Sensitivity variations in the Bayard-Alpert ionization gauge

Sensitivity gauge

variations

in the Bayard-Alpert

ionization

Part two: Simulation of ion collection, for collimated beam input and chaotic gas input, using a digital computer received 2 March 1968; accepted 23 March 1968

D J Turner+ and C Priestland,

Central Research laboratory,

Edwards High Vacuum International

Limited,

Manor Royal, Crawley, Sussex

Editor’s Note

A Bayard-A/pert ionization gauge with end-caps on the grid has been found by many workers to have a higher sensitivity than one with an open-ended grid. Since the assumption of nearly 100 per cent collection efficiency is reasonable for a closed gauge, a simulation of the open gauge has been carried out to determine if this explains the effect satisfactorily. It was found that the loss of sensitivity by not having end-caps on the grid could be only partially explained in this way.

1. Introdllction In experiments described by Priestland and Holland (1968)‘, a Bayard-Alpert gauge with a closed-ended grid structure gave a reading 2.7 times as large as an identical gauge with an open ended grid when a collimated gas beam passed along its axis. Groszkowski (1965)’ has reported an “approximately threefold” sensitivity gain for the same gauge types in an experimental apparatus which would appear to give more chaotic gas conditions. Freytag and S&ram (1963)*, with a slightly smaller gauge, reported a 30 per cent gain for air, and Schulz (1957)p using helium with a gauge similar to Priestland and Holland /

/

efficient ion collection in the open ended gauge. There was the possibility that, due to the different configurations of the electric fields in the two cases (Figure l), there was a difference in the number of ions produced but it was felt that this would not explain the wide variations observed. The first explanation proposed (to account for the effect using a collimated beam) was that the time required for an ion to be collected was greater than that for the ion’s initial axial velocity to carry it out of the end of the gauge. (In the closed gauge the ion would be reflected and thus would not escape.) However, for the particular gauge and gas flow considered (see Figure 2) the maximum time to collection (for an ion produced at the grid) was approximately 1O-6 sect while a gas tthe equation of motion of an ion accelerating transverse plane is:

along a radius-vector

in the

a. Open-ended gauge d2r f -- 0 dt2 -

--

v,1

and this gives the time to collection

b. Closed-ended gauge Figure 1.

T_

Electric field in the gauge

gave a sensitivity “at most 20 per cent higher than the ordinary Bayard-Alpert gauge”. It appeared from these that the difference was due to less*Author’s new address: Industrial Measurement and Control Research Assn, South Hill, Chislehurst,

Vacuum/volume

18lnumber

6.

Group, Kent

Scientific

Instrument

Pergamon Press Ltd/Printed

for an ion produced

at the grid as

2r,Ine) m [

1

-Zn(!i)]

% -PC )I m

(2n + l)n!

n=o

where re -collector radius ra =grid radius l’a -potential difference between collector and grid e =ion charge m =ion mass The infinite series is found to converge quite rapidly

in Great Britain

319

D J Turner and C Priest/and:

Sensitivity

variations

in the Bayard-Alpert

ionization

gauge

I

c

LO.OO238 z

Dimensions in metres

Maximum-length

path

‘X

Figure 2. Layout of the system molecule travelling at the average velocity would take approximately IOW set to traverse the entire length of the gauge. Since this could only explain a small part of the effect it appeared that tangential velocity components due to incomplete collimation were causing ions to spiral round the collector in orbits which did not intersect it. Comsa (1966)5 has analysed ion collection in random gas due to this effect. Using his equations, a collection factor of 74 per cent was obtained for ions formed near the grid with higher factors for ions formed closer in, and an overall collection efficiency of 87 per cent. Similar orbits in a closed gauge would decay due to the field distortion at the gauge ends (Figure 1). Criteria have been given by Turner (1964)” for determining whether a given ion is collected, orbits, or arrives at the grid with sufficient energy to pass through. Since the directions of travel of molecules in the collimated beam could not be specified by any distribution law, the capture probability could not be calculated directly. It was decided therefore to simulate both gauge situations (collimated beam and random gas input) on a computer. These differed only in the way in which ions were generated. The programmes were written in Algol, using ICT input/output procedures. 2. Programme

for collimated gas beam

This commences with an analysis of gas flow in the collimators in order to achieve the correct directional distribution. In determining points of ionization, account had to be taken of the fact that a molecule entering the gauge at a very oblique angle would be in the ionizing field for a much shorter distance than one travelling more nearly parallel with the axis and thus would be less likely to be ionized. Allowance also had to be made for the ionization free region near the collector (Section 2.3). 2.1 Flow in the collimators. The collimators were two tubes each 0.00476 m diameter x 0.028 m long, spaced a distance of 0.017 m apart. Molecules were considered to have been injected with an isotropic distribution and re-emission from a surface was assumed to follow the cosine law. All lines and points were considered on a set of three-dimensional Cartesian co-ordinates with origin in the centre of the entry aperture and z-axis along the axes of the two collimators. Since the system had rotational 320

symmetry it was assumed, for simplicity of the equations, that x -0 at the injection point and at re-emission points. Molecules were considered to have been lost if passing back through the entrance orifice or falling between the two collimators. The direction of motion of the molecule was specified in terms of two angles. Firstly, the angle between the direction of motion and the normal (0). For injection this angle was rectangularly distributed between 0 and n/2 while for reemision it had a cosine distribution over the same range. The angle describes a cone with its apex at the point of emission (or injection) and with the molecule travelling from the apex along its slant surface. The second angle specifying the direction of motion was a rectangularly distributed angle between 0 and ZZ, referred to as 4, which was the angle of rotation of the line around the surface of this cone, from a datum point. For injection, where the normal was the line with direction cosines (O,O,l), the direction cosines of the direction of motion are, I 7 sin 0 . sin 4 171: sin 0 . cos rf,

n

cos 0

For reflection where the normal had direction cosines (O,-l,O), (due to the point of re-emission being at y equals plus 0.00238 m), the direction cosines of the direction of motion are, I L= sin 0 . sin a m = -cos 0 n == sin 0 . cos 4 Finally, when a molecule was found to have been transmitted through the collimators its point of intersection with the entry plane of the grid structure was found to determine whether it entered the gauge or passed outside. The grid was 0.02 m diameter and its entry plane was 0.013 m from the exit plane of the collimators. 2.2 Ionization of the gas entering the gauge. Strictly speaking, an individual molecule has a very low probability of being ionized. Therefore, in order that the programme should not be unreasonably long, it was necessary to consider only those molecules likely to be ionized, while still allowing for different probabilities of ionization due to varying path length in the gauge. The probability that a molecule will be ionized in a distance x,

D J Turner and C Priest/and: Sensitivity variations in the Bayard-Alpert ionization gauge assuming the ionizing efficiency of the field to be the same at all

points, is given by p(x)= 1 -exp

-3 (

L)

where L =mean distance to ionization. Since very few molecules are ionized we know that, for motion in the gauge, xt < < L. In this case expanding the above equation gives us

and the probability becomes $

of ionization

in the range x to (x + dr)

Thus, in the system being considered, the proba-

bility of ionization for a given molecule is proportional to the distance it travels inside the gauge, and ionization is equally likely to occur at all points along its path. The maximum distance a molecule could travel inside the gauge was 0.411 m. This distance is travelled by a molecule being emitted from one lip of the exit aperture of the collimator and passing through the exit aperture of the gauge at a point diametrically opposite to this (see Figure 2). The programme length was reduced by ignoring all molecules travelling farther than this before ionization and assuming that if a molecule travelled a distance 0.0411 m in the gauge the probability of ionization was 1. The probability of ionization for an individual molecule was then equal to the actual distance it travelled in the gauge, divided by 0.0411 m. This ensured that the relative probabilities of ionization for different trajectories was proportional to the path length in the gauge. In fact the dual aim of determining if a molecule was ionized and, if so, where, was achieved by multiplying 0.0411 m by a rectangularly-distributed random number in the range 0 to 1 to obtain the distance travelled by the molecule before ionization. From this, and the molecule’s point of entry into the gauge, and direction of motion, the point of ionization was found and this was examined

I

0

o*oos

Radial distance (m.) Figure 4. Ionizing and collection efficiencies in the experimental gauge

to see if the molecule had already passed out of the gauge. This

was complicated by the possibility of the molecule passing through the ionization free region before being ionized, in which case its trajectory was considered in two parts. 2.3 Ionizing efficiency as a function of radial distance. Due to the collector being negative with respect to the filament, electrons are prevented from approaching closer to it than a certain distance. Furthermore, as electrons approach this limiting radius their energies become too low for them to produce an appreciable number of ions. Figure 3 shows the ionizing efficiency of electrons in argon against their energy (Barnard, 1953)‘, and Figure 4 shows ionizing efficiency plotted against radial distance for the system used. This was obtained from Figure 3 and the known relationship between potential and radial distance. For simplicity it was assumed that ionizing efficiency is zero for radii less than 0.0013 m and constant outside this region. 3. Programme for random gas flow in the gauge

Figure 3. Ionizing efficiency of electrons in Argon

The probability that an ion will be formed at a given point is the product of two probabilities. (a) that a molecule passes through that point (b) that a molecule which does pass through the point is ionized there. The Iirst is, in a sense, a measure of the pressure at the point. Since, for random gas flow, this will be constant throughout the gauge, it follows that the first probability is independent of the position of the point. As has been shown previously, the probability that a molecule entering a uniform ionizing field will be ionized in the distance x to (x + dr) is equal to dx/L, where L is the mean distance to ionization. It should be noted that this is independent of the distance (x) travelled before the point is reached. Thus, the second probability given above is also independent of the position of the point. If a molecule is only in the field for a very short distance, this reduces the probability of it being ionized but does not affect the probability of it being ionized at a given point. It follows from this that the probability of ionization is constant throughout the gauge. 321

0 J Turner and C Priesfland:

Sensitivity variations in the Bayard-Alpert

ionization

gauge

The axial co-ordinate of the point of formation of an ion will be given by a rectangularly distributed random number in the range 0 to 0.04. The radial distance to the point of ionization was considered initially to be rectangularly distributed in the range 0.0013 to 0.01. However, since the probability of ionization or injection within the radii r to (r+dr) depends on the volume within the range this would not be true, and the chaotic gas programme was therefore run using both distributions. (Sections 5.3 and 5.4). The direction of motion of the ion is then specified in terms of the same two angles as described in section 2.1. 4 is generated as before and 0 is now rectangularly distributed in the range 0 to x. From this point on, both programmes proceed in the same way.

4. Ion trajectory in the gauge If the molecule under consideration was ionized it was necessary first to obtain a value for its velocity, which had a Maxwellian distribution. This states that the probability that a molecule has a velocity between I( and (U+du) is given by

Figure 6. Ion-orbit configurations in the transverse plane

4.1 Ion velocity.

P(u,u+du)=$(&~ u2enp( -g)du

(1)

where vz = mass of the molecule k -= Boltzmann’s constant T = temperature of the gas The velocity found was then considered as separate axial and transverse components and, in the case of the transverse component, the angle (A) between the direction of this component and the radius vector was also found (see Figure 5).

inward-moving ion will have a velocity of the same magnitude as an outward moving ion). (b) rmin > r, and r,,,,, > rg (u, i u, and 14~> uR). The ion must pass through the grid whether it is initially outward moving (case 2) or inward moving (case 6). (c) r,i, < r, and r,, r, and r,,, < rg (uB P u, > uJ. In this instance (cases 3 and 7) the ion orbits freely within the gauge. In only three of the eight cases (4, 5 and 8) is the ion collected. For the given direction of motion the critical velocities for collection (u,) and passage through the grid (u,) are given by:

Grid,

These equations, plus the initial direction of motion (ie approach or recession) are then used to determine whether the ion can, or cannot. be collected. Figure 5. Limiting ion-orbits in the transverse plane

4.2 Collection criteria. Figure 6 shows the transverse projections of the different orbits which the ion can follow from its point of formation. These orbits can be summarised in terms of their maximum (r ,,,) and minimum (r min) radial distances or their critical velocities for collection (u,) or escape through the grid (u,). (a) rmin < rC and r,,,,, > rp (u, < uI < u,). If, at the moment of formation, the ion is moving outward it will escape through the grid (case 1) and if it is moving inward it will be collected (case 5). (Nore: The magnitude of the velocity in case 1 is the same as in case 5, since at a given radial distance in a given orbit an 322

4.3 Time-to-collection. To find if a “collectable” ion leaves the gauge before it can be collected, we need to know the time to collection. To find this we consider the general equation for a central orbit, which is d2y _=--y

de2

g

h2y2

where y=-

1 1

h=r2

and

*?=a dt

constant

g = inward acceleration

(2)

D J Turner and C Priest/and:

Sensitivity

variations

in the Bayard-Alpert

If we consider an ion formed at a radial distance r. with a velocity, in the transverse plane, of u, at an angle t to a radius (Figure 5), then the initial conditions are

t=O, O=O, r=r,, Now

(y=y,),

and dy/dO=y,/tan

3,

ionization

gauge

The sign is chosen to make T positive whether r is greater than r,,, or less than r,. An ion which is collected can reach the collector in two ways, and these are shown in Figure 7. For an ion which follows the

dv . dr dfl dr z -=:_ dt dy de Thus, substituting h=-

for the initial conditions in this equation

U, sin 1

(3)

YO Since the inward acceleration is given by

g=-

0-e

V#

m

*Y

In : 0 E

Figure 7. Orbital configurations for a “collected” ion

We have

If we substitute for dy/dO, and integrate conditions for one limit, we have:

0 2= 0e 4)

2Y,2

Z

m

using the initial

v, In 2! -y2+A-

ut2 sin2 IEn 5

0 rc

0”

sin’ L

path AF the time to collection is simply ,,T,, given by the above equation. In the case of an ion following ABCD, the value of ,cT,c is the time taken to travel along CD. (It should be noted that for orbits ABCD and AE the values of i( are complementary, thus giving them the same values of sin ;I). Since the orbit will be symmetrical we know that the times along AB and BC will be equal. Thus, in the case of an ion which recedes initially, the time-to-collection is (2,0T,,,, +,oTrc). The value of r,,, is obtained from equation (5) by putting dr Z =O, thus

(4)

Now

dr dr -=-*-*dt dy dr -= dy

dy

de

de

dt

1

--

y2

dtl_y2u, dt-

sin Iz y,

from equations (2) and (3)

Thus, dr 2

0

(5)

LTt=

Though equation (6) cannot be integrated analytically, the value of ,oT,c can be obtained by using Simpson’s rule to evaluate the integral. In the case of roTrmnr however, the integrand becomes infinite at r=rmax, and the solution is obtained as follows. Consider the term inside the square root sign in equation (6). This is zero when r=r,, (by definition). Thus, we can say that when r is close to rmax, this term becomes linear with respect to r, thus

Re-arranging, and integrating, we obtain the time required for an ion formed at r0 to travel direct to r as

(7)

r Differentiating

this expression, and putting r=r_,

we have

\rc/ 323

D J Turner and C Priesfland:

Sensitivity

variations

in the Bayard-Alpert

We can now write

ionization

gauge

runs to be continued from the point left off or tar modified runs to be carried out using the same random number series. One method of generating numbers with a non-rectangular distribution makes use of the equation

In this number

equation, z ib a rectangularly distributed random in the range 0 to 1 and _f (x) is the probability that a

dr

(rmax-4

+

1Armaa-r) 1

(rmaIh J The value of E is chosen so that (a) the ordinate at (urn,,- &), in the first integral, is not large enough to cause an overflow in the computer, and (b) equation (7) holds true over the range (rmaxmm E) to rmax. ln the above expression the third term can be evaluated analytically. The two parts of the integrand in the second term become equal when r 7 rmax and this is therefore no longer asymptotic. The second term can be evaluated approximately by assuming it to be roughly linear over the range (r,,,~- E) to r,,,,,. Thus,

variate with the given distribution has a value procedure is to generate a value for a and find satisfy the equation. This method applies to though it is not always possible to re-arrange give x as an explicit function of 2.

less than X. The a value for x to all distributions the equation to

5.1 Cosine distribution. The probability that an angle less than 0 is generated in sin*O. Hence the angle is generated from sin20 T. 5.2 Maxwellian distribution. It will be seen, from equation (I) that no explicit equation can be written for the probability of a molecular velocity less than LI. The generating equation has to be written,

In the programme the integral is evaluated, by numerical integration, for successive values of 11 starting at zero and increasing in steps of 1 msec--I. The integrand was assumed to be linear over each interval. At each step the value obtained is compared with the previously generated value of my.When the value of the integral exceeds E the velocity assumed is 0.5 msecm’ less than the value of u reached. This gives an accuracy for the velocity (assuming accuracy in the integral) of 1 0.5 msecp’.

0

+II ” * 2P

5. Generation of random values The usual method of generating numbers with a non-rectangular distribution is to generate rectangularly-distributed numbers and change the form of the distribution by mathematical operations on them. Since the programme was being run on the ICT Atlas at the University of London Atlas Computing Service, it was decided to use the random number generator held on their library tapes. This routine gives a series of rectangularly distributed numbers such that 0 < c~ < 1. An associated routine allows the starting point of the series to be specified while another allows the last number generated to be printed. This enables any later 324

5.3 Radial distance by rectangular distribution. If it is assumed that the probability of a value between r and (rt c/r) is independent of r then the value of r between r, and r2 can be generated from r-r1 -=cI r2 -r I 5.4 Radial distance by area-dependent distribution. If it is assumed that the probability of a value between r and (r +dr) is proportional to the volume between these limits, then r2-r12 -y----=” r 2 ---I 1 2 6. Results 6.1 Collimated gas input. Five separate pieces of information were obtained from this programme. Since earlier runs, during the development of the programme, had shown that only 70-80 ion-histories were considered during the time taken for

D J Turner and C Priest/and:

Sensitivity

variations

in the Bayard-Alpert

the run, it was decided to print out, for each individual ion, the following information: (a) radial distance of the point of formation (b) axial distance to the point of formation (c) ion velocity The final results also included (d) the directional distribution of the output from the collimators (e) the number of ions collected etc. It was found that out of 132 molecules passing through the collimators 59 (44.7 per cent) emerged at less than one degree to the axis and a further 38 (28.8 per cent) emerged at between one and two degrees. Of these 132 molecules, 71 were ionized. As was to be expected ions tended to be formed close to the ionization free region, since this was where the beam of molecules was most intense. Dividing the range of radii from 0.0013 to 0.01 into 10 equal steps it was found that the 24 ions (33.8 per cent) were formed in the innermost region while 29 (40.8 per cent) were formed in the next region and 11 (15.5 per cent) in the third. The axial distribution of ions was found by dividing the length of the gauge into 10 equal sections. There appeared to be a tendency for ions to be produced nearer the exit plane than the entry plane though this was not very great. This could be due to molecules entering the gauge inside the ionization free region, and passing out of it at some point in the gauge. These molecules would tend to be ionized at the far end. The molecular velocities had a mean and standard deviation, respectively of 349.12 msec-’ and 161.16 msec-I. This must be compared with the corresponding expected values (for argon at 20°C) of 394.16 msec- 1and 166.34 msec-I. Application of the “students-t” test gave a level of significance of between 1 and 2 per cent, indicating that the values generated did in fact come from a Maxwellian distribution. Of the 71 ions produced, 55 (77.5 per cent) were collected, 13 (18.3 per cent) entered free orbits, and 3 would have been collected had they not passed out of the gauge first. 6.2 Chaotic gas input. As has already been stated this programme was run using two different radial distributions for ion formation. These were (a) a linear distribution where r=r,+cr(r,-rr,)

and (b) an area-dependent r = [rf +a(r:

distribution

where

ionization

gauge

The results from these two runs are summarized in the following table : IONS Distribution

Produced

Collected

108 109

99 97

(I

361.75 361.80

166.73

’ 165.96 The similarity between the two sets of velocity data occurred because the random number generator was started at the same point for each run. The slight difference is due to the extra ion in the second run. As before, these are compared with the correct mean and standard deviation for argon at 20°C of 394.16 and 166.34 msec-I. Using the “Students-t” test, we obtain a 5 per cent level of significance in each case. This is not as good as in the “collimated beam” programme, though quite acceptable. In order to determine if the difference in the proportions of ions collected in the two cases is significant we consider the standard error of the proportions. If we have two samples N, and N, of which the number fulfilling a given criterion are n1 and n, respectively, then putting b

P=(~I

+n,)l(N,

+NJ

the standard error of the difference in proportion

is given by:

o,=\/Pu-P)(l++~)l

The actual differ&k ‘n o=_1-112

I

in t2heproportions

is, of course

I

IN, NJ

Now, we have n, =99 N, = 108 n,=97 N,=109 Therefore p =0.9032, (I-~ =0.0401 and 0 =0.0268

Thus, the actual difference in the proportions is 0.667 of one standard error, and this suggests that there is no significant difference between the two results. In each of these runs the range of radii from 0.0013 to O.Olm was divided into twenty equal sections and the number of ions collected and ions orbiting were found for each region. It was found that in no case did an ion enter an orbit which would have resulted in collection if it had not passed out through the end of the gauge first. Though the number of ions produced in each region was too low to make any statistical calculations it was noticed that ions produced near the collector were more likely to be collected than those formed near the grid. 7. Discussion Table 1 shows a comparison

- r:)]+

VELOCITY (msec-‘) Mean Standard Deviation

of the results obtained

by the

Table 1. This paper

Gas

Priestland and Holland

A

I

B

Gain

0.02 0.04 0.0001 0.04

0.02 0.04 0.0001524 0.04 f150 -110

I

1.12

I

Freytag and Schram

Schulz

0.02 0.036 0.00012 0.036 +150 -50

0.019 0.038 0.00018 0.038 +140 -30

1.31

<1.20

B

Grid Diameter (m) Grid Length (m) Collector Diameter (m) Collector Length (m) Grid Potential (V) Collector Potential (V) Sensitivity

Groszkowski

Argon

Argon

Flow conditions*

Comsa

1.29

I

2.70

+150 -70

I

1.15

I

approx

3

*A refers to chaotic gas conditions in the gauge. B refers to a collimated beam along the gauge axis.

325

D J Turner and C Priest/and:

Sensitivity

variations

in the Bayard-Alpert

various workers*. In the computer simulation, and in the application of Comsa’s equations**, the gain was found by obtaining a value of collection efficiency for the open-ended gauge and assuming 100 per cent collection efficiency for the closed gauge. This means assuming that in a closed-ended gauge no ion has enough energy to pass through the grid. As has already been stated, argon molecules (mass -6.63 x lO-2a kg) at a temperature of 20°C have a mean velocity of 394.16 msec-I. Assuming no energy exchange at ionization and unit electronic charge (1.6 x lWgC) this is equivalent to acceleration through a potential of 0.03 volts. This means that the average ion would have to be formed extremely close to the grid in order to have enough kinetic energy to escape (the volume of the region within which the ion would need to be formed is only about 0.1 per cent of the total). In the programme for the collimated gas input two assumptions were made which, even when untrue, would not be expected to have an appreciable effect on the results. (a) That the radial distance of the point of input to the collimators was rectangularly distributed between 0 and 0.00238 m, even though the probability of input at a given radial distance is area dependent and not linear. However, since the molecules had to pass through a comparatively long tube before reaching the gauge this is unlikely to have affected the directional distribution of the gas output from the collimator. (b) That re-emission from the inner surfaces of the collimators obeyed a cosine law. The true distribution is not likely to vary much from this. Hurlbut (1957)s has studied molecular beams of nitrogen incident on polished steel and aluminium and found no great divergence from a cosine law. Two further assumptions were made concerning the production of ions and these apply to both collimated and chaotic gas input.

*After this paper was written, Priestland and Holland carried out a further experiment to determine the sensitivity-gain due to end-caps for chaotic gas conditions. The sensitivity gain was 1.55 with outer screen floating and 1.11 with the screen earthed (ie at collector potential). The simulation shows better agreement with experiment in the chaotic case than in the collimated-beam case. **The overall collection efficiency was calculated as follows. The range of radial distances from 0.000762 m (the limit of the ionization-free region) to O.Olm was divided i?to nineteen ranges and the mean collection efficiency was found for each from Comsa’s equation, thus

ionization

gauge

(a) That there was zero ionizing efficiency at radial distances less than 0.0013 m and constant ionizing efficiency outside this limit. This is, of course, not true. In the case of collimated input most ions are formed close to the collector. In a more exact simulation (ie using the correct relationship between ionizing efficiency and radial distance) some ions would be formed at distances between 0.0008 m and 0.0013 m (see Figure 4). Though no conclusions on this point can be drawn from the results of the simulation, the experimental results obtained by Priestland and Holland, suggest that ions formed near the collector are more likely to be collected than those formed farther out and it follows that the true ion collection efficiency in the collimated case would be higher than that found by simulation, and thus the gain would be less. This would increase the divergence between the experimental and simulated systems. In the case of chaotic gas input, more exact simulation would result in an increase in ion production near both the collector and the grid relative to the intermediate region. In this case the effect on the results would not be as great. (b) That ion production is equal in both gauges. The ratio of the sensitivities of the open and closed-ended gauges is not simply equal to the ratio of the collection efficiencies but also involves the relative rates of ion production. In the case of the collimated beam, the “compression” of the field at the ends of the closed gauge would tend to shift more of the high ionizing efficiency field into the path of the gas beam and increase the number of ions produced. However, for this effect to explain the entire difference between the observed gain (2.7) and simulated gain (1.29) it would be necessary for there to be twice as many ions produced in the closed gauge as in the open gauge, which is not likely. For chaotic gas the effect would be similar. Though there is no beam, the high ionizing efficiency field would extend nearer to the collector, resulting in more ion formation in this region. It can be seen therefore, that correction for the errors introduced by the various assumptions would make the results of the experiments reported here, differ from the observed results more, rather than less, and the reason for the divergence must be sought elsewhere. 8. Conclusions

It may be concluded that the difference in sensitivity between an open and a close-ended gauge can be only partially explained by orbiting phenomena. The difference between collection time and transit time would have only a minimal effect. References 1 C Priestland 2 J Groszkowski,

From Figure 4, a value for the ionizing efficiency was found and was multiplied by the difference in the squares of the outer and inner limits of radius (this being proportional to the volume enclosed). This quantity was proportional to the number of ions produced in the region. It was then divided by the total for all regions to give P (i), the proportion formed in that region. The overall collection efficiency was then x-i

) P(i) - P(c)

326

of I.15

3rd

Vacuum,

Irzt

Vat

18 (5), /\fay 1968, 253.

Cony,-.

s J P Freytag and A Schram, 2nd lnst Symp Tubes, Milan, Mm 1963, pp 405-417.

Strrttgart

1965,

sol 2 Prrr-t I

4 G J Schulz, J Appl Phys,

OH Rrsiduol

Guw\

in Ekvtrort

28 (IO), 0c.t 1957, p,, 1149-l 152.

’ G Comsa, J Appl Phys, 37 (2), I;rb 1966, pp 554-556. a D J Turner, 1953, page

This was found to be 0.87, giving a yain, with end-caps

Tram

pp 241-244.

’ G P Barnard,

L

and L Holland,

Vacuum

14 (IZ), Dee 1964. pp 477-47X.

“Modern

Mass

Spectrometry”

(Imtitrttr

87.

L(F C Hurlbut,

J Appl Phys, 28, Arrg 1957, pp 844-850.

of Phmic A).