Hydromagnetic wave propagation in inhomogeneous magnetic fields

Lehane, J.A.; Paoloni, F.J.

doi:10.1088/0032-1028/12/11/001

Cited by 13 publications

(6 citation statements)

References 15 publications

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“…3 (power reflection coefficient of 0.09) for the extreme case of a step change in magnetic field. A recent paper by Cramer [17] gives theoretical calculations that agree favourably with the experimental results of Lehane et al [13].…”

Section: Other Rf Coupling Arrangementssupporting

confidence: 69%

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Some engineering problems of low-frequency heating of fusion reactors

Cato¹,

Kristiansen²,

Hagler³

1972

Nucl. Fusion

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An engineering study of r.f. heating of fusion reactors is described. The frequency range considered is below 100 MHz. Special consideration is given to r.f. structures located between the reactor wall and the plasma in the main fusion region. Possible arcing problems in this region are discussed and it is found that they may not be too serious for neutral pressures below 10−4 torr. It is proposed to feed the r.f. through a slanted vacuum port in order to reduce port area and to protect the voltage insulator from radiation and temperature damage. The cooling of an r.f. coil structure is considered in detail. It is proposed to use a split r.f. coil composed of heat pipes to carry the heat away. Curves are presented which give the maximum r.f. on-time for various coil currents, frequencies, and coil sizes before the coil surface reaches melting temperature. Other coupling schemes involving the use of the vacuum wall as a r.f. structure or locating a wave launcher in the high-field region of a mirror reactor are discussed. In the case of a mirror reactor it is found that this last scheme may be quite attractive since unidirectional couplers can be made and experimental results indicate that the wave reflections may not be too serious in the severe-density and field gradients. This scheme also offers a possible way of launching, for instance, ion-cyclotron waves into very dense plasmas. It is concluded that the engineering problems of fusion-reactor-r. f. heating, albeit formidable, are not impossible.

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Section: Other Rf Coupling Arrangementssupporting

confidence: 69%

“…Reflections due to these gradients could possibly make the plasma region inaccessible. However, in a recent study [13] of the torsional (left hand polarized) and compressional (right hand polarized) waves in an inhomogeneous magnetic field, no reflections were observed for the torsional wave.…”

Section: Other Rf Coupling Arrangementsmentioning

confidence: 85%

Some engineering problems of low-frequency heating of fusion reactors

Cato¹,

Kristiansen²,

Hagler³

1972

Nucl. Fusion

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“…When the local ion cyclotron frequency becomes comparable to the oscillation frequency of the shear wave, additional effects arise such as ion heat-ing, the generation of an axial magnetic field component, and the change from linear to left-hand circular polarization. Stix 62 detailed the cyclotron damping of Alfvén waves in the case of a uniform background magnetic field; experimentally, some of the earliest works on Alfvén waves in nonuniform magnetic fields were performed by researchers [63][64][65] studying the excitation of radial eigenmodes of a cylindrical plasma. The wave propagated axially into a region of decreasing magnetic field to the point where the wave frequency matched the local ion-cyclotron frequency-the socalled ''magnetic beach.''…”

Section: Magnetic Beachmentioning

confidence: 99%

The many faces of shear Alfvén waves

et al. 2011

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One of the fundamental waves in magnetized plasmas is the shear Alfvén wave. This wave is responsible for rearranging current systems and, in fact all low frequency currents in magnetized plasmas are shear waves. It has become apparent that Alfvén waves are important in a wide variety of physical environments. Shear waves of various forms have been a topic of experimental research for more than fifteen years in the large plasma device (LAPD) at UCLA. The waves were first studied in both the kinetic and inertial regimes when excited by fluctuating currents with transverse dimension on the order of the collisionless skin depth. Theory and experiment on wave propagation in these regimes is presented, and the morphology of the wave is illustrated to be dependent on the generation mechanism. Three-dimensional currents associated with the waves have been mapped. The ion motion, which closes the current across the magnetic field, has been studied using laser induced fluorescence. The wave propagation in inhomogeneous magnetic fields and density gradients is presented as well as effects of collisions and reflections from boundaries. Reflections may result in Alfvénic field line resonances and in the right conditions maser action. The waves occur spontaneously on temperature and density gradients as hybrids with drift waves. These have been seen to affect cross-field heat and plasma transport. Although the waves are easily launched with antennas, they may also be generated by secondary processes, such as Cherenkov radiation. This is the case when intense shear Alfvén waves in a background magnetoplasma are produced by an exploding laser-produced plasma. Time varying magnetic flux ropes can be considered to be low frequency shear waves. Studies of the interaction of multiple ropes and the link between magnetic field line reconnection and rope dynamics are revealed. This manuscript gives us an overview of the major results from these experiments and provides a modern prospective for the earlier studies of shear Alfvén waves. V

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“…Experiments have been reported [12,13] for a number of cases treated theoretically above. Excellent agreement with the computed result is shown in Fig.…”

Section: Comparison With Experimentsmentioning

confidence: 99%

On magnetohydrodynamic waves in inhomogeneous magnetic fields

Cramer

1971

Nucl. Fusion

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The theoretical analysis of the propagation of magnetohydrodynamic waves in a cylindrical plasma immersed in a steady inhomogeneous magnetic field is here undertaken by assuming a model field of two constant field regions joined by the field B⃗ = A∇(l/r). We thus consider ‘beach’ and ‘cliff’ magnetic field configurations. The general solution of the coldplasma equations in the central (inhomogeneous field) region must be found numerically, but in the low-frequency case analytic solutions are obtained. The wave reflection and transmission found by applying boundary conditions at the constant field.Solutions are so obtained for a variety of cases, including simple reflection of the compressional and torsional modes, reflection of the compressional mode when the cutoff condition is encountered, absorption of the torsional mode at the ioncyclotron resonance, and conversion of one mode into the other after propagation through both of the above conditions. Finally, comparison is made with several recent experiments, which shows that the above theory is sufficient in the case that the wave frequency is not too close to the resonance frequency.The case of reflection of compressional waves from the cutoff shows good agreement between theory and experiment, except in the high field region, where apparently the waves are not confined by the magnetic field lines. Reflection of torsional waves close to the resonance condition shows disagreement in the transition region, where the experimental wave energy is as great as 4 times as large as that predicted both by the above theory and the WKB method.

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Hydromagnetic wave propagation in inhomogeneous magnetic fields

Cited by 13 publications

References 15 publications

Some engineering problems of low-frequency heating of fusion reactors

Some engineering problems of low-frequency heating of fusion reactors

The many faces of shear Alfvén waves

On magnetohydrodynamic waves in inhomogeneous magnetic fields

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