UCLA BPPL - Helicity Injection and Conservation

EMHD vortices have the unique property that their helicity depends on the direction of propagation along B0. This is demonstrated in the figure below: A pulsed loop antenna excites in the plasma a time-varying field perturbation with (a) a toroidal field and (b) a linked poloidal field. The linkage is right handed when the vortex propagates along B0 and left-handed for propagation against B0. Consequently, (c) the magnetic helicity density (self helicity) reverses sign on either side of the loop antenna.

EMHD vortex

Excitation of a a small-amplitude whistler vortex with a loop antenna. Snapshots of (a) the toroidal field, (b) the poloidal field, and (c) the magnetic helicity density.

Helicity conservation implies that the injection of helicity produces unidirectional emission of vortices. Helicity injection can be accomplished with knotted or linked antenna currents. A magnetic antenna, consisting of a loop linked through a torus, exhibits vacuum fields similar to to plasma fields of EMHD vortices.

Directional antenna

Directional antenna consisting of a wire-wound loop antenna placed in the center of a torus. Current linkage produces helicity whose sign depends on relative current directions. Helicity conservation produces a unidirectional emission of EMHD vortices.

Experiments show that for positive antenna helicity only a vortex propagating along B0 is excited, for negative antenna helicity only a vortex opposite to B0 is produced with typically 20dB directivity (forward/backward energy ratio 100:1).

Directionality of antenna

Directionality of helicity antennas. Solid line shows transmission between two directional antennas with matched helicities. Dashed line shows transmitted signal for antennas with unmatched helicities.

The sign of the antenna helicity is determined by the relative direction of the current flow in the loop and torus. The antenna directionality based on helicity matching also holds for the detection of vortices. Transmission between two identical loop-torus antennas is unidirectional and non-reciprocal. Helicity receiving antennas have also been used to measure the degree of helicity of natural whistler wave noise in the discharge plasma. Observations showed that the magnetic fluctuations in the low frequency whistler branch exhibit more negative than positive helicity, implying preferential propagation against B0 or along the beam of primary electrons emitted by the cathode. The latter excites oblique whistlers by a Cherenkov instability.

Theoretically, magnetic helicity is an invariant in an ideal fluid. However, a dilemma arises when a vortex reflects from a conducting boundary: Its helicity must change sign since the direction of wave propagation changes. This is indeed observed. The violation of helicity conservation is explained by a breakdown of the frozen-in condition near the plasma-boundary interface. Field-line tying is not observed.

Mutual and self helicities

Magnetic helicity of an EMHD vortex before and after reflection from a conducting plate. (a) Contours of mutual helicity and (b) self helicity of the vortex field per axial length. The exciter is located at z = 0 and vortices propagate in ±z direction. The left-going vortex is reflected at z = -25 cm and changes magnetic helicity. During reflection energy is conserved but helicity is not.

Helicity conservation also breaks down when an EMHD vortex propagates through a 3D magnetic null point where the direction of B0 reverses sign. This is demonstrated by inserting a small antenna into the center of a Helmholtz coil field and launching a vortex along the axis of the quasi-dc field-reversed configuration. As the vortex approaches the null point it slows down and its amplitude decays. A small fraction of the incident vortex tunnels through the null point and continues to propagate with opposite helicity. The breakdown of helicity conservation is explained by the fact that at the null point the frozen-in condition is not satisfied and EMHD physics is not applicable.

Mutual and self helicities of wave passing through null point

Magnetic helicity of an EMHD vortex propagating in -z direction through a 3-D magnetic null point at z = -15 cm. (a) Mutual and (b) self magnetic helicity per axial length in the absence of a null point (red data) and presence of a null point, which reverses the sign of the helicity. Both energy and magnitude of the helicity decrease as the vortex tunnels through the null point.

References