Title: 8.3 Plasma Diagnostics
18.3 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
28.3.1 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
3Langmuir 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
4Langmuir 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
5Langmuir 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
6Langmuir 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
7Langmuir 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
8Langmuir Probes (VII)
and
then it is clear that, except for very negative
values of the potential, Is ltlt Ie ,
consequently
and finally
9Langmuir Probes (VIII)
- By assuming the Boltzmann relation for the
electrons, the electron temperature can be then
inferred from a plot of I(f)
- Then the slope of the log of I(f) is
proportional to the inverse of the temperature
10Langmuir 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
11Langmuir Probes (X)
- Typical Langmuir probe characteristic
12Langmuir 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
138.3.2 Gridded Energy Analyzer
The gridded energy analyzer is a more
sophisticated version of a Langmuir probe
14Gridded 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.
15Gridded 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
16Gridded 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
17Gridded Energy Analyzer (V)
- Schematic of a Gridded Ion Analyzer
18Gridded Energy Analyzer (VI)
- Gridded Ion Analyzer Operation
19Gridded 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
20Gridded 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.
21Gridded 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
228.3.3 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
23Interferometry (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
24Interferometry (III)
Tokamak multi-channel laser far-infrared (FIR)
set-up for vertical, line-integrated density
measurements
25Interferometry (IV)
Tokamak top side. Behind the glass, the FIR
channels are apparent. Pressurized air (orange)
and cooling water (black) circuits are also
noticeable
268.3.4 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)
27Polarimetry (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
28Polarimetry (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
298.3.5 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.
30Thomson Scattering (II)
- Thomson scattering setup. Laser light scattered
by the plasma is observed at 25 points (black
circles)
31Thomson Scattering (III)
- Thomson scattering optical fibre bundles
observing a tokamak chamber through three lateral
ports
328.3.6 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.
33Plasma 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.
34Plasma 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