Fully-ionized Plasma Research Articles

Reduced model for direct induction startup scenario development on MAST-U and NSTX-U

A reduced semi-empirical model using time-dependent axisymmetric vacuum field calculations is used to develop the prefill and feed-forward coil current targets required for reliable direct induction (DI) startup on the new MA-class spherical tokamaks, MAST-U and NSTX-U. The calculations are constrained by operational limits unique to each device, such as the geometry of the conductive elements and active coils, power supply specifications and coil heating and stress limits. The calculations are also constrained by semi-empirical models for sufficient breakdown, current drive, equilibrium and stability of the plasma developed from a shared database. A large database of DI startup on NSTX and NSTX-U is leveraged to quantify the requirements for achieving a reliable breakdown (Ip ~ 20 kA). It is observed that without pre-ionization, STs access the large E/P regime at modest loop voltage (Vloop) where the electrons in the weakly ionized plasma are continually accelerating along the open field lines. This ensures a rapid (order millisecond) breakdown of the neutral gas, even without pre-ionization or high-quality field nulls. The timescale of the initial increase in Ip on NSTX is reproduced in the reduced model provided a mechanism for impeding the applied electric field is included. Most discharges that fail in the startup phase are due to an inconsistency in the evolution of the plasma current (Ip) and equilibrium field or loss of vertical stability during the burn-through phase. The requirements for the self-consistent evolution of the fields in the weakly and fully-ionized plasma states are derived from demonstrated DI startup on NSTX, NSTX-U and MAST. The predictive calculations completed for MAST-U and NSTX-U illustrate that the maximum Ip ramp rate (dIp/dt) in the early startup phase is limited by the voltage limits on the poloidal field coils on MAST-U and passive vertical stability on NSTX-U.

A Versatile Numerical Method for the Multi-Fluid Plasma Model in Partially- and Fully-Ionized Plasmas

We present an innovative numerical method that solves for the multi-fluid plasma equations, including the transport, frictional, and chemical reactions terms, coupled to full Maxwell’s equations. The numerical method features a scheme for the electromagnetic field with a proper scaling for the numerical dissipation, a scheme that solves flows at all speeds regimes (from subsonic to supersonic), and implicit time integration to tackle the stiffness of the system. Verification of the numerical scheme is also presented in a wide variety of plasma conditions.

Three-temperature plasma shock solutions with gray radiation diffusion

The effects of radiation on the structure of shocks in a fully-ionized plasma are investigated by solving the steady-state fluid equations for ions, electrons, and radiation. The electrons and ions are assumed to have the same bulk velocity but separate temperatures, and the radiation is modeled with the gray-diffusion approximation. Both electron and ion conduction are included, as well as ion viscosity. When the material is optically thin, three-temperature behavior occurs. When the diffusive flux of radiation is important but radiation pressure is not, two-temperature behavior occurs, with the electrons strongly coupled to the radiation. Since the radiation heats the electrons on length scales that are much longer than the electron-ion Coulomb coupling length scale, these solutions resemble radiative shock solutions rather than plasma shock solutions that neglect radiation. When radiation pressure is important, all three components are strongly coupled. Results with constant values for the transport and coupling coefficients are compared to a full numerical simulation with a good match between the two, demonstrating that steady shock solutions constitute a straightforward and comprehensive verification test methodology for multi-physics numerical algorithms.

Equation of state for magnetized Coulomb plasmas

We have developed an analytical equation of state (EOS) for magnetized fully-ionized plasmas that cover a wide range of temperatures and densities, from low-density classical plasmas to relativistic, quantum plasma conditions. This EOS directly applies to calculations of structure and evolution of strongly magnetized white dwarfs and neutron stars. We review available analytical and numerical results for thermodynamic functions of the nonmagnetized and magnetized Coulomb gases, liquids, and solids. We propose a new analytical expression for the free energy of solid Coulomb mixtures. Based on recent numerical results, we have constructed analytical approximations for the thermodynamic functions of harmonic Coulomb crystals in quantizing magnetic fields. The analytical description ensures a consistent evaluation of all astrophysically important thermodynamic functions based on the first, second, and mixed derivatives of the free energy. Our numerical code for calculation of thermodynamic functions based on these approximations has been made publicly available. Using this code, we calculate and discuss the effects of electron screening and magnetic quantization on the position of the melting point in a range of densities and magnetic fields relevant to white dwarfs and outer envelopes of neutron stars. We consider also the thermal and mechanical structure of a magnetar envelope and argue that it can have a frozen surface which covers the liquid ocean above the solid crust.

Generation and Control of Perpendicular Flow Velocity Shear in a Fully Ionized Collisonless Plasma

Plasma flow velocity and its shear perpendicular to magnetic-field lines are generated by using the tungsten hot plate concentrically three segmented, which can form the radially-different plasma potential, or radial electric field even in a fully-ionized collisionless plasma. A drift-like instability which exists in the peripheral region, where the density gradient is relatively large, is observed to be suppressed by the perpendicular flow velocity shear in the central region.

Plasma Dike Potential Sustained by Local Electron Cyclotron Resonance along Converging Magnetic-Field Lines

Plasma potential formation with electron cyclotron heating is investigated in a fully-ionized collisionless plasma flow along converging magnetic-field lines (monotonously increasing magnetic field) in the presence of a single electron cyclotron resonance (ECR) point. When the ECR point is located in a region of good curvature of the magnetic line, a potential hump (plug potential) with a potential dip (thermal barrier) is generated around the ECR point. This potential structure persists in the steady state, working as a plasma-flow dike potential. In case that the ECR point is located in a region of bad curvature, on the other hand, the dike potential is only transiently formed, and collapses gradually as low frequency curvature-driven instabilities grow.

Nonlocal radiative forces in fully-ionized plasmas

The solution of the Fokker–Planck equation which contains the contribution of high-frequency electric fields is presented. For this, the projection operators of the Krook collision operator and the semicollisional propagator computed with the continued fractions were used. Both elastic and inelastic momentum transfer from the high-frequency electric field to electrons have been considered. The contributions of such high-frequency electric fields to the stress tensor and to the mean change of momentum due to electron–ion collisions are derived in the whole collisionality range. As a result, in the collisionless range, these contributions led to a new force which is 1.6 (instead of 4/3) more important than the Miller force. In the collisional range, the radiative force due to the inverse bremsstrahlung absorption is recovered and a new contribution which arises from the mean change of momentum due to collisions is found.

Temperature estimates for a railgun plasma armature

A free-flowing plasma in a railgun refers to a plasma which is not impeded by a projectile during a firing. One advantage in performing experiments with such plasmas is that spectroscopic measurements can be made when they are ejected. In this paper we analyse absorption and emission spectra of a free-flowing plasma for wavelengths between 300 and 625 nm in several firings. Calculations of the degree of ionization for the various species identified on the spectra are used to produce an estimate for the temperature of a free-flowing plasma in a RAPID railgun that lies between 11 × 103 and 25 × 103 K. This temperature range is reduced to 11 × 103 K by using a special computer code that predicts the thermochemical functions and transport coefficients of partially- and fully-ionized plasmas. The code is then used to develop temperature estimates of the plasma armature in railgun firings with projectiles. For these plasmas, which are expected to be denser than free-flowing plasmas, a temperature estimate of 14 × 103 K is obtained for a RAPID railgun firing at shot-out.

Formation of Plasma-Flow Dike Potential Due to Local ECR along Converging Magnetic-Field Lines

The formation of a plasma potential is experimentally investigated in a fully-ionized collisionless plasma flow along converging magnetic-field lines in the presence of a single ECR point. When the ECR occurs in the region of converging region, the potential profile is observed to be drastically modified. The resultant potential structure consists of a negative potential dip and a subsequent positive potential hump working as a plasma-flow dike potential, which persists in the steady state when the ECR point is located in a region of good curvature of the magnetic configuration. However, this potential structure temporally collapses when the ECR point is located in a bad curvature region. The phenomenon is considered to be caused by low-frequency flute and drift instabilities.

Impulsive Alfven Coupling between the Fully-Ionized Plasma and the Weakly-Ionized Plasma

Basic properties of an impulsive Alfven interaction between the fully-ionized bulk plasma and the weakly-ionized boundary plasma, e.g. , between the magnetosphere and the ionosphere, have been studied by means of a three-dimensional self-consistent simulation of the coupled plasma system. It is found that the duration time of an impulsive perturbation given in the fully-ionized bulk plasma, the spatial distribution of the Alfven propagation time, and the ratio between the impedance of the fully-ionized plasma and the resistance of the weakly-ionized plasma are the key factors that determine the propagation dynamics and the weakly-ionized plasma responses for an impulsive MHD perturbation.

Electric Conductivity of Lower Solar Atmosphere

AbstractElectric conductivity tensor of partly-ionized plasma is deduced. Four atmospheric models are used then to estimate the conductivity in the lower atmosphere. The parallel conductivity reaches its minimum value in the temperature minimum zone, which is 1 to 2 orders smaller than the conductivity of fully-ionized plasmas of the same condition; the effective perpendicular conductivity, or Cowling conductivity, becomes 5 to 6 orders smaller than the fully-ionized value in the lower chromosphere.

The thermal boundary layer of a radiating plasma past a semi-infinite flat plate with suction

The heat transfer in the boundary layer over a hot porous semi-infinite flat plate for a two-component plasma model is computed using an asymptotic series expansion for large suction. The temperature distribution and the Nusselt number are compared with those of a fully-ionized plasma, with and without thermal radiation. Radiative effect increases the range of influence of the temperature and the value of the Nusselt number.

Resistive lower-hybrid instability in current-carrying plasmas

Obliquely propagating lower hybrid waves are found to be unstable in a collisional, fully-ionized plasma carrying a field-aligned current.

Current-Driven Kink-Like Instability in Collisional Plasmas

The stability of left-hand circularly polarized waves propagating along an external magnetic field with wavelengths much larger than the ion Larmor radius is studied for fully-ionized collisional plasmas carrying a field-aligned current. It is found that, in the presence of electron-ion collisions, this "kink-like" instability has two branches of unstable wavenumbers: a main branch and a resistive branch. The resistive branch owes its existence to electron-ion collisions, but its growth rate is much smaller than that of the main branch, which is typically some fraction of the ion cyclotron frequency. The effect of collisions on the main branch is to reduce its maximum growth rate while extending the range of unstable wavenumbers to larger values. However, these changes are significant only when the electron-ion collision frequency is comparable to the electron cyclotron frequency. The dispersion relation is solved numerically for plasma and magnetic field parameters appropriate to the UCLA arcjet plasma. The results show that, within the framework of an infinite and homogeneous theory, the kink-like instability should occur in this plasma device.

Resistive electromagnetic ion cyclotron instability in counterstreaming plasmas

Abstract Obliquely propagating electromagnetic ion cyclotron waves are found to be unstable in a collisional, fully-ionized plasma consisting of two electron beams counterstreaming along an external magnetic field in a background of stationary ions.

Resistive Electrostatic Ion Cyclotron Instability in Plasmas

The stability of electrostatic ion cyclotron waves propagating obliquely with respect to the background magnetic field is studied for collisional, fully-ionized plasmas in which there is a relative field-aligned streaming between electrons and ions. It is found that electron-ion collisions, in conjunction with electron streaming, provides a mechanism for instability. The role of electron streaming is to supply a source of free energy and the role of electron-ion collisions is to restrict the field-aligned mobility of the electrons, thus preventing them from establishing a Boltzmann equilibrium. Ion-ion collisions and finite ion Larmor radius are found to exert a stabilizing influence. The instability is analyzed for both current-carrying plasmas and counterstreaming-beam-plasma systems.

The collisional drift mode in a partly-ionized plasma

The structure of the drift instability is examined in several density regimes. Let λ e be the total electron mean free path, kz the wave-vector component along the magnetic field, and ν ⊥ / ν ∥ the ratio of perpendicular ion diffusion to parallel electron streaming rates. At low densities (kz ν e > 1), the drift mode is isothermal, and should be treated kinetically. In the finite heat conduction regimethe drift instability threshold is reduced at low densities (v⊥/v‖<0·1) and increased at high densities (v⊥/v‖>0·1), as compared with the isothermal threshold. Finally, in the energy transfer limit (kzλe<(m/M)½), the drift instability behaves adiabatically in a fully-ionized plasma, and isothermally in a partly-ionized plasma, for an ion-neutral to Coulomb collision frequency ratio vin/vii>2(m/M)½ at Ti = Tc = Tn.

Wave propagation in a plasma in the presence of a spatially uniform external periodic magnetic field

Starting from the kinetic equation and Maxwell's equations, a dispersion relation is obtained for wave propagation through a fully-ionized plasma along a spatially-uniform, external, periodic magnetic field B0 cos ω0t, and several excitation conditions are deduced. The parametri excitation of waves in a plasma by spatially uniform external periodic electric field has been considered by several authors (Aiev & Silim 1965; Montgomery & Alexeff 1966; Jackson 1967; Prasad 1967, 1968; Nishikawa 1968 a, b). The effect of spatially uniform external periodic magnetic field on wave propagation through a hot plasma was considered by Das (1971), who used hydrodynamic equations to study the effect of wave propagation perpendicular to a spatially-uniform, external, periodic magnetic field.

Kinetic energy corrections for the free electrons in a high-frequency, fully-ionized plasma

It is found that, for a fully-ionized, homogeneous plasma in a high-frequency electric field, the fundamental term 1 in the kinetic-energy correction is defined by the intensity and frequency of the electric field and by the collision frequency v1. We obtain the Debye–Hükel energy correction in 2, too, as did Theimer & Wright, but this term is much smaller than 1, and its coefficient is no longer a constant.

Correlation-function method for the evaluation of plasma transport coefficients: The shear viscosity coefficient

The density dependence of the viscosity coefficient of a dilute fully-ionized plasma is obtained. We associate the viscosity coefficient $\ensuremath{\eta}$ with the autocorrelation function of the off-diagonal elements of the stress tensor. The technique used is essentially equivalent to that used in a previous paper by the authors. The result of our analysis is $\ensuremath{\eta}=\ensuremath{\Sigma}{m=1}^{\ensuremath{\infty}}{U}_{m}(T)\ifmmode\times\else\texttimes\fi{}{(\mathrm{ln}\ensuremath{\rho})}^{\ensuremath{-}m}$, where the ${U}_{m}(T)$ are the solutions to well-defined algebraic equations. If one Sonine polynomial is used, the shear viscosity is given by $\ensuremath{\eta}={[{d}_{1}(T)\mathrm{ln}\ensuremath{\rho}+{d}_{2}(T)]}^{\ensuremath{-}1}$.