Simple Plasma Model Research Articles

Regularized magnetic islands. I. Hyperviscosity and profile functions

The problem of the magnetic island profile functions is analyzed. An idea is suggested that discontinuities of the profile function derivatives at the island separatrix, which appear in simplified plasma models, can be eliminated by means of more complete description, i.e., the profile functions can be regularized. As an example, the regularization of the electrostatic potential profile function is considered for the case of a slab geometry when its formation is governed by the perpendicular viscosity. It is shown that for regularization of such a profile function one should keep in the viscosity expression the terms with higher derivatives of the velocity, usually referred to as hyperviscosity terms. A model expression for the hyperviscosity is derived by the Grad-type method. Physically, the regularization is related to the appearance of a part of the profile function localized in the Larmor transition layer near the island separatrix.

Comparisons and physics basis of tokamak transport models and turbulence simulations

The predictions of gyrokinetic and gyrofluid simulations of ion-temperature-gradient (ITG) instability and turbulence in tokamak plasmas as well as some tokamak plasma thermal transport models, which have been widely used for predicting the performance of the proposed International Thermonuclear Experimental Reactor (ITER) tokamak [Plasma Physics and Controlled Nuclear Fusion Research, 1996 (International Atomic Energy Agency, Vienna, 1997), Vol. 1, p. 3], are compared. These comparisons provide information on effects of differences in the physics content of the various models and on the fusion-relevant figures of merit of plasma performance predicted by the models. Many of the comparisons are undertaken for a simplified plasma model and geometry which is an idealization of the plasma conditions and geometry in a Doublet III-D [Plasma Physics and Controlled Nuclear Fusion Research, 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 159] high confinement (H-mode) experiment. Most of the models show good agreements in their predictions and assumptions for the linear growth rates and frequencies. There are some differences associated with different equilibria. However, there are significant differences in the transport levels between the models. The causes of some of the differences are examined in some detail, with particular attention to numerical convergence in the turbulence simulations (with respect to simulation mesh size, system size and, for particle-based simulations, the particle number). The implications for predictions of fusion plasma performance are also discussed.

Realization, Operation and Results of the Multichannel Far-Infrared Polarimeter on RFX

This paper illustrates the realisation and testing of the multichannel far-infrared polarimeter for the RFX machine, a plasma confinement experiment with the Reversed Field Pinch configuration. The diagnostic is described and the its main sections are outlined: the laser system operating at λ = 118.8μm, the FIR optical line, the beam splitter and the beam detection units, the signal processing electronics and the motion electronics for the calibration halfwave plates. Emphasis is placed on the work performed on the polarimeter to make it operational. We illustrate the preliminary tests of the diagnostic equipment and the activity performed to bring the diagnostic into reliable operation, in particular the reduction of the noise produced by magnetically induced mechanical vibrations during machine shots. An example of the first Faraday angle measurements performed on five chords are presented and discussed. The measured Faraday angle was also compared to a theoretically calculated value, based on a simple plasma model, with satisfactory agreement between measured and predicted data.

Method for the identification of the field configuration in presence of the localized perturbation observed in RFP toroidal plasma devices

A method for the identification of the magnetic field configuration inside a RFP plasma, affected by a localized nonaxisymmetric perturbation, is presented. The knowledge of the magnetic field on a closed surface located around the plasma torus, together with a simplified plasma model, assures a unique solution for this inverse problem.

Comparison between the Landau and Cyclotron Resonances in the Electron Beam-Plasma Interactions

It is well-known that a cool field-aligned electron beam streaming in a plasma can destabilize electrostatic waves, in the frequency ranges of 0<ω< m i n (Ω e ,ω p ) and m a x (Ω e ,ω p )<ω<ω uh , where ω p , Ω e , and ω uh are the plasma, the electron cyclotron, and the upper-hybrid frequencies, respectively. Although both the Landau and cyclotron resonances lead to the generation of the waves, not much attention has been paid to the wave generation via the cyclotron resonance. In this paper we compare the two types of interactions for both non-relativistic and relativistic electron beams by considering a simple plasma model which consists of main and beam electrons and background ions. The plasma is charge neutral and current carrying. The linear theory based on this model predicts that, when the electron beams are non-relativistic, the waves are generated predominantly via the Landau interaction for a wide range of plasma parameters, except for a limited parameter regime with cool main electrons, Ω e /...

Growth-rate calculation of the flute instability of a pure ion channel in a magnetized plasma

A simple plasma model is used to analyze the flute instability of a pure ion channel in a magnetized plasma. In this model, ions are cold and immobile due to heavy mass, while electrons in the plasma have a low temperature so that they can move in the magnetic field. Because of the axially applied magnetic field and the radial electric field in an interface of the ion channel and plasma, an E × B drift occurs in azimuthal direction and this drift causes the flute instability of the ion channel in the interface. In this paper, an approximate growth rate of the instability is obtained and a specific example associated with a plasma lens is given.

Polarization of the high harmonics of radiation in a laser plasma

The polarization of the high harmonics generated in plasmas by the bremsstrahlung of electrons oscillating under the influence of high-power plasma-heating electromagnetic radiation is described on the basis of a simple model of a cold plasma. It is shown that when the polarization of the heating radiation differs from plane polarization by a small but finite amount, the high harmonics are generated with almost perpendicular polarization, and the degree of circular polarization of the harmonics increases with the number of the harmonic.

Reactor modeling of magnetically enhanced capacitive RF discharge

Magnetic and collisional effects on capacitive radio frequency (RF) discharges for magnetically enhanced reactive ion etching (MERIE) are investigated. Using simplified plasma and sheath models, a collisional magnetic-sheath equation that governs the sheath dynamics under a de magnetic field crossed with a sinusoidal RF electric field is obtained. The sheath equation includes global effects of the bulk plasma. Together with the power-balance equation and the particle-conservation equation, the sheath equation is used to extract a circuit model and predict the electrical behavior of MERIE reactors. Numerical results on the plasma density and the power in MERIE reactors agree well with reported experimental results and the circuit model describes the repeated discharge properties well.

A simple model of Davydov-Zakharov class for plasmas in magnetic field: discontinuous solutions

A simple hydrodynamic plasma model, taking into account the electron vorticity effect on the plasma motion and magnetic field behaviour, is expressed in terms of the Davydov-Zakharov formalism. The discontinuities related to the model are obtained. The shock wave corresponds to plasma rarefaction.

Experimental investigation of the matching and impressed electric field of a multipolar electron cyclotron resonance discharge

The experimental performance of an end excited, internally tuned, multipolar electron cyclotron resonance plasma source is investigated versus several independent input variables: (1) incident power (185–350 W), (2) discharge pressure (1–7 mTorr), and (3) microwave matching (applicator length, Ls, varies from 65–170 mm). Plasma source performance in argon gas is determined from measurements of (1) absorbed microwave power, (2) the magnitude, and (3) the spatial variation of the impressed electric field, and the output (4) plasma density and (5) electron temperature. The nonlinear experimental relationships between variations in the input variables and performance variables are established. Two well-matched stable discharge operational regions or modes are identified as Ls is varied. Using the measured impressed electric field patterns, these two modes are identified as TM, Φ symmetric, λg, and λg/2 standing wave modes. As Ls, pressure and power vary, considerable hysteresis in absorbed power and density is observed. However, it is shown that this complex input/output discharge behavior can be approximately explained using simple global plasma models. Despite the multiple steady states and hystereses, it is shown that the discharge can be easily maintained in well-matched, high density (ne&amp;gt;3×1011/cm3) stable operating conditions. The impressed electric field varies between 3 and 4.5 kV/m. An equivalent circuit of the plasma loaded cavity applicator is developed and provides important insights for the plasma matching process. The microwave coupling efficiencies are greater than 98% and the ion production costs vary between 300 and 450 eV/ion versus the experimental inputs. The data presented is useful for plasma source optimization and in developing intelligent plasma processing control strategies.

The plasma properties adjacent to the target in a magnetron sputtering source

Using a simple 1D fluid model of the bulk plasma, the distribution of plasma density, ion and electron velocity and space potential have been determined above the `race-track' of a magnetron sputtering source. Ions generated by electron impact ionization are unaffected by the source magnetic field as they fall to the sheath-edge; however, the electron motion is mobility-limited, in the mutually perpendicular electric and magnetic fields. The results show a peak in the plasma concentration in front of the cathode sheath, the height and position of which is governed by the magnetic field strength and discharge current. With increasing magnetic field, sheath-edge ion fluxes greater than the usual value prescribed by the Bohm criterion are found. For a set of discharge conditions, a reversal in the electron current flow is predicted, indicating a limit in the operating parameters for which physical solutions can be generated. The predicted plasma profiles give good agreement with Langmuir probe measurements made in the magnetron target pre-sheath, demonstrating the usefulness of the simple model approach.

The interaction of the superthermal, thermal electrons and ions beams systems: a simple model for an ionospheric plasma studied by particle simulation

A comparison is made between a plasma system with three components (thermal electrons and superthermal electrons, and also nondrifting ions in a magnetic field, that is taken to be of magnitude of the magnetic field of the yearth) and a four-component system with two species of electrons, (thermal and superthermal) and two species of ions, one nondrifting and one drifting slowly, by using the method of particle simulation. This first 1-D electrostatic approximation used for a simple model of an ionospheric plasma with β < me/mi has the aim to observe the influence of the superthermal electrons on the plasma oscillatory properties, on the electrostatic characteristics and on specific energies of such a periodic plasma system and the interaction between the considered particles species. The observed linear growth in a very short time and the nonlinear stage of the excited instabilities, with specific amplitude fluctuations under the form of successive short growths and Landau-type dampings, demonstrate that the phenomena involved in the two considered systems are essentially nonlinear ones.

Nonlinear instability and chaos in plasma wave–wave interactions. II. Numerical methods and results

In Part I of this work [Phys. Plasmas 2, 1926 (1995)], the behavior of linearly stable, integrable systems of waves in a simple plasma model was described using a Hamiltonian formulation. Explosive instability arose from nonlinear coupling between positive and negative energy modes, with well-defined threshold amplitudes depending on the physical parameters. In this concluding paper, the nonintegrable case is treated numerically. The time evolution is modeled with an explicit symplectic integrator derived using Lie algebraic methods. For amplitudes large enough to support two-wave decay interactions, strongly chaotic motion destroys the separatrix bounding the stable region in phase space. Diffusive growth then leads to explosive instability, effectively reducing the threshold amplitude. For initial amplitudes too small to drive decay instability, slow growth via Arnold diffusion might still lead to instability; however, this was not observed in numerical experiments. The diffusion rate is probably underestimated in this simple model.

Reduction of the power transmission factor and limitation of the secondary-electron inflow at the divertor sheath

A simple model of the collisional divertor plasma indicates that neutral gas collisions should be important in determining the power transmission factor at the transition layer. Inflow of low-energy electrons created by ionization reduces the total potential drop at the transition layer, and the reduction of the power transmission factor is remarkable when the particle amplification factor is much larger than 1. The secondary-electron inflow is effectively diminished due to deflection of the electron by the Lorentz force when the electron cyclotron frequency is much larger than the plasma frequency. The electron emission coefficient under the space-charge limitation is reduced to a value much smaller than 1 due to formation of the magnetic presheath when the magnetic angle approaches 90°.

Model of a laser heated plasma interacting with walls arising in laser keyhole welding.

In laser welding with laser intensities of approximately ${10}^{11}$ W/${\mathrm{m}}^{2}$, a hole, called a keyhole, is formed in the material. In this keyhole a plasma is detected, which is characterized by high pressure as well as being influenced by the boundary of the keyhole. Experimental data on plasma parameters are rare and difficult to obtain [W. Sokolowski, G. Herziger, and E. Beyer, in High Power Lasers and Laser Machining Technology, edited by A. Quenzer, SPIE Proc. Vol. 1132 (SPIE, Bellingham, WA, 1989), pp. 288--295]. In a previous paper [C. Tix and G. Simon, J. Phys. D 26, 2066 (1993)] we considered just a simple plasma model without excited states and with constant ion--neutral-atom temperature. Therefore we neglected radiative transport of excitations and underestimated the ion--neutral-atom temperature and the ionization rate. Here we extend our previous model for a continuous ${\mathrm{CO}}_{2}$ laser and iron and take into account radiative transfer of excitations and a variable ion--neutral-atom temperature. We consider singly charged ions, electrons, and three excitation states of neutral atoms. The plasma is divided in plasma bulk, presheath, and sheath. The transport equations are solved with boundary conditions mainly determined through the appearance of walls. Some effort is made to clarify the energy transport mechanism from the laser beam into the material. Dependent on the incident laser power, the mean electron temperature and density are obtained to be 1.0--1.3 eV and 2.5\ifmmode\times\else\texttimes\fi{}${10}^{23}$--3\ifmmode\times\else\texttimes\fi{}${10}^{23}$ ${\mathrm{m}}^{\mathrm{\ensuremath{-}}3}$. Radiative transport of excitations does not contribute significantly to the energy transport.

Electron inertial effects on geomagnetic field line resonances

A three‐dimensional compressible resistive magnetohydrodynamic simulation code, with inclusion of the fully generalized Ohm's law, has been developed to study the nonlinear evolution of field line resonances in Earth's magnetosphere. A simple Cartesian box model of an inhomogeneous plasma with straight geomagnetic field lines is used, and the Alfvén velocity increases monotonically from the magnetopause boundary layer toward Earth. A monochromatic fast mode compressional oblique wave is applied from the direction of the magnetopause boundary layer, pumping energy into the magnetosphere. The fast mode wave, while propagating toward Earth, is partially reflected at the turning point (located at radial distances between 8 and 10 RE in the equatorial plane) and then couples to shear Alfvén waves, leading to the formation of large‐amplitude field line resonances near Earth. The field line resonances are observed to narrow to several electron inertia lengths within several wave periods of the driver wave, and electron inertial effects become important at this stage. Final profiles near the resonance are very similar to Airy functions, indicating that electron inertial effects become important before possible nonlinear effects. The electron inertial effects lead to oscillating parallel electric field which might be potential accelerators for electrons in some types of auroral arcs.

Studies on microwave coupling into the electron cyclotron resonance ion source Alice

The particular microwave off-axis injection into the electron cyclotron resonance (ECR) ion source Alice, the reflected power and the occasionally observed waveguide arcs, required a careful study both of the waveguide termination and the microwave transmission line. The high-voltage microwave window was redesigned, improving the choke flange and showing the opportunity of treating the teflon insulator to obtain a surface resistivity in the range of 107 Ω. A simple plasma model, unidimensional and based on the Krook model for electron motion, is here considered for the ECR plasma; effects of rapid spatial variation of the external magnetic field are naturally included. Profiles of the waves in the ECR cavity are given, as well as an expression for the impedance of the plasma; no substantial reflections are evidenced for a typical plasma case (ωpl/ω=0.7).

Plasma effects on atomic reaction rates in hydrogen plasmas.

The perturbative effects of plasma electrons and ions on the effective capture and ionization rates in hydrogen plasma are analyzed. A simple model of hydrogen plasma is constructed to extract the salient features of the system, which is assumed to be in local thermal equilibrium. The interplay between the collisional and radiative processes as functions of the electron temperature and density is explicitly demonstrated. A large increase in the collisional radiative recombination rates at high density and low temperature is caused by (i) the shift in the dominant capture mechanism from the radiative to collisional cascade, and (ii) the presence of upper states in Saha equilibrium which act as a reservoir of population flux. Different sets of effective rates which reflect the approximate structure of the rate equations are evaluated, stressing the relationship between the rate coefficients and the rate equations. When the angular-momentum sublevels are averaged over, because of rapid [ital l]-changing collisions, the ion field distortion effect is shown to be negligible, in the lowest order approximation.

Particle transport studies for single-null divertor discharges in DIII-D

In this paper an investigation of the particle confinement for beam-heated single-null discharges in the open divertor configuration of Doublet III-D (DIII-D) [E. J. Doyle et al., Phys. Fluids B 3, 2300 (1991)] is described. Results are based on a Monte Carlo neutral transport model with a relatively simple plasma model that utilizes experimental data on density, temperature, and heat flux profiles in the edge plasma. For a typical discharge, it is found that the particle confinement time in the quiescent H-mode phase is only about a factor of 2 larger than during the L-mode phase, an increase comparable to the energy confinement time increase. For both H-mode and L-mode phases the particle confinement time is about a factor of 4 larger than the energy confinement time. It is also found that the core plasma fueling rate is higher in the H mode due to the increased transparency of a thinner scrape-off layer. The longer particle confinement time and the increased fueling rate both contribute to the observed density rise during the quiescent period following the L–H transition. Flux surface-averaged transport modeling of the time evolution for the core plasma density profile during H mode suggests that a strong inward particle pinch is necessary near the separatrix.

Thermodynamics of Mercury Vapours

AbstractA quantum statistical approach is used to give a unified treatment of the metal‐nonmetal‐ and liquid‐vapour‐transitions in mercury. The limiting cases of the atomic vapour at low densities and the metallic fluid at high densities are included. A simple plasma model with only long range Coulomb forces has to be improved by considering also short range interactions. Estimates are given for the critical point of the liquid‐gas phase transition, as well as for the Mott density indicating the metal‐nonmetal transition.