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An approximate method for determining the emittance of ion sources in quadrupole mass spectrometry
159
AN APPROXIMATE METHOD FOR DETERMINING EMITI’ANCE OF ION SOURCES IN QUADRUPOLE SPECTROMETRY
THE MASS
P.H. DAWSON Division
of Physics, National Research Council of Canada, Ottawa KIA OR6 (Canada)
YU BINGQI Department (China)
of Electronic
(Received 25 February
Engineering,
Nanjing
Institute
of Technolou,
Nanjing,
Jiangsu
1983)
ABSTRACT An approximate method of determining the emittance of an ion source coupled to a quadrupole mass spectrometer is described_ The method combines the conclusions of recent phase space dynamics ca.lculations of quadrupole acceptance and experimentally-measured transmission curves with the d.c. voltage set to zero. The calculation of source emittance is carried out in one dimension and assumes cylindrical symmetry. An exact solution for the emittance, while possible in principle, would be very time consuming and so an iterative approximation was used. The accuracy of the result can be tested by using the calculated emittance to regenerate ion transmission curves. The method described provides a basis for further study of the effective coupling of ion sources to quadrupoles and some improvements to its accuracy are suggested for future work.
INTRODUCTION
In the last few years, design theory for quadrupole mass spectrometers has advanced significantly with the use of phase space dynamics. The new approach not only provides more efficient and convenient ways of expressing the ion-optical properties of quadrupoles, but also provides a new insight into performance evaluation [l-7]. The validity of the theory, including the effects of short fringing fields has been demonstrated by recent experimental measurements of quadrupole acceptance [8]. The application of the design theory to improving quadrupole performance has often been limited by a lack of knowledge of the ion source and its coupling to the quadrupole. In order to achieve a high performance design, attention must 0168-1176/83/$03.&I
0 1983 Elsevier Science Publishers B.V.
160
be paid to the whole optical system from ion source to detector. Little work has been reported on the emittance of ion sourcy--for quadrupoles. In many cases, source design has been done purely empi@zally. It is difficult to measure the etittance directly. One approach& to/use a moveable ion collector equipped with a rotatable collimator sysf& [9]. An alternative is to calculate the distribution of potentials throughout the source and lens system and by plotting a sufficient number of ion trajectories (assuming the positions of ion formation are accurately known) to derive the overall emittance. The method adopted here was to make measurements of ion transmission with the ion source coupled in situ to the quadrupole and to use the known acceptance characteristics of the quadrupole for diagnosis of the source emittance. The measured ion current represents those ions for which the source emittance overlaps with the acceptance of the quadrupole analyser. The acceptance of the analyser varies in nature as the applied voltage is changed and this can be used to give &formation about the relative importance of different parts of the source emittance. THEORETICAL
CONSIDERATIONS
The emittance of an ion source and its lens system is the distribution of ions in phase space at the entrance to the analyser. The ions exciting the source are distributed in a multi-dimensional phase space and the emittance can be expressed as the number of ions in unit phase space volume where x and y are the transverse directions, z is the axial D ~il.ic,,Y;,Y~*L~I direction, and 6 is the phase of the quadrupole field in the usual notation [6,7]. The em&a&e of the source will generally be a static one and independent of the r.f. phase. A reasonable assumption is that the ions have uniform velocity in the axial direction and the density of ions is then Considering an axially symmetric source, the density simply D Xi,~,,Yi,Y;,’ becomes DUi&,where u represents both x and y directions. When the quadrupole is operated along the q axis of the stability diagram (that is, the applied d.c. is zero and a = 0), the ion motion has the same characteristics in the x and y directions and therefore this is an appropriate operating condition for examining axially symmetric sources. The only difference in the X- and y directions is a difference in r.f. phase of 7 radians. This difference is ignored in the results presented here but will be included in future improvements to the method. We have only carried out an approximate calculation for one direction of the average acceptance during a complete r.f. cycle. This probably accounts for some of the inaccuracies of the present results. A second advantage of choosing to use the transmission characteristic with zero d.c. applied is that the analyser of the quadrupole will have its
161
largest acceptance at & = & = 0.5 and so it is likely to encompass all of the source emittance under those conditions. The acceptance of the quadrupole for ions from a particular element of the source emittance at uriCj can be calculated [6,7] as A,_,r,mn 4 g where LJ, depends on the applied r.f. voltage amplitude, and
where Bq E , A, e , rq E and cqrnare the acceptance ellipse parameters of the analyser.mAssu&ng &lindrical symmetry, the ion transmission at a particular 4 value and a particular field phase becomes
(2) where p is the number of segments into which each coordinate is subdivided. If transmission measurements were available for n different r.f. phases, eqn. (2) could be solved provided mn = p2. Unfortunately such information is not readily available, and transmission is normally measured averaged over the complete r-f. cycle. That is, one must consider the average acceptance Aliu,4nlwhere
(3) In the calculations used here, the r.f. cycle was divided into 100 parts so that n, = 100. Equation (2) becomes
To obtain a unique solution to eqn. (4) would require p2 values of 4. A useful subdivision of the phase plane emittance would require p = 20 and direct use of eqn. (4) would demand a large number of measurements and many calculations of A,,y,_ with a correspondingly large computer capacity. In the illustration of the method reported here, m was limited to - 20 and an iterative method of arriving at a possible distribution of D in the phase plane was adopted. COMPUTING The
PROCEDURE
iteration method used the following equations
(5)
162
D(K+l)_ . UiU,.
5 D:,:,;;’ -AuiGiqm
-
m=l
(m=l,2,3...Q) (K=
5
1, 2, 3...)
(6)
AU,k&
m=l
where K is the number of the iteration and 1y1has Q values. The second equation averages the changes in Duihj required across the spectrum. In the first equation, the ratio 1&‘/Zip_ &‘= iD$$) - Au,G,q, serves to normalise the total current to the observed value. The initial values were taken as Diirdj= 1 for all i and j within some selected limits. Equations (5) and (6) were than used iteratively until D,‘f’r) - D(Ef) < 0.05 D(K). This required lo-30 iterations before convergence: All the i%ktrated reI&s are for K = 30. The most useful information in the ion transmission characteristic (the “integrated spectrum”) lies at the two sides of the peak near 4 = 0 and 4 = 0.908. The values of 4, were therefore chosen to correspond to increments of 10% in the ion transmission rather than being equally spaced. The differing character of the acceptance at low and high q values is shown in Fig. 1 which indicates the acceptance ellipses for 10 different initial phases for (a), q = 0.1, (b) q = 0.35, and (c) q.= 0.902 both with.and without a 1.082 cycles linear fringing field. In the former case, an increase in 4 results in a
Fig. 1. Acceptance ellipses for 10 different initial phases of the r.f. field for the cases without fringing fields,(uppet curves) and with a 1.082 cycles linear fringing field (lower curves): from left to right, q = 0.1, 0.35, and 0.902, respectively.
163
rapid increase in transmission of ions with significant transverse velocities. In the latter case, a decrease in 4 makes more probable the transmission of ions that have small transverse velocities but significant initial displacements from the axis. The acceptance ellipse parameters Bq,(,, A,,“, r4,<, and c4mof the perfect field were first calculated in the usual way [6,7] for each 4, and 6,. The matrices for the fringing fields were then calculated with the assumption of a linear ramp [2,6] and the acceptance ellipses transformed to those at the beginning of the fringing field. A SPECIFIC EXAMPLE
The method, even with the limitations of its present form (as discussed above), was tested by using a series of measurements on a quadrupole mass spectrometer model SZH-200 (made in China). The source region is illustrated in Fig. 2. The entrance plate is normally grounded, the axis potential of the quadrupole is U, and the. cage potential at which the ions are created is U, + Uj. Ions are retarded in the fringing field under normal operation so that they spend relatively little time there. The final ion energy is Uj and in the measurements this was kept constant at 8 eV. The r.f. frequency, f, was 2.8 MHz. Transmission measurements were made using EL\ytce Ion cage /
Quadrupole rods
\
/
Ui Fig. 2. The entrance conditions for the quadrupole.
100
60
Y
;1 :
0.0
20
40
I
0.2
I
0.2
I
0.4
I
0.4
q
I
9
0.6
I
0.6
I
0.6
I
0.6
1.0
120
140
0.0
0.2
Ial
.
uI -
0.4
1.2
9
0.6
.
0.6
1.0
-20
-40
- 60
-60
I n
? P 4 ii CT
8 l-i
2 I-
- 100 is z
::
5 - 120 ;:
- 140
giVi?lL
Fig. 3. The experimental data for ion transmission Z as a function of q for various values of U,. (a), U, = 0; (b), U, = 4.2; (c), U, = 25; and (d), U, = 84. The variation of Io.5 and the computed variation of transmission after 10 (0), 20 (0) and 30 (the dotted line) iterations is also
Y) dn
60
120
t, 5
Y
140
iii
0.0
(81 Ud = 0
r w
8 m
6
\ N
d
\
-’
166
nitrogen. The ion current as a function of q is shown in Fig. 3, together with Iom5, for U, = 0, 4.2, 25 and 84 eV. The maximum transmission with U, = 4.2 was arbitrarily taken as 100. The ion transmissions calculated back from the derived source emissivities are also shown for thirty iterations (K = 30). Some points are given for K = 10 and 20 for comparison. The acceptance calculations required estimation of the fringing field length. This was taken to extend over a distance equal to rO, the radius of the quadrupole [8]. The number of cycles in the fringing field is then 2fro(m/2e)0-5((ud+
n= i
v;.)“.‘-
fro{ m/2eq)0.5
q0.5)/C$
(U,*O) (u,=O)
and with r0 = 2.83 X 10e3 metres. For U, = 0, 4.2, 25 and 84 V, the fringing field lengths were 1.082, 0.968, 0.714 and 0.492 cycles, respectively. In the calculation, the source emittance was limited to a region in the phase plane given by the radius of the entrance aperture (= 0.35 ro) and the half-angle a (Fig. 2). The maximum transverse velocity is then given by h
max
=-
sin a
2e(U;,+
‘ITfTg (
m
U,)
Os
i
(7)
The values for U, = 0, 4.2, 25 and 84 V are 0.095 1,0.1175, 0.1932 and 0.3226 r. radian- ‘, respectively. The phase plane was then divided up into segments of AU = 0.025 and Air = 0.025. The estimated emittance distributions are illustrated in Fig. 4 by intensity contours. They have been smoothed from the raw data since the result is not sensitive to small local variations.
DISCUSSION
Figure 4 shows dramatic effects on the source emittance as U, is varied. As might be expected U, alters both the drawout efficiency and the focussing of the beam. With U, = 0, the total ion density is low, and the ions are quite spread out in the phase plane. The ion beam is a hollow cone which is converging (positive displacement tends to be associated with negative transverse velocity). Increasing U, to 4.2 V increases the drawout efficiency considerably, but also the beam is now highly focussed near the axis and is slightly converging. As might be expected from a knowledge of quadrupole acceptance during mass analysis [6] (d.c. * 0), this condition was found experimentally to give the best resolution and highest sensitivity. As U, is further increased to 25 V, the drawout efficiency improves still further but the ions are now drawn directly towards the grounded aperture plate and
167
have a large range of initial displacements, i.e., the beam is defocussed. With U, = 84 V, there is again a hollow beam effect with few ions entering the quadrupole because of large defocussing effects. Despite the limitations of the calculations, the diagnostic value of this type of analysis is evident. The inaccuracies are apparent when the ion transmission curves calculated from the illustrated source emissivities are compared with the experimental transmission curves as in Fig. 3. The main problems are probably due to the artificial limitations of the possible phase plane distributions that were adopted for this ‘particular quadrupole (especially the maximum transverse velocities) and the neglect of the out-of-phase relationship between the x and y directions. For higher precision, the source emittance in two directions-or in a four-dimensional space (xjcyj,)-would have to be considered but a large computing capacity would be required. CONCLUSIONS
By combining experimental measurements of ion transmission characteristics at low resolution (e.g., d.c. voltage = 0) with knowledge of the phase space acceptance of the quadrupole mass filter, it is possible to obtain a knowledge of source emittance and how it changes as lens parameters are varied. The advantages of the method is that the measurements are made in situ. The disadvantage at the present time is the slowness of convergence of the approximate iteration procedure used. If this could be improved, so that more experimental points could be considered, the accuracy would improve. Extensions to account separately for the two transverse directions would then be possible, and by considering transmission curves with small amounts of d.c. applied to the quadrupole, the source symmetry could also be verified. The application described here should be considered as just a first step in developing this diagnostic technique. REFERENCES 1 2 3 4 5 6
M. Baril and A. Septier, Rev. Phys. Appl., 9 (1974) 525. P.H. Dawson, Int. J. Mass Spectrom. Ion Phys., 17 (1975) 423. P.H. Dawson, Int. J. Mass Spectrom. Ion Phys., 17 (1975) 447. R. Baribeau and P.H. Dawson, Int. J. Mass Spectrom. Ion Phys., 22 (1976) 57. P.H. Dawson and C. Lambert, Int. J. Mass Spectrom. Ion Phys., 16 (1975) 269. P.H. Dawson, in L. Marton and C. Marton (Eds.), Advances in’Electronics and Electron Physics, Vol. 53, Academic Press, New York, 1980. 7 P.H. Dawson, in A. Septier (Ed.), Advances in Electronics and Electron Physics, Suppl. 13B, Academic Press, New York, 1980. 8 J.F. Hennequin and R.-L. Inglebert, Int. J. Mass Spectrom. Ion Phys., 26 (1978) 13 1. 9 T. d’Arcy, Ph.D. Thesis, University of Toronto, 1982.
AN APPROXIMATE METHOD FOR DETERMINING EMITI’ANCE OF ION SOURCES IN QUADRUPOLE SPECTROMETRY
THE MASS
P.H. DAWSON Division
of Physics, National Research Council of Canada, Ottawa KIA OR6 (Canada)
YU BINGQI Department (China)
of Electronic
(Received 25 February
Engineering,
Nanjing
Institute
of Technolou,
Nanjing,
Jiangsu
1983)
ABSTRACT An approximate method of determining the emittance of an ion source coupled to a quadrupole mass spectrometer is described_ The method combines the conclusions of recent phase space dynamics ca.lculations of quadrupole acceptance and experimentally-measured transmission curves with the d.c. voltage set to zero. The calculation of source emittance is carried out in one dimension and assumes cylindrical symmetry. An exact solution for the emittance, while possible in principle, would be very time consuming and so an iterative approximation was used. The accuracy of the result can be tested by using the calculated emittance to regenerate ion transmission curves. The method described provides a basis for further study of the effective coupling of ion sources to quadrupoles and some improvements to its accuracy are suggested for future work.
INTRODUCTION
In the last few years, design theory for quadrupole mass spectrometers has advanced significantly with the use of phase space dynamics. The new approach not only provides more efficient and convenient ways of expressing the ion-optical properties of quadrupoles, but also provides a new insight into performance evaluation [l-7]. The validity of the theory, including the effects of short fringing fields has been demonstrated by recent experimental measurements of quadrupole acceptance [8]. The application of the design theory to improving quadrupole performance has often been limited by a lack of knowledge of the ion source and its coupling to the quadrupole. In order to achieve a high performance design, attention must 0168-1176/83/$03.&I
0 1983 Elsevier Science Publishers B.V.
160
be paid to the whole optical system from ion source to detector. Little work has been reported on the emittance of ion sourcy--for quadrupoles. In many cases, source design has been done purely empi@zally. It is difficult to measure the etittance directly. One approach& to/use a moveable ion collector equipped with a rotatable collimator sysf& [9]. An alternative is to calculate the distribution of potentials throughout the source and lens system and by plotting a sufficient number of ion trajectories (assuming the positions of ion formation are accurately known) to derive the overall emittance. The method adopted here was to make measurements of ion transmission with the ion source coupled in situ to the quadrupole and to use the known acceptance characteristics of the quadrupole for diagnosis of the source emittance. The measured ion current represents those ions for which the source emittance overlaps with the acceptance of the quadrupole analyser. The acceptance of the analyser varies in nature as the applied voltage is changed and this can be used to give &formation about the relative importance of different parts of the source emittance. THEORETICAL
CONSIDERATIONS
The emittance of an ion source and its lens system is the distribution of ions in phase space at the entrance to the analyser. The ions exciting the source are distributed in a multi-dimensional phase space and the emittance can be expressed as the number of ions in unit phase space volume where x and y are the transverse directions, z is the axial D ~il.ic,,Y;,Y~*L~I direction, and 6 is the phase of the quadrupole field in the usual notation [6,7]. The em&a&e of the source will generally be a static one and independent of the r.f. phase. A reasonable assumption is that the ions have uniform velocity in the axial direction and the density of ions is then Considering an axially symmetric source, the density simply D Xi,~,,Yi,Y;,’ becomes DUi&,where u represents both x and y directions. When the quadrupole is operated along the q axis of the stability diagram (that is, the applied d.c. is zero and a = 0), the ion motion has the same characteristics in the x and y directions and therefore this is an appropriate operating condition for examining axially symmetric sources. The only difference in the X- and y directions is a difference in r.f. phase of 7 radians. This difference is ignored in the results presented here but will be included in future improvements to the method. We have only carried out an approximate calculation for one direction of the average acceptance during a complete r.f. cycle. This probably accounts for some of the inaccuracies of the present results. A second advantage of choosing to use the transmission characteristic with zero d.c. applied is that the analyser of the quadrupole will have its
161
largest acceptance at & = & = 0.5 and so it is likely to encompass all of the source emittance under those conditions. The acceptance of the quadrupole for ions from a particular element of the source emittance at uriCj can be calculated [6,7] as A,_,r,mn 4 g where LJ, depends on the applied r.f. voltage amplitude, and
where Bq E , A, e , rq E and cqrnare the acceptance ellipse parameters of the analyser.mAssu&ng &lindrical symmetry, the ion transmission at a particular 4 value and a particular field phase becomes
(2) where p is the number of segments into which each coordinate is subdivided. If transmission measurements were available for n different r.f. phases, eqn. (2) could be solved provided mn = p2. Unfortunately such information is not readily available, and transmission is normally measured averaged over the complete r-f. cycle. That is, one must consider the average acceptance Aliu,4nlwhere
(3) In the calculations used here, the r.f. cycle was divided into 100 parts so that n, = 100. Equation (2) becomes
To obtain a unique solution to eqn. (4) would require p2 values of 4. A useful subdivision of the phase plane emittance would require p = 20 and direct use of eqn. (4) would demand a large number of measurements and many calculations of A,,y,_ with a correspondingly large computer capacity. In the illustration of the method reported here, m was limited to - 20 and an iterative method of arriving at a possible distribution of D in the phase plane was adopted. COMPUTING The
PROCEDURE
iteration method used the following equations
(5)
162
D(K+l)_ . UiU,.
5 D:,:,;;’ -AuiGiqm
-
m=l
(m=l,2,3...Q) (K=
5
1, 2, 3...)
(6)
AU,k&
m=l
where K is the number of the iteration and 1y1has Q values. The second equation averages the changes in Duihj required across the spectrum. In the first equation, the ratio 1&‘/Zip_ &‘= iD$$) - Au,G,q, serves to normalise the total current to the observed value. The initial values were taken as Diirdj= 1 for all i and j within some selected limits. Equations (5) and (6) were than used iteratively until D,‘f’r) - D(Ef) < 0.05 D(K). This required lo-30 iterations before convergence: All the i%ktrated reI&s are for K = 30. The most useful information in the ion transmission characteristic (the “integrated spectrum”) lies at the two sides of the peak near 4 = 0 and 4 = 0.908. The values of 4, were therefore chosen to correspond to increments of 10% in the ion transmission rather than being equally spaced. The differing character of the acceptance at low and high q values is shown in Fig. 1 which indicates the acceptance ellipses for 10 different initial phases for (a), q = 0.1, (b) q = 0.35, and (c) q.= 0.902 both with.and without a 1.082 cycles linear fringing field. In the former case, an increase in 4 results in a
Fig. 1. Acceptance ellipses for 10 different initial phases of the r.f. field for the cases without fringing fields,(uppet curves) and with a 1.082 cycles linear fringing field (lower curves): from left to right, q = 0.1, 0.35, and 0.902, respectively.
163
rapid increase in transmission of ions with significant transverse velocities. In the latter case, a decrease in 4 makes more probable the transmission of ions that have small transverse velocities but significant initial displacements from the axis. The acceptance ellipse parameters Bq,(,, A,,“, r4,<, and c4mof the perfect field were first calculated in the usual way [6,7] for each 4, and 6,. The matrices for the fringing fields were then calculated with the assumption of a linear ramp [2,6] and the acceptance ellipses transformed to those at the beginning of the fringing field. A SPECIFIC EXAMPLE
The method, even with the limitations of its present form (as discussed above), was tested by using a series of measurements on a quadrupole mass spectrometer model SZH-200 (made in China). The source region is illustrated in Fig. 2. The entrance plate is normally grounded, the axis potential of the quadrupole is U, and the. cage potential at which the ions are created is U, + Uj. Ions are retarded in the fringing field under normal operation so that they spend relatively little time there. The final ion energy is Uj and in the measurements this was kept constant at 8 eV. The r.f. frequency, f, was 2.8 MHz. Transmission measurements were made using EL\ytce Ion cage /
Quadrupole rods
\
/
Ui Fig. 2. The entrance conditions for the quadrupole.
100
60
Y
;1 :
0.0
20
40
I
0.2
I
0.2
I
0.4
I
0.4
q
I
9
0.6
I
0.6
I
0.6
I
0.6
1.0
120
140
0.0
0.2
Ial
.
uI -
0.4
1.2
9
0.6
.
0.6
1.0
-20
-40
- 60
-60
I n
? P 4 ii CT
8 l-i
2 I-
- 100 is z
::
5 - 120 ;:
- 140
giVi?lL
Fig. 3. The experimental data for ion transmission Z as a function of q for various values of U,. (a), U, = 0; (b), U, = 4.2; (c), U, = 25; and (d), U, = 84. The variation of Io.5 and the computed variation of transmission after 10 (0), 20 (0) and 30 (the dotted line) iterations is also
Y) dn
60
120
t, 5
Y
140
iii
0.0
(81 Ud = 0
r w
8 m
6
\ N
d
\
-’
166
nitrogen. The ion current as a function of q is shown in Fig. 3, together with Iom5, for U, = 0, 4.2, 25 and 84 eV. The maximum transmission with U, = 4.2 was arbitrarily taken as 100. The ion transmissions calculated back from the derived source emissivities are also shown for thirty iterations (K = 30). Some points are given for K = 10 and 20 for comparison. The acceptance calculations required estimation of the fringing field length. This was taken to extend over a distance equal to rO, the radius of the quadrupole [8]. The number of cycles in the fringing field is then 2fro(m/2e)0-5((ud+
n= i
v;.)“.‘-
fro{ m/2eq)0.5
q0.5)/C$
(U,*O) (u,=O)
and with r0 = 2.83 X 10e3 metres. For U, = 0, 4.2, 25 and 84 V, the fringing field lengths were 1.082, 0.968, 0.714 and 0.492 cycles, respectively. In the calculation, the source emittance was limited to a region in the phase plane given by the radius of the entrance aperture (= 0.35 ro) and the half-angle a (Fig. 2). The maximum transverse velocity is then given by h
max
=-
sin a
2e(U;,+
‘ITfTg (
m
U,)
Os
i
(7)
The values for U, = 0, 4.2, 25 and 84 V are 0.095 1,0.1175, 0.1932 and 0.3226 r. radian- ‘, respectively. The phase plane was then divided up into segments of AU = 0.025 and Air = 0.025. The estimated emittance distributions are illustrated in Fig. 4 by intensity contours. They have been smoothed from the raw data since the result is not sensitive to small local variations.
DISCUSSION
Figure 4 shows dramatic effects on the source emittance as U, is varied. As might be expected U, alters both the drawout efficiency and the focussing of the beam. With U, = 0, the total ion density is low, and the ions are quite spread out in the phase plane. The ion beam is a hollow cone which is converging (positive displacement tends to be associated with negative transverse velocity). Increasing U, to 4.2 V increases the drawout efficiency considerably, but also the beam is now highly focussed near the axis and is slightly converging. As might be expected from a knowledge of quadrupole acceptance during mass analysis [6] (d.c. * 0), this condition was found experimentally to give the best resolution and highest sensitivity. As U, is further increased to 25 V, the drawout efficiency improves still further but the ions are now drawn directly towards the grounded aperture plate and
167
have a large range of initial displacements, i.e., the beam is defocussed. With U, = 84 V, there is again a hollow beam effect with few ions entering the quadrupole because of large defocussing effects. Despite the limitations of the calculations, the diagnostic value of this type of analysis is evident. The inaccuracies are apparent when the ion transmission curves calculated from the illustrated source emissivities are compared with the experimental transmission curves as in Fig. 3. The main problems are probably due to the artificial limitations of the possible phase plane distributions that were adopted for this ‘particular quadrupole (especially the maximum transverse velocities) and the neglect of the out-of-phase relationship between the x and y directions. For higher precision, the source emittance in two directions-or in a four-dimensional space (xjcyj,)-would have to be considered but a large computing capacity would be required. CONCLUSIONS
By combining experimental measurements of ion transmission characteristics at low resolution (e.g., d.c. voltage = 0) with knowledge of the phase space acceptance of the quadrupole mass filter, it is possible to obtain a knowledge of source emittance and how it changes as lens parameters are varied. The advantages of the method is that the measurements are made in situ. The disadvantage at the present time is the slowness of convergence of the approximate iteration procedure used. If this could be improved, so that more experimental points could be considered, the accuracy would improve. Extensions to account separately for the two transverse directions would then be possible, and by considering transmission curves with small amounts of d.c. applied to the quadrupole, the source symmetry could also be verified. The application described here should be considered as just a first step in developing this diagnostic technique. REFERENCES 1 2 3 4 5 6
M. Baril and A. Septier, Rev. Phys. Appl., 9 (1974) 525. P.H. Dawson, Int. J. Mass Spectrom. Ion Phys., 17 (1975) 423. P.H. Dawson, Int. J. Mass Spectrom. Ion Phys., 17 (1975) 447. R. Baribeau and P.H. Dawson, Int. J. Mass Spectrom. Ion Phys., 22 (1976) 57. P.H. Dawson and C. Lambert, Int. J. Mass Spectrom. Ion Phys., 16 (1975) 269. P.H. Dawson, in L. Marton and C. Marton (Eds.), Advances in’Electronics and Electron Physics, Vol. 53, Academic Press, New York, 1980. 7 P.H. Dawson, in A. Septier (Ed.), Advances in Electronics and Electron Physics, Suppl. 13B, Academic Press, New York, 1980. 8 J.F. Hennequin and R.-L. Inglebert, Int. J. Mass Spectrom. Ion Phys., 26 (1978) 13 1. 9 T. d’Arcy, Ph.D. Thesis, University of Toronto, 1982.