Schematic of the LAPD (a) and the laser-target configuration (b). The graphite target is located at 5 m axially from the anode and x = 13 cm from the symmetry axis of the cylindrical vacuum vessel. An f/6 lens inserted into the plasma focuses the beam onto the target surface (x = 13 cm, y = 0, z = 0) with an angle of incidence of 43°. The magnetohydrodynamic response of the ambient plasma across and along the field is measured with an array of magnetic flux probes that can be translated in the x-direction.
Magnetic-flux probe measurements of the evolution of the magnetic field ( ) at distances of 4 cm, 9 cm, 14 cm, and 22 cm from the target in at 275 G (a). The field compression increases with distance from the target, reaching a steady from 14 to 22 cm. Inside the bubble, the field is fully expelled but diffuses back into the bubble-volume after about 1 μs. (b) The contour-plot of the same data is a composite of 80 laser shots and shows as a function of time with a spatial resolution of 5 mm. To obtain this data, the perpendicular probe was moved to a different x-location in each shot. The compression of the expelled field at , formation and collapse of the magnetic bubble, and subsequent propagation of a fast magnetosonic pulse are clearly visible. The dimensionless axes represent the spatial and temporal scales with respect to the upstream ion-inertial length and ion-gyroperiod. Downstreaming the length-scales and time-scales are slightly better, considering the compressed field. The left dashed line indicates the time of peak compression.
Ion-saturation-current measurements show electron heating at the edge of the diamagnetic cavity, and the blow-off plasma filling the bubble volume (a). The contours of the magnetic field (for and 50%) as well as the time of peak compression from Fig. 2(b) are shown for comparison. The contour (a) is a composite of 20 separate laser shots with the Langmuir probe moved to different distances from the laser-target (in the direction perpendicular to the external field). (b) Evolution of and the Bdot-probe signal 13 cm from the target. The first negative spike in the Langmuir probe signal coincides with the time of peak-compression, while the second negative spike occurs during field expulsion. The data also display high frequency ( ) oscillations inside the bubble.
Hybrid simulation of the laser-plasma expansion in the preformed plasma and magnetic field. (a) Streak plot of the magnetic field profile during the first along the x-axis. A debris cloud containing explodes spherically into a background in 275 G from x = 0 at . The formation of the diamagnetic cavity and magnetosonic pulse propagating away from the bubble are clearly visible. Plots (b) and (c) show the background and debris ion densities, respectively.
A composite image of the magnetic field strength , a sampling of background ions (blue dots), a sampling of debris ions (red dots), along with trajectories of a couple of background (light blue) and debris (yellow) ion trajectories throughout the course of the simulation. The markers on the trajectories correspond to the test particle's current position at .
A shear-Alfvén wave is launched by the diamagnetic bubble and propagates over several meters along the machine (z-axis) at . A fast wave procedes the shear-wave at , corresponding to electrons with a kinetic energy of 25 eV. (a) Evolution of and at y = 0, from the target, and x = 9 cm from the center of the plasma column. (b) Contour plot of the transverse field component ( ) as a function of time and spatial coordinate along the field (z). The plot is comprised of simultaneous measurements from 9 magnetic pickup coils distributed at longitudinal positions between 2 m and 6.8 m. (c) Total transverse field component as a function of both transverse dimensions in a vertical plane at from the target at . The coaxial current system is clearly visible and is aligned with the center of the plasma column. The arrows indicate the transverse direction of the magnetic field, while the rectangle at (x,y) = (9, 0) cm indicates the probe location for plots (a) and (b).
Evolution of the shear-wave amplitude as a function of distance from the target. The figure shows the magnetic field magnitude at the transverse location where it peaks, at distances of (black), 1.0 m (blue), 2.9 m (green), and 6.8 m (red). The magnitude drops from 80 G near the target to less than 20 G at a distance of several meters.
Evolution of the transverse magnetic field component at y = 0 as a function of transverse position across the plasma column (x), at a distance of from the target in the axial direction (a). The contour plot shows a composite of 45 laser shots where the magnetic probe was moved to a different x-position in each shot. A shear-Alfvén wave passes that probe roughly 15 μs after the laser-trigger, consistent with an Alfvén speed of 330 km/s. A fastwave is also visible preceding the shear-wave. (b) Line-out of as a function of x at the time when the peak of the pulse passes the probe (t = 15 μs). The data are consistent with a pseudo-coaxial current system centered near the middle of the plasma column (x = 3 cm) although the target was located at x = 13 cm. The shear-wave carries a total current around 1 kA distributed over a 20 cm diameter channel, creating a traverse field up to 15 G (or ). We observe current densities around in the center with a return current around carried in a concentric shell.
Auto-spectrum of the magnetic flux probe signal from Figure 6(a) [i.e., at (x,y,z) = (12,0,680) cm]. The exploding laser-plasma creates waves over a large frequency range in the ambient plasma, both above and below the ion cyclotron frequency ( ). The data display a compressional mode at early times around 5–10 μs, decreasing in frequency from 1 MHz to 0.5 MHz, as well as a shear-Alfvén wave at later times around 20 μs at a frequency around 40 kHz .
Variation of the signal with laser-energy 6.8 m axially from the target at (x,y) = (10,0) cm (a). The frequency of the fast wave and the temporal shape and arrival time of the shear-Alfvén pulse are independent of the laser-energy. The transverse field during the passage of the shear-Alfvén pulse at around 20 μs as well as the compressional mode around 10 μs scale linearly with the on-target laser-energy (b). The amplitude of the shear-wave is a factor of two larger than the amplitude of the largest pulse in the compressional wave-train.
Center of the axial current system as a function of longitudinal distance from the target for 275 G, 600 G, and 1800 G (a). The target was located at x = 13 cm with the blow-off directed in the negative x-direction. In each case, the center position was evaluated at the time when the shear-wave field is at maximum for each . The data indicate that the current system that develops into the shear-Alfvén wave is centered around the projection of the bubble edge onto the plasma column (see Table I ). Specifically, the edge of the bubble is located at x = −7 cm for 275 G, x = 2 cm for 600 G, and x = 8 cm for 1800 G, roughly consistent with the current center location upstream from the target. We also observe a fast temporal shift of the current center during the passage of the Alfvénic pulse: (b) shows themagnetic flux probe signal ( ) for at x = 10 cm and cm axially from the target. The location of the current center (i.e., the transverse location x where changes sign) at 1.6 μs during the peak of the pulse is located around x = 8 cm and thus the projection of the edge of the bubble. A few 100 ns after the peak of the pulse the center shifts rapidly towards the center of the vacuum vessel (x = 0) and the wave becomes a plasma column resonance.
Summary of measured key-parameters for experiments with different ambient ion species, external field, and laser-blow-off velocity ( ). The on-target laser energy was kept constant at 20 J for all runs. The blow-off velocity was varied in run 2 by defocusing the laser-beam. The maximum bubble size is defined here as the diameter of the volume with a depth below . At 1800 G, there are not enough fast debris ions to fully expel the field, and the depth of the bubble is at most . The table also lists the peak compression ratio at the edge of the cavity, the total current carried by the shear-wave, the wave amplitude at a distance of 5.2 m from the target, the center location ( ), and the width of the current channel. Also shown are the energy carried by the shear-wave, and the frequencies of the shear-wave ( ) and the fast wave ( ).
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