Helicon Dispersion Research Articles

Helicon waves in a converging-diverging magnetoplasma

Waves propagating along a converging-diverging rf magnetoplasma having the characteristics of a bounded m = 0 helicon mode are reported and characterised. The discharge features a 30cm separation between the region of radiofrequency energy deposition by a single loop antenna and the region of maximum magnetic field applied by a pair of coils. With 200W of rf input power, up to a five-fold increase in axial plasma density between the antenna and the magnetic mirror throat is observed together with an Ar II blue-mode. Two dimensional B-dot probe measurements show that the rf magnetic fields are closely guided by the converging-diverging geometry. The wave is characterised as a m = 0 mode satisfying the helicon dispersion relation on-axis with radial boundary conditions approximately matching the radii of the plasma column. Analysis of the wave phase velocity and wave axial damping failed to identify collisionless or collisional wave-plasma coupling mechanisms. Instead, the wave axial amplitude variations can be explained by local wave resonances and possible reflections from localised rapid changes of the refractive index. A Venturi-like effect owing to the funnel-shaped magnetoplasma and conservation of the wave energy may also explain some level of amplitude variations.

A high power, high density helicon discharge for the plasma wakefield accelerator experiment AWAKE

A plasma cell prototype for the plasma wakefield accelerator experiment AWAKE based on a helicon discharge is presented. In the 1 m long prototype module a multiple antenna helicon discharge with an rf power density of 100 MW m−3 is established. Based on the helicon dispersion relation, a linear scaling of plasma density with magnetic field is observed for rf frequencies above the lower hybrid frequency, ωLH ≤ 0.8ωrf. Density profiles are highest on the device axis and show shallow radial gradients, thus providing a relatively constant plasma density in the center over a radial range of Δr ≈ 10 mm with less than 10% variation. Peak plasma densities up to 7 × 1020 m−3 are transiently achieved with a reproducibility that is sufficient for AWAKE. The results are in good agreement with power balance calculations.

Pseudomagnetic helicons

The existence of pseudomagnetic helicons is predicted for strained Dirac and Weyl materials. The corresponding collective modes are reminiscent of the usual helicons in metals in strong magnetic fields but can exist even without a magnetic field due to a strain-induced background pseudomagnetic field. The properties of both pseudomagnetic and magnetic helicons are investigated in Weyl matter using the formalism of the consistent chiral kinetic theory. It is argued that the helicon dispersion relations are affected by the electric and chiral chemical potentials, the chiral shift, and the energy separation between the Weyl nodes. The effects of multiple pairs of Weyl nodes are also discussed. A simple setup for experimental detection of pseudomagnetic helicons is proposed.

Helicons in Weyl semimetals

Helicons are transverse electromagnetic waves propagating in three-dimensional (3D) electron systems subject to a static magnetic field. We present a theory of helicons propagating through a 3D Weyl semimetal. Our approach relies on the evaluation of the optical conductivity tensor from semiclassical Boltzmann transport theory, with the inclusion of certain Berry curvature corrections that have been neglected in the earlier literature (such as the one due to the orbital magnetic moment). We demonstrate that the axion term characterizing the electromagnetic response of Weyl semimetals dramatically alters the helicon dispersion with respect to that in nontopological metals. We also discuss axion-related anomalies that appear in the plasmon dispersion relation.

Propagation of guided modes in strongly non-uniform helicon-produced plasma

Theoretical as well as numerical analysis of the full set of Maxwell's equations was carried out to study axisymmetric (m = 0) as well as non-axisymmetric (m ≠ 0) guided modes in a helicon discharge (radius R). In detail, the propagation of various guided modes for conditions of strong radial inhomogeneity was treated. The m = 1 helicon dispersion exhibits for kzR≪1 a quadratic frequency dependence on the axial wavenumber, ω∝kz2, if the radial density gradient is steep enough. These modes reveal non-reciprocal behavior with respect to the azimuthal (θ) direction, that is, only modes with positive azimuthal mode numbers, m > 0, can propagate. This is in contrast to the linear dispersion relation, ω∝kz (kzR≪1), for common helicon mode propagation in weakly non-uniform plasma. The results agree reasonably with those obtained from the 2nd-order helicon wave equation derived for Ez = 0. Furthermore, guided electrostatic (ES) modes were analyzed using the 2nd-order wave equation and their eigen mode spectrum wa...

Potential formulation of the dispersion relation for a uniform, magnetized plasma with stationary ions in terms of a vector phasor

The derivation of the helicon dispersion relation for a uniform plasma with stationary ions subject to a constant background magnetic field is reexamined in terms of the potential formulation of electrodynamics. Under the same conditions considered by the standard derivation, the nonlinear self-coupling between the perturbed electron flow and the potential it generates is addressed. The plane wave solution for general propagation vector is determined for all frequencies and expressed in terms of a vector phasor. The behavior of the solution as described in vacuum units depends upon the ratio of conductivity to the magnitude of the background field. Only at low conductivity and below, the cyclotron frequency can significant propagation occur as determined by the ratio of skin depth to wavelength.

Characterization of a helicon plasma source in low diverging magnetic fields

A detailed experimental characterization has been performed of a helicon mode in low nonuniform magnetic fields (B0 < 5 mT) for pressures between 0.04 Pa < p0 < 0.4 Pa and rf powers between 50 W < P0 < 400 W, using a number of electrostatic probes as well as circuit measurements of the antenna and matching network system. The helicon mode is produced over a narrow range of magnetic field values, where a distinct density peak is formed that becomes broader (and higher) as the power or pressure is increased. The density peak is found to shift to larger magnetic fields for increasing powers or pressures, giving an almost linear relationship between the maximum density and the magnetic field at this maximum density, in agreement with helicon dispersion theory. The density within the peak (>1017 m−3) is more than an order of magnitude larger than that before or after, and is associated with a corresponding peak in the measured antenna resistance, thus showing a larger percentage of the input power is deposited within the plasma.

Helicon wave propagation in the SHEILA heliac

The behaviour and structure of waves launched from a novel double-loop antenna in the SHEILA heliac are presented. Radial wave field and azimuthal phase measurements are compared with cylindrical helicon wave theory after an appropriate magnetic coordinate transformation. This comparison provides strong evidence for the involvement of helicon waves. Damping of the waves is investigated by comparing measured spatial damping rates with theoretical estimates. Comparison of measured density with predictions from the helicon dispersion relation reveals how geometry influences propagation of the waves in SHEILA.

Resonance wave discharge and collisional energy absorption in helicon plasma source

The concept of the 'resonance' wave discharge is introduced to explain the high absorption efficiency of inductively coupled helicon plasma source. This discharge is supported by long-scale weakly damped eigenmodes excited in plasma resonator. The RF power absorbed in it is inversely proportional to electron collision frequency. The fields excited by simple single-loop inner antenna and its impedance are calculated in a cylindrical metal resonator. At low collision frequencies the field amplitudes and antenna resistance are shown to peak sharply near the helicon dispersion branches.

Helicon dispersion and damping in aluminium

AbstractThe transmission of helicons through Al slabs has been investigated experimentally and numerically for q ∥ B ∥ [100] and [110]. In the former case oscillations are observed, for B smaller than the cut‐off field for helicons which might be of the Gantmakher‐Kaner type. Finally, the Landau damping for B not parallel to q is investigated. For comparison with the theory the non‐local magnetoconductivity tensor is calculated from Ashcroft's Fermi surface model and the helicon dispersion relation is solved numerically. This leads to a good overall interpretation of the experiments.

Quantum Oscillations of Microwave Helicon Dispersion inn-Type InSb and InAs

The effect of orbital quantization on microwave helicon dispersion in $n$-type InSb and InAs is investigated theoretically and experimentally. In the local limit, the leading term describing helicon dispersion is, unlike helicon damping, unaffected by orbital quantization. Quantum effects enter through the scattering-dependent terms involved in the dispersive part of the helicon propagation constant. The main contribution is shown to be associated with the Shubnikovde Haas-like oscillations of the scattering correction to the dissipationless Hall conductivity. Experimental measurements of the transmitted helicon phase observed at quantizing magnetic fields in highly doped $n$-type InSb and InAs at 35 GHz and liquid-helium temperature are compared with the theory. The magnetic field dependence of the observed oscillations in helicon phase agrees reasonably well with the theoretical analysis. While little can be said analytically about the amplitude of these oscillations (of the order of a few percent), our data does provide an empirical measure of the limits within which the usual classical analysis of helicon dispersion is valid. Finally, the effect of quantum oscillations appears to be considerably stronger in the helicon dispersion than in the related dc problem of the Hall coefficient.

Helicon-Acoustic Dispersion Relations in Metals: Effective-Mass and Relaxation-Time Dependence

The electromagnetic, constitutive, and lattice equations governing propagation of transverse acoustic and electromagnetic waves in a metal with conduction electrons possessing a constant scalar effective mass, and in which there is a uniform magnetic field applied along the propagation direction, are given. These equations are used to derive a secular equation describing the dispersion of interacting helicon and acoustic waves, and in which additional structure arising from the difference between the free-electron mass and the effective electron mass is evident. Magnetoacoustic attenuation, the dispersion and damping of uncoupled helicon waves, and the helicon-acoustic interaction are then analyzed in turn. Numerical solutions of the helicon dispersion relation are presented. The dispersion curve displays a branching in the absorption-edge region. A simple analytic treatment of the relaxation-time and effective-mass dependence of the helicon-acoustic interaction is given. The interaction near and in the absorption-edge region is investigated numerically. A rather large effect of this interaction on the magnetoacoustic absorption of potassium in the edge region is found.

Effect of anisotropy on helicon dispersion relation in tellurium - doped bismuth

Abstract Microwave helicon transmission through Te-doped Bi was measured in a pulsed magnetic field. It was found that the dispersion relation depends strongly on the mass density. The effective mass as well as the carrier density were determined from the experiment.

Interferometric Measurement of Microwave Helicon Dispersion and the Hole Damping Effect in Intrinsic InSb

Interferometric Measurement of Microwave Helicon Dispersion and the Hole Damping Effect in Intrinsic InSb

Instability in the Quantum Helicon Dispersion Relation

The classical stability theorem for the conventional thermal equilibrium state of an electron gas in a uniform magnetic field is generalized to (a) the semiclassical case, (b) the quantum case when there is no magnetic field, and (c) the quantum case in the presence of a magnetic field, provided that only Coulomb interactions, are retained. However, when the quantum gas in a magnetic field is treated with all electromagnetic interactions, at very low temperatures it becomes unstable against transverse excitations propagating in the direction of the field. This instability appears as a root of the quantum helicon dispersion relation in the upper half frequency plane. It is shown that the instability is due to the failure of the conventional Hartreeground state (in which the one-electron states are the ordinary Landau ones) to minimize the ground-state energy, when magnetic current-current interactions are retained along with Coulomb interactions. We have found a state giving a lower energy than the conventional one, in which transverse volume currents exist perpendicular to the magnetic field. Because, however, the magnetic coupling is very weak, the reduction in energy is unobservably small at any realistic field strengths or electronic densities. We conclude that the instability does not lead to any measurable effects, and that for all practical purposes the conventional thermal equilibrium state can be regarded as stable.

Correlation effects and the helicon dispersion relation

Correlation effects and the helicon dispersion relation