different points of silverdielectricsilver nanoshell. Increasing the silver core radius always leads to blue shift of shorter resonance wavelength and red shift of longer resonance wavelength. We observed two distinct local electric field peaks, which are corresponded to the symmetric and antisymmetric coupling between inner and outer surface plasmons. In a system with thick silver shell, local electric field enhancement is greater than a system with thin silver shell. However, the local electric field variations as a function of silver core radius in both systems are different at different points of nanoshell. The effects of the dielectric thickness variations on local electric field are different from those from silver core size variations. As the dielectric thickness is about 3 nm, the highest local electric field enhancement occurs at the surface of the inner silver core, where the symmetric and antisymmetric modes are mixed together.

Gyrokinetic studies of microinstabilities in the reversed field pinch
View Description Hide DescriptionAn analytic equilibrium, the Toroidal Bessel Function Model, is used in conjunction with the gyrokinetic code GYRO to investigate the nature of microinstabilities in a reversed field pinch plasma. The effect of the normalized electron plasma pressure β on the characteristics of the microinstabilities is studied. At a β of 4.5%, a transition between an ion temperature gradient (ITG) and a microtearing mode is observed. Suppression of the ITG mode occurs as in the tokamak, through coupling to shear Alfvén waves, with a critical β for stability higher than its tokamak equivalent due to a shorter parallel connection length. A steep dependence of the microtearing growth rate on the temperature gradient suggests high profile stiffness. There is evidence for a collisionless microtearing mode. The properties of this mode are investigated, and it is found that electron curvature drift plays an important role in the instability.

Bifurcations of nonlinear ion acoustic travelling waves in the frame of a ZakharovKuznetsov equation in magnetized plasma with a kappa distributed electron
View Description Hide DescriptionBifurcations of nonlinear propagation of ion acoustic waves (IAWs) in a magnetized plasma whose constituents are cold ions and kappa distributed electron are investigated using a two component plasma model. The standard reductive perturbation technique is used to derive the ZakharovKuznetsov (ZK) equation for IAWs. By using the bifurcation theory of planar dynamical systems to this ZK equation, the existence of solitary wave solutions and periodic travelling wave solutions is established. All exact explicit solutions of these travelling waves are determined. The results may have relevance in dense space plasmas.

Frequency shift of the propagating ultraintense field in a plasma with a fraction of electronpositron pairs under the conditions of response saturation
View Description Hide DescriptionA model is derived from the Maxwell and fluid dynamics equations to describe the interactions between a relativistically intense electromagnetic wave and a cold unmagnetized plasma composed of an electronion background and a fraction of electronpositron pairs. Combining the envelope approximation for the propagating field and the quasistatic treatment of the plasma dynamics, the model sustains fully nonlinear planewave solutions and shows that saturation of the plasma response occurs at ultrarelativistic intensities of the incident field even for pair concentrations far below those of the electronion background. Stability of the electromagnetic wave under the saturation conditions is demonstrated and an expression is derived to link its interactioninduced frequency shift to the concentration of the electronpositron pairs.

Spontaneous electromagnetic fluctuations in unmagnetized plasmas. II. Relativistic form factors of aperiodic thermal modes
View Description Hide DescriptionGeneral expressions for the electromagnetic fluctuation spectra in unmagnetized plasmas are derived using fully relativistic dispersion functions and form factors for the important class of isotropic plasma particle distribution functions including in particular relativistic Maxwellian distributions. In order to obtain fluctuation spectra valid in the entire complex frequency plane, the proper analytical continuations of the unmagnetized form factors and dispersion functions are presented. The results are illustrated for the important special case of isotropic Maxwellian particle distribution functions providing in particular the thermal fluctuations of aperiodic modes. No restriction to the plasma temperature value is made, and the electromagnetic fluctuation spectra of ultrarelativistic thermal plasmas are calculated. The fully relativistic calculations also provide more general results in the limit of nonrelativistic plasma temperatures being valid in the entire complex frequency plane. They complement our earlier results in paper I and III of this series for negative values of the imaginary part of the frequency. A new collective, transverse, damped aperiodic mode with the damping rate is discovered in an isotropic thermal electronproton plasma with nonrelativistic temperatures.

Collisional effect on the Weibel instability with the biMaxwellian distribution function
View Description Hide DescriptionIn this paper, the Coulomb collision effect of electronion is investigated based on the equilibrium biMaxwellian anisotropic distribution function in dense and unmagnetized plasma. An analytical expression is derived for the real frequency and the growth rate of the Weibel instability for two limiting cases and . In the limit , the quantity η that is due to a collisional term will appear in the growth and condition of the rate of the Weibel instability, which leads to a constraining condition of the growth rate. When η increases, the growth rate will increase and the wave instability will be distant from its own damping mode.

Resistive instability in a Hall plasma discharge under ionization effect
View Description Hide DescriptionA systematic study is presented for low frequency resistive instability in a Hall plasma discharge under the effect of collisions, ionization, and finite temperature of ions and electrons by considering finite axial wave number. For this, a two dimensional dispersion equation is derived and solved numerically. Analytical calculations are also performed for obtaining the expression of growth rate and to discuss the limiting cases of equal axial ( ) and azimuthal ( ) wave numbers. The instability with higher growth rate is realized in the presence of ionization; the same is the case for equal wave numbers ( ). However, the instability is suppressed when the ions and electrons carry higher temperatures, and weak effect of the electron temperature is observed for the case .

Second harmonic effect on geodesic modes in tokamak plasmas
View Description Hide DescriptionResults of a kinetic treatment of Geodesic Acoustic Modes (GAMs) that fully takes into account ion parallel dynamics, including the magnetic field component, are presented. The finiteorbitwidth (FOW) parameter is considered in the calculation of the second harmonic effect on GAMs. For larger values of the FOW parameter, it is shown that dispersive effects related to the m = 2 harmonics is the cause of the mode frequency splitting and the modes appear due to the interaction with the ion sound mode. Furthermore, the modes may have enhanced damping rates due to second harmonic Landau damping.
 Nonlinear Phenomena, Turbulence, Transport

Phase mixing of upper hybrid oscillations in a cold inhomogeneous plasma placed in an inhomogeneous magnetic field
View Description Hide DescriptionWe study phase mixing/wave breaking phenomena of upper hybrid modes in a cold inhomogeneous plasma placed in an inhomogeneous magnetic field. Inhomogeneities both in the background ion density and magnetic field profile are treated as periodic in space but independent in time. The Lagrangian fluid description is employed to obtain an exact solution of this fully nonlinear problem. It is demonstrated that the upper hybrid modes, excited by an initial local charge imbalance, break via phase mixing, induced by the inhomogeneities. It is also shown that it is possible to avoid phase mixing in excited upper hybrid oscillations in an inhomogeneous plasma containing a finite amplitude ion density fluctuation. The choice of external magnetic field is shown to have a key role in avoiding phase mixing in such oscillations. The relevance of our investigation regarding the particle acceleration in an inhomogeneous plasma has also been discussed.

Global twofluid simulations of geodesic acoustic modes in strongly shaped tight aspect ratio tokamak plasmas
View Description Hide DescriptionFollowing recent observations suggesting the presence of the geodesic acoustic mode (GAM) in ohmically heated discharges in the Mega Amp Spherical Tokamak (MAST) [J. R. Robinson et al., Plasma Phys. Controlled Fusion 54, 105007 (2012)], the behaviour of the GAM is studied numerically using the two fluid, global code CENTORI [P. J. Knight et al. Comput. Phys. Commun. 183, 2346 (2012)]. We examine mode localisation and effects of magnetic geometry, given by aspect ratio, elongation, and safety factor, on the observed frequency of the mode. An excellent agreement between simulations and experimental data is found for simulation plasma parameters matched to those of MAST. Increasing aspect ratio yields good agreement between the GAM frequency found in the simulations and an analytical result obtained for elongated large aspect ratio plasmas.

Dynamics of low dimensional model for weakly relativistic Zakharov equations for plasmas
View Description Hide DescriptionIn the present paper, the nonlinear interaction between Langmuir waves and ion acoustic waves described by the onedimensional Zakharov equations (ZEs) for relativistic plasmas are investigated formulating a low dimensional model. Equilibrium points of the model are found and it is shown that the existence and stability conditions of the equilibrium point depend on the relativistic parameter. Computational investigations are carried out to examine the effects of relativistic parameter and other plasma parameters on the dynamics of the model. Power spectrum analysis using fast fourier transform and also construction of first return map confirm that periodic, quasiperiodic, and chaotic type solution exist for both relativistic as well as in nonrelativistic case. Existence of supercritical Hopf bifurcation is noted in the system for two critical plasmon numbers.

Mass dependency of turbulent parameters in stationary glow discharge plasmas
View Description Hide DescriptionA direct current glow discharge tube is used to determine how mass changes the effects of certain turbulence characteristics in a weakly ionized gas. Helium, neon, argon, and krypton plasmas were created, and an axial magnetic field, varied from 0.0 to 550.0 Gauss, was used to enhance mass dependent properties of turbulence. From the power spectra of light emission variations associated with velocity fluctuations, determination of mass dependency on turbulent characteristic unstable modes, energy associated with turbulence, and the rate at which energy is transferred from scale to scale are measured. The magnetic field strength is found to be too weak to overcome particle diffusion to the walls to affect the turbulence in all four types of plasmas, though mass dependency is still detected. Though the total energy and the rate at which the energy moves between scales are mass invariant, the amplitude of the instability modes that characterize each plasma are dependent on mass.