8.3 Plasma Diagnostics

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8.3 Plasma Diagnostics

• 8.3.1 Langmuir Probes
• 8.3.2 Gridded Energy Analyzer
• 8.3.3 Interferometry
• 8.3.4 Polarimetry
• 8.3.5 Thomson Scattering
• 8.3.6 Plasma Spectroscopy

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8.3.1 Langmuir Probes

• If a conducting plate (probe) inserted into an
  equilibrium plasma it will charge negatively and
  a sheath will be formed
• When the sheath is formed a current is flowing
  through the sheath and collected by the probe
• For a sufficiently negative potential of the
  probe (either set naturally because high electron
  temperature or through external bias) the
  electron current can be neglected
• According to the Bohm sheath criterion ions enter
  the sheath with drift velocity

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Langmuir Probes (II)

• If A is the plate collecting area and ns is the
  density at the edge of the sheath the ion current
  will be

• The sheath edge can be defined as the location
  where

• To accelerate ions at this velocity the electric
  potential (with respect to a zero potential
  reference in the plasma body) in the presheath
  region must be

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Langmuir Probes (III)

• For maxwellian electrons following the Boltzmann
  distribution this condition determines the
  density at the sheath

• The value of ns determines the saturation current
  of the probe

• This expression is know as the Bohm current and
  can provide the plasma density from the
  measurement of the current Is in the probe, if
  the temperature is known

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Langmuir Probes (IV)

• The Bohm current (ion saturation current) was
  obtained under the assumption that the electron
  current can be neglected because the potential of
  the plate is highly negative
• If the bias potential of the probe is varied
  towards less negative values the probe current
  will change because some electrons will be able
  to overcome the potential barrier ne ne(f) and

where Ii and Ie are the ion and electron
currents, Iis is the ion saturation current and
ltuegt is the average electron velocity
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Langmuir Probes (V)

• A relationship between the probe current and the
  electron density is then found

• By sweeping the probe with different values of
  bias potential f, the probe current gives the
  electron density as a function of f

• Since the number of electrons with potential
  energy equal to -ef are given by the Boltzmann
  relation

the temperature could be found from the electron
density
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Langmuir Probes (VI)

• The electron current Ie is

• Since the number of electrons with potential
  energy equal to -ef are given by the Boltzmann
  relation

and by expressing ltuegt for a maxwellian the
current Ie can be rewritten as
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Langmuir Probes (VII)

• Since

and
then it is clear that, except for very negative
values of the potential, Is ltlt Ie ,
consequently
and finally
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Langmuir Probes (VIII)

• By assuming the Boltzmann relation for the
  electrons, the electron temperature can be then
  inferred from a plot of I(f)

• By taking the log

• Then the slope of the log of I(f) is
  proportional to the inverse of the temperature

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Langmuir Probes (IX)

• To characterize the plasma first the probe
  characteristic (current vs. bias potential) is
  recorded
• The electron temperature can be measured from the
  slope of the log of the characteristic (this log
  is should be a straight line for Boltzmann
  electrons)
• The ion saturation current is also detected from
  the characteristic
• From the Bohm current formula, by inserting the
  value of the temperature, the electron plasma
  density is found

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Langmuir Probes (X)

• Typical Langmuir probe characteristic

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Langmuir Probes (XI)

• This diagnostic system is called Langmuir probe
  and it is one of the fundamental diagnostics in
  plasma physics
• It can be applied when the size of the probe is
  much greater than the Debye length
• For magnetized plasmas corrections to the
  electron density derivation procedure are
  required if the Larmor radius is in the order of
  the probe size

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8.3.2 Gridded Energy Analyzer
The gridded energy analyzer is a more
sophisticated version of a Langmuir probe
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Gridded Energy Analyzer (II)

• In a gridded energy analyzer, the plasma sheath
  forms around the entrance grid and not the
  collector, like in a Langmuir probe
• Other grids can be used a positively biased grid
  is inserted to repel ions.
• A third grid is biased negatively to selectively
  repel electrons above a particular energy.
• A collector plate collects the electron current.
• This probe can be used to measure the electron
  energy distribution function.

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Gridded Energy Analyzer (III)

• The Langmuir probe does not provide information
  about the ion temperature
• A gridded energy analyzer can be used to measure
  the ion energy distribution
• A negatively biased grid is inserted in front of
  conducting plate (ion collector)
• The collector works as a Langmuir probe
  positively biased but the presence of the grid
  repels all (most) of the electrons
• This prevents the (much larger) electron current
  to cover the ion current variations with the
  potential

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Gridded Energy Analyzer (IV)

• The Langmuir probe does not provide information
  about the ion temperature
• A more sophisticated probe can be designed that
  allows the measurement of the ion energy
• A negatively biased grid is inserted in front of
  conducting plate (ion collector)
• The collector works as a Langmuir probe
  positively biased but the presence of the grid
  repels all (most) of the electrons
• This prevents the (much larger) electron current
  to cover the ion current variations with the
  potential

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Gridded Energy Analyzer (V)

• Schematic of a Gridded Ion Analyzer

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Gridded Energy Analyzer (VI)

• Gridded Ion Analyzer Operation

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Gridded Energy Analyzer (VII)

• The number of grids and grid bias is chosen to
  minimize or avoid secondary electron current at
  the collector.
• Usually an ion probe has from one to four grids
  are used in addition to the front-plate and the
  collector for added flexibility
• The electron repeller grid, G1, is biased
  slightly negative to repel most of the electrons
  entering from the plasma
• The grid G1 may also be left floating, in which
  case the bulk plasma is less perturbed

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Gridded Energy Analyzer (VIII)

• The ion repeller grid, G2, is swept from 0 to 60
  volts.
• Only the ions with parallel energy greater than
  the applied voltage will pass through G2, and
  ions with lower energies will be reflected.
• A constant negative bias is also applied to the
  third grid, G3. If some energetic electrons are
  able to pass through the first potential barrier
  from F and G1, they will be repelled at this
  grid.

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Gridded Energy Analyzer (IX)

• In order to accelerate secondary electrons
  released from the grids and walls out to the
  plasma and not to the collector the bias at grid
  G1 should be positive relative to grid G3 and the
  collector
• The bias on the collector should be positive
  relative to grid G3, so the secondary electrons
  released from the collector are reflected back to
  it.
• The ions passing the ion grid will be accelerated
  towards the collector due to G3 and the collector
  voltage

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8.3.3 Interferometry

• An interferometer measures the phase difference
  (or time difference) between radiation passed
  through the plasma and radiation directed through
  air (no plasma)
• The index of refraction of a plasma is defined as

• From the dispersion relation for e.m. waves in a
  plasma (without external magnetic field)

• Therefore the refraction index depends on the
  plasma frequency and then on the density

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Interferometry (II)

• As the index of refraction of a plasma depends on
  its density, a phase delay will occur between the
  two paths for the radiation (plasma and no
  plasma)
• This phase delay is a function of the integrated
  plasma density along the plasma path.

Attenuator/Phase shifter
Detector
Plasma
mwave Generator
Mixer
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Interferometry (III)
Tokamak multi-channel laser far-infrared (FIR)
set-up for vertical, line-integrated density
measurements
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Interferometry (IV)
Tokamak top side. Behind the glass, the FIR
channels are apparent. Pressurized air (orange)
and cooling water (black) circuits are also
noticeable
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8.3.4 Polarimetry

• An e.m. wave in a magnetized plasma with the wave
  vector parallel to B0 will propagate through
  right- and left-circularly polarized waves
  (R-wave and L-wave)
• The dispersion relation gives the refractive
  index as

• The plasma refractive indexes for both waves are
  then dependent on the magnetic field within the
  plasma and on the density (through the plasma
  frequency)

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Polarimetry (II)

• With a magnetic field along the direction of a
  probing wave, the right and left-circularly
  polarized components of the wave will experience
  different indices of refraction and will cause a
  rotation of the wave polarization plane
• For large frequencies the R-wave has phase
  velocity larger than the L-wave
• Since the R-wave travel faster a phase shift will
  occur after a certain distance through the plasma
• This is known as the Faraday rotation effect and
  is the basis of polarimeter operation

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Polarimetry (III)

• The measure of the rotation of the wave
  polarization plane can be correlated with the
  difference of the left- and right- refraction
  indexes and then with plasma frequency and with
  the density
• This measure provides a line integrated measure
  of the density
• Polarimeter measurements are easier and more
  accurate with laser beams rather than with
  microwaves

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8.3.5 Thomson Scattering

• A laser beam that passes through plasma interacts
  with free plasma electrons so that minute amount
  of the laser light is scattered from them
• The spectral width of the scattered radiation
  depends on the electron temperature (due to
  Doppler line broadening) and its intensity is
  related to the electron density
• Local values of electron temperature and density
  are obtained.

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Thomson Scattering (II)

• Thomson scattering setup. Laser light scattered
  by the plasma is observed at 25 points (black
  circles)

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Thomson Scattering (III)

• Thomson scattering optical fibre bundles
  observing a tokamak chamber through three lateral
  ports

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8.3.6 Plasma Spectroscopy

• In thermal equilibrium, the fraction of atoms or
  electrons found to be in a particular quantum
  state depends on both the temperature and the
  energy of the state in consideration, according
  to the Boltzmann ratio

• Conversely, the populations of known excited
  states, inferred from measurements of
  emission-line intensities, can be used to
  determine the temperature of the plasma.

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Plasma Spectroscopy (II)

• To make a measurement of the plasma temperature,
  the most intense radiation is typically in the
  soft x-ray region of the spectrum, for hot
  plasmas in thermodynamic equilibrium.
• The peak emission for a kT100 eV plasma is at
  about 2.5 nm
• Spectroscopy remains one of the most important
  and powerful diagnostic tools for hot and dense
  plasmas.

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Plasma Spectroscopy (III)

• Visible, UV, VUV (Vacuum Ultra Violet, extends
  from 200 nm), and X-ray regions
• Non-intrusive measurements
• High spatial and temporal resolutions (1 ns, 30
  microns)
• High spectral resolution and flexible spectral
  selectivity
• High detection sensitivity and signal-to-noise
  ratio