On the application of the ideal magnetohydrodynamic linear eigenvalue equation to the Z-pinch

1988 ◽  
Vol 39 (3) ◽  
pp. 521-538 ◽  
Author(s):  
S. Kanellopoulos ◽  
M. Coppins ◽  
M. G. Haines
Keyword(s):  
Growth Rate ◽  
Free Boundary ◽  
Variational Method ◽  
Eigenvalue Equation ◽  
Eigenvalue Spectrum ◽  
Long Wavelength ◽  
Analytic Expression ◽  
Ideal Magnetohydrodynamic ◽  
Z Pinch ◽  
The Ideal

A study of the ideal magnetohydrodynamic linear eigenvalue spectrum for free-boundary modes in the Z-pinch is presented. The application of a variational method to estimate eigenvalues is described and limitations imposed by the nature of the spectrum are discussed. An analytic expression for the long-wavelengthm= 0 growth rate is derived

The large-Larmor-radius Rayleigh–Taylor instability

1998 ◽  
Vol 60 (1) ◽  
pp. 65-68
Author(s):  
M. FAGHIHI ◽  
F. EBRAHIMI
Keyword(s):  
Growth Rate ◽  
Fluid Model ◽  
Taylor Instability ◽  
Larmor Radius ◽  
Rayleigh Taylor Instability ◽  
Magnetohydrodynamic Model ◽  
Ideal Magnetohydrodynamic ◽  
The Ideal

The effect of a large ion Larmor radius on the Rayleigh–Taylor instability is investigated using the Vlasov fluid model. The results are compared with an ideal magnetohydrodynamic model. It is found that this effect reduces the growth rate of the Rayleigh–Taylor instability with respect to the ideal magnetohydrodynamic growth rate.

scholarly journals Magnetohydrodynamic spectrum of gravitating plane plasmas with flow

1999 ◽  
Vol 61 (2) ◽  
pp. 221-240 ◽  
Author(s):  
B. van der HOLST ◽  
R. J. NIJBOER ◽  
J. P. GOEDBLOED
Keyword(s):  
Shear Flow ◽  
Spectral Problem ◽  
Critical Values ◽  
Equilibrium Flow ◽  
Local Extrema ◽  
Ideal Magnetohydrodynamic ◽  
The Ideal

The ideal magnetohydrodynamic spectrum of gravitating plane plasmas with equilibrium flow is investigated. Flow makes the spectral problem non-self-adjoint, so that the spectrum can become overstable. The criteria for cluster spectra to appear are derived analytically and both stable and unstable sides of the spectrum are examined numerically. Above certain critical values of the shear flow at the resonant surface, the gravitating interchange modes disappear. However, the local extrema of the continua can then take over the cluster spectrum.

scholarly journals Kinetic extraordinary-mode eigenvalue equation for relativistic nonneutral electron flow in planar geometry

1989 ◽  
Vol 7 (1) ◽  
pp. 55-84 ◽  
Author(s):  
Ronald C. Davidson ◽  
Han S. Uhm
Keyword(s):  
Electron Flow ◽  
Low Frequency ◽  
Companion Paper ◽  
Field Configuration ◽  
Outer Edge ◽  
Eigenvalue Equation ◽  
Planar Geometry ◽  
Canonical Momentum ◽  
Stability Properties ◽  
Long Wavelength

Use is made of the Vlasov–Maxwell equations to derive an eigenvalue equation describing the extraordinary–mode stability properties of relativistic, non-neutral electron flow in high-voltage diodes. The analysis is based on well-established theoretical techniques developed in basic studies of the kinetic equilibrium and stability properties of nonneutral plasmas characterized by intense self fields. The formal eigenvalue equation is derived for extraordinary-mode flute perturbations in a planar diode. As a specific example, perturbations are considered about the choice of self-consistent Vlasov equilibrium , where . is the electron density at the cathode (x = 0), H is the energy, and Py is the canonical momentum in the Y-direction (the direction of the equilibrium electron flow). As a limiting case, the planar eigenvalue equation is further simplified for low-frequency long-wavelength perturbations with |ω − kvd, ≪ ωυ where and and ⋯c = eB0/mc, and B0ệz is the applied magnetic field in the vacuum region xb < x ≤ d. Here, the outer edge of the electron layer is located at x = xb; ω is complex oscillation frequency; k is the wavenumber in the y-direction; ωυ is the characteristic betatron frequency for oscillations in the x′-orbit about the equilibrium value x′ = x0 = xb/2; and Vd is the average electron flow velocity in the y-direction at x = x0. In simplifying the orbit integrals, a model is adopted in which the eigenfunction approximated by , where x′(t′) is the x′-orbit in the equilibrium field configuration. A detailed analysis of the resulting eigenvalue equation for , derived for low-frequency long-wavelength perturbations, is the subject of a companion paper.

scholarly journals Kinetic ballooning modes in tokamaks and stellarators

2018 ◽  
Vol 84 (6) ◽  
Author(s):  
K. Aleynikova ◽  
A. Zocco ◽  
P. Xanthopoulos ◽  
P. Helander ◽  
C. Nührenberg
Keyword(s):  
Plasma Pressure ◽  
Analytical Prediction ◽  
Ion Temperature ◽  
Ion Temperature Gradient ◽  
Large Pressure ◽  
Equilibrium Configurations ◽  
Mhd Stability ◽  
Ideal Magnetohydrodynamic ◽  
General Geometry ◽  
The Ideal

Kinetic ballooning modes (KBMs) are investigated by means of linear electromagnetic gyrokinetic (GK) simulations in the stellarator Wendelstein 7-X (W7-X), for high-$\unicode[STIX]{x1D6FD}$ plasmas, where $\unicode[STIX]{x1D6FD}$ is the ratio of thermal to magnetic plasma pressure. The analysis shows suppression of ion-temperature-gradient (ITG) and trapped particle modes (TEM) by finite-$\unicode[STIX]{x1D6FD}$ effects and destabilization of KBMs at high $\unicode[STIX]{x1D6FD}$. The results are compared with a generic tokamak case. We show that, for large pressure gradients, the frequency of KBMs evaluated by the GENE code is in agreement with the analytical prediction of the diamagnetic modification of the ideal magnetohydrodynamic limit in W7-X general geometry. Thresholds for destabilization of the KBM are predicted for different W7-X equilibrium configurations. We discuss the relation of these thresholds to the ideal magnetohydrodynamic (MHD) stability properties of the corresponding equilibria.

scholarly journals Weakly nonlinear waves in magnetized plasma with a slightly non-Maxwellian electron distribution. Part 2. Stability of cnoidal waves

2007 ◽  
Vol 73 (6) ◽  
pp. 933-946
Author(s):  
S. PHIBANCHON ◽  
M. A. ALLEN ◽  
G. ROWLANDS
Keyword(s):  
Growth Rate ◽  
Nonlinear Waves ◽  
Electron Distribution ◽  
Magnetized Plasma ◽  
Weakly Nonlinear ◽  
Long Wavelength ◽  
First Order ◽  
Wave Solutions ◽  
Linear Waves ◽  
Weakly Nonlinear Waves

AbstractWe determine the growth rate of linear instabilities resulting from long-wavelength transverse perturbations applied to periodic nonlinear wave solutions to the Schamel–Korteweg–de Vries–Zakharov–Kuznetsov (SKdVZK) equation which governs weakly nonlinear waves in a strongly magnetized cold-ion plasma whose electron distribution is given by two Maxwellians at slightly different temperatures. To obtain the growth rate it is necessary to evaluate non-trivial integrals whose number is kept to a minimum by using recursion relations. It is shown that a key instance of one such relation cannot be used for classes of solution whose minimum value is zero, and an additional integral must be evaluated explicitly instead. The SKdVZK equation contains two nonlinear terms whose ratio b increases as the electron distribution becomes increasingly flat-topped. As b and hence the deviation from electron isothermality increases, it is found that for cnoidal wave solutions that travel faster than long-wavelength linear waves, there is a more pronounced variation of the growth rate with the angle θ at which the perturbation is applied. Solutions whose minimum values are zero and which travel slower than long-wavelength linear waves are found, at first order, to be stable to perpendicular perturbations and have a relatively narrow range of θ for which the first-order growth rate is not zero.

scholarly journals Planet migration and magnetic torques

2015 ◽  
Vol 11 (A29A) ◽  
pp. 14-18
Author(s):  
A. Strugarek ◽  
A. S. Brun ◽  
S. P. Matt ◽  
V. Reville
Keyword(s):  
Numerical Experiments ◽  
Three Dimensional ◽  
Magnetic Star ◽  
Magnetic Topology ◽  
Global Models ◽  
Planet Migration ◽  
Order Of Magnitude ◽  
Ideal Magnetohydrodynamic ◽  
The Impact ◽  
The Ideal

AbstractThe possibility that magnetic torques may participate in close-in planet migration has recently been postulated. We develop three dimensional global models of magnetic star-planet interaction under the ideal magnetohydrodynamic (MHD) approximation to explore the impact of magnetic topology on the development of magnetic torques. We conduct twin numerical experiments in which only the magnetic topology of the interaction is altered. We find that magnetic torques can vary by roughly an order of magnitude when varying the magnetic topology from an aligned case to an anti-aligned case. Provided that the stellar magnetic field is strong enough, we find that magnetic migration time scales can be as fast as ~100 Myr. Hence, our model supports the idea that magnetic torques may participate in planet migration for some close-in star-planet systems.

Effect of Substrate-Surface Orientation on the N Incorporation in GaAsN Films on GaAs Grown by MOVPE

2008 ◽  
Vol 55-57 ◽  
pp. 825-828 ◽  
Author(s):  
P. Klangtakai ◽  
S. Sanorpim ◽  
S. Kuboya ◽  
R. Katayama ◽  
Kentaro Onabe
Keyword(s):  
Growth Rate ◽  
High Performance ◽  
Substrate Surface ◽  
Surface Orientation ◽  
X Ray Diffraction ◽  
N Content ◽  
Long Wavelength ◽  
The Difference ◽  
N Incorporation ◽  
Novel Structures

The GaAs1-xNx alloy semiconductor has been grown on GaAs (001), (111)A and (011) substrates by metalorganic vapor-phase epitaxy. High resolution X-ray diffraction and Raman scattering were employed to examine the effective N content and the growth rate, as a function of the substrate-surface orientation. The growth rate, which was assessed though the clear Pendellösung fringes, and the N content were found to change dramatically with the substrate-surface orientations. The N content was determined in the order (111)A > (001) > (011). While, the growth rate is in the order, (001) > (011) > (111)A. The effect of substrate-surface orientation on the N incorporation found in the present study is interpreted in terms of the difference in the growth rate on each surface orientation and the number of dangling bonds with which the N atoms can be trapped on the growing surface. Our results show that controlled nitrogen incorporating for GaAsN is successfully achieved and can be applied to the fabrication of some novel structures such as a spontaneous N content modulated structure, which is applicable to high performance long wavelength laser diodes.

Wall stabilization in a collisionless bumpy theta-pinch

1977 ◽  
Vol 18 (2) ◽  
pp. 317-337 ◽  
Author(s):  
George Vahala ◽  
Linda Vahala
Keyword(s):  
Growth Rates ◽  
Normal Mode Analysis ◽  
Upper And Lower Bounds ◽  
Mode Analysis ◽  
Well Posedness ◽  
Theta Pinch ◽  
Pressure Anisotropy ◽  
Special Cases ◽  
Ideal Magnetohydrodynamic ◽  
The Ideal

Finite wavelength guiding centre plasma stability of the bumpy θ-pinch is examined by a normal mode analysis. It is shown that previous bumpy θ-pinch calculations are recoverable as special cases of this analysis. The ideal magnetohydrodynamic and guiding centre plasma growth rates are compared for various pressure anisotropies and for various wavenumbers of the field line bumpiness. The well-posedness conditions on the guiding centre plasma equations are shown to give upper and lower bounds on the permissible pressure anisotropy which corresponds to the Aifvén continuum staying on the stable side of the spectrum and to the particle mirror force not having a singularity. It is also found that the higher azimuthal m ≥ 2 modes have growth rates larger than the m = 1 mode.

Axisymmetric Magnetohydrodynamic Equilibria without a Wall

1993 ◽  
Vol 48 (12) ◽  
pp. 1131-1150
Author(s):  
D. Lortz ◽  
W. Haimerl
Keyword(s):  
Magnetic Field ◽  
Homogeneous Magnetic Field ◽  
Mhd Equations ◽  
External Current ◽  
Flux Function ◽  
Plasma Torus ◽  
Ideal Magnetohydrodynamic ◽  
Axisymmetric Configuration ◽  
A Current ◽  
The Ideal

Abstract Starting from the ideal magnetohydrodynamic (MHD) equations, we consider the following axisymmetric configuration: a current-carrying plasma torus in a homogeneous magnetic field that is aligned parallel to the torus axis. At a certain field strength this configuration is in equilibrium without need of external current singularities such as wires or walls.The magnetic flux function is expanded in small inverse aspect ratio. The geometry of this configuration is completely determined to second order as a function of the profile parameters.

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