Plasma
Declan Cockburn: 02038633. Lab partner: William Walshe. April 2005
Abstract:
This experiment is based on the properties of electrons moving through argon. Part (i) with the argon in
gaseous form and part (ii) with it in plasma (ionised gas) form. In part (i) the I-V characteristics across
the gas are used to determine the charge over mass ratio of an electron and the ionisation potential of
argon.
e/m was found to be: 3.9 ×1011 ± 0.2 ×1011C kg -1 Compare with the accepted value of: 1.76 ×1011 C kg -1
The ionisation potential of argon was found to be ~16V
In part (ii) a Langmuir probe (biased against the anode) was used to determine characteristics of the
plasma such as electron temperature and electron density.
The electron temperature was found to be
Te =10,000 K ± 600 K While the density was found to be: ne = 9 ×1015 m -3 ± 2 ×1015 m -3
Introduction:
1. Plasma. An electrically neutral, highly ionized gas composed of ions, electrons, and
neutral particles. It is a phase of matter distinct from solids, liquids, and normal gases.
Sometimes called the “fourth state of matter”, approximately 99% of all visible matter in the universe
is in this form. When stated that it is electrically neutral it is actually quasineutral. i.e. it is a good
approximation to assume that the density of the
negative charges is equal to that of the positive
however, electric fields can and do exist as required
by the physics at hand.
The Child-Langmuir law (for the 884’s geometry):
I =[2π ε0 (4 L
9R
) 2e ]
m
(see appendix for symbols)
Gives the relation between the current and
the voltage between a cathode and the anode
in space (in this case an inert gas) before
ionisation takes place.
In plasmas there exists a Debye screening
effect, which is a damping of electric
fields. This prevents electric fields (but
not magnetic) from considerably
affecting the plasma. It is measured in Debye lengths. Debye lengths tend to be short compared to the
overall size of the plasma. This leads to the concept of a Debye sheath. This sheath is a non-neutral
layer, several debye lengths thick where a plasma contacts a surface. Electrons being of far lesser mass
than their counterpart ions thus possess far greater thermal velocities. So at this interface with the
surface, the electrons will fly out of the plasma and charge the surface negative. The plasma will now
have a potential positive w.r.t. the surface. This potential functions as a barrier allowing the remaining
electrons to be confined electrostatically.
The behaviour of the electrons examined in the plasma relies heavily on the notion of this sheath.
The electrons in the plasma are examined by means of a Langmuir-probe, which is simply a device
used to determine several properties of the plasma such as electron temperature and electron density. A
Maxwell-Boltzmann velocity distribution is assumed for the electrons, thus the I-V characteristic
relation in the plasma is:
I ∝ exp(
eV
)
kTe
At a higher voltage, the current I saturates. The reason it saturates is because when the probe is at this
high bias w.r.t. the anode, no more current can reach the probe so the only current is due to the ions.
This occurs at the value:
I e = Ane e
kTe
(see appendix for symbols)
2π m
Experimental Details:
Part (i)
The aim of this experiment was to measure the electron charge to mass ratio and the ionisation
potential of Argon. The 884 tube was used and a circuit (see fig 1) was set up.
The current was measured in the
range of 0 to 14V. The voltage
was then plotted vs I^(2/3) in
accordance with the ChildLangmuir relation. The linear
part of the graph (before the
first ionisation of Argon took
place) was taken and the slope
found such that the e/m ratio
could be found. The voltage at
I=0 was also determined from
the graph and subtracted from
the breakdown voltage in order
to determine the Ionisation
potential of the argon.
Fig 1
Part (ii)
The aim of this experiment was to determine the plasma (electron) density and the electron temperature.
The Z300T argon filled gas triode was used and a circuit (see fig 2) was set up.
The discharge voltage was set
slowly up to ~100V to set a
stream of high-energy
electrons across from the disc
cathode to the ring anode thus
ionising the gas. This was then
adjusted to give a discharge
voltage of ~10mA. The
(Langmuir) probe current was
then taken for probe voltages
between –9V and +15V. With
special care taken to observe
close readings around the area
of zero-bias (where the current
changes rapidly).
Fig 2
Results and Analysis:
Part (I)
The linear part of the graph mentioned above is shown in fig 3.
Fig.3) Collector voltage against I^(2/3)
16
Collector voltage (V)
14
12
10
8
6
4
2
0
-2 0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
I^(2/3) (A)
The ratio of electron charge to mass is given by the equation:
e
1
9 R 2 Derived from the Child-Langmuir law describing the relation between a current
=
(
)
3
m 2M 8π ε 0 L and voltage between a cathode and anode in space (or in this case; an inert gas).
Where M is the slope of the graph. The value of which (and the intercept) was found to be:
Intercept
Slope
Value Error
-1.556 0.092
211.64 3.047
Thus the relation was given as:
e
=3.9 ×1011 ±0.2 ×1011C / kg
m
Since the breakdown voltage was found to be ~ 14.5V, the ionisation potential of argon was thus
deduced to be ~16V.
Part (ii)
The graph of Probe current vs probe voltage is shown in fig 4.
Fig. 4) I vs V
4.50E-03
4.00E-03
Probe Current (A)
3.50E-03
3.00E-03
2.50E-03
2.00E-03
1.50E-03
1.00E-03
5.00E-04
0.00E+00
0
-5
-5.00E-04
-10
-15
20
15
10
5
Probe Voltage (V)
At low voltages, assuming the electrons have Maxwell-Boltzmann distribution of energy there is an
exponential relationship:
I ∝ exp(
eV
)
kTe
Then a plot (see fig. 5) of the natural logarithm of the current vs. the voltage should yield a linear graph
(before saturation) from which the electron temperature can be calculated.
Fig. 5) Low-voltage, linear part of ln(I) vs V
0
-6
-5
-4
-3
-2
-1
-2
-4
ln(I)
-6
-8
-10
-12
-14
-16
V
0
1
2
Where
Te (the electron temperature) is then given by:
Δ (ln I )
= slope
ΔV
e
Te =
=10,000 K ± 600 K
Δ (ln I )
k(
)
ΔV
if
The saturation current was found to be:
I e = 2.7 ± 0.5 mA And thus the electron density was given by and found to be:
ne =
Ie
= 9 ×1015 m-3 ± 2 ×1015 m-3
kTe
Ae
2π m
Conclusions:
e
= 3.9 ×1011 ± 0.2 ×1011C kg -1
m
The accepted value is:
1.76 ×1011 C kg -1
But Alexeff et al suggest that that with the equipment we use, the typical value obtained will be
somewhat larger. Another reason for the discrepancy may be the effect of the neutral atoms and the fact
that the 884 tube is not equipotential and therefore does not supply an unlimited number of electrons
that theoretically are needed.
The ionising potential of argon was found to be ~16V. The reason for the approximation is that the
breakdown voltage was not well defined. However it did come remarkably close to the 15.2V accepted
value.
The electron temperature was found to be
Te =10,000 K ± 600 K
This value depends on the discharge current but is certainly within the right order of magnitude if not
within error.
The electron density was found to be:
ne = 9 ×1015 m -3 ± 2 ×1015 m -3
Which is the same order of magnitude of Alexeff et al who used a different (but similar) apparatus at
different discharge current/voltage values.
Appendix:
e
Electron charge
k
Boltzmann’s constant
A
Surface area of probe
m
Mass of electron
Te
Electron temperature
ne
Electron density
R
Radius of collector (884 tube)
L
Anode Length (884 tube)
ε0
Permittivity of free space