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  • 1
    Electronic Resource
    Electronic Resource
    Self-consistent electron cyclotron resonance absorption in a plasma with varying parameters (1992)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 72 (1992), S. 3924-3933 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A formalism is developed for numerically calculating reflection and absorption of right-hand polarized waves and reflection of left-hand polarized waves propagating into a cyclotron resonance zone in a medium in which both magnetic field and plasma density are varying. The results are shown to agree with previous analytic calculations in the limit of constant density, weak collisionality, and linearly varying magnetic field, where the analytic calculation applies. The formalism is then applied to a plasma with general field and density variations, and arbitrary collisionality. The absorption and reflections are calculated for various boundary conditions along the propagation path, showing that there is an optimum density for power absorption. The collisionless absorption in the resonance zone, calculated from the single particle heating averaged over the flux is shown to be consistent with the linear wave absorption at low absorption and collisionality. At high absorption a prescription for bringing the two calculation methods into agreement is advanced. The results are used to qualitatively explain some previously puzzling experimental observations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.352244
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  • 2
    Electronic Resource
    Electronic Resource
    Time scale to ergodicity in the Fermi–Pasta–Ulam system (1995)
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 5 (1995), S. 283-297 
    Details
    ISSN: 1089-7682
    Source: AIP Digital Archive
    Topics: Physics
    Notes: We study the approach to near-equipartition in the N-dimensional Fermi–Pasta–Ulam Hamiltonian with quartic (hard spring) nonlinearity. We investigate numerically the time evolution of orbits with initial energy in some few low-frequency linear modes. Our results indicate a transition where, above a critical energy which is independent of N, one can reach equipartition if one waits for a time proportional to N2. Below this critical energy the time to equipartition is exponentially long. We develop a theory to determine the time evolution and the excitation of the nonlinear modes based on a resonant normal form treatment of the resonances among the oscillators. Our theory predicts the critical energy for equipartition, the time scale to equipartition, and the form of the nonlinear modes below equipartition, in qualitative agreement with the numerical results. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.166143
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  • 3
    Electronic Resource
    Electronic Resource
    Modeling a metal–vapor buffer-gas hollow cathode discharge (2000)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 87 (2000), S. 7191-7197 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The operation of a metal–vapor buffer-gas hollow cathode discharge is re-examined using modeling techniques that have been developed for electronegative plasma discharges. It is shown that a previously developed global model can be extended to give spatially resolved densities as well as more accurate values for the plasma parameters. A numerical calculation for a neon–copper (Ne–Cu) discharge is used to illustrate the results of the modeling technique. The density profiles of the neutral and ion components, and their variation with the buffer gas pressure, are similar to those found by numerical solution of the complete equations. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.372968
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  • 4
    Electronic Resource
    Electronic Resource
    Erratum: "Modeling electronegative plasma discharges'' [J. Appl. Phys. 75, 2339 (1994)] (1994)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 76 (1994), S. 625-625 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.358544
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  • 5
    Electronic Resource
    Electronic Resource
    Modeling electronegative plasma discharges (1994)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 75 (1994), S. 2339-2347 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A macroscopic analytic model for a three-component electronegative plasma has been developed. Assuming the negative ions to be in Boltzmann equilibrium, a positive ion ambipolar diffusion equation is found. The electron density is nearly uniform, allowing a parabolic approximation to the plasma profile to be employed. The resulting equilibrium equations are solved analytically and matched to an electropositive edge plasma. The solutions are compared to a simulation of a parallel-plane rf driven oxygen plasma for two cases: (1) p=50 mTorr, ne0=2.4×1015 m−3, and (2) 10 mTorr, ne0=1.0×1016 m−3. In the simulation, for the low power case (1), the ratio of negative ion to electron density was found to be α0≈8, while in the higher power case α0≈1.3. Using an electron energy distribution that approximates the simulation distribution by a two-temperature Maxwellian, the analytic values of α0 are found to be close to, but somewhat larger than, the simulation values. The average electron temperature found self-cosistently in the model is close to that in the simulation. The results indicate the need for determining a two-temperature electron distribution self-consistently within the model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.356252
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  • 6
    Electronic Resource
    Electronic Resource
    Internal sheaths in electronegative discharges (1999)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 86 (1999), S. 4142-4153 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: In three component electronegative discharges a parameter regime can be found in which the positive ions reach the local ion sound velocity at a position where the negative ion density may be significant compared to the electron density. For this regime a quasineutral electronegative core breaks down and a space charge region forms. Solutions in the space charge region are obtained in collisionless and collisional cases, neglecting ionization and positive-negative ion recombination. The structure of the non-neutral region is shown to vary significantly with the ratio of the negative ion and electron densities at the core edge, the ratio of ion and electron temperatures, and the ratio of the electron Debye length to the ion mean free path. If the first ratio is not too large the non-neutral region displays potential oscillations on the electron Debye length spatial scale, which damp away on the scale of the ion–neutral mean free path. The non-neutral region then terminates within the plasma. The change in electric potential across this region is several times the negative ion temperature, which is sufficient to confine the negative ions to the core. The non-neutral region merges with a quasineutral halo containing essentially only positive ions and electrons. If the negative ion density is sufficiently high compared to the electron density the electropositive halo disappears and the non-neutral region extends from the ion sound velocity threshold to the wall. For intermediate values of the negative ion density, a space charge double layer forms between the electronegative and electropositive regions. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.371339
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  • 7
    Electronic Resource
    Electronic Resource
    Self-consistent stochastic electron heating in radio frequency discharges (1988)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 64 (1988), S. 4375-4383 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Fermi acceleration is considered as an underlying mechanism for electron heating in rf discharges, in which the heating arises from the reflection of electrons from moving sheaths. By examining the dynamics of the electron collisions with the sheaths, the map that describes the electron motion is derived. For high-frequency discharges (ω/2π〉50 MHz), the electron motion is shown to be stochastic. By combining these dynamics with collisional effects in the bulk plasma and incorporating self-consistent physical constraints, a self-consistent model of the discharge is developed. The model is used to calculate physically interesting quantities, such as the electron temperature and average lifetime, and to predict the minimum pressure necessary to sustain the plasma. The distribution of electron energies is shown to be non-Maxwellian. These results can be applied to experimentally interesting parallel-plate rf plasma discharges to predict the operating conditions necessary for stochastic heating to occur.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.341286
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  • 8
    Electronic Resource
    Electronic Resource
    Instabilities in low-pressure inductive discharges with attaching gases (1999)
    Woodbury, NY : American Institute of Physics (AIP)
    Applied Physics Letters 75 (1999), S. 3617-3619 
    Details
    ISSN: 1077-3118
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Plasma instabilities at frequencies 1 Hz–900 kHz have been observed in low-pressure inductive processing discharges with attaching gases. Instability windows in pressure and driving power are found. A volume-averaged (global) model of the instability is developed, considering idealized inductive and capacitive energy deposition. As pressure or power are varied to cross a threshold, the instability is born at a Hopf bifurcation, with relaxation oscillations between inductive and capacitive modes causing modulations of charged particle densities, electron temperature, and plasma potential. The oscillations can be so strong that the potential collapses and negative ions flow to the walls. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.125406
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  • 9
    Electronic Resource
    Electronic Resource
    A study of high-beta ballooning modes (1985)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 28 (1985), S. 392-402 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Ballooning instabilities are studied in the Berkeley multiple mirror experiment. Counterstreaming theta pinch and Marshall gun source hydrogen plasmas are used to achieve a high beta ( β〉25%), where β is the ratio of plasma to magnetic pressure at temperatures Te=Ti≈15 eV. Four magnetic field configurations are investigated, each at varying mirror ratios, to explore a range of drive and connection length parameters. In two of these the magnetic field is pulsed from a stable to a locally unstable configuration for initiation of ballooning activity. The other two (static) configurations are a weakly unstable local field region, and the standard linked quadrupole multiple-mirror configuration. Depending on the configuration, critical β's are found for the onset of ballooning that vary from 5% for the most unstable configuration to greater than 25% for the standard multiple-mirror configuration. The m=1 azimuthal mode is predominant, with some admixture of m=2. The experimental results are compared with predictions from a magnetohydrodynamic theory. In the model the pressure is taken to be isotropic and constant along the axis, except in the diverging field regions at the device ends where the pressure falls to maintain beta constant, consistent with experimental observations. The theoretical results generally predict somewhat higher critical betas for the m=1 mode than those observed. Estimates of the effect of finite Larmor radii, nearby conducting walls, axially nonuniform pressure profiles and resistivity, are also given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.865162
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  • 10
    Electronic Resource
    Electronic Resource
    Resistive effects on the rigid mode ballooning instability (1987)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 30 (1987), S. 1416-1428 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: From a set of fluid equations, a second-order differential equation, governing the resistive ballooning instability for a mirror confined plasma with a rigid perturbation, is obtained. The resistive effects on the rigid mode ballooning instability are numerically examined for three tandem mirror configurations; those stabilized by walls, by end cusps, and by end quadrupoles. In the model the pressure is taken to be isotropic and constant along the axis except in the cusps and the diverging field regions, and the plasma has a sharp boundary. The theoretical results indicate that the resistivity can play a major role in determining the growth rate for ballooning for lower temperature devices.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.866255
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