Direct Detection of Resonant Electron Pitch Angle Scattering by Whistler Waves in a Laboratory Plasma

Resonant interactions between energetic electrons and whistler mode waves are an essential ingredient in the space environment, and in particular in controlling the dynamic variability of Earth’s natural radiation belts, which is a topic of extreme interest at the moment. Although the theory describing resonant wave-particle interaction has been present for several decades, it has not been hitherto tested in a controlled laboratory setting. In the present Letter we report on the first laboratory experiment to directly detect resonant pitch angle scattering of energetic ($\sim \mathrm{keV}$) electrons due to whistler mode waves. We show that the whistler mode wave deflects energetic electrons at precisely the predicted resonant energy, and that varying both the maximum beam energy, and the wave frequency, alters the energetic electron beam very close to the resonant energy.

Figure 1

Sketch of the experimental setup (not to scale). A 10 cm diameter electron beam launches electrons with energies up to 5 keV. Whistler waves are launched on the same field lines with a loop antenna in the frequency range $0.2–0.4{\mathrm{\Omega }}_e$. The plasma is diagnosed with Langmuir probes, magnetic field probes and fast particle detectors.

Figure 2

Upper panel: cutaway view of the fast particle detector, showing the grids, collector, housing and $150\hspace{0.17em}\mu \mathrm{m}$ entrance hole. Lower panel: Calculated pitch angle sensitivity of the fast particle detector as a function of electron beam energy. Electrons with $E>0.5\mathrm{keV}$ and pitch angle larger than 10° will hit the side wall and will not be detected.

Figure 3

Profiles of electron beam current density, panel (a), and whistler wave magnetic field, panel (b), in a plane perpendicular to the background field. Beam densities are on the order of ${10}^{-5}$ of the plasma density and whistler amplitudes are on the order of ${10}^{-4}$ the background magnetic field.

Figure 4

Panel (a): time traces of beam voltage and measured electron beam current density both with and without the whistler wave present where $f=180\mathrm{MHz}$. Panel (b): difference of beam current density with/without whistler waves plotted versus beam voltage with $f=180\mathrm{MHz}$. Panel (c): difference signal with maximum beam ramp voltage ranging from 0.5 to 2.5 kV and $f=200\mathrm{MHz}$.

Figure 5

Threshold beam voltage, i.e., resonant electron energy, for signal reduction on the fast particle detector. Shaded region represents the theoretical prediction for $n=1.1\times 10^{12}{\mathrm{cm}}^{-3}$, for a range of $k_{\perp }$ from $0{\mathrm{cm}}^{-1}$ up to $1{\mathrm{cm}}^{-1}$, obtained from the data in Fig. 3. $k_{\parallel }$ at 180 MHz ranges from 1.36 to $1.29{\mathrm{cm}}^{-1}$ inferred from the whistler dispersion relation.

Figure 6

Signal reduction on fast particle detector versus whistler wave input power, taken at $x=1.5\mathrm{cm}$, $y=0.5\mathrm{cm}$.