====== Plasma Impedance Probes (PIPs) ======

=== What it does ===

Measures
  - Plasma frequency [Blackwell2005]
  - Electron density (by measuring plasma frequency) [Blackwell2005]
  - Plasma potential
  - Collision frequency

=== Methods ===

PIPs can be operated in a number of methods

  - Actively driven RF sweeps [Blackwell2005].  Relate the peaks and zero intercepts of Re(Z) and Im(Z) to circuit models and dispersion relationships to get the plasma frequency.
  - Plasma oscillation (excite a two stream instability) [Blackwell2005].  Drive weak beam of electrons into the plasma to excite a two stream instability.  Under correct conditions, its frequency is close to the plasma frequency.  An FFT of passive PIP measurements reveals the frequency.  


=== Advantages ===

  * [Blackwell2005] An improvement over Langmuir probes because contamination of the probe has a larger impact on its measurements than on the PIP.
  * Better resolution and accuracy than traditional Langmuir probes [citation]

=== Disadvantages ===

  * More complicated.  Requires careful setup/calibration and the use of an expensive network analyzer.
  * (Check this) Cannot be used in real-time because the network analyzer data can only be post-processed.  

=== Sources of error ===

  * [Blackwell2005] recommends "choosing sufficiently shielded coax cables so that the impedance characteristics are not changed as cables are moved around during the experiment. "
  * [Blackwell2005] Nearby objects to the probe reflected radiation
  * [Blackwell2005] At frequencies related to certain wavelengths, standing waves can form in the chamber.

=== Types of electrodes used ===

  * Planar probes
  * Spherical probes - leads to a simpler analysis [Blackwell2005]
  * Monopole antenna [Bilen1999]


=== [Blackwell2005] ===

Blackwell2005 discusses a PIP in a cold (cold ions) and unmagnetized plasma using a spherical probes.  Provides a derivation of the circuit model (I reproduce part of it below) that captures the impedance of the sheath and the plasma.   

Derivation of Eq. 2.   Also citing Piel2009.  

{{ :private:writeups:img_20200701_140114.png?nolink&600 |}}

=== Calibration ===

A calibration is common to remove the impedance of the non-plasma components (coax feedlines, network analyzer, etc).  
  * [Blackwell2005] does this by attaching a 50ohm load and then a short at the end of the feedline with the other end attached to a network analyzer.  "the calibration consists of programming the analyzer to add phase shifts to the value of G to cancel out the phase shift from the cable."