Lecture on Interferometry in Plasma Physics

Overview of Interferometry with Plasma

• Interferometry involves using a probing laser beam through a plasma.
• Part of the laser (probe) is transmitted through the plasma, while part (reference) is routed around.
• Interference occurs when recombining probe and reference beams.
• The phase difference ($\Delta \phi$) is key, calculated as: [ \Delta \phi = -\frac{\omega}{c} \times n_{critical}(\lambda) \times \int n_e , dl ] where $n_e$ is the electron density.

Homodyne and Heterodyne Techniques

• Homodyne: Involves detecting interference of beams with same frequency $\omega_1 = \omega_2$.
  • Results in phase ambiguity (e.g., phase changes more than $2\pi$ are indistinguishable).
• Heterodyne: Involves probes with different frequencies $\omega_1 \neq \omega_2$.
  • Introduces a beat frequency $\omega_1 - \omega_2$ that resolves phase ambiguity.
• Measurement results in signals that depend on frequency differences and temporal changes in electron density.

Spatially Heterodyne Techniques

• Expanding the beam through plasma creates an image with interference fringes.
• Spatial heterodyne adds a slight tilt to the reference beam's wavefronts.
  • This adjustment helps measure how the wavefronts are misaligned due to plasma.
• Allows resolving ambiguities by shifting frequency in spatial domain.

Practical Considerations

• Wavelength Choice:
  • Different wavelengths are sensitive to different electron density ranges.
  • Using shorter wavelengths (e.g., visible light) results in higher sensitivity to vibrations.
• Two-Color Interferometry:
  • Combines measurements from two different wavelengths to distinguish vibrational effects from actual phase shifts.

Measurement of Neutrals and Electrons

• Neutrals affect refractive index: $n = 1 + 2\pi\alpha n_A$, with $\alpha$ being the polarizability.
  • Neutrals' contribution to phase shift can be determined by using two wavelengths.
  • Challenges arise due to variability in $\alpha$ and potential resonances.

Key Challenges and Solutions

• Disambiguation of Phase:
  • Homodyne systems are plagued by phase ambiguity, which heterodyne systems resolve through frequency shifts.
• Handling Vibrations:
  • Utilize a fast laser with short wavelength as a reference to correct for vibrations.
• Neutrals and Ionized States:
  • Differentiating between contributions to refractive index from neutrals and electrons using distinct wavelengths.

Advanced Examples and Applications

• Spatially Heterodyned Interferograms:
  • Analysis involves tracing fringes to infer electron density.
  • Challenges include refractive loss (high density gradients) and dealing with overlapping fringes.
• Real Data Examples:
  • Tokamak experiments utilizing spatial heterodyning.
  • Temporal and spatial resolutions depend heavily on technology (e.g., detector speed).

Questions and Further Discussion

• Examples of practical applications in plasma experiments were provided.
• Further inquiries addressed the handling of complex fringe patterns and resolution limits.

This lecture provided a comprehensive overview of interferometry in plasma physics, focusing on techniques for measuring electron density and addressing challenges such as phase ambiguity and vibrational interference. It also introduced advanced methods for resolving these issues using heterodyne and spatially heterodyne techniques.