EXPERIMENT 12
LANGMUIR PROBES
1. SAFETY FIRST
There are two DC power supplies used in this experiment, a grey Fluke
3.5 kV power supply for providing the discharge current for the glow discharge you will be using,
and a 100 V power supply for adjusting the Langmuir probe potential. Both are potentially able to
deliver a fatal electric shock. Please, remember:
 Do not disconnect the coaxial cable between the grey Fluke power supply and the black





ballast box on top of this power supply.
Do not turn on the grey Fluke power supply when connecting the red and black leads to the
discharge tube.
To minimize damage to the probes the Langmuir probe power supply should be set to 50 V
before connecting the power leads, and increased to reduce the probe current to < 300 µA
immediately after connecting these leads.
Avoid touching the red and black wires connecting the ballast box to the discharge tube, and
the Langmuir probe power supply to the probe.
Always hold the connectors when connecting the Langmuir probe power supply – not the
wires - and keep your fingers away from the sockets connected to the probes (on the
Perspex cover of the discharge tube) as well as the front of the plug.
Report any apparent damage to the lab technician and/or your tutor.
2
 There is a very small possibility that the discharge tube will implode. The Perspex cover of
the equipment will contain most of the glass splinters. Should this happen, turn off the
mechanical vacuum pump immediately.
If you do not understand all of these points, speak to a tutor before turning on any equipment.
2. AIM
In this experiment a Langmuir probe (a fine metal wire) is used to investigate the plasma of the
positive column of a glow discharge in nitrogen. In addition to the main power supply which
produces the glow discharge, a smaller auxiliary power supply is connected between the probe and
the anode of the discharge tube, and the current to the probe is measured as a function of the probeanode voltage. Using a simple model for the operation of the probe, it is possible to determine from
the current-voltage curve the plasma potential, the electron density, and the electron temperature at
the probe location.
3. THE GLOW DISCHARGE
A glow discharge consists of a number of bright and dark regions (see the Appendix for more
detail). For the discharge used in this experiment only the positive column is visible, as the various
cathode glows and dark spaces are hidden in the hollow cathode. The hollow cathode arrangement
minimises sputtering of metal from the cathode on to the walls of the discharge tube. The greater
part of the voltage drop across a glow discharge (and hence the region of strongest electric field)
occurs across the dark space adjacent to the cathode where there is considerable positive space
charge. In contrast, measurements show that the electric field in the positive column is relatively
2
small and uniform, which implies that the resultant space charge  is small (    0 E   0 V );
that is, the electron density is closely equal to the positive ion density. An ionised gas which
maintains a close equality of positive and negative space charge is called a plasma.
For nitrogen filling gas, the electron mass is some 50,000 times less than the mass of the positive
ions and the electrons are thus much more mobile. Moreover in elastic collisions they lose only a
very small fraction of their energy to the neutrals or ions. On the other hand a positive ion loses the
greater part of its excess energy at each collision with a neutral molecule, as the masses of the ion
and neutral are essentially equal. Thus the kinetic energy of the ions is much the same as that of the
neutral molecules which are close to room temperature, while the average electron energy is some
100 times that of the neutral gas. Thus the average electron velocity is of the order of 2,000 times
that of a neutral molecule or a positive ion. The electrons are very fast and mobile; the positive ions
are very sluggish.
At a typical filling pressure of 0.3 Torr (~ 40 Pa), the number of neutral gas molecules at room
temperature is approximately 1022 m-3 or 1016 cm-3. The mean free path of a typical electron at this
pressure is of the order of half a millimetre. The electron motion is thus highly erratic, being a
random walk diffusion on which is superimposed a slow drift velocity in the applied electric field.
The electron drift velocity is of the order of 1/10 of its total velocity.
4. PLASMA BEHAVIOUR
If an electrically isolated probe is inserted in the plasma, it is rapidly charged to a negative potential
as it collects the electrons which quickly diffuse to it. When it is sufficiently negatively charged
3
most of the electrons will be repelled as only the most energetic can reach the probe. Being
negatively charged the probe now attracts the sluggish positive ions which diffuse into its vicinity,
and the probe potential stabilizes when this small positive ion current equalizes the small electron
current due to the high energy tail of the electron distribution. In such circumstances the probe is
said to be floating and its potential is called the floating potential. Such a process also occurs at the
glass walls of the tube: the loss of electrons due to diffusion is thus considerably reduced by the
negative charge built up on the walls. The diffusion of electrons to the walls is therefore limited by
the rate at which positive ions can diffuse to the walls where they neutralize and can then re-enter
the discharge as atoms. Electron diffusion controlled by the slow rate of diffusion of the sluggish
positive ions is called ambipolar diffusion.
Thus between the relatively undisturbed, neutral plasma (where the electron density ne is equal to
the positive ion density ni) and the boundary wall there is a region in which the electrons are
repelled and the positive ions are attracted. This region has positive space charge and, consequently,
a rapidly changing potential. Its thickness is the order of the Debye shielding length D where
 kT 
T 
D   02 e   7.4  103  eV 
 e ne 
where
k
is the Boltzmann constant
Te
is electron temperature in kelvin
TeV 
kTe
e
 ne 
is the electron temperature in electron volts (11,600 K  1 eV)
e
is the electron charge
ne
is the electron density in m-3
The temperature T of particles in plasma is often expressed as the value of the energy kT in units of
electron volts. Thus a ‘temperature’ of 1 eV corresponds to 11,600 K. Note that this energy value is
3
not the average energy of the particles, which would be kT .
2
Since the degree of ionization in a glow discharge is around 1 part in a million, electron-ion
collisions are rare and very little electron-ion recombination occurs. Most of the electron loss is by
diffusion to the walls. The electron loss is made up in the discharge by the very high energy
electrons in the tail of the electron energy distribution, which are energetic enough to ionize the
neutral molecules. The light from the plasma is due to molecules and atoms excited by the more
energetic electrons.
The positive column is usually striated into bright and dark bands a few centimetres apart. They
result from not very large periodic fluctuations in electron density and energy initiated in the
cathode region.
5. THE LANGMUIR PROBE
The Langmuir probe is a small metal wire. It is named after Irving Langmuir (1881-1957), an
American physicist who was one of the pioneers of the study of the plasma state, and coined the
term plasma. An ideal plasma for investigation by the Langmuir probe is one where the electrons
and ions are fully thermalized at equal temperatures and where the particle mean free paths greatly
4
exceed the Debye length. Under these conditions the Langmuir probe current-voltage
characteristics may be expected to conform to a simple theory. In the glow discharge the electronelectron collision probability is small, and the electron gas cannot be expected to be in thermal
equilibrium. Under these conditions the electrons in the plasma can only be approximately
described by an electron temperature. Moreover the ion temperature is many folds less than the
electron temperature, and the Debye length is of the order of an electron-neutral mean free path.
It is to be expected that the Langmuir probe characteristics taken under the plasma conditions of this
experiment do not closely agree with textbook idealisation. A further cause of departure from
idealised characteristics is the effects of impurities in the gas and on the probes themselves. Careful
experiments under ultra high vacuum conditions of cleanliness with ultrapure gases indicate that
minute traces of impurities in the gas and on the probe surfaces have large effects on the probe
characteristics. But in spite of all its problems and difficulties the Langmuir probe has proved a
most valuable tool for plasma diagnostics, and is of great value in probing plasmas in the laboratory
and in space.
6. LANGMUIR PROBE THEORY
The probe current-voltage characteristic shown in Figure 2 can be divided into three regions:
(a)
for V  V f (the floating potential, for which the current collected is zero) the probe current is
mainly positive ion current.
(b)
for Vf  V  Vs (the space or plasma potential), the current is mostly due to electron
diffusion to the probe. It is expected to vary exponentially with the probe voltage. Note that
when the probe is at potential Vs it is at the same potential as the plasma; thus electrons and
ions diffuse to the probe as if they were unaffected by its presence.
(c)
For V  Vs the current is space charge limited electron current, and for a cylindrical probe in
an ideal plasma the square of the current is expected to vary linearly with the probe voltage.
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Vs
Ionization
near probe
Log I p
Positive ion current
Vf
Logarithmic Variation
Slope = 1/TeV
-100
0
Probe Volts
FIGURE 1
Current voltage characteristic for Langmuir probe.
It is assumed that the probe current does not disturb the plasma equilibrium, the probe diameter is
less than the electron mean free path, and that the electrons are in thermal equilibrium among
themselves at a temperature Te with a Maxwellian kinetic energy distribution. Let
ne = electron density in the undisturbed plasma at potential Vs.
n = electron density in the immediate vicinity of the probe surface at potential V < Vs.
Then from the Boltzmann law
e(Vs  V) 
(V  V) 
  ne exp  s

n  ne exp 
 kTe

 TeV 
(1)
The electron current diffusing to the probe will be given from kinetic theory by
Ip 
1
Anev
4
(2)
where v is the average electron speed and A is the surface area of the probe:
v
8kTe 
8eTeV 
5
1

 6.7  10 TeV ms
 m 
 m 
(3)
Taking natural logarithm of equation (1), and with the aid of equation (2):
ln I p  ln I ps 
Vs
V

TeV TeV
(4)
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where Ips is the probe current at V  Vs and is given by
I ps 
1
Aneev
4
(5)
and the slope of the curve ln Ip versus V is given by
d ln I p
dV

1
TeV
(6)
Thus a plot of the natural logarithm of the probe current, lnIp, against probe voltage, V, should be
linear in the region between the space potential and the floating potential. The slope of this line
determines the electron temperature from equation (6). This analysis assumes that the positive ion
current is small and can be neglected in most of this region; this is a reasonable assumption except
very close to Vf .
Using the value obtained for TeV the mean electron speed can be obtained from equation (3) and
then the electron density from equation (5).
A second method of calculating the electron density, described in Hoag & Korff, Electron and
Nuclear Physics, Chapter 8, involves plotting Ip2 as a function of V for V > Vs.
For V < Vf the positive ion current to the probe can be investigated. This is discussed in Heald &
Wharton, Plasma Diagnostics with Microwaves, page 380.
An alternative to the single probe is the double probe which involves using two probes close to each
other in the plasma and plotting the Ip : V characteristic between them. This is also discussed in
Heald and Wharton.
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7. EXPERIMENTAL PROCEDURE
6.1 The Apparatus
0 - 3500 V supply
-
0 - 100 V supply
+
Anode
Cathode
+
(SCHEMATIC ONLY)
Probes
Vacuum isolation tap
Reduced
pressure
Bottle
pressure
Needle valve
Air inlet
Bottle valve
key operated N
2
Pressure
reducing
e valve
g
Backing
pump
FIGURE 2
Block diagram of Langmuir apparatus.
A block diagram of the apparatus is shown in Figure 2.





Close the air inlet tap to the backing pump, start the pump, and after 1 minute open the tap
to evacuate the discharge tube.
When the thermocouple vacuum gauge indicates a pressure below 0.08 Torr, nitrogen gas
can be admitted. Ensure that a technician or demonstrator has turned on the gas supply and
has adjusted it so that the reducing valve on the gas cylinder reads about 10 lb/in2 (not
above).
Slowly open the needle valve to admit nitrogen to a pressure of 0.2 Torr into the discharge
tube.
Switch on the main voltage supply (Fluke 3.5 kV) and adjust to about 1500 V which should
be more than adequate to establish a discharge across the tube.
Re-adjust the voltage to set up a discharge current of 10 mA and allow 15 minutes to
stabilise before proceeding with any measurements (during this time the current may drop
somewhat).
The positive terminal of the auxiliary 0-100 volt probe supply is connected to the anode of the
discharge tube, the negative terminal to the probe being investigated, with the current meter set at its
highest range.
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
Adjust the probe voltage to give zero probe current on the most sensitive current range.
The probe is then at its floating potential where the electron and ion currents are equal. At more
positive probe voltages (decrease in the auxiliary supply voltage) the probe draws mostly electron
current, whereas at more negative probe voltages the probe will draw mostly positive ion current.
QUESTIONS:
1)
The Thermocouple Pirani vacuum gauge uses the variation of thermal conductivity of a gas
with change of pressure.
How does the thermal conductivity of a gas vary with pressure and with the nature of the
gas? Over what range of pressure is such a gauge useful and what is the limitation for high
and low pressures?
2)
Make a diagrammatic sketch illustrating the operation of a mechanical backing pump. What
is the ultimate pressure to be expected from such a pump and what determines its pumping
speed?
6.2
Langmuir Probe Characteristic

Using probe 4 measure probe current as a function of probe voltage and plot the results on a
log-linear graph of the probe current versus probe voltage. This is best done using QtiPlot.
From your graph estimate

The probe floating potential.

The electron temperature in electron volts and in K. If using QtiPlot this can be done by
making a linear fit to the appropriate section of the data. Alternatively this section of data
can be reploted separately.
Then

Calculate the average electron speed (Eq. 3) and then determine the electron density from an
estimate of Ips (Eq. 5).
Tutor checkpoint. Obtain tutor's signature before proceeding.
6.3
Electric Field in the Positive Column

Measure floating potentials with two probes (use 4 and 6) and then estimate the electric field
in the positive column.

Calculate the average electron drift velocity from the electron density as determined by the
Langmuir probe, the discharge current, and the estimated cross section of the gas discharge.

Compare the drift velocity of the electrons with the mean thermal speed of the electrons as
calculated from the measured electron temperature.
Tutor checkpoint. Obtain tutor's signature before proceeding.
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6.4
Sparking Potential
This is the minimum potential required to produce breakdown in a gas, and is a function of the
pressure and the electrode spacing and shape.





Disconnect the high voltage supply from the discharge tube.
Connect the high voltage supply between probe 4 (positive terminal) and the nickel cylinder
(negative terminal).
Vary the pressure and determine the sparking potential as a function of pressure. Such plots
are called Paschen curves.
Stop the discharge immediately when it strikes, as sputtering of the nickel onto the glass
walls will occur if the discharge is left running.
Determine the minimum sparking potential.
SHUTDOWN.
 Turn off both the high voltage and probe supplies.
 Close off the nitrogen supply at the needle valve and the gas bottle.
 Close the vacuum valve between the discharge tube and the pump.
 Stop the pump, and admit air to the pump through the air admittance valve.
Tutor checkpoint.
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Appendix: The Glow Discharge
A glow discharge is a self sustaining discharge through gas which occurs at pressures well below
atmospheric pressure. It has obvious glowing regions and fills the full cross-section of the tube. The
discharge in a fluorescent light is a glow discharge (in which the current alternates at 50 Hz).
Figure A1 shows the variations of electric potential, electric field, and space charge density along
the length of the discharge from the cathode (negative electrode) on the left to the anode (positive
electrode) on the right. Note that most of the potential drop occurs near the cathode over a region
called the cathode fall. In this region ions are accelerated into the cathode at sufficient energy to
cause emission of secondary electrons from the cathode. These electrons are accelerated away from
the cathode producing further electrons and ions as a result of ionising collisions. The condition for
a self sustaining discharge is that each electron which leaves the cathode produces sufficient ions so
that when these ions strike the cathode they result in one secondary electron to replace the original
electron.
Figure A1 The glow discharge (from A.M. Howatson, An Introduction to Gas Discharges )
Since most of the potential difference across the discharge occurs across the cathode fall, the
electric field in the cathode fall is much higher than in the rest of the discharge. The field in the
cathode fall is due to the net positive space charge in this region.
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In the positive column the electric field is weak, and as a consequence the net space charge is
negligible. This region, which maintains a close equality between positive and negative charge
density, is called plasma.
The cathode fall region is essential for the existence of the discharge. The positive column provides
a conducting connection to the anode. Thus if the separation between the electrodes is varied
(keeping pressure and current constant) the cathode fall will remain unchanged and the length of the
positive column will vary.
In a glow discharge the discharge fills the cross-section of the tube. As pressure is increased the
current increases and its cross-section constricts to a narrow channel. The discharge is then called an
electric arc.
More detailed descriptions of glow discharges can be found in A.M. Howatson, An Introduction to
Gas Discharges, Pergamon Press (Oxford, 1965).
References
M.A. Lieberman and A.J. Lichtenberg, Principles of Plasma Discharges and Materials Processing,
Wiley & Sons (New York, 1994), section 6.6
J.B. Hoag and S.A. Korff, Electron and Nuclear Physics, Van Norstrand (New York, 1952),
Chapter 8
M.A. Heald and C.B. Wharton, Plasma Diagnostics with Microwaves, Wiley (New York, 1965),
page 380.
A.M. Howatson, An Introduction to Gas Discharges, Pergamon Press (Oxford, 1965)