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Design modifications to reduce duodecapole components in the fringe field region of magnetic quadrupole lenses
NUMB
Nuclear Instruments and Methods in Physics Research B77 (1993) 35-38 North-Holland
Beam Interactions with Materials&Atoms
Design modifications to reduce duodecapole field region of magnetic quadrupole lenses
components in the fringe
G.R. Moloney, D.N. Jamieson and G.J.F. Legge School of Physics,Universityof Melbourne,Park&e 3052,Australia
An investigation into minimisat~on of the duodecapole (fifth order) fringe field components of magnetic quad~~le lenses has been conducted at Melbourne. Detailed measurement and analysis of the fringe field region of the Melbou~e magnetic quadrupole lenses has revealed the presence of significant fifth order multipole fields. A program of design modifications to the pole tip profiles has been conducted with the aim of reducing the duodecapole component of the fringe field. The design changes made and the results of detailed magnetic field mapping are presented.
1. Introduction
A well constructed magnetic quadrupole lens should suffer no ~ntam~ation by parasitic sextupole and octupole magnetic fields. It will, in general, suffer contamination by higher order multipole fields. The most significant of these are the duodecapole and 20-pole components. The 20-pole components have a very high order radial dependence (B, a r’). Hence the 20-pole magnetic field is only significant very close to the pole tips. The duodecapole components have a lower order radial dependence (B, a ?), and are more significant at lower values of r. In general, the ions in a microprobe beam do not pass close to the pole tips. Hence the duodecapole components are of most significance in dete~ining ion trajectories. The duodecapole component of the magnetic field within the lens will contribute to the fifth order aberration coefficients of the lens. Parzen [l] showed the duodecapole and 20-pole contamination could be minimised by using cylindrical pole tips, with a suitable ratio of pole tip radius to lens bore radius. Magnetic field mapping of the fringe field region of the Melbourne quadrupole lenses has shown the presence of significant duodecapole cont~ination in the fringe field region of magnetic quad~pole lenses 121. The amplitude of the duodecapole profile can increase up to several orders of magnitude in the fringe field region of a magnetic quadrupole lens. These fringe field components will contribute to the fifth order aberration of the lens. The new two-stage proton microprobe [3], under construction at Melbourne, will be very sensitive to lens aberrations. We wish to reduce the fifth order aberrations of the lenses due to the fringe field duodecapole components.
The grid shadow method has been used extensively by Jamieson 14-71 to measure the aberrations of microprobe systems. This method, however, yields no information on the axial profiles of the multipole components of a lens. The axial profile of all m~tipole field components in a magnetic quadrupole lens can be determined by detailed magnetic field measurements. At Melbourne we have performed such measurements with a Hall effect probe mounted on a computer controlled translation and rotation stage. The small sampling area of the Hall effect probe (= 1 mm2) enables the complex multipole profiles to be determined to a high degree of accuracy. Following Szilagyi @I,the magnetic scalar potential, u, may be expressed in the cylin~cal coordinate system, (I, IY, z), as a Fourier series in cy, u(r, a, 2) = _,[a-(r, +b,(r,
z) cos(mcu) z) sin(mcr)],
(1)
where a,(r,
2) = 2 Am,k(z)r2k+m, k=O
bm(r, 2) = 2
Bm,k(z)r”k+m,
k=O
and (-l)%! A
B
m,k = 4%!(m
+ k)!
u;Zk’( z),
(3)
(-qkrrz! m,k = 4%!(m
0168-583X/93/$~.~ 0 1993 - Elsevier Science Publishers B.V. All rights reserved
+ k)!
V@k’( Z))
I. TECHNOLOGY
where the superscripts, (2k), on U and W denote the 2kth derivative with respect to z. The U,(z) and W,(z) represent the profiles of the mth order multipole in the multipole expansion. For a magnetic quadrupole lens, assuming no constructional or excitational asymmetries, u satisfies the foltowing symmetry conditions, zL(r,a,
z)=zL--Y,ff, = --u(r,
.z)=L1(r,(7i-/2)-ff,z) -a,
(4)
m = 2, 6, 10, 14, . . . .
&W;(z)r’+
&WF(z)r6]
+ W6(z)r” sin(&). of the
magnetic
cy, z) = V$L(r, cr, z).
(6) field,
(7)
Hence, to sixth order in r, B,(r,
r-R
/
60’
!
@
f 7.25nm
1 I
sured showing the radius which was cut into the pole ends. The bore radius of the lens is 6.35 mm. Pole tip profiles were measured for values of R = 0, 1.5875, 3.175, 4.7625, 6.35, 7.9375 and 9.525 mm.
in r, for an ideal magnetic
The radial component B,.(r, a, z>, is defined by BJr,
.~
(5)
u(r, rr, 2) = [W,(z)?Xsin(2a)
AXIS
Pig. 1. Diagram of the pole pieces used in the lenses mea-
z).
The only terms in u satisfying these symmetry conditions are those such that,
Thus, to sixth order quadrupole lens,
-_. -7 v4 I-=BEAM
cl!, z) = [2W,(z)r
- +w;l(z)r”
+ &w:(z)?]
Xsin(&)
I- 6W,(z)r5
sin(&).
(8)
In the central region of a quadrupole, u(r, LY,al is independent of z, and the W,(z) are constant. Thus the derivatives in z vanish and we obtain the familiar two-dimensional multipole expansion for u(r, (Y): u(r, in) = E rm[U, cos(ma) m=O
+ W;, sin(mcu)].
(9)
In the fringe field region of a quadrupole lens these derivatives do not vanish, and must be considered when calculating the higher order ion optical properties of the system. The W; term in u will contribute to the intrinsic spherical aberration coefficients of the lens. The Wz and W, terms will contribute to the fifth order aberrations of the lens.
the magnetic axis. The data are Fourier tranformed in LYto yield the a,&+, z) and b,,(r, z) values in eq. (1). In each z-plane, a pol~omial in r is fit to each of the a,(r, z) and b,(r, z) by the least squares method. This yields values for the A,,,(z) and B,,,(z) coefficients in eq. (3). The multipole field profiles, U,(z) = A,,,(z) and W,(z) = B,,o(z), are thus obtained. Note the necessity of measuring the angular dependence of B$r, a, z). Measuring B, over only the radial and axial coordinates, r and z, leaves an ambiguity between the r’sin(2Lu) and r5sin(6a) terms in eq. (8). Previous calculations 191 and measurements [IO] have mapped B, over r and z, at constant ty, in the fringe field region. This has led to the r3 sin(2a) and r5 sin(2a) terms in eq. (8) being mistakenly identified as due to higher order multipole fields (octupole and duodecapole). Indeed, it is only by mapping B,(r, cx, z> over the three coordinates, r, a and z, that we can remove the ambiguity between the r5sin(2a) and r5sin(6a) terms in eq. (8). The Melbourne magnetic quadrupole lenses have been described by Legge et al. 1111. The lenses analysed in the current work use a modified pole piece design. The pole pieces used are constructed from a single piece of iron, as shown in fig. 1. The NC digital mill in the School of Physics at Melbourne has been used to mill a “radius” onto the ends of the pole pieces, as shown in fig. 1. The magnetic multipole profiles have been measured for various values of the pole end radius, R.
2. Experimental The field mapping apparatus and technique have been described previously 121. The field mapping instrument enables us to map the radial component of the magnetic field, B, = Vq as a function of I, a! and z. The measurements are analysed by the computer to produce the field profiles presented. At a given value of r and z, the computer rotates the Hall probe about
3. Measu~men~
and results
The measured quadrnpole and duodecapole profiles are shown in figs. 2-5. The data points shown represent the B, ,(z) in eq. (3). All the profiles shown have been normalised so that B,,,(z) = 1.0 in the centre of the lens.
,R=OILUD
,R=1.%75mm R = 3.175 mm _ R = 4.7625 mm ,R=6.35mm + R = 7.9375 mm -ftR = 9.525 mm
i
w
/
0
5
10
15
20
25
-l.OE-05
z (mm)
-10
Fig. 2. Normalised magnetic quadrupole B,(r, (Y, z) = 2W,(r) sin(2cu) profiles measured at the indicated values of the pole end radius, R.
0
-5 Ihlance
5 10 From end of pole tip, z (mm)
15
Fig. 3. Normalised magnetic duodecapole 8, = 6W&) sin(6a) profiles.
..,..R=Omm __*__R=
0.0030 -
0.0030
1.5875mm
o R=3,75rnnl __sL~ R=4.7625rnrn
..o..R=6.35nm ..,..R=7,9375mm o R = 9.525 mm
0.0020 *-
?G-
2
4
0.0010
f
I o_
OI
m
rt
_______
0
._...
_.
-O.ooLO -0.0020 .o.oo-_;. DiSwmx fivm end of pole tip, z hm)
Fig. 4. (a) Normalised &(Y, LY,z) = - $W;r3(z)
Distance
Fig. 5. (a) Normalised
fromen*Of pole
tip, z (rnrn,l
i
;
i.
Distancefrom end of pale tip, 2 (mm)
sin(2ru) profiles for R < 5 mm. (b) Normalised B,(r, (Y,z) = - ;W;Ir3(z) sin&) profiles for R > 5 mm.
Disrwce
B,(r, cy, z) = &WFr5(z) sin(2cu) profiles for R < 5 mm. (b) Normal&d profiles for R > 5 mm.
fromend
ofpole
lip,
z
(mm,
&(T, (Y,z) = &W,i”r5(z) sin(2ac)
I. TECHNOLOGY
G.R Maloney et al. / Duodecapole components in the fringe field
38
An empirical field profile function has been fit to the quadrupole profile data by the least squares method. The function fit is OS.2
P
f(Z) =
I/( 1 + exp(c, + cis I- c2s2 + css3)) z* IZIZ2,
i0
(IO]
z,
where s = z/r,, and rO = 6.35 mm, is the lens bore radius. The profiles for each of the B%,(z) and B,,,(z) components have been split into two plots for greater clarity. The profiles for lower values of R are shown on the left, and higher values on the right. The dashed and dotted lines are cubic splines drawn through the data points and are intended to guide the eye. The solid line curves in the plots of B,,,(z) and B,,,(z) are those expected from the function fitted to the quadrupole, B,,,(z), profile. From eq. (3), we expect %1(z)
= - %l(z>~
(II)
and &z(r)
The B,,,(z) and B,,,(z) profiles have also decreased in amplitude, although we do measure an increase in amplitude of the B,,,(z) profile for very large values of R. The poor agreement between the measured and expected values of the B&z) and B,,,(z) profiles for large values of R merits further investigation. Accurate determination of these profiles places high demands on the magnetic field mapping instrumentation. The &i(z) components contribute directly to the intrinsic third order spherical aberration of the lens. The B,,,(z) and B,,(z) components contribute to the fifth order geometric aberration of the lens. We will continue this work with complete, numerical calculations of the ion optical properties of the measured field profiles. The numerical ray tracing program OXRAY 1121 is ideally suited to perform these calculations.
References IN G. Parzen, Magnetic Fields for Transporting Charged
Beams, BNL 50536, ISA 76-13 (3.976). 121 G.R. Maloney, D.N. Jamieson and G.J.F. Legge, Nuci.
= &i&V,&).
(12)
The dashed and dotted lines are cubic splines through the data points intended to guide the eye. The agreement is quite good for R < 7 mm in the &i(z) plots. However, the measured profiles begin to increase in amplitude for R > 7 mm, while the expected profiles (solid lines) continue to decrease. The measured and predicted profiles in the B&z) plots show somewhat poorer agreement. In general, the predicted profiles appear to be too low by a factor of 2. The solid Line curves drawn in the plot of &,,a(~) are cubic splines through the data points of Ql, and are intended only to guide the eye.
4. Discussion It is evident from the data that the modified pole tip has reduced the amplitude of all the measured multipole fields. The duodecapole field decreases sharply in amplitude at first, then more slowly, with increasing pole end radius, R.
Instr. and Meth. 854 (1991) 24. 131 G.R. Maloney, D.N. Jamieson and G.J.F. Legge, ibid., p. 68. [41 D.N. Jamieson and G.J.F. Legge, Nucl. In&r. and Meth. B29 (1987) 544. I.51D.N. Jamieson, G.W. Grime and F. Watt, Nucl. Instr. and Meth. B40/41 (1989) 669. [61 D.N. Jamieson, C.G. Ryan and S.H. Sie, Nucl. Instr. and Meth. B54 (1991) 33. [71 D.N. Jamieson and U.A.S. Tapper, Nucl. Instr. and Meth. B44 (1989) 227. I81 M. Szilagyi, Electron and Ion Optics; Microdevices: Physics and Fabrication Technologies, eds. I. Brodie and 3.5. Murray (Plenum, 1988). [9] K. Inoue, M. Takai, K. Ishibashi, Y. Kawata and S. Namba, Jpn. J. Appl. Phys., 28 (1989) 1307. [lo] T. Kamiya and E. Minehara, Proc. JAERI Conf. Tokamura, JAERI (1990). [ll] G.J.F. Legge, D.N. Jamieson, P.M.J. O’Brien and A.P. Mazzolini, Nucl. Instr. and Meth. 197 (1982) 563. [12] G.W. Grime, F. Watt, G.D. Blower, J. Takacs and D.N. Jamieson, ibid., p. 97.
Nuclear Instruments and Methods in Physics Research B77 (1993) 35-38 North-Holland
Beam Interactions with Materials&Atoms
Design modifications to reduce duodecapole field region of magnetic quadrupole lenses
components in the fringe
G.R. Moloney, D.N. Jamieson and G.J.F. Legge School of Physics,Universityof Melbourne,Park&e 3052,Australia
An investigation into minimisat~on of the duodecapole (fifth order) fringe field components of magnetic quad~~le lenses has been conducted at Melbourne. Detailed measurement and analysis of the fringe field region of the Melbou~e magnetic quadrupole lenses has revealed the presence of significant fifth order multipole fields. A program of design modifications to the pole tip profiles has been conducted with the aim of reducing the duodecapole component of the fringe field. The design changes made and the results of detailed magnetic field mapping are presented.
1. Introduction
A well constructed magnetic quadrupole lens should suffer no ~ntam~ation by parasitic sextupole and octupole magnetic fields. It will, in general, suffer contamination by higher order multipole fields. The most significant of these are the duodecapole and 20-pole components. The 20-pole components have a very high order radial dependence (B, a r’). Hence the 20-pole magnetic field is only significant very close to the pole tips. The duodecapole components have a lower order radial dependence (B, a ?), and are more significant at lower values of r. In general, the ions in a microprobe beam do not pass close to the pole tips. Hence the duodecapole components are of most significance in dete~ining ion trajectories. The duodecapole component of the magnetic field within the lens will contribute to the fifth order aberration coefficients of the lens. Parzen [l] showed the duodecapole and 20-pole contamination could be minimised by using cylindrical pole tips, with a suitable ratio of pole tip radius to lens bore radius. Magnetic field mapping of the fringe field region of the Melbourne quadrupole lenses has shown the presence of significant duodecapole cont~ination in the fringe field region of magnetic quad~pole lenses 121. The amplitude of the duodecapole profile can increase up to several orders of magnitude in the fringe field region of a magnetic quadrupole lens. These fringe field components will contribute to the fifth order aberration of the lens. The new two-stage proton microprobe [3], under construction at Melbourne, will be very sensitive to lens aberrations. We wish to reduce the fifth order aberrations of the lenses due to the fringe field duodecapole components.
The grid shadow method has been used extensively by Jamieson 14-71 to measure the aberrations of microprobe systems. This method, however, yields no information on the axial profiles of the multipole components of a lens. The axial profile of all m~tipole field components in a magnetic quadrupole lens can be determined by detailed magnetic field measurements. At Melbourne we have performed such measurements with a Hall effect probe mounted on a computer controlled translation and rotation stage. The small sampling area of the Hall effect probe (= 1 mm2) enables the complex multipole profiles to be determined to a high degree of accuracy. Following Szilagyi @I,the magnetic scalar potential, u, may be expressed in the cylin~cal coordinate system, (I, IY, z), as a Fourier series in cy, u(r, a, 2) = _,[a-(r, +b,(r,
z) cos(mcu) z) sin(mcr)],
(1)
where a,(r,
2) = 2 Am,k(z)r2k+m, k=O
bm(r, 2) = 2
Bm,k(z)r”k+m,
k=O
and (-l)%! A
B
m,k = 4%!(m
+ k)!
u;Zk’( z),
(3)
(-qkrrz! m,k = 4%!(m
0168-583X/93/$~.~ 0 1993 - Elsevier Science Publishers B.V. All rights reserved
+ k)!
V@k’( Z))
I. TECHNOLOGY
where the superscripts, (2k), on U and W denote the 2kth derivative with respect to z. The U,(z) and W,(z) represent the profiles of the mth order multipole in the multipole expansion. For a magnetic quadrupole lens, assuming no constructional or excitational asymmetries, u satisfies the foltowing symmetry conditions, zL(r,a,
z)=zL--Y,ff, = --u(r,
.z)=L1(r,(7i-/2)-ff,z) -a,
(4)
m = 2, 6, 10, 14, . . . .
&W;(z)r’+
&WF(z)r6]
+ W6(z)r” sin(&). of the
magnetic
cy, z) = V$L(r, cr, z).
(6) field,
(7)
Hence, to sixth order in r, B,(r,
r-R
/
60’
!
@
f 7.25nm
1 I
sured showing the radius which was cut into the pole ends. The bore radius of the lens is 6.35 mm. Pole tip profiles were measured for values of R = 0, 1.5875, 3.175, 4.7625, 6.35, 7.9375 and 9.525 mm.
in r, for an ideal magnetic
The radial component B,.(r, a, z>, is defined by BJr,
.~
(5)
u(r, rr, 2) = [W,(z)?Xsin(2a)
AXIS
Pig. 1. Diagram of the pole pieces used in the lenses mea-
z).
The only terms in u satisfying these symmetry conditions are those such that,
Thus, to sixth order quadrupole lens,
-_. -7 v4 I-=BEAM
cl!, z) = [2W,(z)r
- +w;l(z)r”
+ &w:(z)?]
Xsin(&)
I- 6W,(z)r5
sin(&).
(8)
In the central region of a quadrupole, u(r, LY,al is independent of z, and the W,(z) are constant. Thus the derivatives in z vanish and we obtain the familiar two-dimensional multipole expansion for u(r, (Y): u(r, in) = E rm[U, cos(ma) m=O
+ W;, sin(mcu)].
(9)
In the fringe field region of a quadrupole lens these derivatives do not vanish, and must be considered when calculating the higher order ion optical properties of the system. The W; term in u will contribute to the intrinsic spherical aberration coefficients of the lens. The Wz and W, terms will contribute to the fifth order aberrations of the lens.
the magnetic axis. The data are Fourier tranformed in LYto yield the a,&+, z) and b,,(r, z) values in eq. (1). In each z-plane, a pol~omial in r is fit to each of the a,(r, z) and b,(r, z) by the least squares method. This yields values for the A,,,(z) and B,,,(z) coefficients in eq. (3). The multipole field profiles, U,(z) = A,,,(z) and W,(z) = B,,o(z), are thus obtained. Note the necessity of measuring the angular dependence of B$r, a, z). Measuring B, over only the radial and axial coordinates, r and z, leaves an ambiguity between the r’sin(2Lu) and r5sin(6a) terms in eq. (8). Previous calculations 191 and measurements [IO] have mapped B, over r and z, at constant ty, in the fringe field region. This has led to the r3 sin(2a) and r5 sin(2a) terms in eq. (8) being mistakenly identified as due to higher order multipole fields (octupole and duodecapole). Indeed, it is only by mapping B,(r, cx, z> over the three coordinates, r, a and z, that we can remove the ambiguity between the r5sin(2a) and r5sin(6a) terms in eq. (8). The Melbourne magnetic quadrupole lenses have been described by Legge et al. 1111. The lenses analysed in the current work use a modified pole piece design. The pole pieces used are constructed from a single piece of iron, as shown in fig. 1. The NC digital mill in the School of Physics at Melbourne has been used to mill a “radius” onto the ends of the pole pieces, as shown in fig. 1. The magnetic multipole profiles have been measured for various values of the pole end radius, R.
2. Experimental The field mapping apparatus and technique have been described previously 121. The field mapping instrument enables us to map the radial component of the magnetic field, B, = Vq as a function of I, a! and z. The measurements are analysed by the computer to produce the field profiles presented. At a given value of r and z, the computer rotates the Hall probe about
3. Measu~men~
and results
The measured quadrnpole and duodecapole profiles are shown in figs. 2-5. The data points shown represent the B, ,(z) in eq. (3). All the profiles shown have been normalised so that B,,,(z) = 1.0 in the centre of the lens.
,R=OILUD
,R=1.%75mm R = 3.175 mm _ R = 4.7625 mm ,R=6.35mm + R = 7.9375 mm -ftR = 9.525 mm
i
w
/
0
5
10
15
20
25
-l.OE-05
z (mm)
-10
Fig. 2. Normalised magnetic quadrupole B,(r, (Y, z) = 2W,(r) sin(2cu) profiles measured at the indicated values of the pole end radius, R.
0
-5 Ihlance
5 10 From end of pole tip, z (mm)
15
Fig. 3. Normalised magnetic duodecapole 8, = 6W&) sin(6a) profiles.
..,..R=Omm __*__R=
0.0030 -
0.0030
1.5875mm
o R=3,75rnnl __sL~ R=4.7625rnrn
..o..R=6.35nm ..,..R=7,9375mm o R = 9.525 mm
0.0020 *-
?G-
2
4
0.0010
f
I o_
OI
m
rt
_______
0
._...
_.
-O.ooLO -0.0020 .o.oo-_;. DiSwmx fivm end of pole tip, z hm)
Fig. 4. (a) Normalised &(Y, LY,z) = - $W;r3(z)
Distance
Fig. 5. (a) Normalised
fromen*Of pole
tip, z (rnrn,l
i
;
i.
Distancefrom end of pale tip, 2 (mm)
sin(2ru) profiles for R < 5 mm. (b) Normalised B,(r, (Y,z) = - ;W;Ir3(z) sin&) profiles for R > 5 mm.
Disrwce
B,(r, cy, z) = &WFr5(z) sin(2cu) profiles for R < 5 mm. (b) Normal&d profiles for R > 5 mm.
fromend
ofpole
lip,
z
(mm,
&(T, (Y,z) = &W,i”r5(z) sin(2ac)
I. TECHNOLOGY
G.R Maloney et al. / Duodecapole components in the fringe field
38
An empirical field profile function has been fit to the quadrupole profile data by the least squares method. The function fit is OS.2
P
f(Z) =
I/( 1 + exp(c, + cis I- c2s2 + css3)) z* IZIZ2,
i0
(IO]
z,
where s = z/r,, and rO = 6.35 mm, is the lens bore radius. The profiles for each of the B%,(z) and B,,,(z) components have been split into two plots for greater clarity. The profiles for lower values of R are shown on the left, and higher values on the right. The dashed and dotted lines are cubic splines drawn through the data points and are intended to guide the eye. The solid line curves in the plots of B,,,(z) and B,,,(z) are those expected from the function fitted to the quadrupole, B,,,(z), profile. From eq. (3), we expect %1(z)
= - %l(z>~
(II)
and &z(r)
The B,,,(z) and B,,,(z) profiles have also decreased in amplitude, although we do measure an increase in amplitude of the B,,,(z) profile for very large values of R. The poor agreement between the measured and expected values of the B&z) and B,,,(z) profiles for large values of R merits further investigation. Accurate determination of these profiles places high demands on the magnetic field mapping instrumentation. The &i(z) components contribute directly to the intrinsic third order spherical aberration of the lens. The B,,,(z) and B,,(z) components contribute to the fifth order geometric aberration of the lens. We will continue this work with complete, numerical calculations of the ion optical properties of the measured field profiles. The numerical ray tracing program OXRAY 1121 is ideally suited to perform these calculations.
References IN G. Parzen, Magnetic Fields for Transporting Charged
Beams, BNL 50536, ISA 76-13 (3.976). 121 G.R. Maloney, D.N. Jamieson and G.J.F. Legge, Nuci.
= &i&V,&).
(12)
The dashed and dotted lines are cubic splines through the data points intended to guide the eye. The agreement is quite good for R < 7 mm in the &i(z) plots. However, the measured profiles begin to increase in amplitude for R > 7 mm, while the expected profiles (solid lines) continue to decrease. The measured and predicted profiles in the B&z) plots show somewhat poorer agreement. In general, the predicted profiles appear to be too low by a factor of 2. The solid Line curves drawn in the plot of &,,a(~) are cubic splines through the data points of Ql, and are intended only to guide the eye.
4. Discussion It is evident from the data that the modified pole tip has reduced the amplitude of all the measured multipole fields. The duodecapole field decreases sharply in amplitude at first, then more slowly, with increasing pole end radius, R.
Instr. and Meth. 854 (1991) 24. 131 G.R. Maloney, D.N. Jamieson and G.J.F. Legge, ibid., p. 68. [41 D.N. Jamieson and G.J.F. Legge, Nucl. In&r. and Meth. B29 (1987) 544. I.51D.N. Jamieson, G.W. Grime and F. Watt, Nucl. Instr. and Meth. B40/41 (1989) 669. [61 D.N. Jamieson, C.G. Ryan and S.H. Sie, Nucl. Instr. and Meth. B54 (1991) 33. [71 D.N. Jamieson and U.A.S. Tapper, Nucl. Instr. and Meth. B44 (1989) 227. I81 M. Szilagyi, Electron and Ion Optics; Microdevices: Physics and Fabrication Technologies, eds. I. Brodie and 3.5. Murray (Plenum, 1988). [9] K. Inoue, M. Takai, K. Ishibashi, Y. Kawata and S. Namba, Jpn. J. Appl. Phys., 28 (1989) 1307. [lo] T. Kamiya and E. Minehara, Proc. JAERI Conf. Tokamura, JAERI (1990). [ll] G.J.F. Legge, D.N. Jamieson, P.M.J. O’Brien and A.P. Mazzolini, Nucl. Instr. and Meth. 197 (1982) 563. [12] G.W. Grime, F. Watt, G.D. Blower, J. Takacs and D.N. Jamieson, ibid., p. 97.