The UCD Plasma Diagnostics Group, in collaboration with LLNL researchers, pursues a comprehensive theoretical, computational, and experimental program which is elucidating the physics of reflectometry and producing innovative instruments.
To quantify this information, we have performed the first calculations of the scattering phase shift in S-polarized O-mode fluctuation reflectometry both within and beyond the Born approximation. This work has resulted in analytic expressions for the scattering phase shift, identification of the controlling nondimensional parameters for the validity of the Bragg resonance picture and the Born approximation, and indications of the challenges to interpretation posed by fluctuations that cause scattering beyond the Born approximation.
The fluctuation model we use in our calculations is inspired by controlled laboratory plasma experiments performed at UCLA and UC Davis.
Using 1-D profiles of plasma density and artificial damping in our SOFTSTEP simulations we show the effects on the electric field of density perturbations in the Bragg resonance regime or near the cutoff. A perturbation in the Bragg scattering region does not affect the field's amplitude, whereas an oscillating mirror models the effect of perturbations near the critical density and indicates why they modify the electric field amplitude.
By moving a narrow fluctuation wavepacket down a perturbed density profile we can see the influence of a stationary density perturbation on the phase shift of the scattered electric field.
Because the location of the Bragg scattering region depends on the wavenumber of the density fluctuation (scattering occurs farther from the critical density when the fluctuation wavenumber is higher), the Born approximation breaks down at lower values of as the fluctuation wavenumber decreases and the scattering occurs closer to the cutoff, where a given perturbation is larger compared to the background profile density.
Scattering near the critical density caused by larger density perturbation levels exhibits nonlinear effects different from those seen in the Bragg resonance regime. Large phase jumps can occur when a density perturbation forms a new critical surface (which subsequently disappears) in front of the original one as it travels down the density profile.
The profiles of density and artificial damping used in 2-D SOFTSTEP simulations are analogous to those used in the 1-D cases. A new effect not possible in 1-D is diffraction, which is seen in the differences between electric fields that result from using a wide vs. a narrow field source in the simulation.
Because of diffraction, the electric field that is measured by a reflectometer's receiving antenna travels along a multitude of paths from its origin at the transmitting antenna to the scatterer somewhere in the plasma and back to the receiver. The receiving antenna physically performs an averaging process over all the field information it receives as it directs freely propagating electric fields into the waveguide to which it is attached. Inside the waveguide the field is in a single waveguide mode, which is measured by a detector. It is this field whose phase shift is measured relative to the reference phase of the transmitting waveguide's field. Therefore, the phase shift will be influenced by the various path lengths through which the fields propagated from the transmitter to the receiver.
With a wide source we can see already that even a small amount of diffraction causes the field to travel along paths with different lengths. The wider the region over which the received field is averaged, the more the ultimate measured signal differs from that measured at a single spatial point. The effect is similar at a higher density perturbation level; an oblique trajectory for the fluctuation wavepacket produces a signal even more difficult to decipher.
These effects are similarly present for scattering near the critical density. Signals produced by head-on wavepacket trajectories at low and high perturbation levels are shown.
Interestingly, narrow wavepackets do not suffer as much from the averaging effect. The shape of the electric field profile is self-similar despite increasing the size of the region over which averaging is performed.