Experimental Characterization of Electron Acoustic Waves (EAW)

1. Trivelpiece Gould EAW Electron Acoustic Waves (EAW)EAW’s are novel kinetic waves that exist only because nonlinear trapping turns off Landau damping. We recently provided the first experimental characterization of EAW’s, showing that they are easily excited by low a amplitude drive applied at the theoretically predicted frequency. The driver automatically creates the required trapped particle distribution. Surprisingly, large amplitude drives excite the modes off resonance over a broad range of frequencies. The driver modifies the particle distribution until a kinetic wave can exist at the driver frequency. The results are summarized in the figure on the right. The blue crosses and squares are linear Langmuir waves (called Trivelpiece-Gould waves for a magnetized plasma column), and the red dots and crosses are the EAW’s. Both sets of points lie close to the theoretically predicted dispersion curve. The broad purple bar shows the frequency range over which EAW-like waves (KEEN waves ?) are excited by a large amplitude drive.

2. 2000 velocity [ m/s ] -2000 0 90 180 270 360 Wave phase EAW’s continued.To measure the trapped particle velocity distribution we developed a post-hoc coherent detection technique for our laser induced fluorescent measurements, in which the arrival time of every photon is recorded and later binned according to wave phase. The figure on the left shows a schematic of the pure ion plasma device and associated LIF system, and the figure on the right shows the measured phase space velocity distribution for an EAW. A trapped particle region is clearly visible at the wave phase 180 degrees. (Note that electron acoustic wave is a misnomer; the wave dynamics involves only a single species, so the wave exists in a pure ion plasma.)

3. Axial trapping separatrices are ubiquitous in plasmas, and traditional Neo-Classical Transport theory calculates transport effects from collisional separatrix crossings. Recent experiments and theory show that "chaotic" separatrix crossings may dominate, arising from plasma rotation across a "ruffled" separatrix s = V0 +Vmcos(m), or from wave-induced separatrix fluctuations. Chaotic Neo-Classical Transport from a "Ruffled" Separatrix Here, a magnetic tilt "error field" causes plasma expansion at rate P. The chaotictransport shows an un-ambiguous sin2 signature, where is the angle between the separatrix ruffle and the magnetic tilt. Chaotic transport is proportion to the ruffle Vm, and adds to the collisional transport. Two different magnetic scalings are observed: Chaotic  B-1 Collisional  B-1/2 P

4. Wave damping from separatrix dissipation We observe strong plasma wave damping due to both magnetic and electric separatrices. At left, a very weak magnetic ripple, Bz/Bz ~ 10-3, causes damping of a kz=1, m=1 plasma wave at rate 11(M) (red), greatly exceeding Landau damping. Adding a positive anti-squeeze does nothing (blue) Adding a negative squeeze (blue) makes a separatrix, causing proportional increase in damping (black). Wave damping can be further increased by chaotic dissipation on separatrix ruffles. At right, the "Trapped Particle Diocotron Mode" damping rate 1a is increased (a) by a static applied ruffle Vm ; or (b) by a wave-induced ruffle, from wave amplitude Q. Damping experiments spanning 0.4 < B < 20.kG show the same scalings as transport: Chaotic  B-1 Collisional  B-1/2

5. Measurement of Salpeter enhancement factorSalpeter predicted that the nuclear fusion rate in a dense, strongly correlated plasma (e.g., a white dwarf star) is enhanced because of Debye shielding, or more generally correlation. The enhancement factor f() is approximately exp(), where  is the correlation strength. We have measured this enhancement factor using the cyclotron energy of ions in a cryogenic pure ion plasma as a stand-in for nuclear energy. The cyclotron energy is bound up in an adiabatic invariant that is well conserved in most collisions and is released only in close energetic collisions (just like the fusion energy). We showed theoretically that the equipartion rate for collisional scattering between velocity components parallel and perpendicular to the magnetic field is enhanced by exactly the same Salpeter factor as in the fusion rate.

6. Measurement of Salpeter enhancement factor continued The figure on the left shows the measured equipartion rate for 3 values of density, 2 values of magnetic fields, and a range of 5 orders of magnitude in temperature. For cryogenic temperatures, the adiabatic invariant become effective and the rate drops exponentially. The solid curves are theory predictions for the rate without the enhancement factor and the dashed curves with the enhancement factor. Correlation strength is shown by the diagonal lines at the bottom. The measurements show strong enhancement for the larger density, more strongly correlated cases (green and red). Collecting the data on a single graph shows a measured enhancement up to 9 orders of magnitude for large . The solid curve is theory and the points are experiment.

7. Theory of recombination rate of antihydrogen in a strong magnetic field. Atoms initially are weakly-bound "guiding center atoms"; radiation plus collisions with background plasma cause recombination. Guiding center atom Distribution of binding energies at different times-- power law tails  Atoms recombine most rapidly at weaker B, lower T Steady-state flux to deeper binding (recombination rate):