COMPUTER CALCULATIONS OF A SOLENOID LENSFUR FOCUSSING MEV PROTON BEAMS
H. Koyama and L. Grodzins*
The Institute of Medical Science, The University
Massachusetts Institute of Technology*ofTokyoandABSTRACT
A superconducting solenoid lens for focussing proton beams up
to 5 MeV to the order of one micron is installed on a scanning
proton microprobe facility. The expected performance of the lens
including' the effect of the spherical, chromatic and mechanicalaberrations on the resolution and throughput, studied by ray
trace computer calculation is described.
The recent interest in developing a scanning proton microprobe(SPM) is prompted by its advantages over the well developed
scanning electron microprobe (SEM) such as its high sensitivity
to trace elements or its capability of in air analysis ofhydrated or even live samples (1). The resolution of one micronispractical
and important in the elemental analysis of
biological samples in air.
Hitherto, the magnetic quadrupole
lenses have been used in SPM facilities (2 ,3) to focuss a few MeV
proton beam to a few microns level.
Simple solenoids have not previously been used for focussing
heavy ions principally because the thin lens requires an order ofmagnitude higher magnetic fields for focussing than does theanalogous quadrupole lens. A 2 MeV proton has the same momentum,
hence magnetic rigidity, as a 61 MeV electron and conventim~a.J.
magnetic solenoids cannot produce sufficient field strength.s togive the short focal lengths desired for a focussing system.
Onthe other hand,a state of the art superconducting solenoid canproduce fields more than ample for the present application.
The focussing system is installed on a beamlineofMIT-Lincoln Lab. 4 MeV Van de Graaff generator. A shematic viewof the beam optics is shown in Fig.l.
The object and image
distances measured from the center of the lens, are 405 em and16 em respectively, with the implication of a demagnetization of25.
The actual size of the solenoid coil is shown in Fig.2. A
maximum field of 6.5 Tesla on the axis is attainable for 23 A.
Calculations were performed using a ray trace program (4), in
which a subroutine to calculate .the magnetic fields of a sheet
solenoid coil was replaced by one to calculate the fields of athick coil by the method of Garrett (5). The field distribution
on the axis is shown in Fig.2. The ray trace results are asdescribed below.
Results and Discussions
Detailed calculations were performed for 2 MeV protons, acommonly used energy in PIXE, under the geometry shown in Fig.l.
The spherical aberration constant Cs defined by~ = MGs8t ..5+ MCs I e. ,t + •..
is 3.08 x 107 em, where fs is the radius of the aberration disk
at the gauss plane with the demagnification M and (), ... is theincident angle spread.
Fbr an image with diameter, d, theoptimum object radius and limiting angle spread are proportional
to d and d 113 , respectively, so the throughput is proportional tod 8/3.
In order to get a 1 pm diameter beam spot with the maximum
throughput for the geometry shown in Fig.2, the object diameter-313-

must be limited to 19 }Jln and the angle spread must·· be limited by
an appropriate aperture to ± 0.34 mr.
The effect of the chromaticaberration
wasestimatedseparately.
The chromatic aberration constant Cck defined interms of the ~e radius, fc,.. asfc.~o. = MCcJ.. B._H·(E - E.,)/Eo
is 9.41 x 10 3 em at Eo = 2 MeV and with the same lens parameters.
Fbr example, the energy spread of 0.1 % deteriorates a 1 }Jln beam,effectively to a 2 J..Un beam.
The optimum intensity of the 1 }Jln dia. beam is expected to be
mre than 0.1 nA for the incident beam of 100 J.lA with theemittance of nretn _...., 0.25TC cm·mr. Such a focussing ability andother advantages- simplicity of design and operation, rapidcha.nge of focal length-make the superconduc ting lens a strongcontender for ion beam focussing application s. More detailed
description will be found elsewhere (6).
We thank S.B.Kowalsk i for the use of his ray trace code andthank him, R.J.Weggel and H.Ehge for many helpful discussions.
Focus Point
Angle Limiting:\Aperture-'/Beam Size LimitingH•eeam from
Vart de Graof.f

F'jg.l.
A shematicview
ofthebeamoptics.

~~o""

Aperture ............... 'Quadrupales -.,/v

'I \ //~/

4...._1.5m-'

Fig.2.
Calculated
magnetic fields on theaxis of the coil .

·10.8-6-4-20Position (em)References(1) P.Horowitz and L.Grodzins, Science 1~ (1975) 795.
(2) J.A.Cookson et al., J. Radioanal. Chem. 12 (1972) 39.
(3) F.Bosch et al., Nucl. Instrum. and MethodSl49 (1978) 665.
(4) H.A.Ehge and S.B.Kowalsk i, Third Int. Conf. '"'On Magnet··
Technology (1970) and private cormnunicati ons.
.
(5) M. W. Garret, J. Appl. Phys. _38 (1967) 2563.
(6) H.Koyama and L. Grodzins, Nucl. ·-rnstrum. and Methods, in press.

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