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  • 1
    Electronic Resource
    Electronic Resource
    WKB theory of wave tunneling for Hermitian and nearly Hermitian vector systems of integral equations (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 2527-2544 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A general theory of wave tunneling in one dimension for Hermitian and nearly Hermitian vector systems of integral equations is presented. It describes mode conversion in terms of the general dielectric tensor of the medium and properly accounts for the forward and backward nature of the waves without regard to specific models. Energy conservation in the WKB approximation can be obtained for general Hermitian systems by the use of modified Furry rules that are similar to those used by Heading for second-order differential equations. Wave energy absorption can then be calculated perturbatively using the conservation properties of the dominant Hermitian operator. Operational graphical rules are developed to construct global wave solutions and to determine the direction of energy flow for spatially disconnected roots. In principle, these rules could be applied to systems with arbitrary mode complexity. Coupling coefficients for wave tunneling problems with up to four interacting modes are calculated explicitly.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528534
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  • 2
    Electronic Resource
    Electronic Resource
    Spontaneous hole–clump pair creation (1999)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 6 (1999), S. 3102-3113 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Numerical simulations and quantitative theoretical explanations are presented for the spontaneous formation of a hole–clump pair in phase space. The equilibrium is close to the linear threshold for instability and the destabilizing resonant kinetic drive is nearly balanced by either extrinsic dissipation or a second stabilizing resonant kinetic component. The hole and clump, each support a nonlinear wave where the trapping frequency of the particles is comparable to the kinetic linear growth rate from the destabilizing species alone. The power dissipated is balanced by energy extracted by trapped particles locked to the changing wave-phase velocities. With extrinsic dissipation, phase space structures always form just above the linear instability threshold. With a stabilizing kinetic component, an electrostatic interaction is considered with varying mass ratios of the stabilizing and destabilizing species together with collisional effects. With these input parameters, various nonlinear responses arise, only some of which sweep in frequency. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.873550
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  • 3
    Electronic Resource
    Electronic Resource
    Growth and saturation of toroidal Alfvén eigenmode modes destabilized by ion cyclotron range of frequency produced tails (1998)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 5 (1998), S. 2781-2796 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The linear growth rates of TAE (toroidal Alfvén eigenmode) modes destabilized by ICRF (ion cyclotron range of frequency) heating are calculated over a range of plasma parameters. Nonlinear saturation of a single unstable mode is investigated both analytically and numerically when wave–particle trapping is the dominant saturation mechanism. A numerical code has been developed based on a reduced resonance description of the wave–particle interaction (using a Hamiltonian formalism). A delta-f algorithm was incorporated to allow a low-noise description of mode evolution with particle sources and sinks present. The numerically observed saturation amplitudes correlate well with theoretical predictions to within 20%. Self-excited frequency sweeping resulting from the excitation of many simultaneous wave–particle resonances at different energies is demonstrated and explained as an extension of previous published theory [Berk et al., Phys. Lett. A 234, 213 (1997)]. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.872966
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  • 4
    Electronic Resource
    Electronic Resource
    On the theory of internal kink oscillations (1998)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 5 (1998), S. 2326-2333 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: In this paper a time evolution equation for internal kink oscillations is derived. It is valid for both stable and unstable plasma regimes, and incorporates the response of an energetic particle population. A linear analysis reveals a parallel between (i) the time evolution of the spatial derivative of the internal kink radial displacement and (ii) the time evolution of the perturbed particle distribution function in the field of an electrostatic wave (Landau problem). It is shown that diamagnetic drift effects make the asymptotic decay of internal kink perturbations in a stable plasma algebraic rather than exponential. However, under certain conditions the stable root of the dispersion relation can dominate the response of the on-axis displacement for a significant period of time. The form of the evolution equation naturally allows one to include a nonlinear, fully toroidal treatment of energetic particles into the theory of internal kink oscillations. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.872906
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  • 5
    Electronic Resource
    Electronic Resource
    Nonlinear response of driven systems in weak turbulence theory (1996)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 3 (1996), S. 1827-1838 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A method is presented for predicting the saturation levels and particle transport in weakly unstable systems with a discrete number of modes. Conditions are established for either steady-state or pulsating responses when several modes are excited for cases where there is and there is not resonance overlap. The conditions for saturation and the associated transport are discussed. Depending on parameters, the saturation level can be low, with only a small fraction of the available free energy released to waves and with no global transport, or the saturation level can be quite high, with almost complete conversion of free energy to wave energy coupled with rapid transport. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.871978
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  • 6
    Electronic Resource
    Electronic Resource
    Critical nonlinear phenomena for kinetic instabilities near threshold : The 38th annual meeting of the Division of Plasma Physics (DPP) of the American Physical Society (1997)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 4 (1997), S. 1559-1568 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A universal integral equation has been derived and solved for the nonlinear evolution of collective modes driven by kinetic wave particle resonances just above the threshold for instability. The dominant nonlinearity stems from the dynamics of resonant particles that can be treated perturbatively near the marginal state of the system. With a resonant particle source and classical relaxation processes included, the new equation allows the determination of conditions for a soft nonlinear regime, where the saturation level is proportional to the increment above threshold, or a hard nonlinear regime, characterized by explosive behavior, where the saturation level is independent of the closeness to threshold. In the hard regime, rapid oscillations typically arise that lead to large frequency shifts in a fully developed nonlinear stage. The universality of the approach suggests that the theory applies to many types of resonant particle driven instabilities, and several specific cases, viz. energetic particle driven Alfvén wave excitation, the fishbone oscillation, and a collective mode in particle accelerators, are discussed. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.872286
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  • 7
    Electronic Resource
    Electronic Resource
    Finite beta plasma equilibrium in toroidally linked mirrors (1994)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 1 (1994), S. 881-890 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The problem of finite pressure plasma equilibrium in a system with closed magnetic field lines consisting of quadrupole mirrors linked by simple toroidal cells with elliptical cross sections is analyzed. An appropriate analytical procedure is developed, that uses conformal mapping techniques, which enables one to obtain the magnetic field structure for the free boundary equilibrium problem. This method has general applicability for finding analytic solutions of the two-dimensional Dirichlet problem outside an arbitrary closed contour. Using this method, the deformations of the plasma equilibrium configuration due to finite plasma pressure in the toroidal cell are calculated analytically to the second order in a λ expansion, where λ∼β/εE, β is the ratio of plasma pressure to the magnetic field pressure, ε is the inverse aspect ratio, and E is the ellipticity of the plasma cross section. The outer displacement of the plasma column is shown to depend nonlinearly on the increase of plasma pressure, and does not prevent the achievement of substantial β∼10% in the toroidal cells.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.870747
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  • 8
    Electronic Resource
    Electronic Resource
    Instability due to axial shear and surface impedance (1994)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 1 (1994), S. 1199-1213 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The stability of plasma flow in the scrape-off layer of a tokamak, taking into account the surface sheath impedance and the axial shear in the E×B flow is analyzed. An interesting stability problem arises in the limit that end plates are sufficiently far apart, so that stability can be analyzed when the plasma is taken to interact with a single end plate. As parameters are varied, windows of instability are found, and it is shown that growth rates are maximized for an insulating end plate and are also quite sensitive to the ratio of the ion diamagnetic and E×B drift frequencies. Mixing-length estimates of the diffusivity are comparable to experimentally observed values.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.870717
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  • 9
    Electronic Resource
    Electronic Resource
    Toroidal plasma beta-finite Larmor radius limit in a toroidally linked mirror system (1994)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 1 (1994), S. 3622-3634 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The ballooning stability limit in one toroidal section of the recently proposed toroidally linked neutron source is investigated within the framework of the Wentzel–Kramers–Brillouin (WKB) approximation. Rotational effects induced by radial electric fields present in the equilibrium are neglected. The equilibrium pressure and density profiles are taken to be linear in the flux variable. For a reasonable set of design parameters, ideal ballooning instability limits the toroidal plasma beta to less than 1%. However, the inclusion of stabilizing kinetic effects due to finite ion Larmor radius approximately doubles the predicted critical beta limit, and makes possible a choice of design parameters compatible with ballooning stability.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.870897
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  • 10
    Electronic Resource
    Electronic Resource
    Nonlinear modeling of kinetic plasma instabilities : The 40th annual meeting of the division of plasma physics of the american physical society (1999)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 6 (1999), S. 1822-1829 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Many kinetic plasma instabilities, in quite different physical systems, share a genuinely similar mathematical structure near isolated phase-space islands. For this reason, dynamical features such as faster-than-exponential growth of the instability, as well as nonlinear frequency sweeping, are found to be universal. Numerical δf methods, which follow the evolution of the (nonlinear) perturbed distribution function along single-particle orbits, have been applied to analytic models, which include a continuous particle source, resonant particle collisions, and wave damping. The result is a series of codes that can reliably model the nonlinear evolution of kinetic instabilities, including some specific to tokamak plasmas, over experimentally relevant time scales. New results include (i) nonlinear simulations of two-species, one-degree-of-freedom plasmas; (ii) simulations of fishbone bursts in tokamak plasmas; (iii) nonlinear modeling of beam-driven toroidal Alfvén eigenmode activity in tokamaks. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.873440
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