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Spherotron — a new concept in mass spectrometry
International Journal of Mass Spectrometry and Ion Processes, 121 (1992) R I - R I 0 Elsevier Science Publishers B.V., Amsterdam
RI
Rapid C o m m u n i c a t i o n Spherotron - - a new concept in mass spectrometry V. Cherepin Metal Physics Institute, Academy of Sciences of Ukraine, 252142 Kiev (Ukraine) (First received 24 February 1992; in final form 1 September 1992)
ABSTRACT A new concept of a static multi-transit mass analyzer based on the use of the ion optical properties of a spherical condensor immersed in a magnetic field is proposed. Computer modeling data on the optical and mass dispersive properties and achievable mass resolving power are discussed. Preliminary results from experimental tests of the first laboratory prototype instrument are shown.
Keywords: multi-transit; spherical condensor; mass analyzer; spherotron.
INTRODUCTION
A conventional static mass spectrometer contains a magnetic sector field usually combined with an electrostatic sector field and quadrupole lenses [1], and the ion beam is mass separated during a single transit through this combination of fields. High mass resolution is achieved in this instrument by using narrow (up to a range of 1-5 #m) slits and magnetic sectors of large mean radius. For a wide mass range, a high magnetic field strength is required and hence a magnetic sector type mass spectrometer is always a bulky and heavy instrument. The magnetic field may be used more effectively in a multi-transit mass spectrometer in which an ion beam passes several times through the same magnetic field surrounded by a number of electrostatic mirrors [2]. However, this approach seems to be not very realistic for practical instruments because of the complicated design and the precision machining and positioning required. A new concept of a static multi-transit mass analyzer based on the use of the ion optical properties of a spherical condensor immersed in a magnetic field is proposed in the present paper.
Correspondence to: V. Cherepin, Metal Physics Institute, Academy of Sciences of Ukraine, 252142 Kiev, Ukraine. 0168-1176/92/$05.00
© 1992 Elsevier Science Publishers B.V. All rights reserved.
V. Cherepin/lnt. J. Mass Spectrom. Ion Processes 121 (1992) R1-RIO
R2
Fig. 1. Equatorial projection of an ion trajectory in a spherotron. OPTICAL AND MASS DISPERSIVE PROPERTIES The optical and energy dispersive properties of a spherical condensor are well known and such a system is widely used as an energy analyzer for charged particles [3]. For the most frequently used hemispherical configuration the energy dispersion is De = 2re, where r e is the mean radius of the spherical electrodes. This configuration also provides for a first order stigmatic imaging of the entrance slit [4]. It is important to note for the present discussion that, if the first hemisphere is immediately followed by an identical second one, an energy-dispersed image is convoluted again to the initial shape, since each trajectory is circular and hence, after a 360 ° revolution, an ideal refocusing of the primary beam is produced i.e. an image of the entrance slit is formed. Now let us immerse this field configuration and the ion beam (with an appropriate combination of energy and voltages to produce orbiting of the ions in the gap of the spherical condensor) into a homogeneous magnetic field parallel to the polar axis of the spherical condensor. The ion beam is injected along the normal to the equatorial plane in the inter-electrode space. Under the effect of the Lorentz force, the ion trajectories are oppositely 2 i
Fig. 2. Computer modeling of the spherical spiral.
V. Cherepin/lnt. J. Mass Spectrom. Ion Processes 121 (1992) R1-RIO
R3
/,0 ~s¢~.
,~ ,~,ro /
coo 2oo
~,ro ~,'o!
~? J
6
~
6
?
o
0
cp
Norn~er Of eevMu~.ons Fig. 3. Total angle of deflection vs. number of resolutions for ions of different masses.
deflected in the upper ("northern") and lower ("southern") hemispheres following a curve which may be called a "spherical spiral". Projections of the trajectories on the equatorial plane are close to circular arcs and their radius, Rm, is simply defined as R~ =
(4.79 x 107/-/2) [MI
(1)
where V is the ion accelerating voltage (V), M is the ion mass number (u) and /-/is the magnetic field (T). From simple geometrical considerations it is clear that, during the first half of the revolution in the sphere, the equatorial projection of the trajectory corresponds to a deflection by a polar angle ® = 2re/Rm(rad) while during the second half, the ion beam is deflected by the same angle but in the opposite direction (Fig. 1). This means that ions with mass numbers M~ < M2 < M3
~3
y V / f / / / / / |
!
L tttra#d Fig. 4. Schematic diagram of the spherotron structure: 1, ion source; 2, yoke; 3, spherical condensor; 4, SEM; 5, magnet coil.
V. Cherepin/Int. J. Mass Spectrom. 1on Processes 121 (1992) R1-RIO
R4
Jerromagnet~c
"af
ci Fig. 5. Homogeneous (a) and divergent (b) magnetic field in a spherical gap.
will be deflected by the angles 4ro 4r e 201 = ~ > 2@2 = ~ > 203 =
4re/RM,
and an exit slit or diaphragm positioned in the equatorial plane at an angular distance of for example 202 with respect to the entrance slit separates ions with mass number M~ and thus converts this arrangement into a mass filter set for transmission of mass M2. Since after a 360 ° revolution in the spherical capacitor a complete convolution of the primary beam and an ideal refocusing take place, the procedure just described may be repeated with a corresponding accumulation of the mass dispersion but without accumulation of aberrations. Computer simulation of the ion motion in a combination of a spherical electrostatic field and a homogeneous magnetic field is shown in Fig. 2, and the effect of the accumulation of the mass dispersion is shown in Fig. 3. If now a series of the selection slits is positioned in the equatorial plane,
".. s,
he2f an~£e ~dc ver~ence, de~ Fig. 6. Effect of divergent magnetic field on the energy focusing: S~ corresponds to an ideal field; $2 takes into account fringing field effects.
II. Cherepin/lnt. J. Mass Spectrom. Ion Processes 121 (1992) RI-RIO
R5
Fig. 7. The coordinate system used for description of the fringing field outside the gap.
equally spaced with an angular separation of 2 0 2 , only ions with mass M2 remain orbiting, while the rest are eliminated and the system becomes a mass filter. Scanning of the magnetic field creates favorable conditions for ions with other mass numbers to be deflected by an angle of 202. In this way, the mass spectrum may be obtained. This mass filter may be called a "spherotron". Optical properties of the spherotron are dominated by the optical properties of the spherical condensor. At small angles of deflection in the magnetic field the achievable phase-space transmission is completely defined by the geometrical dimensions of the condensor and the energy spread of the ion beam being analyzed. Direct computer modeling has shown that 100% transmission may be obtained for a radial slit length up to 0.35 of the inter-electrode separation and an ion beam half angle of divergence of 3.5 ° . The achievable phase-space transmission AXY = Sh~ 2, where S and h are the slit width and height (radial length) respectively and ~ is the maximum half divergence angle (assumed to be equal in both main sections). This value was estimated for r e = 10cm, Ar e = l cm, S = 0.01 cm, and h = 0.35cm. In this case, ~ = 1o and AXY = 10 -3 mster cm 2 which is several orders of magnitude better than the phase-space transmission of a high resolution magnetic sector mass spectrometer. Two directions of mass dispersion may be expected in this system of crossed fields. The first one corresponds to deflection of the ions with respect to the polar axis and may be called lateral dispersion. This dispersion is responsible for the achievable mass dispersion Dm. F r o m Figs. 1 and 3 one finds
Dm=2nOre(~)
(2)
where 2n® is the total polar angle of deflection during n orbits. If2nO = 2.616 rad (150 °) and re = 200 mm, then Dm = 2.67 m m for 1% of the mass variation. The image magnification is equal to unity and, for an entrance-exit slit width of 0.005 mm, the achievable mass resolving power, M/AM, is about 27 000. The second possible direction of the mass dispersion is the radial direction of the spheres (longitudinal dispersion). According to our computer modeling
R6
V. Cherepin/lnt. J. Mass Spectrom. Ion Processes 121 (1992) R1-RIO .3
~
.9
"~
i I p
.8
.I
.?
Dlmenslon of ssctlon:
s t l t 0.1 x 0 . 1 u ~
0.2
1
3
2
1
4
7
8
9
7
(a)
x 0.2 mm ~
2
3
c°
8
$
9
(b)
I
I 0.5"xo.5" a )
j,
2
i
Dimension of section:
P
0.~ x 0,1 rmm~
I I
7
3
~
~"
(c)
. . . .
~
(d)
Fig. 8. The slit image distortion ((a) and (b)) and the effect of the angular spread of ___0.5 ° in two main sections without (c) and with (d) taking into account fringing field effects; ( - - - ) , equatorial line.
data, this type of mass dispersion is not observed and, for a permanent magnetic field, the images of the radial entrance slit corresponding to ions of different mass (in a certain mass range limited by the width of an intermediate diaphragm or slit) are positioned at the equatorial line and hence the instrument may be used for parallel detection of part of the mass spectrum (mass spectrographic mode). It should be pointed out that the magnetic field necessary to produce total deflection of the ion beam by an angle 2n® is n times lower than that in a
V. Cherepin/lnt. J. Mass Spectrom. Ion Processes 121 (1992) R1-RIO
R7
e.j
/'1#11 /'lum~lf',
#.~,Q.
Fig. 9. Low mass portion of a residual gas mass spectrum. magnetic sector field with the same total angle of deflection and mean radius equal to re. Hence the same ultimate magnetic field makes it possible to analyze a mass range n 2 times broader, or, alternatively, to use much less powerful magnets. A homogeneous magnetic field can be produced in a long coil inside which the spherical condensor is placed. The problem of magnetic fringing field effects does not exist in this case. However, complete immersion of the spherical condensor in a magnetic field is inconvenient because of the large dimensions of the corresponding magnet coil and the effect of the field on the ion source and ion detector. More practical is the formation of the magnetic field in a cylindrical portion of the sphere concentric to the polar axis where deflection of the ions and the mass dispersion is performed. This configuration is created by making ferromagnetic inserts into non magnetic spherical electrodes and placing a magnet coil inside the inner sphere with a ferromagnetic yoke around the outer one (Fig. 4). In this case, a near homogeneous magnetic field can be produced using ferromagnetic inserts of the same cylindrical cross-section with equidistant spherical surfaces (Fig. 5a). If the cross-section of the outer insert is of a larger diameter, magnetic field, H, becomes divergent and may be approximately described as /1 =/-/1 rg ~3,
(3)
where ~ is the strength of the field near the surface of the inner insert, r0 is the distance from the apex of the cone described through the boundaries of inserts at the spherical electrodes and ~ is the radius vector of a point in the
V. Cherepin/lnt. J. Mass Spectrom. Ion Processes 121 (1992) R1-RIO
R8
magnet gap (Fig. 5b). In this case, divergence of the magnetic field is characterized by the cone half angle, 0c. EFFECT OF ENERGY DISPERSION AND EXPERIMENTAL RESULTS The energy spread of the ions being analyzed produces an energy focal line coinciding with the radius after orbiting 180° in the sphere. This line is convoluted again after 360 ° into a point for a point source, i.e. an achromatic image of the entrance slit is formed. However, in the homogeneous magnetic field, deflection of ions with different energies occurs in such a way that ions with higher energies are deflected through larger angles because they traverse a longer path and lose the kinetic energy while approaching the outer electrode. As a result the energy focal lines are tilted with respect to the corresponding radius and the respective convoluted image becomes broadened, thus reducing the mass resolution. This difficulty may be overcome by making the magnetic field divergent in the polar direction to such an extent that it compensates for the variation of the ion energy. Computer simulation makes it possible to obtain geometrical parameters for a magnetic field producing complete and simultaneous angular and energy focusing, thus providing achromatic stigmatic imaging together with a high energy band pass (Fig. 6). The effect of the magnetic fringing fields have been estimated by introducing corresponding data [5] into the description of the magnetic field for the computer modeling. If a coordinate system shown in Fig. 7 is used, then the z component of the magnetic field in the central plane between the pole faces depends only on the x coordinate
Hz(x) = Hoh(x)
0 <~h(x) ~< 1
(4)
For infinitely thick pole sections, h(x) may be described by a relation suggested by Coggeshall [6]:
+ l
:
(5)
where do is the width of the gap. In the plane z = 0 only the z component of the field,/-/:, is present. In the other points, the/-/. (x, z) component is an even function of z and the Hx (x, z) component is an odd function of z. Close to the median plane, z = 0, these components may be presented in the following form
[ dh(x) dx z Hz(x, z) = Ho [ h(x) k
1 d3h(x) z3 + ] 6 dx 3 "'" A 1 dZh(x)z2 + ] 2 dx 2 "'"
(6) (7)
V. Cherepin/Int. J. Mass Spectrom. Ion Processes 121 (1992) RI-RIO
R9
For computer simulation of a particle path, the fringing field distribution outside the gap was calculated using two members in the series (5) and do = 10 mm. Since the Hx components in points symmetric with respect to the plane z = 0 are opposite, i.e.//x(x,, Zk) = --FIx(Xi, - - Zk), the fringing field deflects differently the ions moving higher and lower on the equilibrium trajectory i.e. high and low energy ions, thus producing a weak energy focusing effect in the convolution plane Y® = 2zn even with a homogeneous magnetic field ($2 = 0.7 mm) (Fig. 6). But the best effect is produced by a combined action of the divergent field with 0~= 7.9 ° and the fringing field. The field inside the gap was estimated in this case by using/-) as H0 in eqns. (6) and (7). The effect of the fringing field on the imaging properties of the spherotron has also been studied. The images of a square (0.1 m m × 0.1 mm) entrance slit, in the convolution plane after 10 orbits in an ideal divergent field with = 25.8 ° and in the field with ~ = 7.9 ° taking into account fringing field effects are shown in Fig. 8a and b respectively. The image is distorted in the direction of lateral dispersion, i.e. mass resolution is deteriorated but by a factor of no more than 1.5. The effect of the angular spread of _+0.5 ° in two main sections without and with taking into account fringing field effects is shown in Fig. 8c and d respectively. In the second case, broadening is smaller and does not exceed 0.06 ram. These values will probably define the achievable mass resolution of the spherotron. The first laboratory prototype of the spherotron with re = 40 m m and a slit width of 0.15 m m was put into operation in August 1991 and an example of an actual residual gas mass spectrum is shown in Fig. 9. Mass resolving power is about 2 0 0 ( M ] A M ) and a mass range of 500 u can easily be achieved. A more complex and larger instrument is under construction. If the resolution is proportional to r e and reciprocal of the slit width, S, one may expect, by increasing re to 2 0 0 m m and decreasing S to 0.005 mm, to achieve a mass resolving power of about 30 000. It should be noted that the spherotron concept is also promising for the time of flight (TOF) mode of operation. In this case, the selection slits may be made wide enough to pass a broad portion of the mass spectrum poorly resolved in the magnetic field but preselected by corresponding settings of the field. A long drift space is easily obtained in the spherotron differing from any other type of T O F by a complete absence of field free region, so that an ion bunch is permanently retained in the electrostatic field with periodic stigmatic and energy focusing. A combination of the static mode for low masses and T O F mode for high masses makes the spherotron a very promising instrument for various analytical, physical and chemical applications.
R10
II. Cherepin/lnt. J. Mass Spectrom. Ion Processes 121 (1992) R1-RIO
REFERENCES 1 2 3 4 5 6
T. Matsuo, T. Sakurai, M. Ishihara, Nucl. Instrum. Methods Phys. Res. A, 298 (1990) 134. M. Baril, Nucl. Instrum. Methods, 187 (1981) 153. K. Serier, Low Energy Electron Spectrometry, Wiley, New York, 1972, p. 397. H. Ebel, M.F. Ebel and M. Mantler et al., Surf. Sci., 231 (1990) 233. H. Wollnik, Optics of Charged Particles, Academic Press, New York, 1987, p. 387. N.D. Coggeshall, J. Appl. Phys., 18 (1947) 855.
RI
Rapid C o m m u n i c a t i o n Spherotron - - a new concept in mass spectrometry V. Cherepin Metal Physics Institute, Academy of Sciences of Ukraine, 252142 Kiev (Ukraine) (First received 24 February 1992; in final form 1 September 1992)
ABSTRACT A new concept of a static multi-transit mass analyzer based on the use of the ion optical properties of a spherical condensor immersed in a magnetic field is proposed. Computer modeling data on the optical and mass dispersive properties and achievable mass resolving power are discussed. Preliminary results from experimental tests of the first laboratory prototype instrument are shown.
Keywords: multi-transit; spherical condensor; mass analyzer; spherotron.
INTRODUCTION
A conventional static mass spectrometer contains a magnetic sector field usually combined with an electrostatic sector field and quadrupole lenses [1], and the ion beam is mass separated during a single transit through this combination of fields. High mass resolution is achieved in this instrument by using narrow (up to a range of 1-5 #m) slits and magnetic sectors of large mean radius. For a wide mass range, a high magnetic field strength is required and hence a magnetic sector type mass spectrometer is always a bulky and heavy instrument. The magnetic field may be used more effectively in a multi-transit mass spectrometer in which an ion beam passes several times through the same magnetic field surrounded by a number of electrostatic mirrors [2]. However, this approach seems to be not very realistic for practical instruments because of the complicated design and the precision machining and positioning required. A new concept of a static multi-transit mass analyzer based on the use of the ion optical properties of a spherical condensor immersed in a magnetic field is proposed in the present paper.
Correspondence to: V. Cherepin, Metal Physics Institute, Academy of Sciences of Ukraine, 252142 Kiev, Ukraine. 0168-1176/92/$05.00
© 1992 Elsevier Science Publishers B.V. All rights reserved.
V. Cherepin/lnt. J. Mass Spectrom. Ion Processes 121 (1992) R1-RIO
R2
Fig. 1. Equatorial projection of an ion trajectory in a spherotron. OPTICAL AND MASS DISPERSIVE PROPERTIES The optical and energy dispersive properties of a spherical condensor are well known and such a system is widely used as an energy analyzer for charged particles [3]. For the most frequently used hemispherical configuration the energy dispersion is De = 2re, where r e is the mean radius of the spherical electrodes. This configuration also provides for a first order stigmatic imaging of the entrance slit [4]. It is important to note for the present discussion that, if the first hemisphere is immediately followed by an identical second one, an energy-dispersed image is convoluted again to the initial shape, since each trajectory is circular and hence, after a 360 ° revolution, an ideal refocusing of the primary beam is produced i.e. an image of the entrance slit is formed. Now let us immerse this field configuration and the ion beam (with an appropriate combination of energy and voltages to produce orbiting of the ions in the gap of the spherical condensor) into a homogeneous magnetic field parallel to the polar axis of the spherical condensor. The ion beam is injected along the normal to the equatorial plane in the inter-electrode space. Under the effect of the Lorentz force, the ion trajectories are oppositely 2 i
Fig. 2. Computer modeling of the spherical spiral.
V. Cherepin/lnt. J. Mass Spectrom. Ion Processes 121 (1992) R1-RIO
R3
/,0 ~s¢~.
,~ ,~,ro /
coo 2oo
~,ro ~,'o!
~? J
6
~
6
?
o
0
cp
Norn~er Of eevMu~.ons Fig. 3. Total angle of deflection vs. number of resolutions for ions of different masses.
deflected in the upper ("northern") and lower ("southern") hemispheres following a curve which may be called a "spherical spiral". Projections of the trajectories on the equatorial plane are close to circular arcs and their radius, Rm, is simply defined as R~ =
(4.79 x 107/-/2) [MI
(1)
where V is the ion accelerating voltage (V), M is the ion mass number (u) and /-/is the magnetic field (T). From simple geometrical considerations it is clear that, during the first half of the revolution in the sphere, the equatorial projection of the trajectory corresponds to a deflection by a polar angle ® = 2re/Rm(rad) while during the second half, the ion beam is deflected by the same angle but in the opposite direction (Fig. 1). This means that ions with mass numbers M~ < M2 < M3
~3
y V / f / / / / / |
!
L tttra#d Fig. 4. Schematic diagram of the spherotron structure: 1, ion source; 2, yoke; 3, spherical condensor; 4, SEM; 5, magnet coil.
V. Cherepin/Int. J. Mass Spectrom. 1on Processes 121 (1992) R1-RIO
R4
Jerromagnet~c
"af
ci Fig. 5. Homogeneous (a) and divergent (b) magnetic field in a spherical gap.
will be deflected by the angles 4ro 4r e 201 = ~ > 2@2 = ~ > 203 =
4re/RM,
and an exit slit or diaphragm positioned in the equatorial plane at an angular distance of for example 202 with respect to the entrance slit separates ions with mass number M~ and thus converts this arrangement into a mass filter set for transmission of mass M2. Since after a 360 ° revolution in the spherical capacitor a complete convolution of the primary beam and an ideal refocusing take place, the procedure just described may be repeated with a corresponding accumulation of the mass dispersion but without accumulation of aberrations. Computer simulation of the ion motion in a combination of a spherical electrostatic field and a homogeneous magnetic field is shown in Fig. 2, and the effect of the accumulation of the mass dispersion is shown in Fig. 3. If now a series of the selection slits is positioned in the equatorial plane,
".. s,
he2f an~£e ~dc ver~ence, de~ Fig. 6. Effect of divergent magnetic field on the energy focusing: S~ corresponds to an ideal field; $2 takes into account fringing field effects.
II. Cherepin/lnt. J. Mass Spectrom. Ion Processes 121 (1992) RI-RIO
R5
Fig. 7. The coordinate system used for description of the fringing field outside the gap.
equally spaced with an angular separation of 2 0 2 , only ions with mass M2 remain orbiting, while the rest are eliminated and the system becomes a mass filter. Scanning of the magnetic field creates favorable conditions for ions with other mass numbers to be deflected by an angle of 202. In this way, the mass spectrum may be obtained. This mass filter may be called a "spherotron". Optical properties of the spherotron are dominated by the optical properties of the spherical condensor. At small angles of deflection in the magnetic field the achievable phase-space transmission is completely defined by the geometrical dimensions of the condensor and the energy spread of the ion beam being analyzed. Direct computer modeling has shown that 100% transmission may be obtained for a radial slit length up to 0.35 of the inter-electrode separation and an ion beam half angle of divergence of 3.5 ° . The achievable phase-space transmission AXY = Sh~ 2, where S and h are the slit width and height (radial length) respectively and ~ is the maximum half divergence angle (assumed to be equal in both main sections). This value was estimated for r e = 10cm, Ar e = l cm, S = 0.01 cm, and h = 0.35cm. In this case, ~ = 1o and AXY = 10 -3 mster cm 2 which is several orders of magnitude better than the phase-space transmission of a high resolution magnetic sector mass spectrometer. Two directions of mass dispersion may be expected in this system of crossed fields. The first one corresponds to deflection of the ions with respect to the polar axis and may be called lateral dispersion. This dispersion is responsible for the achievable mass dispersion Dm. F r o m Figs. 1 and 3 one finds
Dm=2nOre(~)
(2)
where 2n® is the total polar angle of deflection during n orbits. If2nO = 2.616 rad (150 °) and re = 200 mm, then Dm = 2.67 m m for 1% of the mass variation. The image magnification is equal to unity and, for an entrance-exit slit width of 0.005 mm, the achievable mass resolving power, M/AM, is about 27 000. The second possible direction of the mass dispersion is the radial direction of the spheres (longitudinal dispersion). According to our computer modeling
R6
V. Cherepin/lnt. J. Mass Spectrom. Ion Processes 121 (1992) R1-RIO .3
~
.9
"~
i I p
.8
.I
.?
Dlmenslon of ssctlon:
s t l t 0.1 x 0 . 1 u ~
0.2
1
3
2
1
4
7
8
9
7
(a)
x 0.2 mm ~
2
3
c°
8
$
9
(b)
I
I 0.5"xo.5" a )
j,
2
i
Dimension of section:
P
0.~ x 0,1 rmm~
I I
7
3
~
~"
(c)
. . . .
~
(d)
Fig. 8. The slit image distortion ((a) and (b)) and the effect of the angular spread of ___0.5 ° in two main sections without (c) and with (d) taking into account fringing field effects; ( - - - ) , equatorial line.
data, this type of mass dispersion is not observed and, for a permanent magnetic field, the images of the radial entrance slit corresponding to ions of different mass (in a certain mass range limited by the width of an intermediate diaphragm or slit) are positioned at the equatorial line and hence the instrument may be used for parallel detection of part of the mass spectrum (mass spectrographic mode). It should be pointed out that the magnetic field necessary to produce total deflection of the ion beam by an angle 2n® is n times lower than that in a
V. Cherepin/lnt. J. Mass Spectrom. Ion Processes 121 (1992) R1-RIO
R7
e.j
/'1#11 /'lum~lf',
#.~,Q.
Fig. 9. Low mass portion of a residual gas mass spectrum. magnetic sector field with the same total angle of deflection and mean radius equal to re. Hence the same ultimate magnetic field makes it possible to analyze a mass range n 2 times broader, or, alternatively, to use much less powerful magnets. A homogeneous magnetic field can be produced in a long coil inside which the spherical condensor is placed. The problem of magnetic fringing field effects does not exist in this case. However, complete immersion of the spherical condensor in a magnetic field is inconvenient because of the large dimensions of the corresponding magnet coil and the effect of the field on the ion source and ion detector. More practical is the formation of the magnetic field in a cylindrical portion of the sphere concentric to the polar axis where deflection of the ions and the mass dispersion is performed. This configuration is created by making ferromagnetic inserts into non magnetic spherical electrodes and placing a magnet coil inside the inner sphere with a ferromagnetic yoke around the outer one (Fig. 4). In this case, a near homogeneous magnetic field can be produced using ferromagnetic inserts of the same cylindrical cross-section with equidistant spherical surfaces (Fig. 5a). If the cross-section of the outer insert is of a larger diameter, magnetic field, H, becomes divergent and may be approximately described as /1 =/-/1 rg ~3,
(3)
where ~ is the strength of the field near the surface of the inner insert, r0 is the distance from the apex of the cone described through the boundaries of inserts at the spherical electrodes and ~ is the radius vector of a point in the
V. Cherepin/lnt. J. Mass Spectrom. Ion Processes 121 (1992) R1-RIO
R8
magnet gap (Fig. 5b). In this case, divergence of the magnetic field is characterized by the cone half angle, 0c. EFFECT OF ENERGY DISPERSION AND EXPERIMENTAL RESULTS The energy spread of the ions being analyzed produces an energy focal line coinciding with the radius after orbiting 180° in the sphere. This line is convoluted again after 360 ° into a point for a point source, i.e. an achromatic image of the entrance slit is formed. However, in the homogeneous magnetic field, deflection of ions with different energies occurs in such a way that ions with higher energies are deflected through larger angles because they traverse a longer path and lose the kinetic energy while approaching the outer electrode. As a result the energy focal lines are tilted with respect to the corresponding radius and the respective convoluted image becomes broadened, thus reducing the mass resolution. This difficulty may be overcome by making the magnetic field divergent in the polar direction to such an extent that it compensates for the variation of the ion energy. Computer simulation makes it possible to obtain geometrical parameters for a magnetic field producing complete and simultaneous angular and energy focusing, thus providing achromatic stigmatic imaging together with a high energy band pass (Fig. 6). The effect of the magnetic fringing fields have been estimated by introducing corresponding data [5] into the description of the magnetic field for the computer modeling. If a coordinate system shown in Fig. 7 is used, then the z component of the magnetic field in the central plane between the pole faces depends only on the x coordinate
Hz(x) = Hoh(x)
0 <~h(x) ~< 1
(4)
For infinitely thick pole sections, h(x) may be described by a relation suggested by Coggeshall [6]:
+ l
:
(5)
where do is the width of the gap. In the plane z = 0 only the z component of the field,/-/:, is present. In the other points, the/-/. (x, z) component is an even function of z and the Hx (x, z) component is an odd function of z. Close to the median plane, z = 0, these components may be presented in the following form
[ dh(x) dx z Hz(x, z) = Ho [ h(x) k
1 d3h(x) z3 + ] 6 dx 3 "'" A 1 dZh(x)z2 + ] 2 dx 2 "'"
(6) (7)
V. Cherepin/Int. J. Mass Spectrom. Ion Processes 121 (1992) RI-RIO
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For computer simulation of a particle path, the fringing field distribution outside the gap was calculated using two members in the series (5) and do = 10 mm. Since the Hx components in points symmetric with respect to the plane z = 0 are opposite, i.e.//x(x,, Zk) = --FIx(Xi, - - Zk), the fringing field deflects differently the ions moving higher and lower on the equilibrium trajectory i.e. high and low energy ions, thus producing a weak energy focusing effect in the convolution plane Y® = 2zn even with a homogeneous magnetic field ($2 = 0.7 mm) (Fig. 6). But the best effect is produced by a combined action of the divergent field with 0~= 7.9 ° and the fringing field. The field inside the gap was estimated in this case by using/-) as H0 in eqns. (6) and (7). The effect of the fringing field on the imaging properties of the spherotron has also been studied. The images of a square (0.1 m m × 0.1 mm) entrance slit, in the convolution plane after 10 orbits in an ideal divergent field with = 25.8 ° and in the field with ~ = 7.9 ° taking into account fringing field effects are shown in Fig. 8a and b respectively. The image is distorted in the direction of lateral dispersion, i.e. mass resolution is deteriorated but by a factor of no more than 1.5. The effect of the angular spread of _+0.5 ° in two main sections without and with taking into account fringing field effects is shown in Fig. 8c and d respectively. In the second case, broadening is smaller and does not exceed 0.06 ram. These values will probably define the achievable mass resolution of the spherotron. The first laboratory prototype of the spherotron with re = 40 m m and a slit width of 0.15 m m was put into operation in August 1991 and an example of an actual residual gas mass spectrum is shown in Fig. 9. Mass resolving power is about 2 0 0 ( M ] A M ) and a mass range of 500 u can easily be achieved. A more complex and larger instrument is under construction. If the resolution is proportional to r e and reciprocal of the slit width, S, one may expect, by increasing re to 2 0 0 m m and decreasing S to 0.005 mm, to achieve a mass resolving power of about 30 000. It should be noted that the spherotron concept is also promising for the time of flight (TOF) mode of operation. In this case, the selection slits may be made wide enough to pass a broad portion of the mass spectrum poorly resolved in the magnetic field but preselected by corresponding settings of the field. A long drift space is easily obtained in the spherotron differing from any other type of T O F by a complete absence of field free region, so that an ion bunch is permanently retained in the electrostatic field with periodic stigmatic and energy focusing. A combination of the static mode for low masses and T O F mode for high masses makes the spherotron a very promising instrument for various analytical, physical and chemical applications.
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II. Cherepin/lnt. J. Mass Spectrom. Ion Processes 121 (1992) R1-RIO
REFERENCES 1 2 3 4 5 6
T. Matsuo, T. Sakurai, M. Ishihara, Nucl. Instrum. Methods Phys. Res. A, 298 (1990) 134. M. Baril, Nucl. Instrum. Methods, 187 (1981) 153. K. Serier, Low Energy Electron Spectrometry, Wiley, New York, 1972, p. 397. H. Ebel, M.F. Ebel and M. Mantler et al., Surf. Sci., 231 (1990) 233. H. Wollnik, Optics of Charged Particles, Academic Press, New York, 1987, p. 387. N.D. Coggeshall, J. Appl. Phys., 18 (1947) 855.