,
LANGMUIR PROBES IN A FLOWING WW DENSITY PLASMA BY
J. B. FRENCH
AUGUST, 1961 UTIA REPORT NO. 79
BY
J. B. FRENCH
AUGUST, 1961 UTIA REPORT NO. 79
'v'
' 1"
ACKNOWLEDGMENTS
The author wishes to th ank Dr. G. N. Patterson and Dr.!.!, Glass for their continued interest and support.
The work was supervised by Dr. J. H. deL eeuw, whose discussions, suggestions and support during the course of this investiga-tion are gratefully acknowledged.
The financial assistance of the Defence Research Board of Canada, and the UnitedStates Air Force Office of Scientific Research (Contract AF 49( 638)- 82 3) made this study possible.
\ •
.
,
Two aspects of the use of Langmuir probes have been
investigated. First, a Langmuir probe free-molecular with respect to all species, and in a plasma in which the ion temperature is higher than the electron temperature, is considered. Theoretical predictions are that both the ion current and the electron current Qutside the retarding field region are controlled by ion energy, instead of electron energy. Hence directed ion energy in the form of plasma mass motion is expected to influence collection. The retarding field method of measuring electron temperature is uninfluenced. Experiments in the form of comparisons between ion collecting cylindrical probes parallel and transverse to the supersonic plasma stream agree quantitatively with these predictions.
Second, the situation is considered in which the electrons have much higher thermal energy than the ions, and in which the probe is free-molecular with respect to neutral particles but in continuum flow with respect to the ions and electrons. The smaller electron and ion
mean free paths are calculated to have little effect on the current collected by the probe, unless mass motion is present. In this case experiments indicate that a region of increased ion density exists in front of a probe biased to reflect ions back into the oncoming stream.
I. 11.
lIl.
IV.
V.
(i) TABLE OF CONTENTS NOTATION INTRODUCTIONGENERAL DESCRIPTION OF PROBLEM 2. 1 Basic Flow Parameters
2.2 Description of a Typical Probe Characteristic ANALYSIS OF PROBE THEORY
Page (iii) 1 2 2 4 6 3. 1 Introductory Remarks Regarding Collisions 6
3.2 The Retarding Field Operation 7
3. 3 Ion Collection 9
3.3. 1 Effect of Ion Energies on Collection 12 3. 3. 2 The Effect of Small Ion and Electron Mean
Free Paths 14
3. 4 Effect of Mass Motion 17
3.4.1 All Mean Free Paths Larger Than the Probe 17 3.4.2 Combined Effect of Mass Motion. and Small
Ion Mean Free Path 20
DESCRIPTION OF EXPERIMENT AL WORK 4. 1 The Interim Plasma Tunnel
4.1.1 The Plasma Source
4. 1. 2 Operation of the Plasma Jet 4. 2 Langmuir Probes
4.2.1 The Probe Circuit
4. 2. 2. Probe- Traversing Gear
4.2.3 Oscilloscope Trace Triggering System EXPERIMENTAL RESULTS AND DISCUSSION
21 21 22 22 23 24 25 25 26 5. 1 Probe in a Low Ion Density Plasma 27 5.1.1 Cylindrical Probe, Axis Aligned with Flow 27 5.1.2 Comparison of Cylindrical Probes Parallel 31
and Transverse to the Flow
Page
VI. CONCLUDING REMARKS 36
APPENDIX A 38
"
APPENDIX B 39 APPENDIX C 40 REFERENCES 43 TABLES I to V FIGURES 1 to 16a A Cm C d e e F, G h J j K M m+ m n N p Q T V x (iii) NOTATION speed of sound area
most probable random molecular speed mean random molecular speed
Child-Langmuir sheath thickness (metres), Eq. 2.6 unit of electronic·charge (1. 5921 x 10-19 coulombs) base of natural logarithms
integrals defined by Eq. 5. 1 Debye length (Eq. 2. 5) total current (amp)
current per unit area (amp / metre2)
Boltzmann constant (1. 3804 x 10-23 newton-metres/oK) Mach number
mass of argon ion (6. 63 x 10 -26 kilogram) electron rest mass (9.108 x 10- 31kilogram) particle concentration
total number of incident particles/sec. (Eq. 5.1)
pressure mass flow
temperature (oK)
potential difference (volts) dimension
ratio of specific heat, cp/Cv
dielectric constant of free space (8.85 x 10- 12 farad/ metre) viscosity (gm cm- 1 sec -1)
conductivity of a Lorentz gas (ohm-metre), Eq. 3.18 mean free path (cm)
(Debye length) / (impact parameter for 900 deflection) (Eq. 2.2) electron ion direction coordinates free stream stagnation conditions
•
(1) 1. INTRODUCTION
A low density plasma tunnel has been under development at the Institute of Aerophysics (Ref. 1), which makes use of a high energy plasma stream produced by expanding in a supersonic nozzle the plasma from an electrical arc jet. The basic problem considered here is the appli-cation of the Langmuir probe as an analytical tooI to investigate a flowing argon plasma. This plasma is expected to have the following general pro-perties:
ionization: up to 10%
ion concentration: 10 11 to 10 15 ions/cm 3 pressure range: 1 - 200 microns Hg. speed ratio: up to 5
stagnation temperature: 5000 - 15000 oK
The Langmuir probe, or electrostatic probe as it is sometimes called, is conventionally used in glow discharge and other stationary low density plasmas to measure ion concentration and electron temperature. These quantities are of basic interest in possible studies in the plasma tunnel involving heat transfer to bodies, microwave radar and radio interactions, plasma oscillations, plasma electrical conductivity and magnetogasdynamics. Hence, if the effects of mass motion and elevated temperature on the probe characteristic could be understood, the Langmuir probe would appear to be an attractive analytical tooI, particularly so because it can provide local measurements in a flow field of varying properties. In contemplating the application of the Langmuir probe to such high energy low density plasma flows, several considerations become apparent.
First, an important aspect of the present application is the plasma mass motion, which is in the range where ion directed energies are somewhat greater than their random kinetic energies. It will be shown that the effect of this mass motion on plasma concentration measurements de-pends on the ion concentration, on whether the probe is attracting ions or electrons, and on whether the ions or electrons have higher thermai energies.
Second, while certain portions of the probe characteristic (electrical current drawn by the probe from the stream as a function of the voltage applied to the probe) are reasonably well understood for the case of stationary low energy plasmas, a general theory for the whole probe charac-teristic is not available at present. Hence the approximations used in the analyses of the various regions of the characteristic have to be carefully
reviewed in this more general application involving flows and higher energies. In particular, it is normally assumed that ion thermal energies can be ne-glected (or approximated) in comparison to electron energies, reflecting the
situation in conventional glow discharges. In contrast, it is shown later that under certain conditions ion energies can exceed electron energies, a fact which requires inversion of much of the normal analysis.
Third, an advantage of the low density aspect of the present application is that it makes feasible the construction of a free-molecular Langmuir probe. The meaning of free-molecular is discussed in Sec. 2.1. Basically it im plies two things:
(1) conditions can be such that electrons or ions flowing to the probe have a negligible probability of · .. ~uridergoing any collision while under the influence of the probe' s field, a fact which aids greatly in interpreting
probe data.
(2) the probe.is free-molecular in the conventional sense in that collisions between incoming and reflected neutral particles occur at such distances that the incoming stream is not appreciably altered.
Finally, the experimental difficulties in the use of such a
probe must be overcome. Earlier work on Langmuir probes has given them areputation for unreliability, largely as a result of unsuspected probe
effects such as work function changes. Such effects have recently been systematically studied (Ref. 2) and as aresult could readily be recognized in the experiments and allowed for. The aim of the present work is to study all these various aspects in order to show that the free-molecular Langmuir
probe can provide useful information in a flowing low density plasma. 11. GENERAL DESCRIPTION OF PROBLEM
2. 1 Basic Flow Parameters
Because the low density plasma tunnel was under construc -tion at the time the present experimental work was carried out, an interim vacuum facility was used in which the efflux from the plasma jet was
ex-panded only to the 200 - 400 micron Hg pressure range. This pressure was dictated by the size of the mechanical vacuum pumps available and the argon mass flow range to which the plasma jet was limited for stabie operation
(.06 to 0.125 gms/sec.).
However, because of the elevated static temperatures
characteristic of the plasma jet efflux (:> 1500oK, see Appendix C) the argon atom mean free paths were still of the order of O. 10 cm or greater, as
indicated in Fig. 1. The curves of Fig. 1 are calculated from the standard
kinetic theory result relating the mean free pa th to the viscosity, in C. g. s. units
mean free path
=
1. 845 x 103fT
"l
•
(3 )
where ~ , the viscosity in gm. / cm -sec, was calculated from the Lennard-Jones 6 - 12 potential model, using data tabulated in Ref. 3. It was found feasible to manufacture Langmuir probes from O. 01 cm. diameter wire, small enough to be free-molecular in the plasma stream available in the interim facility.
The term free-molecular is used here in the conventional sense, implying that the probe presents no disturbance to the incident flow of argon atoms. However, the argon plasma is basically a three-component gas: argon atoms, singly charged positive argon ions, and electrons, and six distinct mean free paths exist. Thus the possibility arises that a probe may be free-molecular with respect to argon atoms but in continuum or transition flow with respect to the ions, for example. Ordinary continuum flow occurs when the mean free path in question is very much smaller than the body characteristic dimension.
The atom -ion collisions may be grouped with the atom -atom collisions so far as momentum collision cross-section~and hence mean free path are concerned, but the ion-ion, ion-electron, and electron-electron collisions are distinct. In Fig. 2, ion-ion mean free paths are plotted, based on calculations by Spitzer (Ref. 4), for the "self-collision time" of a group of like-charged particles interacting with each other. In c. g. s. units the mean free path formula adapted from Ref. 4 beco.mes
(2. 2) 3 ( k'3
r'!J )
't2,
where
..A
=
2.e
~
.?:;;
n.
and is tabulated in Ref. 4. For the same concentration and kinetic temperature, electron-electron mean free paths are the same as ion-ion, whereas electron-ion mean free paths are approximately half the ion-ion mean free paths.Test section ion concentrations from 10 15 ions/cm 3 down to 10 11 ions/cm 3 or lower have been produced in the interim plasma facility, and will be studied in the low density plasma tunnel. From Fig. 2 it is seen that this range of concentration will represent, for a typical probe of O. 01 cm diameter and an ion and electron temperature range of 500 to 150000K,
the complete gamut of conditions from free-molecular flow to continuum flow with respect to ions and electrons, in spite of the fact that the probe may be free-molecular with respect to the neutral atoms throughout. In this paper attention wil! be confined to the two limits of free-molecular and contin:uum flow with respect to the charged particles, the probe always being free-molecular with respect to the atoms.
*
Charge exchange cross-sections are difficult to estimate because of the scarcity of data at low energies. Extrapolation of existing data suggests mean free paths that are of the same order as those for momentumLangmuir probes usually consist of a small collecting area such as a tungsten sphere, disc or cylinder, immersed in the plasma and fitted with ancillary circuitry so that the probe's potential with respect to the plasma can be varied and the resulting current measured. Before con
-siderin'g the various regions of the resulting voltage-current plot, it is use-ful to review the situation at the boundary of a plasma.
The basic characteristic of a plasma is its very strong tendency to maintain electrical neutrality. In a plasma such as the present one where no electronegative ions are considered, neutrality implies that the ion concentration n.. and electron concentration n._ are almost iden-tic al, and are in fact often termed the plasma concentration n How strong this tendency to neutrality is may be seen by applying Poisson1 s equation to a region of uniform net charge density
(2. 3) so that over a slab of thickness % , integration yields
v
(2.4)To prodl ce a voltage difference of 10000 volts in one metre, insertion of numerical values shows that the concentration difference necessary is only
10 6 /crn 3. Hence in a plasma of 10 12 ions/cm 3 concentration, a difference between the ion and electron concentrations of one in one million is all that is necessary.
Now, if an insulated body or wall is placed in contact with the plasma, the basic condition th at must be satisfied is that no net elec-trical current flow to the wall, or in other words that the number of posi-tive and negaposi-tive particles reaching the wall must be equal. The random kinetic speed of the electrons being much greater than that of the ions, many more electrons would reach the wall than ions except for the: fact that this quickly produces a potential gradient normal to the wall which turns back all but a smal! number of electrons , sufficient to balance the ion flow. Since this total potential drop V must be equivalent to nearly all of the mean electron thermal energy in one direction,
eV=
'~KT
and assurning partic1es of one sign only this value of V may be inserted in Eq. (Z. 4) to obtain a rough measure of the thickness of the region of large potential drop at the wall:
•
.
'
(5 )
=
69.0)
~
(2.5)where n is the plasma concentration and
h.
is called the Debye length,since Debye has shown tha t
h.
is the distance in which the field of a pointcharge in an electrolyte is shielded by adjustment in position of particles of opposite sign.
Thus the sheath which develops whenever a plasma is in
contact with an insulated wall is characterized by potential gradients re
-lated to the electron temperature, and a deviation from the charge equality
which is characteristic for a plasma. The boundary between the plasma
and sheath will be discussed more fully in Sec. 3.3.
The qualitative features of the characteristic of a probe
immersed in a plasma are indicated in Fig. 3. If the probe is made
sufficiently negative with respe ct to the plasma to prevent any electrons reaching it, only ions will be collected, the magnitude of the ion current being almost independent of the probe voltage. This independence is due to the presence of the ion sheath region, which shields the plasma from most of the probe's electric field. The thickness of the sheath is given in the case of space-charge-limited current flow for particles of one sign by the
Langmuir-Child relation (Ref. 5, p. 620):
'3/4
(V
p~obe)
d
(2. 6)where Vprobe is the potentialof the probe with respect to the local plasma potential.
Since the she ath edge effectively replaces the metal surface
as the collecting area, an increasing ion collection with increasing negative
probe potential may be at least partially ascribed to the increasing sheath thickness, for probes of spherical or cylindrical geometry.
If the probe is made sufficiently negative, the ions ga in
enough energy in falling through the potential gradient to the probe to cause surface emission of electrons by impact; the current flow due to this effect is equivalent to additional ion collection. This effect rapidly increases
with increasing n~gative probe potential, as indicated in Fig. 3. If the
probe is made less negative, a potential will be reached close to the plasma potential at which the most energetic electrons in the surrounding plasma can reach the probe against the retarding field. The variation of collected electron current with probe potential in this region provides information about the electron energy distribution; this technique is referred to as the retarding field rn ethod.
Ion thermal energies are usually such that at a probe poten-tial a small fraction of a volt positive with respect to the plasma no ions are able to reach the probe. and an electron sheath develops. Increase in probe potential beyond this .value causes a much more gradual increase in electron collection than in the retarding field region, due to the shielding effect of the sheath. At high enough probe potentials the probe field extends far enough to have collisions within its range, and the electrons accelerated in the probe field have sufficient energy to cause secondary ionization, so that a rapid increase in electron collection ensues.
In this paper, informa tion obtainable from the retarding field region of the probe characteristic and from the magnitude of the current during ion-sheathed and electron-sheathed probe operation is con
-sidered.
lIl. ANALYSIS OF PROBE THEORY
3. 1 Introductory Remarks Regarding Collisions
Collisions involving ions or electrons may have important effects on the magnitude of the current collected by the probe. Conven
-tional probe theory has been developed for the conditions under which no collisions ofthe charged particles occur once they are under the influence of the probe's electric field. However, this condition may be satisfied
and the probe still not measure undisturbed plasma conditions. For example, when the sheath extends one-one hundredth of the probe radius, and the
charged particle mean free paths are one tenth of the probe radius, the conventional probe theory will apply, but the plasma which the probe is sampling will be that which exists at the imaginary surface one tenth of the probe radius away from the probe. The charged particle nurnber densities, temperatures and plasma potential at this distance will be controlled by conductivity and flow of the charged particles. and the measured quantities may be different from those of the undisturbed plasma.
Only when all m ean free paths are m uch larger than the probe radius wiU the probe measure undisturbed plasma properties. In other words, at a point a mean free path distant from the probe, the probe must subtend such a small solid angle that the flux of particles to that point is negligibly disturbed by the presence of the probe.
In the analysis of Sections 3.2 and 3. 3, only the first con-dition above need be satisfied. The probe will only measure true plasma conditions, however, if the second condition is satisfied.
,
r
'
.
(7 ) 3. 2 The Retarding Field Operation
The free electrons in any sample volume of plasma will normally have a distribution of random kinetic velocities about some most probable value. If the plasma is free from such factors as high fluid shear stress, imposed magnetic or electric fields as in an arc, or shock waves, then this velocity distribution will be Maxwellian,
3/2.
-(o/r)~
' ) Cttl I.f
= (
,
.
e
1T
CmWh en a probe is at a potential such that some but not all of the electrons are repelled, only those which have sufficient energy in their motion to-ward the probe, i. e. whose energy is equal to or greater than that given by
V
',1.C
2e
=
2. rYl_ VIcan reach the probe. V is the probe voltage with respect to the plasma,
Yrl_ the electron mass, and Cv, the component of random motion normal to the element of probe surface. Then a basic relationship of kinetic theory states that the electron current density collected by the element of probe surface is obtained by integrating over all velocities which permit the electrons to reach the probe.
If the electrons have a Maxwellian velocity distribution function this integrates to
eV
- KT_
J
e
(Yl4
C_)
e
where C_
=
average speed=
2.)
2. K.T-11" )'\1_ Converting to logarithms and differentiating,
11700
T_
(3. 1)
(3. 2)
Thus if the logarithm of the electron current is plotted against probe voltage, a linear variation indicates that the electrons have a Maxwellian velocity distribution function at one electron m ean free path from the probe. Further, by measuring the slope of this linear portion, the electron temperature is found.
Regardless of the magnitude of the cur rent collected when the probe is electron or ion sheathed, it is evident that when the probe potential is exactly that of the plasma, the electron and ion fluxes will be those determined by ra~dom kinetic motion, i. ~.---f~) ions per unit area per unit time and
(Yl.+C_)
electrons.Thu~
if the electrons and ions have the same temperature the electron cur rent will be greater than the ion current by the factorjm+/m_
For argon this ratio is 271. As soon as the probe is made slightly positive with respect to the plasma, the ion current drops to zero, but no kink appears in the probe characteristic at this point because at the ordinary magnification used to obtain the electron current, the ion current is negligible. What does occur, however, is the development of the electron sheath, and consequently a more or less abrupt change in slope of the probe characteristic, especially when plotted semi-logarithmically. The plasma potential is conventionally determined by the intersection of the extrapolations of the two regions of the semi-Iogarithmic plot.When the sheath thickness is much larger than the probe diameter (i. e. the ion density is low), and the electron temperature is high, the electron collection is limited by orbital motion. That is, many of the electrons entering the she ath follow an open traject.ory around the probe and leave (Ref. 6). For example, in the case of the cylindrical probe, the square of the electron current versus voltage provides a linear region which when taken together with the linear retarding field region of the semi-logarithmic plot serves to define a plasma potential. Since these conditions were not obtained in the present set of experiments, this point is not pursued.
As noted, the electron flux to the probe when it is at plasma potential is
('Y\ÏJ,..ë_)
per unit probe area, or(~)
= e(Y1
4
C-)
y=O
O'3~8
e
n_J
KT_m_
(3.3)Having determined th is
J_
from the ordinate corresponding to the intersection of the extension of the two linear regions, Yl._ is deter-mined, since G_ is known from the previous retarding field measurement. In this case the value of A is exactly the probe area, since the electron sheath, while incipient, does not form until the probe becomes positive.This is the conventional formulation of the Rroblem. The implicit assumption that it contains is that the flux of
(Yl
4
C_)
electrons, which certainly occurs when the probe is at plasma potential, also occurs when the probe is electron attracting, so that all the field which exists when the probe is positive is assumed to be confined to the sheath, and the electrons arrive at the sheath edge by random kinetic diffusion alone. This assumption is va lid when the ions have negligible thermal energy•
't
(9)
in relation to the electrons, but its validity is less certain when ion energies are appreciabIe. It will be shown later (Sec. 3.3) that only when ion
energies approach one half the electron energies does their energy begin to affect ion collection. It would seem to be areasonabIe assumption that the influence of ion energy on electron collection is not any more severe, so that in the following work it will be assumed that the conventional extra-polation to plasma potentialof the current collection curve for operation of the probe at positive potentials yields the random kinetic flux of electrons.
Thus, so long as the various mean free paths are larger than the range of influence of the probe's field, the following may be de-termined:
(1) whether or not the electrons have alocal Maxwellian veloci ty distribution function
if they have, then
(2) the local electron temperature (3) the local ion number density
(4) the local plasm a potential
These will be the conditions which exist at approximately one mean free path distant from the probe, but they will be the conditions of the loc al undisturbed plasma only if the mean free paths are much larger than the probe. Otherwise these measured conditions will have to be related back to undisturbed plasma conditions by full solution of equations involving the conductivity of the plasma.
3. 3 Ion Collection
The flat portion of the characteristic corresponding to posi-tive probe potentials is extrapolated to the plasma potential to determine
~_ from Eq. (3. 3). This procedure implies that all field effects of the probe are limited to the sheath (which affects the computed value of the effective probe area A), so that electrons arrive at the sheath edge by ran-dom kinetic motion alone. It also implies that the electrons have a Max-wellian velocity distribution function at one m ean free path from the probe.
Similar reasoning applied to the collection current when the probe is negative and ion-sheathed extrapolated to plasma potential would indicate that from
the ion temperature could be determined, since
n
+ ~ 1'\._ However, Tonks and Langmuir (Ref. 7, p. 879) noted that such a procedure led to the anomolous experimental result of ion temperatures over half the value of the electron tem peratures (i. e. 150000K) in plasmas in wh ich the ions were known to be approximately at room temperature . .Later in the same paper Tonks and Langmuir studied the complete plasma and sheath system and deduced that in general a small amount of the field of the probe extends beyond the edge of the sheath into the body of the plasma, thus increasing the ion collection over the value which would be expected for random kinetic motion. The effect of this pre-sheath on the probe collection current was not considered. however. until the studies of Bohm, Burhop and Massey (Ref. 8) and Allen, Boyd and
Reynolds (Ref. 9). The treatment in Ref. 9 is most pertinent to the present case, and is reviewed briefly here.
Consider a spherical probe immersed in a plasma in which all molecular collisions_oc;cur.at a distanee much greather than the extent of the probe's field,and in which the ion temperature is negligible in com-parison to the electron temperature. The spherically symmetrie field will accelerate ions toward the probe, and at radii where initial ion thermal energies are negligible in comparison to the energy due to the field, the ion velocity will be
J
-2.e
V
/m ... )
directed toward the probe centre, where V is the potential relative to the plasma. Hence the ion density at that radius can be written-l
n ...
=
J
t [411"
t'2.e
J-2.
eV/m ... ]
(3.4)Since the probe is biased so that no electrons can reach it, the local population of electrons must be in thermodynamic equilibrium with the local potential, and the Boltzmann equation relates electron density to
potential
_e
y
KT_
(3.5)
Poisson's equation relates the Laplacian of the potential to the local net charge density
Substituting for the values of Y\.... and Yl._ , one form of the general
"plasm~-sheath" equation is found
(3. 6)
•
(11)
-~~-J
-1\
e
0_ (3.7)
This differs from the equation originally developed by Tonks and Langmuir because they were considering the situation in a cylindrical discharge tube where the walls were ion-sheathed and the pre-sheath field extended toward the tube centre. lons were assumed to be continuously created uniformly throughout the pre-sheath and plasma with zero initial velocity and thus fell varying distances under the influence of the wall po-tential. On the other hand, in the probe case, all the ions are attracted from infinity, and no collisions or ionizing events within the field region are considered.
Allen, Boyd and Reynolds solved Eq. (3.7) by numerical integration. Their results are reproduced in Fig. 4. The curves are for various magnitudes of probe current, normalized by a current related to the current crossing a sphere whose radius is the Debye length, so that the curves correspond to different probe sizes. Actually,
J.
= êo (K T_ )~/~
which is 2J-ff
m(~
times the current crossing a Debyesp~ere.
eJ
2. m -t )It is seen that for probes that are very large in relation to the Debye length, the curve marked "plasma approximation" provides an
accurate solution outside the radius corresponding to
ev/
KT_=
1/2.. Thus for these probes the solution can conveniently be split into two parts, the plasma approximation applying up to the sheath edge and the Child-Langmuir relation applying in the sheath.This plasma approximation involves a technique first used by Langmuir and Tonks, in which they noted that for the moderate fields exist-ing in the pre-sheath the plasma equality n+~ Y\,_ is very closely true. Hence from Eqs. (3.4) and (3.5), th is equality yields
110
e
(3.8)This is plotted as the "plasma approximation" in Fig. 4. From Fig. 4 or by differentiation of Eq. (3.8) it is seen that
av
èl
r
asThe radius at which this occurs may be taken as the point of breakdown of the plasma approximation. At this radius, the current reaching the sheath edge is obtained by substituting eV /KT_ =.
Y,
into Eq. (3.8)(3. 9)
Other authors considering the plasma-to-sheath transition (Ref. 10) have
shown th at mathematically a stable sheath is only possible when the ions have been accelerated to a kinetic energy equivalent to at least half the
electron temperature. Thus it may be concluded th at the case in which the
probe is much larger than the De.bye length may be treated by splitting the
field into two parts, the plasma approximation embodied in Eq. (3. 9)
applying up to the sheath edge, and the Child-Langmuir relation (Eq. (2.6»
applying in the sheath. This approximate treatment may be applied to the
present experimental work since the characteristic probe areas used.were
always much greater than the surface area of a Debye sphere.
Equation (3. 9) implies that. ion collection at potentials which
exclude all electrons from the probe is independent of the probe voltage,
except for the effect of voltage on the effective probe area A, which is
con-ventionally assumed to be the sheath edge area. Since this sheath grows
with increasing negative potential, as governed by the Child-Langmuir
relation, it is customary to extrapolate the ion collection curve to plasma
potential, at which no sheath is assumed to exist. Then by using the ion
current so found together with the probe surface area A, the calculation in
Eq. (3.9) becomes independent of this sheath-growth effect. Experimentally
the uncertainties. involved are usually small because the ion collection curve approximates a nearly horizontal straight line when the probe dia-meter is much larger than the Debye length.
By comparing Eqs. (3.3) and (3. 9), and noting that for argon
Jm./W'I_
=
271, the implied ratio of electron to ion current is found to be=
271 x O. 398=
178 0.6073.3. 1 Effect of Ion Energies on Collection
(3. 10)
Analyses are available which attempt to treat the situation when the ion thermal energies must be taken into account. Reference 8
does this in an approximate manner, but in Ref. 11 the complete plasma
-sheath equation has been solved numerically for spherical and cylindrical
probes, the only approximation being that the ions are taken as monoenergetic.
The technique used is to characterize the orbits of the individual charged particles in terms of the constants of their motion - their energies 'and
angular momenta. The computations were carried out on a digital computer for ratios of probe diameter to Debye length which are very much smaller than in the present experim ents, but they indicate that in general an
increase in ion energy leads to a small decrease in ion collection. For example, when the probe has a diameter of ten Debye lengths, an increase
i
/
'r
(13)
in
ï""/T _
from 0.01 to O. 10 causes a 10% decrease in ion current collection.From the trend in the curves it is evident that for larger probe sizes the effect is even less important.
To summarize, for probes large with respect to a Debye length, both Refs. ;9 and ;11. yield Eqs. (3.9) ant§ (3. 10) in the limit
,..
~ /T_~ 0 , and Ref. ~8: indicates increases in the value of 'J_ / J-tfrom 178 of only a few per cent, right up to T+/, ..
=
~.For any probe, however, increasing the value of
4/T_
must eventually cause large changes in the value of ;r-/;r't The case
T+/T_">
I
is not usually considered because this condition has not been common in experimental plasmas. Biondi (Ref. 12) points out, however, that in plasmas where the charged particle density is dropping due to ambi-polar diffusional los ses, the electron temperature can readily drop below the gas temperature, which the ions share. In fact, this condition was obtained in some of the present experiments.When T+
/T_
>
2. ,
the arguments leading to the equations for ion-sheathed and electron-sheathed probes are inverted. The retarding field region still affords a measure of the electron energy distribution be-cause regardless of field details {wi th the possible exception of fields that do not decrease monotonically) it determines how many electrons can over-come any specific potential. But just as previously the electrons were assumed to arrive at the electron sheath by random kinetic motion so now the ions arrive solely by virtue of their random kinetic motion. HenceJ
=
0-39 8
e
n
A
j
K T++
0 m+ (3. 11)On the other hand the electrons now require acceleration to at least one half the ion energy for a stable sheath to form, and equations analogous to (3. 9) and (3. 10) result
J-/A.
(3. 12)so that for argon the electron-to-ion current ratio becomes
412
500
400
2.00
100
0·01
The effect of Ti'
/-C
is illustrated in sketch 1.0'1 I I I I NO TH~ORYI I AVÁI LÁBLE: I I I I I SKETCH 1 10 100
It is apparent that sketch 1 provides a criterion whereby experiment can at least determine whether the ions or electrons have more random energy.
3. 3. 2 The Effect of Smal! Ion and Electron Mean Free Paths
All of the previous analyses apply to probe collection under the condition that no collisions occur within the radius of the resulting electrostatic field of the probe. It is of interest to consider the situation in which the neutral particle mean free path remains much larger than the body dimension, but the plasma concentration increases to the point that charged particle mean free paths are much smaller than the body dimension. This situation may be written as
A
neutrals probe diameter ~ ). ions ::>electrons
Roughly speaking, the problem may then be considered in two parts, as indicated in Sketch 2. The probe will be sampling the plasma one ion mean free path away from the surface, where the ion concentration
n,
(15) PItOB.E
SVR ~ACE
SHEAïH
SKETCH 2
and plasma potential VI will be measured, subject to all the previous dis-cussions. However, these will not in general be the same as the local un-disturbed plasma conditions 11.0 and Vo , and the second problem will be to relate conditions 'h" V, to
na) Va
Stated another way, in the pre-vious analysis the pre-sheath voltage gradient goes asymptotically to zero at infinity. The assumption here is that the bulk. of the pre-sheath voltage drop occurs in a collision-free distance so that the previous analysis still applies, but that the charged particle collisions m ay alter the voltage gradient beyond this distance.Since ion-neutral and electron-neutral mean free paths are much larger than the diameter of the probe, this second problem is not one of diffusion of charged particles through a neutral gas, but of their flow which is caused by electrostatic fields and concentration differences, and is impeded by collisions with oppositely charged particles. When the probe is collecting electrons and rejecting ions, the flow may be considered as that of a Lorentz gas, which consists of non-interacting electrons colliding with fixed ions. The problem is: given the electron flow
j_
= :J~/A through the spherical surface one electron-ion mean free path away from the probe sur-face, and having measured 'Yl-, andv:
by the probe, what areno
and ~ ? The ions will be very close to equilibrium:
-e~-Vo)
Kï~
or since th is whole region is a plasma,
(3. 14)
n,
=
'hoe
This implies that the ion density has to decrease as the higher potential permits fewer ions to penetrate, and that in. order to pre-serve plasma neutrality the electrons must very closely follow this con-centra tion profile.
Consider a spherical probe. Beyond r, (n, I
V,) ,
the voltage drop across an incremental stripd
r will be given bydV
(3. 15)where ~ is the resisitivity in m. k. s. units of a Lorentz gas. Then. integrating:
00
v
,-V
0 (3. 16)But from Eq. (3.3)
(3. 17)
and using Spitzer's calculation of resisitivity for a Lorentz gas (Ref. 4) in m. k. s. units,
3 3 ~
d [
3(K T_)
J
(3. 18)...&n. 2
e
3111\
or using Eq. (2. 5), (17 ) _3
8-16
x
10er,
hL
(3. 19)Numerical values typical of the present experiments may be substituted into Eq. (3. 19) to estimate the importance of this effect.
Using
h
r,
-4t
10 me ... es Eq. (3. 19) becomes -8 0-5 )(io
mettes(liberal estimate of radius of pre-sheath "edge" )
4 x 10- 5 volts
Hence the local plasma potential is not measurably different from the undisturbed value. As a corollary, Eq. (3. 14) indicates that the local plasma density is even less disturbed, so that it may be concluded that, under the conditions of the present experiment, charged particle
collisions do not constitute a measurable source of error in probe measure
-me nts. How the presence of mass motion complicates this conclusion is discussed in Sec. 3.4.2.
3.4 Effect of Mass Motion,
3.4. 1 All Mean Free Paths Larger Than the Probe
Attention will be confined to probes that are large in relation to the Debye length. Additionally, consideration is limited in this section to situations in which the probe is free -molecular wi th respect to all species.
In the limit of very high speed ratios, such as would occur in the case of a satellite or in some types of laboratory facilities, the thermal motion of the ions can be neglected, and the .analysis can be based on the concept of the probe collecting the flux of ions which essentially cross the projected frontal area:.of the probe. This case is considered in Refs. 13, 14, and 15. Here, the case is considered in which this simpli-fying limit is not applicable.
For plasmas having mass motion the essential change is that the energy of the ions will be non-isotropic, implying that non-spherical or non-cylindrical fields will result in genera!. Hence analyses of ion
collection such as Ref. ll/which depend on conservation of angular momen-turn I will be difficult to apply.
In the absence of exact theory there is still much useful in-formation that can be obtained. Because of the mass difference between argon atoms and electrons, the electron speed ratio is negligible in re-lation to the argon speed ratio. For instance when S = 27 for argon, if the electrons have the same temperature and mass motion their speed ratio is O. 10. Hence it is expected that the norm al retarding field relations apply and that the measurement of electron temperature will be unaffected by mass motion. This may be checked experimentally by comparing, for example, the retarding field portion of the characteristics of two long free-molecular cylindrical probes, one whose axis is parallel to the flow and one whose axis is transverse. Except for end effects which may be made
arbitrarily small, the probe in the parallel orientation will be unaffected by mass motion.
Consider the probe operation when the ions have more
thermal energy than the electrons, since this condition was available experi-mentally. When the probe is biased to accept electrons and reject ions, the analysis in the previous section has indicated that a pre-sheath field will exist which will now be complicated by the asymmetry in the ion energy. Additionally, a probe area transverse to the flow will reflect ions back into the oncoming stream, causing an increased ion density in front of the probe and a decreased density behind the probe. Elementary gas kinetic calcu-lations indicate that the net density variation from the stationary case inte-grates approximately to zero for all speed ratios, so that electron collection would be uninfluenced if it only depended on this factor. However, the
electron collection depends on a combination of local plasma density and an effective ion "temperature". The influence of the ion temperature originates in the pre-sheath field and intuitively it would be expected that some amount of similar compensation in the pre-sheath field effect around the probe would also take place, but there is no approximate theoretical treatment available to justify this statement, and appeal must be made to experiment • .
When the probe is biased to accept ions the situation is per-haps more' tractable. The analysis in the previous section has indicated that no pre-sheath field should exist, so that the ions should arrive at the sheath edge in an amount governed by simple kinetic theory. For example, a plane:. element of probe surface whose normal is inclined at an angle 9 to the flow direction of a plasma of speed ratio S should receive an ion current
- S"" sin2.
e
(l9)
The case of a cylindrical probe transverse to the flow may be similarly treated, and was studied experimentally to determine whether simple kinetic theory governs ion collection under these conditions.
Although experimental limitations prevented experiments being performed in which the electrons had more thermal energy than the ions, and in which the probes were free-molecular with respect to all species, it is of interest to apply the previous considerations to this con-dition. Here, pre-sheath fields should be associated with ion collection, so that because of the anticipated field asymmetry due to ion energy asymmetry, the ion collection will be subject to the same measure of un-certainty as was the electron collection wh en the ions were the more
energetic species . . When electro ns are being collected, the reflected ions will cause a density variation in the plasma concentration around the probe but, as before, this will integra te very closely to zero around the probe.
To summarize, the approximate theories available have
allowed prediction of the effects of mass motion only under some conditions, which may be tabulated as follows. The uncertain areas require exact
analysis.
Summary of Predicted Effects of Mass Motion (All mean free paths) >::> (Probe Dia. ) "» (Debye Length)
(T-y, )">.> ,
T_
(T
yT_)
« ,
Retarding Field unaffected unaffected
Region
Ion C ollection follows_ siI!lple uncertain
kinetic theory
3.4.2 Combined Effect of Mass Motion and Small Ion Mean Free Path So far, the discussion of the effect of mass motion has been limited to the completely free-molecular case, and the discussion of the effect of small charged particle mean free paths has been limited to sta-tionary plasmas. In this section the combined effects of mass motion and small charged particle mean free paths is discussed.
Consider a plane probe such as would be formed by the ex-posed end of a wire facing into the flow, having insulated sides. Whenthe probe is electron-sheathed, ions undergo specular reflection at the more-or-less plane .... sheath edge. Consider the case that the ratio of the ion-ion mean free path to the probe diameter is less than one tenth, so that con
-tinuum flow with respect to the ions will exist. A shock wave composed only of ions and electrons is predicted whenever the plasma is supersonic.
When the ionization level of the plasma is only a few per cent the increased plasma concentration behind the shock wave wiU have negligible effect on the ion-neutral mean free paths, so that the probe wil! remain free
-molecular wi th respect to the neutral particles. The electrons have a negligible speed ratio and hence would not form a shock wave, but are con-strained to follow the concentration profile of the ions in order to maintain approximate plasma neutrality. It is not intended to study here the interest-ing details of the shock front, which wil! undoubtedly be affected by the diffusion and mobility of the éle.Ctrons. It would be expected however that because of the ease of energy flow in the electron population the electron compression would tend to produce an electron temperature gradient that extends over a region large in relation to the shock thickness based on the concentration profile. In the present situation, a smal! region of com-pressed plasma exists in front of the probe, from which the electrons can readily lose energy in three directions to the surrounding cooler electron population. Rough estimates indicate that the electron temperature may be expected to change very little in crossing the shock front.
When the probe is biased to attract ions, no shock wiU be formed since the probe is a sink for ions, and the electrons have a negligible speed ratio. Any floating body or insulator s uch as the quartz shield around the probe wil! al ways be ion attracting and hence form no shock.
To summarize, Langmuir probes used under the conditions
( À neutrais) >"> (Probe Dia.)
»
(h
ions)
electrons>:> (
h, )
should have the foUowing behaviour. An area parallel to the flow wiU cause no shock whe.n reflecting ions, and the electron current can be used to determine
n.
'
which wil! very closely be 'Yl-o as discussed pre-viously. Further, the electron temperature can be determined to conven-tional Langmuir probe accuracy, so th at a comparison of this temperature with that of the electrons in the shocked region in front of a transverse probe(21)
area will indicate to what extent the electron compression through the shock is isothermal.
The transverse probe should measure a considerably higher plasma concentration when the probe is reflecting ions. This number density will be somewhat less than that predicted by the Rankine-Hugoniot normal shock relation,
I
1t
I[Cr-I)
+
(3. 21)
because the probe constitutes the whole area causing the ion shock and will hence begin drawing electron current from regions of lower plasma density than that on the stagnation stream line. Hence, without solving the whole ion flow field to obtain ion concentration at one ion mean free path fr om the probe, the only prediction with re gard to experiment that can be made is that a comparison between transverse and parallel probes will yield an apparent density ratio somewhat less than the Rankine Hugoniot ratio for a normal shock . This result would serve to substantiate the existence of an ion shock.
A study of the utility of a Langmuir probe buried in the stag-nation point of a blunt body, making use of solutions of the flow field near the stagnation point, has been made by Talbot (Ref. 16). In this case the Langmuir probe was large in relation to the various near free paths. The details of the flow field itself have been studied by Sonin (Ref. 17), using Langm uir probes that were free -molecular with respect to the neutral particles.
IV. DESCRIPTION OF EXPERIMENTAL WORK 4.1 The Interim Plasma Tunnel
The facility is shown in Figs. 5 and 6. It consists of an electric-arc-powered plasma source, or plasma jet, which discharges through a supersonic nozzle (either with or without an intervening settling chamber) into the test section. The test section has a simple rectangular shape and opens directly into a 3000 litre surge tank. The test section and tank are evacuated by three mechanical vacuum pumps totalling 500 litre / sec pumping capacity. The instrumentation of direct interest in the present experiments is shown in Fig. 5. The experimental paramet~rs
(1) arc voltage and current
(2) high frequency arc current fluctuation, measured by an oscilloscope
(3) arc chamber peripheral static pressure (4) mass flow
(5) static pressure of intermediate settling chamber (6) test section static pressure (McLeod gauge) (7) nozzle exit static pressure
(8) impact pressure at any point in the nozzle exit plane.
(5), (7) and (8) were measured with a precision three-tube butyl phthalate manometer.
4. 1. 1 The Plasma Source
A cross-sectional view of the plasma source used is shown in Fig. 6. This unit has been evolved from a commercial model*, and is basically a swirl stabilized arc of the type pioneered in Germany at Kiel by Finkelnberg et al. The electrodes consist of an indented disc anode and a sleeve cathode made of thoriated tungsten and silver-soldered into water
-cooled copper holders. The working fluid, which in all the present work was argon, is introduced tangentially at the periphery of the arc chamber. The centrifugal action of the swirling gas helps to constrain the much-Iess-dense arc column to a central position. The anode spot was observed to remain centrally located in the depression, but the remainder of the current pathis uncertain. Power up to 25 KW is supplied by either rectifier power packs or an AC - DC arc welding generator.
4. 1. 2 Operation of the Plasma Jet
For the purpose of the present investigation, it was of pri-mary importance to run the plasma jet under reproducible conditions and
:,with complete freedom from fluctuation in the arc process and fr om electrode contamination. Unfortunately the last two conditions were not perfectly achieved and proved to be an experimental limitation in some respects. The development of the arc to a stability satisfactory for aero and thermodynamic measurements has been discussed in Ref. H). Briefly, an ad hoc experimental program showed various stabIe modes of arc
operation, depending on m ass flows, power settings, electrode geometry
(23)
etc. The plasma jet design shown in Fig. 6, run at 0.05 to 0.1 gm/sec of argon mass flow, over a current range fro.m 80 to 400 amps, showed the highest stability to date. The arc still showed a persistent tendency to wander between close limits, (see Appendix A).
4.2 Langmuir Probes
The usual shapes of the collecting surfaces of Langmuir
probes are spheres, cylinders or plane discs, these being the most amenable to analysis. Freedo.m of choice was limited in the present work by the
high energy and high ion density of the strea.m, and by the limitation on size imposed by the desire to have the probe in free -molecular flow wi th respect to the argon atoms.
Two types of probes that proved feasible are shown in Sketch 3. Both are formed fro.m 0. 1016 mm diameter tungsten wire mounted in an insulating quartz or nonex holder. The cylindrical collect-ing area was preferred but was found to draw such a large electron current in the high ion density plasma that it vapourized.
NOWE)( OR QUA.RTZ SHE,\TI1
0·01 ~\"tl €3
a
p
~==~==~==~
.
_t--i
~
~~==========:!l
'
-
'::.=
\
~
.
-t-
-=.--=-
t
I Q-/OlbHltt. 0-2. ,~M O.O. fun~$te.n wit·eLANGMUIR PROBE CONSTRUCTION SKETCH 3
The probe in the form of a circular plane area formed by the exposed wire end was made as follows. Working under a 40-power micro-scope, the wire was clamped in soft plastic inserts in a jeweller' s vise
and the end ground to a smooth circular cross-section, using the finest grade of Arkansas stone available. Quartz tubing of 2 mm outer diameter was separately drawn down in an oxy-acetylene flame to a long slender taper. The tungsten wire was inserted until it just jammed in the taper, and the tubing cracked off just past this point, providing an outer diam eter of the quartz of about 0.2 mmo With the wire removed, the quartz sheath was ground back to a flat end, again using the Arkansas stone. The grinding was continued until the wire would just pass through, leaving an annular gap of about 0.01 mm clearance. With the end of the wire carefully aligned flush with the end face of the quartz, the oxy-acetylene flame was gently applied about 5 mm from the tip until the quartz shrunk down in this region onto the tungsten wire. Alternatively nonex glass and a small propane torch flame could be used. The probe was then bent through 900 about 40 mm back from the tip and mounted in a slender stainless steel support.
The probe utilizing the length of
o
.
1016 mm diameter wire as a cylindrical surface was made in the same manner except that the quartz was fused onto the wire with the appropriate length left exposed, usually to provide a length to diameter ratio greater than 50.4.2. 1 The Probe Circuit
The basic probe circuit is shown in Fig. 7. A sine wave voltage signalof any desired frequency was amplified by a 10 watt audio power amplifier and applied to the primary winding of an isolating trans-former, selected for a minimum of stray capacitive coupling. One ter-minalof the secondary winding was connected to ground through a 300 ohm resistor, and the other side connected to the probe, so th at the probe volt-age oscillated about ground potential at any desired amplitude and frequency. By applying the instantaneous probe voltage signal to the external horizontal drive of a suitable oscilloscope and applying the probe current signal
(voltage developed across the 300 ohm resistor) to the vertical input, the complete probe characteristic was traced out on the oscilloscope screen, twice for every sine wave cycle. Because the plasma stream was normally at about +12 to +15 volts, the range of interest of the probe voltage swing was usually from +10 volts to +20 volts, and the oscilloscope horizontal drive was calibrated so th at this was the range displayed.
Because of the wide disparity between the electron and ion currents, a "chopping" or two-trace preamplifier was used, one trace being set to a scale to display conveniently the electron current and the other the ion current.
(25) 4.2.2 Probe-Traversing Gear
The higher ion density stream contained enough kinetic and latent energy to vapourize any small uncooled body in the flow. Since it was mechanically impractical to cool probes of such small dirnensions, it was decided to traverse the probe rapidly across the stream, relying on the thermal capacity of the tungsten and quartz to allow only a tolerable temperature rise.
The system used for this purpose is shown in Fig. 6. The probes were rnounted on a hollow shaft parallel to the flow axis of the plasma strearn but 15. 2 cm beneath it, so that rotation of the shaft caused the probe to be swung across the plasma strearn. The shaft was actuated by a synchronous motor whose speed was exactly 72 r. p. m ., so that the linear motion of the probe was 1. 15 mm/millisec. Alternatively the probe rotational speed could be reduced through a 5/1 gear ratio.
An external "o-ring" seal was used to prevent air leakage into the test section around the shaft. and the probe leads were .. potted in epoxy resin inside the shaft. The leads passed out through holes in the shaft to connect to slip ririgs dipping into troughs of mercury. frorn which the probe signals were taken. This system proved reliable. and introduced no contact noise or variable resistance to falsify the probe signal.
4.2. 3 Oscilloscope Trace Triggering System
The probe voltage oscillator was normally set at 500 c. p. s . • so that the full voltage swing (i. e. one half cycle) occurred in one rnilli-second, corresponding to a probe movement of 1. 15 mrn. Since the strearn width was approximately 3. 2 cm. this movement amounted to 3% of the total width and was thus considered to be a good approximation to a point me asurement. Since the probe voltage oscillated continuously as the probe crossed the stream. the oscilloscope trace, if permanently brightened (or "unblanked") would paint an agglomerate picture of all the probe characteristics taken across the stream.
In order to obtain a single probe characteristic corres-ponding to a known position in the plasma strearn. the procedure was adopted of allowing the trace to be unblanked only for the duration of one trace at any desired point in the traverse. This was done in the following way. First. the Tektronix type 551 dual beam oscilloscope used provides a permanent unblanking bias to the grid which controls trace brightness in the cathode ray tube. whenever the external horizontal drive is used. This feature was removed so that unless further steps were taken the trace would remain blanked. However) another unblanking signal is ·provided in conjunction with the internal sawtooth generator normally used to sweep the trace horizontally, the trace being brightene d for its normal display
as it crosses the screen and blanked as it flies back. This internal feature is still available even when the external horizontal drive is being used, so that if the internal sweep is set so that it makes a single sweep upon receipt of a triggering signal, then an unblanking signal is provided, the duration of which corresponds to the time normally taken for the disconnected internal
sweep to cross the screen once. .
The required triggering pulse was obtained by the system shown schematically in Fig. 6. A disc having an adjustable narrow radial
slit in it was mounted on the shaft. The angular displacement between the
probe and the sUt could be adjusted so that, for example, when the probe was just entering the plasma stream the sUt coincided with a similar slit in the wall of a Ught-tight housing containing a type 929 photocell, allowing light from a suitable lamp to reach the photocell. The signal from the photocell was amplified, fed to a calibrated variable delay circuit, and then shaped in a pulse shaper to provide positive triggering of the oscillo-scope. Thus at any desired time corresponding to any desired position, af ter the probe reached the stream edge the trace could be unblanked by the delayed triggering pulse, and the duration of the unblanking pulse varied to provide either a single probe characteristic at the desired position, or a succession of characteristics from that position on across the stream.
V. EXPERIMENTAL RESULTS AND DISCUSSION
The analysis of the previous section has indicated that the way in which a Langmuir is used and the data interpreted is predicated on the physical conditions of the plasma. Limiting discussion to plasmas in which the neutral particle mean free paths are much larger than the probe dimensions, two basic criteria determine the flow regime. First, the
probe may be in continuum, transition, or free-molecular flow with respect to the charged particles, depending on their number density and tempera-tures. Second, probe currents during ion and electron sheathed probe operation in a stationary plasma may be ion-temperature controlled or electron-temperature controlled, depending on which species has more energy.
Experimentally it would be desirable to investigate a range of flows representing the extreme conditions under each criterion, but this proved to be impractical with the available equipment. With the plasma
jet dis charging directly through the nozzle into the test section, the
avail-able stavail-able arc operating conditions provided a flow in which the plasm a concentration and tempera tures were suc h as to impose "plasma continuum" conditions on even the smallest practical probes. At the same time the electrons were invariably much more energetic than the ions, as may be seen by comparing the electron temperatures reported in Section 5. 2. 1 with the ion temperature estimates given in Appendix C.
(27 )
The only effective method found to lower the plasma concen-tration (in order to have a Langmuir probe free-molecular with respect to all particles) was to interpose a settling chamber between the plasma jet and expansion nozzle. However, it was found that this allowed the electron population to cool to a temperature below that of the ions at the nozzle exit conditions, presumably by ambipolar diffusion in the settling chamber.
Thus the two operating conditions available were high plasma concentration coupled with the condition that the electrons had more thermal energy than the ions, and lower plasma concentration coupled with the con-dition that the ions had more energy than the electrons. The experimental results for the latter condition are reported first, in Sec. 5. 1. 1.
5. 1 Probe In a Low Ion Density Plasma
If a long cylindrical Langmuir probe which was free-molecular with respect to all species we re to be used with its long axis parallel to the flow direction, the situation would approximate that of a Langmuir probe in a stationary plasma. The approximation would be valid to the extent that the probe surface approximates an infinite cylinder, since mass mot ion along the axis of such a cylinder should have no effect on the collection, in the absence of any collisional effects near the probe. The procedure adopted was to use such a probe, and from the electron current obtain an indication of the local ion density to check that the probe was in free-molecule flow with respect to all species. This probe was then used as a standard with which to compare other probes mounted trans-verse to the flow. The test section conditions, as measured by methods outlined in Appendix C, were
static pressure: 400 microns Hg. centreline Mach number: 1. 41
static temperature: 1500 rv 20000K
5. 1. 1 Cylindrical Probe, Axis Aligned with Flow
The lower pair of curves shown in Fig. 8 is typical of a number of characteristics obtained for cylindrical Langmuir probes
parallel to the low ion density stream. The probe was made of O. 1016 mm diameter wire wi th a nonex shield as described in Section 4. 2, leaving a 5. 21 mm length of wire exposed, corresponding to a length-to-diameter ratio of 51. The characteristic was taken at the stream centreline in a time interval of 10 ms during which the probe moved 2.4 mmo
It is apparent from the wander of the trace in the retarding field region that the plasma stream properties were fluctuating during the
