Betatron-modified ion-acoustic instability of the Bennett equilibrium

Krishnamurthi, U.; Sen, Abhijit; Sharma, A. S.; Sundaram, A. K.

doi:10.1088/0029-5515/25/8/008

Cited by 3 publications

(6 citation statements)

References 17 publications

(26 reference statements)

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“…In the Bennett equilibrium of a cylindrical plasma column, an axial current produces the confining azimuthal magnetic field. The equilibrium, particle orbits and stability analysis of the Bennett pinch have already been presented in Refs [10,11,15]. The essential features of the analysis are presented here, and then the case of the low frequency MHD stability is developed.…”

Section: Kinetic Stability Theorymentioning

confidence: 98%

“…dTV z (r)A lz (r')exp(i^) (10) where \J/ = -COT + k(z' -z) -I-m(0' -0), are to be integrated along the betatron orbits discussed earlier [10,15]. When the particle orbits have small excursions the functions ^i(r') and A u (r') may be Taylor expanded, and this leads to the differential equations for the radial eigenmode, Eqs ( 7) and ( 8).…”

Section: Kinetic Stability Theorymentioning

confidence: 99%

“…This self-consistent magnetic field vanishes on the plasma axis and, consequently, the particles have large excursion betatron orbits [10]. The ion betatron motion in the Bennett equilibrium has been found to have a stabilizing influence on the ion acoustic instability [15]. In this paper, the kinetic stability of the low frequency electromagnetic mode with the azimuthal mode number m = 1 in the Bennett pinch is analysed.…”

Section: Introductionmentioning

confidence: 98%

“…Secondly, the use of a diffuse profile, such as the Bennett profile, is important since the growth rate of MHD instability for the diffuse profile is about onethird the growth rate for the sharp boundary case [17]. The kinetic integral stability theory developed earlier [10,15] is used to derive the matrix dispersion relation for this low frequency MHD mode. The eigenvalues are then obtained by using methods for finding matrix eigenvalues.…”

Section: Introductionmentioning

confidence: 99%

“…The eigenvalues are then obtained by using methods for finding matrix eigenvalues. As in the low frequency electrostatic case [15], this matrix dispersion relation can be approximated by a simplified dispersion relation. The eigenvalues obtained from this dispersion relation are found to be very close to those obtained from' the matrix dispersion relation.…”

Section: Introductionmentioning

confidence: 99%

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Kinetic theory of the m = 1 kink instability in Z-pinches

1988

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The kinetic theory of the m = 1 kink instability of a Z-pinch with Bennett profile is presented. The dominant particle trajectories in the equilibrium field are the large excursion betatron orbits. To deal with these orbits, an integral formulation of the stability analysis is adopted. In this case, the dispersion relation is expressed as the determinant of a matrix. In the limit where the electrostatic perturbation is neglected, the eigenmodes are computed numerically from this dispersion relation. Two methods are used to obtain the growth rates, and the computed values agree very well. The Landau damping of the mode is found to be strong enough to stabilize the mode at shorter wavelengths. This may explain the stability of the kink mode in some experiments.

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Section: Kinetic Stability Theorymentioning

confidence: 98%

Section: Kinetic Stability Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Kinetic theory of the m = 1 kink instability in Z-pinches

1988

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Finite Larmor radius effects on the stability properties of internal modes of aZ-pinch

Åkerstedt

1988

Phys. Scr.

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are considered. In Section 3 we consider the stability of those From the Vlasov-fluid model a set of approximate stability equations describing the stability of a cylindrically symmetric z-pinch is derived. The equations are derived in the limit of small gyroradius and include first order kinetic effects such as finite ion Larmor radius effects and resonant ion effects. Neglecting the resonant ion terms, we explicitly solve this set of equations for a constant current density profile leading to a dispersion relation. FLR effects are shown for the case of m = 1 internal mode to be stabilizing and for large wavenumbers k, using a trial function approach, absolute stabilization is found.

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Non-local theory of the resistive hose instability of beams with the Bennett profile

1991

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The resistive hose instability of nonrelativistic counter-streaming electron and ion beams propagating through a background plasma with finite conductivity is analyzed by a non-local kinetic theory. The beam as well as the plasma have the Bennett profile and the dominant orbit of the beam particles is taken to be betatron orbits. The eigenmodes are expressed in terms of the zeroes of a Bessel function, and the non-local effects are taken into account by this integral formulation of the stability analysis. In general the eigenvalues of the resistive hose mode are numerically computed from a matrix dispersion relation. A reduced dispersion relation is derived from the general case and this may be solved analytically in the long wavelength limit. The new physical effect considered in this paper is the Landau damping due to the spread in the axial velocity. Thi effect has significant stabilizing influence on the hose eigenmode.

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Betatron-modified ion-acoustic instability of the Bennett equilibrium

Cited by 3 publications

References 17 publications

Kinetic theory of the m = 1 kink instability in Z-pinches

Kinetic theory of the m = 1 kink instability in Z-pinches

Finite Larmor radius effects on the stability properties of internal modes of aZ-pinch

Non-local theory of the resistive hose instability of beams with the Bennett profile

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