Helicons in Unbounded Plasmas

Helicons are whistler modes with helical phase fronts. They have been studied in solid state plasmas and in discharge tubes where boundaries and nonuniformities are ever present. The present work shows that helicons also exist in unbounded and uniform plasmas, thereby bridging the fields of laboratory and space plasma physics. First measurements of helicon field lines in three dimensional space are presented. Helicons with negative and positive mode numbers can propagate with equal amplitudes.

Figure 1

Picture of the discharge plasma produced by a 1 m diam oxide coated cathode. A 4 cm diam loop antenna is inserted down into the uniform plasma center to excite helicon modes. A circular array for exciting $\pm m$ helicons is shown schematically.

Figure 2

Measured fields of an $m=0$ whistler mode. (a) Contours of the axial field component $B_z(y,z)$ in arbitrary units (arb. units) excited by a dipolar field from the loop antenna. It is the axial component of a poloidal field of a vortex (see black line). (b) Contours of the azimuthal field $B_x(y,z)$ which forms a toroidal field in the $x\text{−}y$ plane (see black line). The poloidal and toroidal fields are linked, which produces positive magnetic helicity. (c) 3D view of the semitransparent conical isosurfaces of $B_z$ with embedded field lines. The field lines are confined to half wave sections of opposite field directions. On the central axis spiral null points are formed where $B_z\simeq 0$. (d) 3D field lines in sections of positive and negative $B_z$ showing field line spirals with opposite directions but same right-handed field line rotation or positive helicity. The color of the lines reflects the sign of $B_z$. Here, arb. units stands for arbitrary units.

Figure 3

Properties of $m=1$ whistler modes. (a) Schematic picture of fields and currents near a loop antenna with dipole moment across ${\mathbf{B}}_0$. (b) Schematic picture of the wave fields decomposed into linked loops for purpose of simplification. (c) Contours of the three measured field components in the $y\text{−}z$ plane of the loop ($x=0$). The $V$-shaped phase fronts indicate oblique propagation in the Gendrin mode. The $B_x$ and $B_y$ components are shifted by $\lambda /4$ indicating circular polarization. (d) Contours of the axial field component $B_z$ and vector field of $(B_x,B_y)$ in the $x\text{−}y$ plane at different times within one rf period. The field rotates in the same sense and rate as electrons rotate around ${\mathbf{B}}_{\mathbf{0}}$, i.e., clockwise in space. (e) Selected 3D field line for an $m=+1$ helicon mode which forms two left-handed spiraling helices of opposing field line direction with closure at left side. (f) Isosurfaces of $B_z=\mathrm{const}$ indicating the helical phase fronts of a helicon mode. Field lines lie inside the phase fronts. (g) Multiple 3D field lines started in different $x\text{−}y$ planes, showing field line closure and formation of the helical spirals. On the left side, the spiral closes via transverse fields through the axis. As the starting plane is shifted in $z$, the transverse field rotates consistent with circular polarized whistlers. Off axis, the field lines are guided by the rotating $B_z$ field into spirals tangential to the phase fronts or isosurfaces. The color of the field lines indicates the field strength which peaks near the axis of the spirals.

Figure 4

Field lines and $B_z$ components of a dipole field generated by two adjacent $m=0$ loop antennas. (a) $B_z(x,y)$ contours and isosurfaces and a closed field line in an axial half wavelength segment of the wave train. The field line is traced from a point near a null in $B_z$. (b) Multiple isosurfaces showing no rotation of $B_z$ which can be considered a superposition of $m=1$ and $m=-1$ modes. A field line is launched at the peak of $B_z$ and meanders through the isosurfaces along the whole wave train. The transverse $B$ vector on axis rotates left handed in space or right handed in time appropriate for whistlers. Thus, the helicon can be considered an $m=\pm 1$ mode.

Figure 5

Rotating field of a hexapole antenna exciting $m=\pm 3$ helicon modes. (a) Contours of $B_z(x,y)$ and 3D field lines showing six left-handed spirals characteristic for an $m=+3$ helicon. (b) Isosurfaces $B_z(x,y,z)=\mathrm{const}$ showing spiraling phase fronts of the propagating helicon wave. The pitch is three axial wavelengths. Field lines are nearly parallel to the phase front. (c) Same as (a) but with reverse rotation of the antenna field. It creates an $m=-3$ helicon mode which is just as strong as the $m=3$ mode. (d) Same as (b) but for clockwise rotation which produces an $m=-3$ helicon.