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Wien Filter Applications to Ions
CHAPTER FIVE
Wien Filter Applications to Ions Damaschin Ioanoviciu1 and Katsushige Tsuno2 1
Physics Faculty and Institute of Doctoral Studies, Babes-Bolyai University, M. Kogalniceanu Str. Nr. 1, 400084 Cluj-Napoca Romania, National Institute for Research and Development of Isotopic and Molecular Technologies) Donath Str, Nr. 65-103, 400293 Cluj-Napoca, Romania, E-mail: [email protected] 2 Electron Optics Solutions Tsuno, 2-10-11, Mihori, Akishima, Tokyo 196-0001, Japan, E-mail: [email protected]
Contents 1. Wien Filters as Independent Mass Analyzers 1.1. The Colutron 1.2. Volcano Field Ionization Mass Spectrometer 1.3. Inhomogeneous Field Wien Filter Mass Spectrometer 2. Double-Focusing Mass Spectrometers 2.1. Mass Spectrometer of Jordan 2.2. Electric Deflector-Wien Filter Double-focusing Geometries 2.3. The Triple-focusing Mass Spectrometer of Taya et al. 2.4. Electric SectordWien Filter Mass Spectrometer 2.5. Compact Geometries with a Common Magnet Gap 2.6. Triple-focusing Compact Geometries 2.7. Double-focusing Mass Spectrometers with Simple Geometry 2.8. Simplest Compact Geometry 3. Wien Filter in Accelerator Mass Spectrometry 4. Micro Wien Filters as Leak Detectors 5. Wien Filters for Radioactive Ions 6. Reaction Product Separators 6.1. Reaction Products of Major Interest for Astrophysics 6.2. Heavy Ion Mass Spectrometer of Enge and Horn 6.3. Reaction Product Mass Separator at MSU 6.4. LISE 3 6.5. The Daresbury Recoil Separator 6.6. ARES 6.7. ERNA 6.8. St. Georges 6.9. VAMOS 6.10. IGISOL 7. Multiple Wien Filters
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) retired Advances in Imaging and Electron Physics, Volume 176 ISSN 1076-5670, http://dx.doi.org/10.1016/B978-0-12-408142-0.00005-5
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1. WIEN FILTERS AS INDEPENDENT MASS ANALYZERS As a charged particle analyzer, the Wien filter can be associated with a roughly constant-energy charged particle source to ensure mass analysis. In this very simple configuration, the Wien filter becomes a direction (angle)–focusing mass spectrometer or mass separator. For such an instrument, there are two basic characterizing quantities: the resolution and the sensitivity. While the sensitivity is closely connected to the processes happening inside the ion source, the resolution can be defined clearlydat least theoreticallydfor an ion beam with well-defined properties. The mass resolution is given by the ratio of the mass dispersion coefficient divided by the sum of the image and detector slit width, at the peak basis, or to the image width alone for the peak half height definition (Figure 1) from Ioanoviciu (1989). These, expressed in simple mathematical formulas, are Rbasis ¼
Dg Dg and R1=2 ¼ ; I þD I
where Rbasis and R1/2 are the resolution at the basis and at peak half height, respectively; Dg is the mass dispersion coefficient of the analyser; and I and D are the image and detector slit width, respectively. R1/2 is given for D ¼ I. In the figure, Ds/s must be substituted for g. At the site
Figure 1 Resolved different mass ion beams at the detector slit. Reproduced with permission.
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of the image, its width is expressed as a mixture of small terms, up to second order: I ¼ Md þ Dd d þ Dg g þ Axx d 2 þ Axa xa þ Axd xd þ Aaa a2 þ Aad ad þ Add d2 þ Ayy y2 þ Ayb yb þ Abb b2 : Besides the object slit width d, the relative energy deviation d, and mass deviation g, with respect to a main path (beam axis) particle, the string contains terms generated by the radial a and axial b angles and by the height 2y of the object slit. M is the absolute value of the analyzer magnification along the x direction. We limited the development to second-order terms, except those concerning the mass difference, because for the mass spectrometer analyzers, the total image width is important, as the resolution formula shows. The Wien filter use in the area of chemistry has been described by Aberth and Wollnik (1990).
1.1. The Colutron The colutron isotope separator got its name because of its similarity to the calutrons of the Manhattan Project. The colutron of Wahlin (1964) included an ExB (Wien) filter in a versatile device that could switch quickly from one group of isotopes to another. The first version was modified by Wahlin (1965) and continued to be under improvement and in production for various customers. The colutron consists of the following main parts which we enumerate along the ion path from creation to neutralization: the ion source followed by a three-cylinder electrostatic lens, the Wien filter, separated by a field-free space from the detector. The electrostatic lens usually is the only axially (y direction) focusing element on the ion path. The Wien filter has the role of mass dispersion. However, the Wien filter electrodes can be used to create some electrostatic field gradients by appropriately connecting the shims of the deflectors or by connecting one of the deflecting plates to the ground potential. There are 18 guard rings in the 1964 model and 22 in the 1965 model, isolated by Teflon tape (of 0.254 mm thickness in the last case). By these procedures inducing electric gradients all along the beam or by lenses at the filter ends, the beam can be rounded at the detector; i.e., the astigmatism can be eliminated. These Wien filters were assembled from pole pieces and electrodes that were 39.5 cm in length. The pole gaps were of 3.175 cm for the magnet and 3.81 for the electrodes For isotope separators, the mass dispersion is a parameter of prime
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importance. We find the mass dispersion coefficient Dg for the Wien filter field, for a free space lr0 in front of the collector: c1 s Dg ¼ l, that for Wien filters shorts with respect to the Wien 2 2 radius r0. It transformsinto W W Dg ¼ lþ , a formula that gives the distance between two 2 2 isotope beams Dizo differing in mass by DM: DM DM E Z Z Lþ ¼ ; Dizo ¼ r0 Dg M 4M Vacc 2 where Z ¼ Wr0 while L ¼ lr0. As an example, which appears on the Colutron Corporation website (www. colutron.com), we see a distance of 1.9 mm between the beam of Ca40 and Ca42 for an applied deflector field E ¼ 16,853 V/m, filter length Z ¼ 0.152 m, and L ¼ (0.3 – 0.152/2) if Vacc ¼ 5 kV (the exact relation is 1.81 mm). If DM/M ¼ 1/83, as for the Kripton isotopes 83 and 84 parameter values close to those of the 1964 and 1965 colutrons: Z ¼ 0.395 m, E ¼ 12,500 V/m, give for Vacc ¼ 7 kV Dizo ¼ 4.66 mm if L ¼ 2 m and 6.79 mm for L ¼ 3 m. The Colutron attractive properties include the adjustable dispersion and low cost. The range of working parameters includes magnetic field up to 12,000 Gauss, accelerating voltage up to 60 kV, focusing voltage from 0 to 30 kV, and electrostatic plates fed by 0 to 3 kV. As an illustrative example, the Kripton peak is obtained on ions accelerated to 25 keV when the electric field between plates is 920 V/cm.
1.2. Volcano Field Ionization Mass Spectrometer The Volcano Field Ionization mass spectrometer of Aberth (1980) is a 3.5-mlong instrument incorporating a 0.69-m Wien filter followed by a 2 m fieldfree space in front of the detector. For an accelerating voltage of 30 kV, the 2 eV energy spread ion-generating source allowed the spectrometer to be operated at 3,500 peak half height resolution at the 92 and 93 mass per charge ratio for the toluene. The usual operating resolution is 1,500 and the sensitivity 105 ion/molecule. The spectrometer operates with two lenses. As for the colutron, the mass dispersion can be varied.
1.3. Inhomogeneous Field Wien Filter Mass Spectrometer A Wien filter mass spectrometer with inhomogeneous fields Ioanoviciu and Cuna (1977) (shown in Figure 2) attained a resolution of 4,100 measured on þ 16 the C2Hþ A detected current. 4 -N2 mass 28 doublet (Figure 3) at 1.28 x 10 The Z ¼ 0.3 m effective length inhomogeneous field Wien filter was located
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Figure 2 Single focusing arrangement of an inhomogeneous-field Wien filter. Reproduced with permission.
between two 0.41-m-long, field-free spaces. Parallel electrodes were inserted in a wedge magnetic field with an axial magnetic force line radius rm ¼ 10 cm. A Nier-type ion source working at 4 kV accelerating voltage was used, and the magnetic field on the beam axis was 7,700 Oe. The axial electrostatic equipotential radius on the beam axis was estimated at 16.5 cm.
2. DOUBLE-FOCUSING MASS SPECTROMETERS A simple look at the resolution formula accounting for the image components reveals that the most harmful term is that of the first order, due to the relative energy difference (spread). The general drawback of the resolution increase of mass spectrometers was eliminated by using the double-focusing principle. First proposed by Mattauch and Herzog (1934), this principle consists of obtaining energy focusing at the image site or, in other words, cancelling both Aa and Ad at a glance. It was put in practice by combining two charged particle analyzers of different types. The most frequently encountered is the association of an electrostatic cylindrical condenser with a homogeneous magnetic field sector.
2.1. Mass Spectrometer of Jordan Jordan (1941) constructed a double-focusing mass spectrometer by combining a homogeneous fields Wien filter with a 60 deflecting magnetic sector. The basic geometric parameters of his instrument were Wien filter effective length Z ¼ 1.15 m, and magnetic field main path radius rB ¼ 0.366 m. The magnet was located symmetrically between the intermediate image situated at the
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8
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4
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2
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0 þ Figure 3 Record of the mass 28 C2Hþ 4 -N2 mass doublet. Reproduced with permission.
Wien filter end and the detection photographic plate. The mass dispersion coefficient was Dg ¼ 1.4 m, an amazingly high resolution, especially at the level in 1941, was obtained: 28,000.
2.2. Electric Deflector-Wien Filter Double-focusing Geometries Another combination of analyzers allowing double focusing is that of a Wien filter with an electrostatic condenser that is cylindrical or toroidal. In this case, a single magnet is needed. A weight saving was assumed to result in a weight saving with respect to a Wien filter-magnetic sector configuration of Jordan’s type, Jordan (1941). The basic properties of these geometries were detailed for both the direct and the reversed geometries [see Ioanoviciu and Cuna (1974a); Figure 4]. We call direct a configuration with the Wien
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EB
E
Δ ℓ″1
ℓ′2
ℓ″2
h
Z
r0 φ ℓ′ 1
Figure 4 Double-focusing mass spectrometer geometry schematic. Reproduced with permission.
filter located after the deflector along the ion path from source to collector. As direct geometry was considered that having the electrostatic deflector before the Wien filter on the ion beam path. The possibility of combining only one angular focusing analyzer with another non-focusing or diverging analyser was considered in the discussion. The double-focusing condition, the mass dispersion coefficient, and the needed field areas, as well as the second-order aberration coefficients, were also determined. Here, we focus on only the first-order basic formulas. If we consider as “direct” the configuration with the electric condenser on the source side and the Wien filter on the detector side, let Md and Dgd be its radial magnification and mass dispersion, respectively. Then the reversed geometry magnification Mr and mass dispersion Dr will be connected with the above by the relations 1 Mr ¼ Md Dgr ¼
Dgd : Md
There are three possible analyzer combinations that can ensure double focusing: converging-converging, converging-dispersing, and convergingdiverging. The focusing conditions to be fulfilled take different forms accordingly. Only the condition for the first combination is given here. The energy focusing condition is as follows: r0e r0 1 : ð1 Me Þ ¼ 2 1 1 ne 2k Mw Here the index e refers to the electrostatic deflector (including its nonhomogeneity index ne), while Mw means the magnification of the Wien filter. The mass dispersion of the double-focusing mass spectrometer assembly is r0e Dg ¼ Mw ð1 Me Þ: 1 ne
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2.3. The Triple-focusing Mass Spectrometer of Taya et al. The mass spectrometer of Taya et al. (1978) had the purpose to ensure high sensitivity along with double focusing. This adds a new dimension: triple focusing. The instrument offered angular radial, energy, and axial focusing together; i.e., it is a design satisfying three first-order focusing conditions. The focusing of the beam along the direction normal to the dispersion plane was achieved by two means: the spherical analyzer and the unique Wien filter having oblique beam entry. No other such Wien filter played such a focusing role by using fringing fields. Otherwise, the theory of such oblique-incidence Wien filters seems to be still at the first level of the approximation stage. The triple-focusing mass spectrometer is defined ion optically at first order by the following geometric quantities: field-free space lengths, counted from the ion source toward the detector at 46 cm, 30 cm, and 43.3 cm, with the Wien filter at an effective length of 38 cm with an entrance angle of 28 (magnetic deflector definition), r0 ¼ 33.7 cm, spherical condenser deflector with 18 cm main path radius, and a 30 effective deflexion angle. The mass spectrometer was able to handle high-intensity (on mass spectrometric scale) currents of Argon ion beams from a duoplasmatron ion source with 68% transmission and 10 mA to 150 mA currents from a microvawe ion source with 5 kV acceleration. Resolutions of 120 at 10% level were obtained with 3 mm source and 1 mm collector slits, respectively. Among the various technical solutions on the prototype, the appropriate homogeneity in the electric and magnetic fields was obtained with longitudinal shims.
2.4. Electric SectordWien Filter Mass Spectrometer A Wien filter cylindrical deflector with Matsuda plates [Cuna and Ioanoviciu (1983)] was constructed and tested (Figure 5). The basic parameters of the
Figure 5 A Wien filter electric deflector geometry used for a 5,500 resolution instrument. Reproduced with permission.
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instrument were k ¼ 0.03873i /cm (divergent regime), r0 ¼ 12.25 cm, first field-free space ¼ 40.2 cm, last field-free space ¼ 34.4 cm, distance between analyzers ¼ 8 cm, effective length of the Wien filter ¼ 30 cm, radius of main path inside the electrostatic deflector ¼ 20 cm, and angle of deflexion ¼ 31 . The magnification of the first analyzer was 0.25, 1 of the second. A resolution of 5,600 was measured at half the height of the Arþ peak with a 0.1-mm-wide source slit.
2.5. Compact Geometries with a Common Magnet Gap A possibility to create compact, small, double-focusing mass spectrometers useful in space research or as RGA is to locate an electrostatic plate pair inside a magnet gap common with a magnetic deflector [Ioanoviciu and Cuna (1974b)]. These very attractive arrangements introduce an additional feature: how to master fringing fields of only electrostatic nature at the end of the Wien filter, where the pure magnetic field analyzer begins. As a general rule, knowing that the electrostatic fringing fields are less extended would lead you to expect fewer problems. However, inside the electrostatic fringing field, the Wien condition cannot be satisfied. The transition region must be reduced to a minimum. In a study of the double-focusing mass spectrometers created by introducing a parallel plate pair in a homogeneous magnet gap, the ion optical properties were analyzed, including mass dispersion, second-order aberration coefficients, and needed magnetic field area for a given beam angular opening. The magnification of such a double-focusing mass spectrometer is M ¼ –1; while the mass dispersion is Dg ¼ r0, the energy dispersion being cancelled. The field spaces, which are of equal length L, are L ¼ r0c/s, with r0 the main path radius inside the homogeneous magnetic field, s ¼ sin(4) ¼ sin(Z/r0) and c ¼ cos(4) ¼ cos(Z/r0). The basic second-order aberration coefficients are r0 1 1 1 r0 2 3 þ ðx=aaÞ ¼ 3 2sð1 þ 2c Þ þ r0 c þ þ 2s Re2 Rm1 Re1 Rm2 r 2 c 1 c3 r0 ðx=adÞ ¼ ð2 þ c c 2 þ c 3 Þ þ 0 2 s 2s Re2 r0 4 r02 ð1 cÞ2 r02 1 c c 3 3 2 ðx=ddÞ ¼ ð2c 4c þ 2c þ 4c 3Þ þ þ : 4 8sRe2 2sRm2
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Re1, Re2, Rm1, Rm2 are the radii of the boundaries of the electric (e) and magnetic (m) of the electrodes and pole pieces. “1” means “entry,” while “2” means “exit limit.” The area covered in the median plane by a beam of a 2a radial angular opening is the same inside the pure magnetic field as inside the Wien filter: 2ar20,which allows us to establish the needed area for the pole faces. Estimations were made for r0 ¼ 5 cm, source slit width of 0.25 mm, a ¼ 1/20, and d ¼ 1/100. If boundaries are selected to cancel the (x/aa) aberration, then resolutions around 100 can be expected, while for straight boundaries, around 50 can be expected.
2.6. Triple-focusing Compact Geometries Another study [Ioanoviciu et al. (1992)] explored the possibility of using oblique entry and exit for homogeneous magnetic fields. The considered geometries are conceived to ensure stigmatic focusing by using oblique incidence at the entry end of the Wien filter and at the exit from the homogeneous magnetic field. The first-order conditions to be satisfied are: L ¼
1 Z and 4 ¼ tan 4 tan ε r0
f or My ¼ 1 when Dg ¼ Ltan f and tan ε ¼
1=4 þ tan f f or My ¼ þ1 2
while tan ε ¼
tan 4 if My ¼ 1: 2
Two specific cases were calculated: • For the configuration with positive unitary axial magnification, the following basic parameters were selected: 4 ¼ 88 , ε ¼ 86.09 , and L ¼ 0.071r0. The basic aberration coefficients are (x/aa) ¼ 12.88r0, (x/ad) ¼ 6.31r0, (x/dd) ¼ –0.95r0, (x/yy) ¼ –412/r0, (x/yb) ¼ –903, and (x/bb) ¼ –1.539r0. A calculation for a stigmatic double-focusing geometry, with axial magnification –1, ensures much more advantageous aberration coefficients. Its basic parameters are 4 ¼ 60 , ε ¼ 40.89 , and L ¼ 1.1547r0, while the aberration coefficients (x/aa) ¼ 20.0r0, (x/ad) ¼ 8.948r0, (x/dd) ¼ –0.219r0, (x/yy) ¼ –0.717/r0, (x/yb) ¼ –0.538, and (x/bb) ¼ –3.333r0.
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• Other configurations put plane parallel plate condensers inside wedge magnetic field gaps for normal entry and exit. The relations contain an additional free parameter K, the ratio of the main particle momentum to that of one moving on a circular path in a specified point of the magnetic field. A numerical example will be reproduced: basic parameters 4 ¼ 110 , Z/r0 ¼ 1.891, K ¼ 0.5867, L2 ¼ 0.241r0, L1 ¼ 0.577r0, Dg ¼ 1.10r0, with the aberration coefficients (x/aa) ¼ 3.119r0, (x/ad) ¼ 3.183r0, (x/dd) ¼ –1.314r0, (x/yy) ¼ –0.57/r0, (x/yb) ¼ –0.451, and (x/bb) ¼ 0.17r0.
2.7. Double-focusing Mass Spectrometers with Simple Geometry The simplest double-focusing mass spectrometer geometries result by introducing a pair of parallel plates inside the gap created by two longer rectangular pole pieces that are parallel [Ioanoviciu (1995)]. Then the ion beam normally approaches the Wien filter entry limit and leaves the homogeneous magnetic field, laterally obliquely at an exit angle ε (Figure 6). The deflexion of the beam and this oblique exit angle must satisfy the relation: ε ¼ 4-p/2, while double focusing is obtained when 4 ¼ Z/r0. The first-order parameters are Dg ¼ r0 sin2 f M ¼ sin2 f y=y ¼ 1 þ cos2 f ðy=bÞ ¼ 2r0 ½fðy=yÞ þ cot anf; while the aberration coefficients of second order are
L1
Z r0 θ
L2
Figure 6 Layout of the compact, oversimplified, double-focusing mass spectrometer. (For color version of this figure, the reader is referred to the online version of this book).
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r0 3 1 1 1 1 x=aa ¼ þ þ þ c 2s Re1 Rm1 Rm2 s3 Re2 1 3c 2 1 þ ð3 mÞc 2 þ 3 2m þ 2 2s2 r0 1 2c 3 3 sm ðc 1Þ þ fm ð2 þ cÞ ðx=adÞ ¼ þ 3 2 Re2 s Rm2 4 4 1 ðc 1Þð3c 4 þ 5c 3 þ 4c 2 6c 4Þ 2s3 r0 1 4c 3 3 s2 m sðc 1Þ2 þ scfm þ 3 ðx=ddÞ ¼ ð2c þ 1Þ 8 Re2 s Rm2 8 8 þ
þ
1 ð1 cÞð2c 3 þ 7c 2 2c 3Þ 4ð1 þ cÞ
2 c c2 ðx=yyÞ ¼ sGyy þ 1 þ c 2 Fyy þ ð1 þ c 2 Þ Fyb þ 2 Fbb s s c ðx=ybÞ ¼ sGyb þ 4ð1 þ c 2 ÞFyy fð1 þ c 2 Þ þ s 1 2fc 2c c 2 2 þ ð1 þ c Þ 2 þ þ fð1 þ c Þ þ Fyb s s s s c 1 þ 2 2 þ 2fc Fbb s s h c i2 ðx=bbÞ ¼ sGbb þ 4 fð1 þ c 2 Þ þ Fyy s 2 c 1 2 þ fð1 þ c Þ þ þ 2fc Fyb s s s 1 1 2 þ 2 2fc þ Fbb ; s s with the abbreviations: Gyy
r0 1 1 1 s þ ð3m 1Þ ¼ þc þ 2 Re2 Re1 Rm1 2
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2c r0 F Gyy þ 3ð1 cÞm s 2Re2 c 2 c 1 r0 F2 ¼ Gyb Gyy þ 3mF þ 3m s 2Re2 s s 2 Gyb ¼
Gbb
1 þ c2 r0 c Fyy ¼ 2 2Rm2 s2
Fyb ¼ 2FFyy þ
Fbb ¼ F2 Fyy þ F
c3 s
c 3 s2 : s 2
2.8. Simplest Compact Geometry A double-focusing compact mass spectrometer resulting by replacing half of the Dempster 180 magnetic deflector by an appropriate Wien filter in the same gap was constructed and tested [Ioanoviciu and Cuna (1995), and see Figure 7]. A (p/2)56 mm long Wien filter has been created in front of a 56 mm main path radius magnetic 90 deflector. The 88-mm-long iron plates were slid inside the vacuum chamber containing the electrodes in a sandwich structure. The electrodes were profiled in a way that creates a field close to homogeneous. The plates were located finally at an 8-mm gap. The aberration coefficients of the entire double-focusing mass spectrometer can be influenced only by non-homogeneities of the electric field created by small height plates, and an almost homogeneous magnetic field created between wide pole pieces. The ion source was immersed inside the magnetic field; therefore, the electric fringing fields being present at both the entry and exit of the Wien filter. Accounting for these structural properties, the ion optical properties of the apparatus can be synthetized as follows:
Z r0 Φ
Figure 7 Half of a Dempster mass spectrometer deflector combined with a Wien filter to ensure double focusing. (For color version of this figure, the reader is referred to the online version of this book).
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Radial magnification M ¼ –1, mass dispersion coefficient Dg ¼ r0; second-order aberration coefficients: Aaa Add
r0 r0 m 3p ¼ 1mþ Aad ¼ 2 þ 1 2Re 2Re 2 4 1 m r0 ¼ 3þ þ 4 2 2Re Ayy ¼
Abb
3m r0 2Re 2
Ayb ¼ 3m
pr0 2Re
p p2 r0 ¼ 3m 1 8Re 2
In these formulas, the non-homogeneity coefficient m has been defined in the manner of Wollnik et al. (1972): m ¼
r02
d 1 ; dx Rax
with Rax as the radius of curvature of the potential surface passing the beam axis. The attempt to ensure electric field homogeneity was associated by creating straight boundaries to the electric electrode limits. For these particular conditions, the aberration coefficients were simplified as the mass resolution R1/2 formula: Ayy ¼ Ayb ¼ Abb ¼ 0 while Aaa ¼ 1 . Aad ¼ 2 . Add ¼
3 4
R1=2 ¼
: 1 s þ a2 þ 4ad þ 0:75d2
For a source object slit width sr0 of 0.25 mm, a radial beam opening angle a ¼ 1.5 . For d ¼ 0.05, which is a pretty realistic value, a resolution of 175 was predicted and measured in the methane mass spectrum. Around 1 keV ions were detected when ionizing electron currents of 260 mA were used. Ion currents of the order of 1010A were collected with a 0.1-mm-wide, 8-mm, high-source slit.
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3. WIEN FILTER IN ACCELERATOR MASS SPECTROMETRY The Wien filter also was used in accelerator mass spectrometry. A Wien filter was included in the accelerator mass spectrometry system of the Australian National University to improve mass resolution [King et al. (1997)]. The basic layout of the assembly includes a caesium sputtering ion source. The first 90 deflecting magnet selects the aluminium ions entering the accelerator column, next in another 90 deflector are measured by a gas ionization detector. The system determined the presence of a 26Al isotope in biological materials as aluminium oxide or phosphate from blood or soft tissues. The Wien filter was inserted between the last deflector and the detector, that was set to leave undeviated 26Al ions. It reduced substantially the levels of other ions in the mass spectrum of C, O, and Mg.
4. MICRO WIEN FILTERS AS LEAK DETECTORS Micromachined Wien filters Sillon, Baptist (2002) were created to serve as leak detectors. Such small instruments would allow the increase of work pressure for leak detection. As the molecule free path at 0.5 Pa is about 1 cm, this should be the length of the mass analyser. Chips with six channels of 200 mm and 1 cm long were prepared in silicone wafers. Tests were performed on He with a magnetic field of 5,500 G, the distance between rods being 200 mm with 6.37 V for 70 eV ion acceleration. Good separation has been obtained for the He peak, but the separation of 14 þ N from 28Nþ 2 is bad. Detection on the plate showed a sensitivity of 107A/Pa. The filter dimensions (lateral) are 200 mm x 400 mm, and the ion entrance diameter is 150 mm.
5. WIEN FILTERS FOR RADIOACTIVE IONS Simulations of Wien filters destined for mass analysis of radioactive ions were reported by Pierret et al. (2008). The single-filter solution has been discarded as unsatisfactory. The solution of two consecutive Wien filters, the mass dispersion planes normal each other was recommended: two consecutive Wien filters having the dispersion plane rotated by 90 one with respect to the another. The two filters of 400 mm length each should be located 100 mm apart. A beam from a MONO 1000 ECR ion source was
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considered. The simulated configuration contained the MONO 1000 ECR ion source, an unipotential lens, and the Wien filters. The use of the system as a mass separator, with one Wien filter of a 750-mm-long beam of 180 pmm mrad and 150 p mm mrad emittance at 15 kV, gave good separation for masses of 20 u, 34 u, and 79 u. The system was considered as a mass separator to eliminate part of the undesired ions. Electrodes symmetrically fed by 2,000 V were simulated. As an on-line mass analyser, the two Wien filters of 400 mm placed 10 mm apart should be used. Good simulated results were obtained for a mass of 79 u and for a 5-mm aperture with about 1% transmission.
6. REACTION PRODUCT SEPARATORS 6.1. Reaction Products of Major Interest for Astrophysics The purpose of the recoil mass separators is to distinguish the focusing plane among the various reaction products after their mass, and to suppress the primary projectiles from the beam. This separation is accomplished by Wien filters, among other types of analyzers [Davids (2003)]. The knowledge of the cross sections of the nuclear a particle and proton capture reactions are of paramount importance in the description of the stellar processes from red giants to supernova explosions, and in building a correct image of how various elements were created in the universe. Many efforts have been made over time to determine the cross-section of the 12 C(a,g)16O reaction with an accuracy of better than 10%. Let us see what ion-optical conditions must satisfy the recoil mass analyzers to approach this goal. The projectile ions and the recoil ones have almost identical momenta. Projectiles and recoils of identical momenta cannot be distinguished after the collision. If the recoils from the reaction will be detected only partially, errors will be introduced in the resulting cross-section value. Based on these preliminary observations, a careful selection of the projectiles is recommended, with the suppression of those that are identical to the followed reaction products. The recoil mass analyzer must offer complete acceptance for the emitted recoils Rogalla et al (2003), these arising inside of a cone of half angle q: q ¼ arc tan[Ug/(pc)] and having a relative momentum spread of Dp/p. Here, Ug is the emitted g ray photon energy resulting from the capture process, and p the recoil, as well as the projectile momentum. For the specific case of the 12C(a,g)16O capture reaction, Ug ¼ 7.9 MeV, then q ¼ 1.8 and Dp/p ¼ 0.062 for an energy of U ¼ 0.7 MeV, while q ¼ 1 ,
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Dp/p ¼ 0.03 for U ¼ 5 MeV. As the cross sections we are looking for are of the order of s ¼ 1 pb, the projectiles contaminating the primary beam must be in a concentration of less than 1018 from those generating the recoils (or less than 1014 if the detector ensures itself an additional discrimination from the projectiles) Recoil separators handling high energy charged particles result in big installations ensuring compensation of electric and magnetic deviations successively or simultaneously in Wien filters [Wollnik (1987)].
6.2. Heavy Ion Mass Spectrometer of Enge and Horn In Enge and Horn (1977), an energy-mass spectrograph for heavy ions resulting from fusion reactions was constructed, tested, and used at Brookhaven National Laboratory (Figure 8). The spectrograph combined a Wien filter with a split pole magnetic spectrograph (SP1, SP2). The Wien filter, WF, has the dispersion plane normal to the deflection plane of the spectrograph. The magnetic field inside the Wien filter has been directed against the deflection sense inside the spectrograph. Special attention was paid to the fringing field in an effort to make to reconcile both the electric and magnetic field distributions (at least as a common effective boundary). Expressions for the offset resulted at the entry and exit boundaries were derived (Salomaa and Enge 1977). The instrument had a horizontal plane acceptance of 2 mr, in the vertical plane of 8 mr with the total solid angle 0.64 msr, horizontal dispersion 2.15 m, vertical 0.37-0.52 m, horizontal magnification 0.26–0.342 (ends of focal plane), and vertical magnification 0.662–1.867. The best resolution
Figure 8 Enge’s Wien filter split-pole energy mass spectrograph. (For color version of this figure, the reader is referred to the online version of this book).
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attained was 425 (360 for evaporation residues from the reaction 32Sþ70Ge at 3 ). The Wien filter was put together from pole pieces with a 1.016-m length and a 152-mm gap. In the gap were installed two 1.11-m-long plates (which is longer than the magnet pole pieces) in an attempt to match the electric and magnetic fringing fields to each other. The plates were fed by voltages up to 60 kV. The magnetic field can be increased up to 4,000 G to cope with the primary beam particles moving along the evaporation residues. As the velocity of these last items is two or four times lower than that of the primaries depending of the products, these should be stopped inside the Wien filter on four berilium-covered baffles attached to one stainless steel plate.
6.3. Reaction Product Mass Separator at MSU The Reaction Product Mass Separator (RPMS) at Michigan State University in East Lansing [Harwood and Nolen (1981)] was constructed to study nuclei far from the stability valley. The separator (Figure 9) ensures triple focusing at the focusing plane; i.e., both radial and axial angular focusing, as well as momentum focusing of the first order. The projectiles from the K500 Cyclotron hit the target in front of the separator. The two magnetic quadrupoles Q1 and Q2 in the RPMS first focus the resulted and primary ions to the Wien filter (WF) of an unusual 5-m length. Next, a deflecting magnet (MD) is located in front of another magnetic quadrupole doublet (Q3, Q4) and arrives to the detector (Det), flying a total path of 14.3 m. Depending upon the measurement, the products can be observed directly or deviated, the last quadrupole doublet and detector moving accordingly. For the prototype, the maximum allowed energy was 30 MeV/u a mass resolution of 100 at the peak base level being presumed for a 1-msr solid angle and 16% energy range, respectively, 200 for energy range
Figure 9 Basic configuration of the RPMS at MSU. (For color version of this figure, the reader is referred to the online version of this book).
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reduced twice. The parameters anticipated for the next development phase of the RPMS were length 30 m, maximum energy 300 MeV/u, accepted solid angle 0.8 msr, energy acceptance 8%, dispersion 8.5 mm/%, mass resolution 180 to 320 for 0.6 to 0.4 msr, and a 2 to 4% energy spread.
6.4. LISE 3 The program dealing with super heavy elements at GANIL involves the Wien filter called LISE3. The Wien filter selects charged particles from a reaction chamber that uses two wheels with targets and with carbon stripper foils, respectively. The LISE3 Wien filter has an angular acceptance of 36p mrad. It has two halves: the upper electrode placed at a position 2 cm higher to admit beam particles is suppressed without hitting electrodes and generating background. The undesired beam is absorbed on a collimator composed from two pairs of mobile slits. The background suppression is achieved by a deflecting magnet located before detectors (carbon foils and MCP detectors) [Grevy et al. (2002)].
6.5. The Daresbury Recoil Separator The Daresbury recoil separator was used by Rogers et al. (2008) to study reactions of (p,g) type proton capture products. The Oak Ridge National Laboratory at the Holifield Radioactive Ion Beam Facility A dipole magnet preceding a last three-quad group was placed between the target and the detector groups of quads before and after the two consecutive Wien filters.
6.6. ARES The Astrophysic Recoil Spectrometer (ARES) of the Cyclotron Research Center in Louvain-la-Neuve (Figure 10). Couder et al. (2003) was designed as a tool to determine the cross sections of the (p,g) capture reactions.
Figure 10 Assembly scheme of the ARES. (For color version of this figure, the reader is referred to the online version of this book).
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We distinguish a part of the system creating the projectile beam that interacts with the target T (of CH2, polyethylene) followed by the reaction product mass separator. The projectiles are accelerated to 0.2–0.8 MeV/u energies, focused on the target by a doublet of magnetic quadrupoles. The reaction product separator focuses first by a quadrupole triplet (QT) on the ions, a magnet MD deflecting them by 40 before a selection on a slit. Next, a quadrupole doublet (QD1) precedes the 1-m-long Wien filter (WF), which in turn sends the velocity-separated products on a new slit system. Finally the separated products come to the last quadrupole doublet (QD2) in front of an DE-E detector (Det). The product ions from proton captures in inverse kinematics are emitted in a cone with about a 10-mrad angle half opening, the beam opening increasing along its path due to multiple scattering. During the tests performed on 12F2þ ions, the transmission of ARES was around 70%. This transmission was maintained for a particularly broad range of applied fields on the Wien filter: 2.5-20 kV/cm and 176–1407 G in constant ratio. When transmitted the 20Ne7þ, the deflecting magnet field was changed by 0.4% compared to 19F ions, while that of the Wien filter was increased by 6%.
6.7. ERNA The recoil separator at Bochum (Figure 11) was called the European Recoil Separator for Nuclear Astrophysics (ERNA) [Rogalla et al. (1999b)]. A sputtering ion source working at 130 kV is used to inject through a deflecting magnet the created negative ions into the 4 MV Tandem accelerator. There, ions are stripped, and the resulted ions must be focused
Figure 11 Schema of the basic components of the ERNA. (For color version of this figure, the reader is referred to the online version of this book).
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and selected before being directed against a jet gas target [of He gas if (a,g) reactions are studied]. The process of projectile purification is directed to eliminate the wrong charge state and undesired mass projectiles. It is performed by the following ion-optical components located along the beam path: a doublet of magnetic quadrupoles (QD1), a first Wien filter (FW1), an analyzing magnet (MD1), a switching magnet, a second quadrupole doublet (QD2), and a second Wien filter (WF2). The first Wien filter selects ions according to their velocities, the magnet separates the various electric charge states, and finally, the second Wien filter eliminates the undesired mass projectiles from the primary ion beam. This is the purificating part of the assembly and is not a constituting section of the recoil separator itself [Rogalla et al. (1999a)]. A simplified configuration for beam purification reported by Rogalla et al. (1999a) was assembled, where after the tandem accelerator, the analyzing magnet directs the projectiles through a quadrupole doublet after an aperture through a Wien filter to the telescope detector. The Wien filter, which is obviously homogeneous, uses two parallel electrodes of 0.85 m long and 48 mm wide, located over and under the beam. These electrodes were fed by 20 kV, applied symmetrically with respect to the ground. The pole pieces were only 0.79 m long, with a width of 117 mm and a gap of 110 mm. The single Wien filter indicates that a purification of the 12C3þ beam of 16O ions can be obtained up to a 2 x 1017 level. As it is certainly not enough, a second Wien filter was included in the purification part. The assembly concentrating the projectiles onto the jet create a minimal size object for the ERNA recoil separator itself. This last uses a magnetic quadrupole triplet (QT) to shape the virtual beam of recoils from the gas target onto a slit system followed by the third Wien filter (WF3). This Wien filter has the important role of mass-analyzing the recoils. A 60 deflector magnet (MD2) preceded by a focusing quadrupole (Q), slits, and a Faraday cup with a last doublet, direct the reaction product ions towards the fourth Wien filter (WF4) in a parallel beam to the detector telescope (Det) [Gialanella et al (2007)]. The last deflecting magnet and Wien filter ensure a supplementary momentum and mass separation, as well as the elimination of the background ions resulting from the projectile beam scattering on residual gas and on the various slits along the beam path. The third Wien filter has deflectors of 0.5 m length, 120 mm wide, located 70 mm apart, creating an electric field directed horizontally and plates fed by 50 kV stable voltage units. The magnet pole faces of the Wien filter have the same 0.5-m effective length, being 320 mm wide and creating a 100-mm gap.
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For 16O3þ 0.7 MeV ions, the needed field was calculated to be of 0.08 T, while for 16O6þ ions of 5 MeV, it is 0.11 T. The last Wien filter on the recoil path, from Cal Tech, has the geometry defined by 0.578-m effective lengths, the condenser plates of 63 mm width creating a horizontally directed electric field in a 70-mm gap, while the pole faces of 77 mm width have a 95-mm gap. The calculated magnetic fields to be applied (16O3þ recoils of 0.7 MeV and 16 6þ O of 5 MeV) are 0.12 T and 0.11 T, respectively [Rogalla et al. (1999b)]. The ion optical optimization of the recoil separator has been performed with the help of the computer code COSY Infinity, up to fourth-order small quantities. From the diagrams of the ion paths, we can see how act the various recoil separator components. The quadrupole triplet next to the target horizontally acts as a convergent/divergent/convergent combination of quadrupole lenses, creating a waist in this plane at the single quadrupole site. The third Wien filter has a weak focusing action. The diverging trajectories remain so through the magnetic dipole being drastically refocused by the first quadrupole in the quadrupole doublet. Next, the beam remains almost parallel. It maintains this trend in the last Wien filter and through the last quadrupole. The beam is directed parallel in both horizontal and vertical planes toward the telescope detector. The focusing role of the Wien filter is limited in the horizontal plane, as naturally it is absent in the vertical one. We can define Wien filters as being weak if their length Z is small compared to the cyclotron radius r0. Then, sin (Z/r0) – Z/r0 will be a small quantity. Certainly, the Wien filter embodied in the Jordan mass spectrometer is a hard Wien filter because for it, the Z/r0 ratio is p. For the discussed Wien filters for the m ¼ 16 recoils with 3 charges and 0.7 MeV, the difference Z/r0 sin(Z/r0) is 2.56 x 103 for 0.08 T and 8.63x103 for 0.12 T, while for six charges and 5 MeV, the same difference takes the value 2.8 x 103 for B ¼ 0.11 T. The acceptance of the system has been measured by using a beam of ions having the energy, mass, and charge of the expected recoils. With the ERNA recoil separator, over 96% of the products created at 70 mm around the target center (energy acceptance).
6.8. St. Georges The recoil mass separator St. Georges was designed by Couder et al. (2008a) and Couder et al. (2008b) for the detection of the products of nuclear reactions with an a particle and proton capture. The cross-sections of these reactions are
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of major interest for the understanding of the burning processes in stars. The St. Georges recoil separator was conceived to have three sections with three distinct functions. The first section has the purpose of selecting the charge state of the reaction product (helium) to be detected, coming from the interaction site. This part contains two magnetic quadrupoles and a pair of magnetic dipoles. The second section ensures mass separation with the help of a Wien filter as equal- or almost-equal-momentum projectiles pass through the magnetic deflectors. Here, the projectile beam suppression occurs with a very high efficiency, to the 10-`15 level. The second section already fits the transparency for the particles with the help of five magnetic quadrupoles located there, two after another pair of magnetic dipoles, all in front of the Wien filter. The final section was included with the purpose of matching the phase space of recoils to the detector, and also to reduce further the background by the longitudinally symmetric pairs of two quadrupoles and a dipole assembly. The paramount importance of the Wien filter is obvious: ensuring the analysis after mass with a resolution of around 100, and acting as a suppressor of the primary particle beam. The Wien filter has been designed to ensure the homogeneity of both magnetic and electric fields inside the volume where reaction product ions are passing. The relative homogeneities will be of 2 x 103 in a space extending 130 mm in the dispersion plane, (the normal length is 60 mm). This will be obtained in a magnet gap of 320 mm, the electrodes being 200 mm high and located 132 mm apart. The electrodes to the vacuum chamber distances are 48 mm long. The electrodes, which have a carefully studied shape, have four homogeneizer electrodes to warranty the prescribed field uniformity, in addition to Rose shims. The highest voltage to be connected to the two main electrodes will be of 110 kV, while that to the auxiliary electrodes is 37 kV. The effective length of the Wien filter (i.e., of both magnetic and electric fields) is 1.1 m. Additionally, the magnetic field effective boundary can be adjusted to 10 mm with field clamps. In the determination of the electric field’s effective boundary, the vacuum chamber position at 218 mm from the main electrode ends was accounted for. The electric fringing fields’ harming effects were overcome by shaping the main electrodes with the auxiliary electrodes to reduce the electric field intensity similarly as the magnetic field reduction proceeds there. Toward the electrode ends, the electrode gap increases in a hyperbolic electrode manner, In this way, the electric field to magnetic field ratio variation inside the fringing fields region is reduced to 35% or less of the value inside the main fields where the Wien
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condition is satisfied (much less than for Wien filters without constructive improvements).
6.9. VAMOS The VAMOS (Variable MOde Spectrometer) (Figure 12) was created to ensure a great versatility to cover a wide range of reaction product analysis as elastic and inelastic scattering, transfer, deep inelastic, fusion evaporation reactions (Pullanhiotan 2008). The VAMOS includes a quadrupole doublet (Q1, Q2) with a high aperture, a second quadrupole with an elliptic aperture, a Wien filter (WF), and a deflecting magnet (MD) before the detector. The entire assembly ensures high acceptance, and the components can be configured according to the experiment’s needs (the magnet deflection angle can be adjusted as the target quadrupole distance). The Wien filter is activated only for a special category of experiments of type beam rejection, and for specific charge resolution by velocity analysis (http://ganil/vamos/design.html). The basic characteristics and performances of VAMOS are acceptances: solid angle 130 msr, angular 200 mr, momentum 5%, dispersion 2 cm/%, mass resolution 14%, target-detector distance 4 m, and magnet deflection less than 57 on a 1-m radius. The Wien filter having the length of 1 m with a gap of 150 mm has been designed to withstand 150 kV on the electrodes even inside the magnetic field. To ensure homogeneity of the electric field, 15 intermediary electrodes of aluminium alloy were constructed. The geometry was defined by using the computer program Poisson at first, and later by Tosca. The fields were limited to less than 60 kV/cm. The magnet was designed to ensure an 18-kG maximal field. The high voltage applied to the electrodes has been created by a formatting process, a first formation to 150 kV being accomplished in six hours. The magnetic field of 18 kG did not cause troubles on the electrodes under 140 kV [Malard et al (2000-2001)].
Det T
Q1 Q2
WF
MD
Figure 12 Main components of the VAMOS and its configuration. (For color version of this figure, the reader is referred to the online version of this book.)
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6.10. IGISOL Another homogeneous-field Wien filter is the velocity analyzer of the Ion Guide Isotope Separator On Line (IGISOL) [Nummela et al. (2002)]. It deals with the reaction products by the following successive components: the beam coming from the cyclotron enters in the ion guide, and the products penetrate inside a separating magnet and then are redirected by the “switchyard” to a radio frequency quadrupole. In this cooler, the doubly charged ions will capture most of the electrons. After deflection in a quadrupole deflector at 90 , they will come to the Wien filter, where their separation will be completed by slits, and admitted reaching the detectors. The Wien filter was assembled from permanent magnets of Norem having 2 x 2 x 0.5-in.3 pieces with remanence Br ¼ 1.12 T. The induction inside the gap, calculated with the formula 1 ð2d=hÞ 0:05 B ¼ Br ; 1þ 1 þ ð2d=hÞ 1 þ ð2d=hÞ was 0.71 T (compared to the value 0.663 T obtained by simulating with the Poisson code) with h ¼ 14.6 mm and d ¼ 12.7 mm. The electric field to pass undeviated mass 70 u ions is 2.19 kV/cm, and for mass 80 is 2.05 kV/cm for B ¼ 0.66 T. These values can be applied at 106 mbar pressure levels inside the vacuum vessel. The electric field homogeneity was ensured by nine evenly spaced strips that are 1 mm wide, located at 2-mm intervals between the two main plates. The resulting field was homogeneous enough in a 20 x 10 mm2 transversal section of the useful volume, ensuring safe handling of a 2-mm-wide beam. The distance between plates is 25 mm for nine strips at the left, and are absent on the right, with 2.6 kV simulated showing good homogeneity. The 50.5-mm-long filter was located at 276.75 mm distance from the slits.
7. MULTIPLE WIEN FILTERS A focused ion beam system ensures the use of a liquid metal ion source for application in the microfabrication of semiconductors, maskless doping, and micromachining. A four Wien filter assembly, two dispersing in one sense (first and last) and two in the opposite sense, was used to handle the beam. The two pairs of Wien filters are separated by a field-free space of 34 mm, the total length of the block being 172 mm [Kawanami, Ishitani,
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and Umemura (1989)]. The pole gap is 12 mm, while the length of the electrodes was 8 mm. The system operated at accelerating voltages of 40 kV and showed a resolution of 100 on the 58Ni2þ and 60Ni2þ peaks. A simplified analysis of a four Wien filter assembly with no field-free spaces, neglecting fringing field effects, was performed in a second-order approximation in the dispersion plane. Let us consider first four homogeneous field Wien filters with all the fields directed to be parallel (or, in other words, a single Wien filter with the total length of all four). The final image is obtained if the individual Wien filters have the following possible values of the W ¼ Z/r0 ratio: p/4, p/2, or p. The p/4 version has many nonvanishing aberrations, as follows. The p/2 case cancels all the aberrations except the xd term, which is –3, and that of d2, which is –3/2. For the four Wien filters of pr0 length, all the second-order aberrations disappear, which already happens at the intermediate image located at the halfway point of the device. For the single Wien filter of pr0 length, the x2, a2, xd and d2 are nonvanishing at 1/r0, 3/2r0, 1, and r0/4, respectively. For the other cases, all aberration coefficients vanish. If we consider the case of two end Wien filters dispersing in one sense, the central two in the opposite sense, we obtain the following aberration coefficient values for Z/r0 ¼ p/2: Axa ¼ –8, Axd ¼ 5, Aad ¼ 10r0, and Add ¼ 10r0, with others vanishing. For Z/r0 ¼ p, the assembly is second-order x, a, d aberration exempt.
Wien Filter Applications to Ions Damaschin Ioanoviciu1 and Katsushige Tsuno2 1
Physics Faculty and Institute of Doctoral Studies, Babes-Bolyai University, M. Kogalniceanu Str. Nr. 1, 400084 Cluj-Napoca Romania, National Institute for Research and Development of Isotopic and Molecular Technologies) Donath Str, Nr. 65-103, 400293 Cluj-Napoca, Romania, E-mail: [email protected] 2 Electron Optics Solutions Tsuno, 2-10-11, Mihori, Akishima, Tokyo 196-0001, Japan, E-mail: [email protected]
Contents 1. Wien Filters as Independent Mass Analyzers 1.1. The Colutron 1.2. Volcano Field Ionization Mass Spectrometer 1.3. Inhomogeneous Field Wien Filter Mass Spectrometer 2. Double-Focusing Mass Spectrometers 2.1. Mass Spectrometer of Jordan 2.2. Electric Deflector-Wien Filter Double-focusing Geometries 2.3. The Triple-focusing Mass Spectrometer of Taya et al. 2.4. Electric SectordWien Filter Mass Spectrometer 2.5. Compact Geometries with a Common Magnet Gap 2.6. Triple-focusing Compact Geometries 2.7. Double-focusing Mass Spectrometers with Simple Geometry 2.8. Simplest Compact Geometry 3. Wien Filter in Accelerator Mass Spectrometry 4. Micro Wien Filters as Leak Detectors 5. Wien Filters for Radioactive Ions 6. Reaction Product Separators 6.1. Reaction Products of Major Interest for Astrophysics 6.2. Heavy Ion Mass Spectrometer of Enge and Horn 6.3. Reaction Product Mass Separator at MSU 6.4. LISE 3 6.5. The Daresbury Recoil Separator 6.6. ARES 6.7. ERNA 6.8. St. Georges 6.9. VAMOS 6.10. IGISOL 7. Multiple Wien Filters
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) retired Advances in Imaging and Electron Physics, Volume 176 ISSN 1076-5670, http://dx.doi.org/10.1016/B978-0-12-408142-0.00005-5
Ó 2013 Elsevier Inc. All rights reserved.
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1. WIEN FILTERS AS INDEPENDENT MASS ANALYZERS As a charged particle analyzer, the Wien filter can be associated with a roughly constant-energy charged particle source to ensure mass analysis. In this very simple configuration, the Wien filter becomes a direction (angle)–focusing mass spectrometer or mass separator. For such an instrument, there are two basic characterizing quantities: the resolution and the sensitivity. While the sensitivity is closely connected to the processes happening inside the ion source, the resolution can be defined clearlydat least theoreticallydfor an ion beam with well-defined properties. The mass resolution is given by the ratio of the mass dispersion coefficient divided by the sum of the image and detector slit width, at the peak basis, or to the image width alone for the peak half height definition (Figure 1) from Ioanoviciu (1989). These, expressed in simple mathematical formulas, are Rbasis ¼
Dg Dg and R1=2 ¼ ; I þD I
where Rbasis and R1/2 are the resolution at the basis and at peak half height, respectively; Dg is the mass dispersion coefficient of the analyser; and I and D are the image and detector slit width, respectively. R1/2 is given for D ¼ I. In the figure, Ds/s must be substituted for g. At the site
Figure 1 Resolved different mass ion beams at the detector slit. Reproduced with permission.
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of the image, its width is expressed as a mixture of small terms, up to second order: I ¼ Md þ Dd d þ Dg g þ Axx d 2 þ Axa xa þ Axd xd þ Aaa a2 þ Aad ad þ Add d2 þ Ayy y2 þ Ayb yb þ Abb b2 : Besides the object slit width d, the relative energy deviation d, and mass deviation g, with respect to a main path (beam axis) particle, the string contains terms generated by the radial a and axial b angles and by the height 2y of the object slit. M is the absolute value of the analyzer magnification along the x direction. We limited the development to second-order terms, except those concerning the mass difference, because for the mass spectrometer analyzers, the total image width is important, as the resolution formula shows. The Wien filter use in the area of chemistry has been described by Aberth and Wollnik (1990).
1.1. The Colutron The colutron isotope separator got its name because of its similarity to the calutrons of the Manhattan Project. The colutron of Wahlin (1964) included an ExB (Wien) filter in a versatile device that could switch quickly from one group of isotopes to another. The first version was modified by Wahlin (1965) and continued to be under improvement and in production for various customers. The colutron consists of the following main parts which we enumerate along the ion path from creation to neutralization: the ion source followed by a three-cylinder electrostatic lens, the Wien filter, separated by a field-free space from the detector. The electrostatic lens usually is the only axially (y direction) focusing element on the ion path. The Wien filter has the role of mass dispersion. However, the Wien filter electrodes can be used to create some electrostatic field gradients by appropriately connecting the shims of the deflectors or by connecting one of the deflecting plates to the ground potential. There are 18 guard rings in the 1964 model and 22 in the 1965 model, isolated by Teflon tape (of 0.254 mm thickness in the last case). By these procedures inducing electric gradients all along the beam or by lenses at the filter ends, the beam can be rounded at the detector; i.e., the astigmatism can be eliminated. These Wien filters were assembled from pole pieces and electrodes that were 39.5 cm in length. The pole gaps were of 3.175 cm for the magnet and 3.81 for the electrodes For isotope separators, the mass dispersion is a parameter of prime
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importance. We find the mass dispersion coefficient Dg for the Wien filter field, for a free space lr0 in front of the collector: c1 s Dg ¼ l, that for Wien filters shorts with respect to the Wien 2 2 radius r0. It transformsinto W W Dg ¼ lþ , a formula that gives the distance between two 2 2 isotope beams Dizo differing in mass by DM: DM DM E Z Z Lþ ¼ ; Dizo ¼ r0 Dg M 4M Vacc 2 where Z ¼ Wr0 while L ¼ lr0. As an example, which appears on the Colutron Corporation website (www. colutron.com), we see a distance of 1.9 mm between the beam of Ca40 and Ca42 for an applied deflector field E ¼ 16,853 V/m, filter length Z ¼ 0.152 m, and L ¼ (0.3 – 0.152/2) if Vacc ¼ 5 kV (the exact relation is 1.81 mm). If DM/M ¼ 1/83, as for the Kripton isotopes 83 and 84 parameter values close to those of the 1964 and 1965 colutrons: Z ¼ 0.395 m, E ¼ 12,500 V/m, give for Vacc ¼ 7 kV Dizo ¼ 4.66 mm if L ¼ 2 m and 6.79 mm for L ¼ 3 m. The Colutron attractive properties include the adjustable dispersion and low cost. The range of working parameters includes magnetic field up to 12,000 Gauss, accelerating voltage up to 60 kV, focusing voltage from 0 to 30 kV, and electrostatic plates fed by 0 to 3 kV. As an illustrative example, the Kripton peak is obtained on ions accelerated to 25 keV when the electric field between plates is 920 V/cm.
1.2. Volcano Field Ionization Mass Spectrometer The Volcano Field Ionization mass spectrometer of Aberth (1980) is a 3.5-mlong instrument incorporating a 0.69-m Wien filter followed by a 2 m fieldfree space in front of the detector. For an accelerating voltage of 30 kV, the 2 eV energy spread ion-generating source allowed the spectrometer to be operated at 3,500 peak half height resolution at the 92 and 93 mass per charge ratio for the toluene. The usual operating resolution is 1,500 and the sensitivity 105 ion/molecule. The spectrometer operates with two lenses. As for the colutron, the mass dispersion can be varied.
1.3. Inhomogeneous Field Wien Filter Mass Spectrometer A Wien filter mass spectrometer with inhomogeneous fields Ioanoviciu and Cuna (1977) (shown in Figure 2) attained a resolution of 4,100 measured on þ 16 the C2Hþ A detected current. 4 -N2 mass 28 doublet (Figure 3) at 1.28 x 10 The Z ¼ 0.3 m effective length inhomogeneous field Wien filter was located
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Figure 2 Single focusing arrangement of an inhomogeneous-field Wien filter. Reproduced with permission.
between two 0.41-m-long, field-free spaces. Parallel electrodes were inserted in a wedge magnetic field with an axial magnetic force line radius rm ¼ 10 cm. A Nier-type ion source working at 4 kV accelerating voltage was used, and the magnetic field on the beam axis was 7,700 Oe. The axial electrostatic equipotential radius on the beam axis was estimated at 16.5 cm.
2. DOUBLE-FOCUSING MASS SPECTROMETERS A simple look at the resolution formula accounting for the image components reveals that the most harmful term is that of the first order, due to the relative energy difference (spread). The general drawback of the resolution increase of mass spectrometers was eliminated by using the double-focusing principle. First proposed by Mattauch and Herzog (1934), this principle consists of obtaining energy focusing at the image site or, in other words, cancelling both Aa and Ad at a glance. It was put in practice by combining two charged particle analyzers of different types. The most frequently encountered is the association of an electrostatic cylindrical condenser with a homogeneous magnetic field sector.
2.1. Mass Spectrometer of Jordan Jordan (1941) constructed a double-focusing mass spectrometer by combining a homogeneous fields Wien filter with a 60 deflecting magnetic sector. The basic geometric parameters of his instrument were Wien filter effective length Z ¼ 1.15 m, and magnetic field main path radius rB ¼ 0.366 m. The magnet was located symmetrically between the intermediate image situated at the
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9
8
7
6
5
4
3
2
1
0 þ Figure 3 Record of the mass 28 C2Hþ 4 -N2 mass doublet. Reproduced with permission.
Wien filter end and the detection photographic plate. The mass dispersion coefficient was Dg ¼ 1.4 m, an amazingly high resolution, especially at the level in 1941, was obtained: 28,000.
2.2. Electric Deflector-Wien Filter Double-focusing Geometries Another combination of analyzers allowing double focusing is that of a Wien filter with an electrostatic condenser that is cylindrical or toroidal. In this case, a single magnet is needed. A weight saving was assumed to result in a weight saving with respect to a Wien filter-magnetic sector configuration of Jordan’s type, Jordan (1941). The basic properties of these geometries were detailed for both the direct and the reversed geometries [see Ioanoviciu and Cuna (1974a); Figure 4]. We call direct a configuration with the Wien
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EB
E
Δ ℓ″1
ℓ′2
ℓ″2
h
Z
r0 φ ℓ′ 1
Figure 4 Double-focusing mass spectrometer geometry schematic. Reproduced with permission.
filter located after the deflector along the ion path from source to collector. As direct geometry was considered that having the electrostatic deflector before the Wien filter on the ion beam path. The possibility of combining only one angular focusing analyzer with another non-focusing or diverging analyser was considered in the discussion. The double-focusing condition, the mass dispersion coefficient, and the needed field areas, as well as the second-order aberration coefficients, were also determined. Here, we focus on only the first-order basic formulas. If we consider as “direct” the configuration with the electric condenser on the source side and the Wien filter on the detector side, let Md and Dgd be its radial magnification and mass dispersion, respectively. Then the reversed geometry magnification Mr and mass dispersion Dr will be connected with the above by the relations 1 Mr ¼ Md Dgr ¼
Dgd : Md
There are three possible analyzer combinations that can ensure double focusing: converging-converging, converging-dispersing, and convergingdiverging. The focusing conditions to be fulfilled take different forms accordingly. Only the condition for the first combination is given here. The energy focusing condition is as follows: r0e r0 1 : ð1 Me Þ ¼ 2 1 1 ne 2k Mw Here the index e refers to the electrostatic deflector (including its nonhomogeneity index ne), while Mw means the magnification of the Wien filter. The mass dispersion of the double-focusing mass spectrometer assembly is r0e Dg ¼ Mw ð1 Me Þ: 1 ne
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2.3. The Triple-focusing Mass Spectrometer of Taya et al. The mass spectrometer of Taya et al. (1978) had the purpose to ensure high sensitivity along with double focusing. This adds a new dimension: triple focusing. The instrument offered angular radial, energy, and axial focusing together; i.e., it is a design satisfying three first-order focusing conditions. The focusing of the beam along the direction normal to the dispersion plane was achieved by two means: the spherical analyzer and the unique Wien filter having oblique beam entry. No other such Wien filter played such a focusing role by using fringing fields. Otherwise, the theory of such oblique-incidence Wien filters seems to be still at the first level of the approximation stage. The triple-focusing mass spectrometer is defined ion optically at first order by the following geometric quantities: field-free space lengths, counted from the ion source toward the detector at 46 cm, 30 cm, and 43.3 cm, with the Wien filter at an effective length of 38 cm with an entrance angle of 28 (magnetic deflector definition), r0 ¼ 33.7 cm, spherical condenser deflector with 18 cm main path radius, and a 30 effective deflexion angle. The mass spectrometer was able to handle high-intensity (on mass spectrometric scale) currents of Argon ion beams from a duoplasmatron ion source with 68% transmission and 10 mA to 150 mA currents from a microvawe ion source with 5 kV acceleration. Resolutions of 120 at 10% level were obtained with 3 mm source and 1 mm collector slits, respectively. Among the various technical solutions on the prototype, the appropriate homogeneity in the electric and magnetic fields was obtained with longitudinal shims.
2.4. Electric SectordWien Filter Mass Spectrometer A Wien filter cylindrical deflector with Matsuda plates [Cuna and Ioanoviciu (1983)] was constructed and tested (Figure 5). The basic parameters of the
Figure 5 A Wien filter electric deflector geometry used for a 5,500 resolution instrument. Reproduced with permission.
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instrument were k ¼ 0.03873i /cm (divergent regime), r0 ¼ 12.25 cm, first field-free space ¼ 40.2 cm, last field-free space ¼ 34.4 cm, distance between analyzers ¼ 8 cm, effective length of the Wien filter ¼ 30 cm, radius of main path inside the electrostatic deflector ¼ 20 cm, and angle of deflexion ¼ 31 . The magnification of the first analyzer was 0.25, 1 of the second. A resolution of 5,600 was measured at half the height of the Arþ peak with a 0.1-mm-wide source slit.
2.5. Compact Geometries with a Common Magnet Gap A possibility to create compact, small, double-focusing mass spectrometers useful in space research or as RGA is to locate an electrostatic plate pair inside a magnet gap common with a magnetic deflector [Ioanoviciu and Cuna (1974b)]. These very attractive arrangements introduce an additional feature: how to master fringing fields of only electrostatic nature at the end of the Wien filter, where the pure magnetic field analyzer begins. As a general rule, knowing that the electrostatic fringing fields are less extended would lead you to expect fewer problems. However, inside the electrostatic fringing field, the Wien condition cannot be satisfied. The transition region must be reduced to a minimum. In a study of the double-focusing mass spectrometers created by introducing a parallel plate pair in a homogeneous magnet gap, the ion optical properties were analyzed, including mass dispersion, second-order aberration coefficients, and needed magnetic field area for a given beam angular opening. The magnification of such a double-focusing mass spectrometer is M ¼ –1; while the mass dispersion is Dg ¼ r0, the energy dispersion being cancelled. The field spaces, which are of equal length L, are L ¼ r0c/s, with r0 the main path radius inside the homogeneous magnetic field, s ¼ sin(4) ¼ sin(Z/r0) and c ¼ cos(4) ¼ cos(Z/r0). The basic second-order aberration coefficients are r0 1 1 1 r0 2 3 þ ðx=aaÞ ¼ 3 2sð1 þ 2c Þ þ r0 c þ þ 2s Re2 Rm1 Re1 Rm2 r 2 c 1 c3 r0 ðx=adÞ ¼ ð2 þ c c 2 þ c 3 Þ þ 0 2 s 2s Re2 r0 4 r02 ð1 cÞ2 r02 1 c c 3 3 2 ðx=ddÞ ¼ ð2c 4c þ 2c þ 4c 3Þ þ þ : 4 8sRe2 2sRm2
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Re1, Re2, Rm1, Rm2 are the radii of the boundaries of the electric (e) and magnetic (m) of the electrodes and pole pieces. “1” means “entry,” while “2” means “exit limit.” The area covered in the median plane by a beam of a 2a radial angular opening is the same inside the pure magnetic field as inside the Wien filter: 2ar20,which allows us to establish the needed area for the pole faces. Estimations were made for r0 ¼ 5 cm, source slit width of 0.25 mm, a ¼ 1/20, and d ¼ 1/100. If boundaries are selected to cancel the (x/aa) aberration, then resolutions around 100 can be expected, while for straight boundaries, around 50 can be expected.
2.6. Triple-focusing Compact Geometries Another study [Ioanoviciu et al. (1992)] explored the possibility of using oblique entry and exit for homogeneous magnetic fields. The considered geometries are conceived to ensure stigmatic focusing by using oblique incidence at the entry end of the Wien filter and at the exit from the homogeneous magnetic field. The first-order conditions to be satisfied are: L ¼
1 Z and 4 ¼ tan 4 tan ε r0
f or My ¼ 1 when Dg ¼ Ltan f and tan ε ¼
1=4 þ tan f f or My ¼ þ1 2
while tan ε ¼
tan 4 if My ¼ 1: 2
Two specific cases were calculated: • For the configuration with positive unitary axial magnification, the following basic parameters were selected: 4 ¼ 88 , ε ¼ 86.09 , and L ¼ 0.071r0. The basic aberration coefficients are (x/aa) ¼ 12.88r0, (x/ad) ¼ 6.31r0, (x/dd) ¼ –0.95r0, (x/yy) ¼ –412/r0, (x/yb) ¼ –903, and (x/bb) ¼ –1.539r0. A calculation for a stigmatic double-focusing geometry, with axial magnification –1, ensures much more advantageous aberration coefficients. Its basic parameters are 4 ¼ 60 , ε ¼ 40.89 , and L ¼ 1.1547r0, while the aberration coefficients (x/aa) ¼ 20.0r0, (x/ad) ¼ 8.948r0, (x/dd) ¼ –0.219r0, (x/yy) ¼ –0.717/r0, (x/yb) ¼ –0.538, and (x/bb) ¼ –3.333r0.
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• Other configurations put plane parallel plate condensers inside wedge magnetic field gaps for normal entry and exit. The relations contain an additional free parameter K, the ratio of the main particle momentum to that of one moving on a circular path in a specified point of the magnetic field. A numerical example will be reproduced: basic parameters 4 ¼ 110 , Z/r0 ¼ 1.891, K ¼ 0.5867, L2 ¼ 0.241r0, L1 ¼ 0.577r0, Dg ¼ 1.10r0, with the aberration coefficients (x/aa) ¼ 3.119r0, (x/ad) ¼ 3.183r0, (x/dd) ¼ –1.314r0, (x/yy) ¼ –0.57/r0, (x/yb) ¼ –0.451, and (x/bb) ¼ 0.17r0.
2.7. Double-focusing Mass Spectrometers with Simple Geometry The simplest double-focusing mass spectrometer geometries result by introducing a pair of parallel plates inside the gap created by two longer rectangular pole pieces that are parallel [Ioanoviciu (1995)]. Then the ion beam normally approaches the Wien filter entry limit and leaves the homogeneous magnetic field, laterally obliquely at an exit angle ε (Figure 6). The deflexion of the beam and this oblique exit angle must satisfy the relation: ε ¼ 4-p/2, while double focusing is obtained when 4 ¼ Z/r0. The first-order parameters are Dg ¼ r0 sin2 f M ¼ sin2 f y=y ¼ 1 þ cos2 f ðy=bÞ ¼ 2r0 ½fðy=yÞ þ cot anf; while the aberration coefficients of second order are
L1
Z r0 θ
L2
Figure 6 Layout of the compact, oversimplified, double-focusing mass spectrometer. (For color version of this figure, the reader is referred to the online version of this book).
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r0 3 1 1 1 1 x=aa ¼ þ þ þ c 2s Re1 Rm1 Rm2 s3 Re2 1 3c 2 1 þ ð3 mÞc 2 þ 3 2m þ 2 2s2 r0 1 2c 3 3 sm ðc 1Þ þ fm ð2 þ cÞ ðx=adÞ ¼ þ 3 2 Re2 s Rm2 4 4 1 ðc 1Þð3c 4 þ 5c 3 þ 4c 2 6c 4Þ 2s3 r0 1 4c 3 3 s2 m sðc 1Þ2 þ scfm þ 3 ðx=ddÞ ¼ ð2c þ 1Þ 8 Re2 s Rm2 8 8 þ
þ
1 ð1 cÞð2c 3 þ 7c 2 2c 3Þ 4ð1 þ cÞ
2 c c2 ðx=yyÞ ¼ sGyy þ 1 þ c 2 Fyy þ ð1 þ c 2 Þ Fyb þ 2 Fbb s s c ðx=ybÞ ¼ sGyb þ 4ð1 þ c 2 ÞFyy fð1 þ c 2 Þ þ s 1 2fc 2c c 2 2 þ ð1 þ c Þ 2 þ þ fð1 þ c Þ þ Fyb s s s s c 1 þ 2 2 þ 2fc Fbb s s h c i2 ðx=bbÞ ¼ sGbb þ 4 fð1 þ c 2 Þ þ Fyy s 2 c 1 2 þ fð1 þ c Þ þ þ 2fc Fyb s s s 1 1 2 þ 2 2fc þ Fbb ; s s with the abbreviations: Gyy
r0 1 1 1 s þ ð3m 1Þ ¼ þc þ 2 Re2 Re1 Rm1 2
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2c r0 F Gyy þ 3ð1 cÞm s 2Re2 c 2 c 1 r0 F2 ¼ Gyb Gyy þ 3mF þ 3m s 2Re2 s s 2 Gyb ¼
Gbb
1 þ c2 r0 c Fyy ¼ 2 2Rm2 s2
Fyb ¼ 2FFyy þ
Fbb ¼ F2 Fyy þ F
c3 s
c 3 s2 : s 2
2.8. Simplest Compact Geometry A double-focusing compact mass spectrometer resulting by replacing half of the Dempster 180 magnetic deflector by an appropriate Wien filter in the same gap was constructed and tested [Ioanoviciu and Cuna (1995), and see Figure 7]. A (p/2)56 mm long Wien filter has been created in front of a 56 mm main path radius magnetic 90 deflector. The 88-mm-long iron plates were slid inside the vacuum chamber containing the electrodes in a sandwich structure. The electrodes were profiled in a way that creates a field close to homogeneous. The plates were located finally at an 8-mm gap. The aberration coefficients of the entire double-focusing mass spectrometer can be influenced only by non-homogeneities of the electric field created by small height plates, and an almost homogeneous magnetic field created between wide pole pieces. The ion source was immersed inside the magnetic field; therefore, the electric fringing fields being present at both the entry and exit of the Wien filter. Accounting for these structural properties, the ion optical properties of the apparatus can be synthetized as follows:
Z r0 Φ
Figure 7 Half of a Dempster mass spectrometer deflector combined with a Wien filter to ensure double focusing. (For color version of this figure, the reader is referred to the online version of this book).
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Radial magnification M ¼ –1, mass dispersion coefficient Dg ¼ r0; second-order aberration coefficients: Aaa Add
r0 r0 m 3p ¼ 1mþ Aad ¼ 2 þ 1 2Re 2Re 2 4 1 m r0 ¼ 3þ þ 4 2 2Re Ayy ¼
Abb
3m r0 2Re 2
Ayb ¼ 3m
pr0 2Re
p p2 r0 ¼ 3m 1 8Re 2
In these formulas, the non-homogeneity coefficient m has been defined in the manner of Wollnik et al. (1972): m ¼
r02
d 1 ; dx Rax
with Rax as the radius of curvature of the potential surface passing the beam axis. The attempt to ensure electric field homogeneity was associated by creating straight boundaries to the electric electrode limits. For these particular conditions, the aberration coefficients were simplified as the mass resolution R1/2 formula: Ayy ¼ Ayb ¼ Abb ¼ 0 while Aaa ¼ 1 . Aad ¼ 2 . Add ¼
3 4
R1=2 ¼
: 1 s þ a2 þ 4ad þ 0:75d2
For a source object slit width sr0 of 0.25 mm, a radial beam opening angle a ¼ 1.5 . For d ¼ 0.05, which is a pretty realistic value, a resolution of 175 was predicted and measured in the methane mass spectrum. Around 1 keV ions were detected when ionizing electron currents of 260 mA were used. Ion currents of the order of 1010A were collected with a 0.1-mm-wide, 8-mm, high-source slit.
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3. WIEN FILTER IN ACCELERATOR MASS SPECTROMETRY The Wien filter also was used in accelerator mass spectrometry. A Wien filter was included in the accelerator mass spectrometry system of the Australian National University to improve mass resolution [King et al. (1997)]. The basic layout of the assembly includes a caesium sputtering ion source. The first 90 deflecting magnet selects the aluminium ions entering the accelerator column, next in another 90 deflector are measured by a gas ionization detector. The system determined the presence of a 26Al isotope in biological materials as aluminium oxide or phosphate from blood or soft tissues. The Wien filter was inserted between the last deflector and the detector, that was set to leave undeviated 26Al ions. It reduced substantially the levels of other ions in the mass spectrum of C, O, and Mg.
4. MICRO WIEN FILTERS AS LEAK DETECTORS Micromachined Wien filters Sillon, Baptist (2002) were created to serve as leak detectors. Such small instruments would allow the increase of work pressure for leak detection. As the molecule free path at 0.5 Pa is about 1 cm, this should be the length of the mass analyser. Chips with six channels of 200 mm and 1 cm long were prepared in silicone wafers. Tests were performed on He with a magnetic field of 5,500 G, the distance between rods being 200 mm with 6.37 V for 70 eV ion acceleration. Good separation has been obtained for the He peak, but the separation of 14 þ N from 28Nþ 2 is bad. Detection on the plate showed a sensitivity of 107A/Pa. The filter dimensions (lateral) are 200 mm x 400 mm, and the ion entrance diameter is 150 mm.
5. WIEN FILTERS FOR RADIOACTIVE IONS Simulations of Wien filters destined for mass analysis of radioactive ions were reported by Pierret et al. (2008). The single-filter solution has been discarded as unsatisfactory. The solution of two consecutive Wien filters, the mass dispersion planes normal each other was recommended: two consecutive Wien filters having the dispersion plane rotated by 90 one with respect to the another. The two filters of 400 mm length each should be located 100 mm apart. A beam from a MONO 1000 ECR ion source was
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considered. The simulated configuration contained the MONO 1000 ECR ion source, an unipotential lens, and the Wien filters. The use of the system as a mass separator, with one Wien filter of a 750-mm-long beam of 180 pmm mrad and 150 p mm mrad emittance at 15 kV, gave good separation for masses of 20 u, 34 u, and 79 u. The system was considered as a mass separator to eliminate part of the undesired ions. Electrodes symmetrically fed by 2,000 V were simulated. As an on-line mass analyser, the two Wien filters of 400 mm placed 10 mm apart should be used. Good simulated results were obtained for a mass of 79 u and for a 5-mm aperture with about 1% transmission.
6. REACTION PRODUCT SEPARATORS 6.1. Reaction Products of Major Interest for Astrophysics The purpose of the recoil mass separators is to distinguish the focusing plane among the various reaction products after their mass, and to suppress the primary projectiles from the beam. This separation is accomplished by Wien filters, among other types of analyzers [Davids (2003)]. The knowledge of the cross sections of the nuclear a particle and proton capture reactions are of paramount importance in the description of the stellar processes from red giants to supernova explosions, and in building a correct image of how various elements were created in the universe. Many efforts have been made over time to determine the cross-section of the 12 C(a,g)16O reaction with an accuracy of better than 10%. Let us see what ion-optical conditions must satisfy the recoil mass analyzers to approach this goal. The projectile ions and the recoil ones have almost identical momenta. Projectiles and recoils of identical momenta cannot be distinguished after the collision. If the recoils from the reaction will be detected only partially, errors will be introduced in the resulting cross-section value. Based on these preliminary observations, a careful selection of the projectiles is recommended, with the suppression of those that are identical to the followed reaction products. The recoil mass analyzer must offer complete acceptance for the emitted recoils Rogalla et al (2003), these arising inside of a cone of half angle q: q ¼ arc tan[Ug/(pc)] and having a relative momentum spread of Dp/p. Here, Ug is the emitted g ray photon energy resulting from the capture process, and p the recoil, as well as the projectile momentum. For the specific case of the 12C(a,g)16O capture reaction, Ug ¼ 7.9 MeV, then q ¼ 1.8 and Dp/p ¼ 0.062 for an energy of U ¼ 0.7 MeV, while q ¼ 1 ,
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Dp/p ¼ 0.03 for U ¼ 5 MeV. As the cross sections we are looking for are of the order of s ¼ 1 pb, the projectiles contaminating the primary beam must be in a concentration of less than 1018 from those generating the recoils (or less than 1014 if the detector ensures itself an additional discrimination from the projectiles) Recoil separators handling high energy charged particles result in big installations ensuring compensation of electric and magnetic deviations successively or simultaneously in Wien filters [Wollnik (1987)].
6.2. Heavy Ion Mass Spectrometer of Enge and Horn In Enge and Horn (1977), an energy-mass spectrograph for heavy ions resulting from fusion reactions was constructed, tested, and used at Brookhaven National Laboratory (Figure 8). The spectrograph combined a Wien filter with a split pole magnetic spectrograph (SP1, SP2). The Wien filter, WF, has the dispersion plane normal to the deflection plane of the spectrograph. The magnetic field inside the Wien filter has been directed against the deflection sense inside the spectrograph. Special attention was paid to the fringing field in an effort to make to reconcile both the electric and magnetic field distributions (at least as a common effective boundary). Expressions for the offset resulted at the entry and exit boundaries were derived (Salomaa and Enge 1977). The instrument had a horizontal plane acceptance of 2 mr, in the vertical plane of 8 mr with the total solid angle 0.64 msr, horizontal dispersion 2.15 m, vertical 0.37-0.52 m, horizontal magnification 0.26–0.342 (ends of focal plane), and vertical magnification 0.662–1.867. The best resolution
Figure 8 Enge’s Wien filter split-pole energy mass spectrograph. (For color version of this figure, the reader is referred to the online version of this book).
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attained was 425 (360 for evaporation residues from the reaction 32Sþ70Ge at 3 ). The Wien filter was put together from pole pieces with a 1.016-m length and a 152-mm gap. In the gap were installed two 1.11-m-long plates (which is longer than the magnet pole pieces) in an attempt to match the electric and magnetic fringing fields to each other. The plates were fed by voltages up to 60 kV. The magnetic field can be increased up to 4,000 G to cope with the primary beam particles moving along the evaporation residues. As the velocity of these last items is two or four times lower than that of the primaries depending of the products, these should be stopped inside the Wien filter on four berilium-covered baffles attached to one stainless steel plate.
6.3. Reaction Product Mass Separator at MSU The Reaction Product Mass Separator (RPMS) at Michigan State University in East Lansing [Harwood and Nolen (1981)] was constructed to study nuclei far from the stability valley. The separator (Figure 9) ensures triple focusing at the focusing plane; i.e., both radial and axial angular focusing, as well as momentum focusing of the first order. The projectiles from the K500 Cyclotron hit the target in front of the separator. The two magnetic quadrupoles Q1 and Q2 in the RPMS first focus the resulted and primary ions to the Wien filter (WF) of an unusual 5-m length. Next, a deflecting magnet (MD) is located in front of another magnetic quadrupole doublet (Q3, Q4) and arrives to the detector (Det), flying a total path of 14.3 m. Depending upon the measurement, the products can be observed directly or deviated, the last quadrupole doublet and detector moving accordingly. For the prototype, the maximum allowed energy was 30 MeV/u a mass resolution of 100 at the peak base level being presumed for a 1-msr solid angle and 16% energy range, respectively, 200 for energy range
Figure 9 Basic configuration of the RPMS at MSU. (For color version of this figure, the reader is referred to the online version of this book).
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reduced twice. The parameters anticipated for the next development phase of the RPMS were length 30 m, maximum energy 300 MeV/u, accepted solid angle 0.8 msr, energy acceptance 8%, dispersion 8.5 mm/%, mass resolution 180 to 320 for 0.6 to 0.4 msr, and a 2 to 4% energy spread.
6.4. LISE 3 The program dealing with super heavy elements at GANIL involves the Wien filter called LISE3. The Wien filter selects charged particles from a reaction chamber that uses two wheels with targets and with carbon stripper foils, respectively. The LISE3 Wien filter has an angular acceptance of 36p mrad. It has two halves: the upper electrode placed at a position 2 cm higher to admit beam particles is suppressed without hitting electrodes and generating background. The undesired beam is absorbed on a collimator composed from two pairs of mobile slits. The background suppression is achieved by a deflecting magnet located before detectors (carbon foils and MCP detectors) [Grevy et al. (2002)].
6.5. The Daresbury Recoil Separator The Daresbury recoil separator was used by Rogers et al. (2008) to study reactions of (p,g) type proton capture products. The Oak Ridge National Laboratory at the Holifield Radioactive Ion Beam Facility A dipole magnet preceding a last three-quad group was placed between the target and the detector groups of quads before and after the two consecutive Wien filters.
6.6. ARES The Astrophysic Recoil Spectrometer (ARES) of the Cyclotron Research Center in Louvain-la-Neuve (Figure 10). Couder et al. (2003) was designed as a tool to determine the cross sections of the (p,g) capture reactions.
Figure 10 Assembly scheme of the ARES. (For color version of this figure, the reader is referred to the online version of this book).
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We distinguish a part of the system creating the projectile beam that interacts with the target T (of CH2, polyethylene) followed by the reaction product mass separator. The projectiles are accelerated to 0.2–0.8 MeV/u energies, focused on the target by a doublet of magnetic quadrupoles. The reaction product separator focuses first by a quadrupole triplet (QT) on the ions, a magnet MD deflecting them by 40 before a selection on a slit. Next, a quadrupole doublet (QD1) precedes the 1-m-long Wien filter (WF), which in turn sends the velocity-separated products on a new slit system. Finally the separated products come to the last quadrupole doublet (QD2) in front of an DE-E detector (Det). The product ions from proton captures in inverse kinematics are emitted in a cone with about a 10-mrad angle half opening, the beam opening increasing along its path due to multiple scattering. During the tests performed on 12F2þ ions, the transmission of ARES was around 70%. This transmission was maintained for a particularly broad range of applied fields on the Wien filter: 2.5-20 kV/cm and 176–1407 G in constant ratio. When transmitted the 20Ne7þ, the deflecting magnet field was changed by 0.4% compared to 19F ions, while that of the Wien filter was increased by 6%.
6.7. ERNA The recoil separator at Bochum (Figure 11) was called the European Recoil Separator for Nuclear Astrophysics (ERNA) [Rogalla et al. (1999b)]. A sputtering ion source working at 130 kV is used to inject through a deflecting magnet the created negative ions into the 4 MV Tandem accelerator. There, ions are stripped, and the resulted ions must be focused
Figure 11 Schema of the basic components of the ERNA. (For color version of this figure, the reader is referred to the online version of this book).
Wien Filter Applications to Ions
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and selected before being directed against a jet gas target [of He gas if (a,g) reactions are studied]. The process of projectile purification is directed to eliminate the wrong charge state and undesired mass projectiles. It is performed by the following ion-optical components located along the beam path: a doublet of magnetic quadrupoles (QD1), a first Wien filter (FW1), an analyzing magnet (MD1), a switching magnet, a second quadrupole doublet (QD2), and a second Wien filter (WF2). The first Wien filter selects ions according to their velocities, the magnet separates the various electric charge states, and finally, the second Wien filter eliminates the undesired mass projectiles from the primary ion beam. This is the purificating part of the assembly and is not a constituting section of the recoil separator itself [Rogalla et al. (1999a)]. A simplified configuration for beam purification reported by Rogalla et al. (1999a) was assembled, where after the tandem accelerator, the analyzing magnet directs the projectiles through a quadrupole doublet after an aperture through a Wien filter to the telescope detector. The Wien filter, which is obviously homogeneous, uses two parallel electrodes of 0.85 m long and 48 mm wide, located over and under the beam. These electrodes were fed by 20 kV, applied symmetrically with respect to the ground. The pole pieces were only 0.79 m long, with a width of 117 mm and a gap of 110 mm. The single Wien filter indicates that a purification of the 12C3þ beam of 16O ions can be obtained up to a 2 x 1017 level. As it is certainly not enough, a second Wien filter was included in the purification part. The assembly concentrating the projectiles onto the jet create a minimal size object for the ERNA recoil separator itself. This last uses a magnetic quadrupole triplet (QT) to shape the virtual beam of recoils from the gas target onto a slit system followed by the third Wien filter (WF3). This Wien filter has the important role of mass-analyzing the recoils. A 60 deflector magnet (MD2) preceded by a focusing quadrupole (Q), slits, and a Faraday cup with a last doublet, direct the reaction product ions towards the fourth Wien filter (WF4) in a parallel beam to the detector telescope (Det) [Gialanella et al (2007)]. The last deflecting magnet and Wien filter ensure a supplementary momentum and mass separation, as well as the elimination of the background ions resulting from the projectile beam scattering on residual gas and on the various slits along the beam path. The third Wien filter has deflectors of 0.5 m length, 120 mm wide, located 70 mm apart, creating an electric field directed horizontally and plates fed by 50 kV stable voltage units. The magnet pole faces of the Wien filter have the same 0.5-m effective length, being 320 mm wide and creating a 100-mm gap.
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For 16O3þ 0.7 MeV ions, the needed field was calculated to be of 0.08 T, while for 16O6þ ions of 5 MeV, it is 0.11 T. The last Wien filter on the recoil path, from Cal Tech, has the geometry defined by 0.578-m effective lengths, the condenser plates of 63 mm width creating a horizontally directed electric field in a 70-mm gap, while the pole faces of 77 mm width have a 95-mm gap. The calculated magnetic fields to be applied (16O3þ recoils of 0.7 MeV and 16 6þ O of 5 MeV) are 0.12 T and 0.11 T, respectively [Rogalla et al. (1999b)]. The ion optical optimization of the recoil separator has been performed with the help of the computer code COSY Infinity, up to fourth-order small quantities. From the diagrams of the ion paths, we can see how act the various recoil separator components. The quadrupole triplet next to the target horizontally acts as a convergent/divergent/convergent combination of quadrupole lenses, creating a waist in this plane at the single quadrupole site. The third Wien filter has a weak focusing action. The diverging trajectories remain so through the magnetic dipole being drastically refocused by the first quadrupole in the quadrupole doublet. Next, the beam remains almost parallel. It maintains this trend in the last Wien filter and through the last quadrupole. The beam is directed parallel in both horizontal and vertical planes toward the telescope detector. The focusing role of the Wien filter is limited in the horizontal plane, as naturally it is absent in the vertical one. We can define Wien filters as being weak if their length Z is small compared to the cyclotron radius r0. Then, sin (Z/r0) – Z/r0 will be a small quantity. Certainly, the Wien filter embodied in the Jordan mass spectrometer is a hard Wien filter because for it, the Z/r0 ratio is p. For the discussed Wien filters for the m ¼ 16 recoils with 3 charges and 0.7 MeV, the difference Z/r0 sin(Z/r0) is 2.56 x 103 for 0.08 T and 8.63x103 for 0.12 T, while for six charges and 5 MeV, the same difference takes the value 2.8 x 103 for B ¼ 0.11 T. The acceptance of the system has been measured by using a beam of ions having the energy, mass, and charge of the expected recoils. With the ERNA recoil separator, over 96% of the products created at 70 mm around the target center (energy acceptance).
6.8. St. Georges The recoil mass separator St. Georges was designed by Couder et al. (2008a) and Couder et al. (2008b) for the detection of the products of nuclear reactions with an a particle and proton capture. The cross-sections of these reactions are
Wien Filter Applications to Ions
173
of major interest for the understanding of the burning processes in stars. The St. Georges recoil separator was conceived to have three sections with three distinct functions. The first section has the purpose of selecting the charge state of the reaction product (helium) to be detected, coming from the interaction site. This part contains two magnetic quadrupoles and a pair of magnetic dipoles. The second section ensures mass separation with the help of a Wien filter as equal- or almost-equal-momentum projectiles pass through the magnetic deflectors. Here, the projectile beam suppression occurs with a very high efficiency, to the 10-`15 level. The second section already fits the transparency for the particles with the help of five magnetic quadrupoles located there, two after another pair of magnetic dipoles, all in front of the Wien filter. The final section was included with the purpose of matching the phase space of recoils to the detector, and also to reduce further the background by the longitudinally symmetric pairs of two quadrupoles and a dipole assembly. The paramount importance of the Wien filter is obvious: ensuring the analysis after mass with a resolution of around 100, and acting as a suppressor of the primary particle beam. The Wien filter has been designed to ensure the homogeneity of both magnetic and electric fields inside the volume where reaction product ions are passing. The relative homogeneities will be of 2 x 103 in a space extending 130 mm in the dispersion plane, (the normal length is 60 mm). This will be obtained in a magnet gap of 320 mm, the electrodes being 200 mm high and located 132 mm apart. The electrodes to the vacuum chamber distances are 48 mm long. The electrodes, which have a carefully studied shape, have four homogeneizer electrodes to warranty the prescribed field uniformity, in addition to Rose shims. The highest voltage to be connected to the two main electrodes will be of 110 kV, while that to the auxiliary electrodes is 37 kV. The effective length of the Wien filter (i.e., of both magnetic and electric fields) is 1.1 m. Additionally, the magnetic field effective boundary can be adjusted to 10 mm with field clamps. In the determination of the electric field’s effective boundary, the vacuum chamber position at 218 mm from the main electrode ends was accounted for. The electric fringing fields’ harming effects were overcome by shaping the main electrodes with the auxiliary electrodes to reduce the electric field intensity similarly as the magnetic field reduction proceeds there. Toward the electrode ends, the electrode gap increases in a hyperbolic electrode manner, In this way, the electric field to magnetic field ratio variation inside the fringing fields region is reduced to 35% or less of the value inside the main fields where the Wien
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Damaschin Ioanoviciu and Katsushige Tsuno
condition is satisfied (much less than for Wien filters without constructive improvements).
6.9. VAMOS The VAMOS (Variable MOde Spectrometer) (Figure 12) was created to ensure a great versatility to cover a wide range of reaction product analysis as elastic and inelastic scattering, transfer, deep inelastic, fusion evaporation reactions (Pullanhiotan 2008). The VAMOS includes a quadrupole doublet (Q1, Q2) with a high aperture, a second quadrupole with an elliptic aperture, a Wien filter (WF), and a deflecting magnet (MD) before the detector. The entire assembly ensures high acceptance, and the components can be configured according to the experiment’s needs (the magnet deflection angle can be adjusted as the target quadrupole distance). The Wien filter is activated only for a special category of experiments of type beam rejection, and for specific charge resolution by velocity analysis (http://ganil/vamos/design.html). The basic characteristics and performances of VAMOS are acceptances: solid angle 130 msr, angular 200 mr, momentum 5%, dispersion 2 cm/%, mass resolution 14%, target-detector distance 4 m, and magnet deflection less than 57 on a 1-m radius. The Wien filter having the length of 1 m with a gap of 150 mm has been designed to withstand 150 kV on the electrodes even inside the magnetic field. To ensure homogeneity of the electric field, 15 intermediary electrodes of aluminium alloy were constructed. The geometry was defined by using the computer program Poisson at first, and later by Tosca. The fields were limited to less than 60 kV/cm. The magnet was designed to ensure an 18-kG maximal field. The high voltage applied to the electrodes has been created by a formatting process, a first formation to 150 kV being accomplished in six hours. The magnetic field of 18 kG did not cause troubles on the electrodes under 140 kV [Malard et al (2000-2001)].
Det T
Q1 Q2
WF
MD
Figure 12 Main components of the VAMOS and its configuration. (For color version of this figure, the reader is referred to the online version of this book.)
Wien Filter Applications to Ions
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6.10. IGISOL Another homogeneous-field Wien filter is the velocity analyzer of the Ion Guide Isotope Separator On Line (IGISOL) [Nummela et al. (2002)]. It deals with the reaction products by the following successive components: the beam coming from the cyclotron enters in the ion guide, and the products penetrate inside a separating magnet and then are redirected by the “switchyard” to a radio frequency quadrupole. In this cooler, the doubly charged ions will capture most of the electrons. After deflection in a quadrupole deflector at 90 , they will come to the Wien filter, where their separation will be completed by slits, and admitted reaching the detectors. The Wien filter was assembled from permanent magnets of Norem having 2 x 2 x 0.5-in.3 pieces with remanence Br ¼ 1.12 T. The induction inside the gap, calculated with the formula 1 ð2d=hÞ 0:05 B ¼ Br ; 1þ 1 þ ð2d=hÞ 1 þ ð2d=hÞ was 0.71 T (compared to the value 0.663 T obtained by simulating with the Poisson code) with h ¼ 14.6 mm and d ¼ 12.7 mm. The electric field to pass undeviated mass 70 u ions is 2.19 kV/cm, and for mass 80 is 2.05 kV/cm for B ¼ 0.66 T. These values can be applied at 106 mbar pressure levels inside the vacuum vessel. The electric field homogeneity was ensured by nine evenly spaced strips that are 1 mm wide, located at 2-mm intervals between the two main plates. The resulting field was homogeneous enough in a 20 x 10 mm2 transversal section of the useful volume, ensuring safe handling of a 2-mm-wide beam. The distance between plates is 25 mm for nine strips at the left, and are absent on the right, with 2.6 kV simulated showing good homogeneity. The 50.5-mm-long filter was located at 276.75 mm distance from the slits.
7. MULTIPLE WIEN FILTERS A focused ion beam system ensures the use of a liquid metal ion source for application in the microfabrication of semiconductors, maskless doping, and micromachining. A four Wien filter assembly, two dispersing in one sense (first and last) and two in the opposite sense, was used to handle the beam. The two pairs of Wien filters are separated by a field-free space of 34 mm, the total length of the block being 172 mm [Kawanami, Ishitani,
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and Umemura (1989)]. The pole gap is 12 mm, while the length of the electrodes was 8 mm. The system operated at accelerating voltages of 40 kV and showed a resolution of 100 on the 58Ni2þ and 60Ni2þ peaks. A simplified analysis of a four Wien filter assembly with no field-free spaces, neglecting fringing field effects, was performed in a second-order approximation in the dispersion plane. Let us consider first four homogeneous field Wien filters with all the fields directed to be parallel (or, in other words, a single Wien filter with the total length of all four). The final image is obtained if the individual Wien filters have the following possible values of the W ¼ Z/r0 ratio: p/4, p/2, or p. The p/4 version has many nonvanishing aberrations, as follows. The p/2 case cancels all the aberrations except the xd term, which is –3, and that of d2, which is –3/2. For the four Wien filters of pr0 length, all the second-order aberrations disappear, which already happens at the intermediate image located at the halfway point of the device. For the single Wien filter of pr0 length, the x2, a2, xd and d2 are nonvanishing at 1/r0, 3/2r0, 1, and r0/4, respectively. For the other cases, all aberration coefficients vanish. If we consider the case of two end Wien filters dispersing in one sense, the central two in the opposite sense, we obtain the following aberration coefficient values for Z/r0 ¼ p/2: Axa ¼ –8, Axd ¼ 5, Aad ¼ 10r0, and Add ¼ 10r0, with others vanishing. For Z/r0 ¼ p, the assembly is second-order x, a, d aberration exempt.