8.3 Plasma Diagnostics - PowerPoint PPT Presentation

1 / 34
About This Presentation
Title:

8.3 Plasma Diagnostics

Description:

This is known as the Faraday rotation effect and is the basis of polarimeter operation ... Polarimeter measurements are easier and more accurate with laser ... – PowerPoint PPT presentation

Number of Views:749
Avg rating:3.0/5.0
Slides: 35
Provided by: Alfonso73
Category:

less

Transcript and Presenter's Notes

Title: 8.3 Plasma Diagnostics


1
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

2
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

3
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

4
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

5
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
6
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
7
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
8
Langmuir Probes (VII)
  • Since

and
then it is clear that, except for very negative
values of the potential, Is ltlt Ie ,
consequently
and finally
9
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

10
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

11
Langmuir Probes (X)
  • Typical Langmuir probe characteristic

12
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

13
8.3.2 Gridded Energy Analyzer
The gridded energy analyzer is a more
sophisticated version of a Langmuir probe
14
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.

15
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

16
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

17
Gridded Energy Analyzer (V)
  • Schematic of a Gridded Ion Analyzer

18
Gridded Energy Analyzer (VI)
  • Gridded Ion Analyzer Operation

19
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

20
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.

21
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

22
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

23
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
24
Interferometry (III)
Tokamak multi-channel laser far-infrared (FIR)
set-up for vertical, line-integrated density
measurements
25
Interferometry (IV)
Tokamak top side. Behind the glass, the FIR
channels are apparent. Pressurized air (orange)
and cooling water (black) circuits are also
noticeable
26
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)

27
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

28
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

29
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.

30
Thomson Scattering (II)
  • Thomson scattering setup. Laser light scattered
    by the plasma is observed at 25 points (black
    circles)

31
Thomson Scattering (III)
  • Thomson scattering optical fibre bundles
    observing a tokamak chamber through three lateral
    ports

32
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.

33
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.

34
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
Write a Comment
User Comments (0)
About PowerShow.com